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Energy Peak/average brightness/ ph/(s*mrad*mm2*0.1%Bw Linewidth
Injector - amplifier project ≤ 1 ps/ 100 Hz 10 - 20 nm full/~0.5 mm 0.1 mW ~ 5 - 10 µJ 1026 /1015 300 fs). The general architecture of the Ti:Sa laser is schematically represented in figure 2.
Fig. 2. Schematic view of the LASERIX driver architecture
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The front-end is designed as a customized laser based on standard modules, developed by French companies (THALES LASER and AMPLITUDE TECHNOLOGIES). It is composed by two parts, one for the shaping and pre-amplification of the oscillator pulse, the other for two cryogenic amplifiers. The output energy at the front-end is more than 2J at the 10Hz repetition rate. The front-end beam (2.5 J) is then injected in the main amplifier, which is composed by the large Ti:Sa crystal (diameter 100 mm), shown in figure 3. The crystal is pumped by a 4-module Nd:glass laser delivering 100 Joules of 2ω green light, developed by the French laser company QUANTEL. The energy deposition on each side of the crystal is homogenized using lens arrays. The crystal is held in a mount in which a special liquid is circulating all around to cool the crystal and limit the transverse lasing. After 4 successive passes through the crystal, the expected output before compression is ≅ 40 Joules at the repetition rate of 10 Hz. Basically, as shown in figure 2, the 40-joule beam is divided in two parts, respectively 20 Joules of 500 ps and 10 Joules of 50 fs-1 ps (after compression). Besides, two more beams are offered at the final stage. Thus, the zero-order rejected by the compressor may be itself compressed to give a beam of ≅ 1 J in 50 fs. Besides, a weak part of the energy at the exit of the front-end, ≅50 mJ in 50 fs at the repetition rate of 10Hz, can be offered to the users
Fig. 3. The large titanium-doped sapphire crystal (diameter : 100 mm) of the LASERIX driver amplifier is shown on the left. On the right image, we can see the crystal and its mount, including a liquid all around the mount.
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4 Description of the beam-lines possibility Owing to our choice of the Ti:Sa technology for the driver, LASERIX will offer the largest experimental possibilities. Thus, as shown in figure 4, the main beams represented in the part (a) give a long pulse and a short pulse leading to TCE X-ray lasers at 0.1 Hz repetition rate. Beside these two beams, several infrared beam-lines will be useable for applications in the IR range and/or for producing auxiliary XUV beamlines. For instance, the zero-order issuing from the compressor will be itself compressed to produce an auxiliary beam of 1 Joule in 50 fs, as shown in part (b) of figure 4. In addition the energy of the uncompressed beam will be generally larger than needed, so a part of it will be available. Finally, leaks taken in the front-end offer the possibility to have other auxiliary IR beam-lines, as shown in part (c) of the figure 4. Such beams can be used again for applications at 10Hz repetition rate. But, particularly they offer possibility to produce XUV beams by high-order harmonic generation (HHG). Such beams may be amplified in TCE plasmas to produce intense XRL beams of high optical quality [10]. All these beam-lines open a large field of applications, especially because they all are synchronized with the main beam
Fig. 4. Configuration of the main beam-lines in the experimental area.
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5 Applications of X-ray lasers and LASERIX project X-ray lasers can be employed to excite matter, to diagnose solid surfaces, or probe high-density plasmas. Indeed, the unique XRL properties (very large brightness, coherence, short duration) add to good beam collimation, and make XRLs attractive with respect to the other soft XUV sources. Owing to their high brightness, XRLs are well suited as diagnostic tools for various purposes, in particular in microscopy and interferometry [11,12,13]. As a widely used diagnosing tool in the research of laser-produced plasma, interferometry has many advantages in the accurate measurement of the plasma electron density because it directly gives refraction index mapping from the interference pattern processing. Indeed, due to the high intensity and short wavelength, X-ray lasers applied as a probing beam for the interferometry provides better penetration into high density plasma (1019–1022 cm-3) with small refraction, which is a main limitation of interferometry in the UV range for high-density gradient plasma diagnosis. In this paper, we just ullustrate the interest of X-ray lasers for laserproduced plasmas investigations from the results of an X-ray interference microscopy diagnosis using a wavefront-division imaging Fresnel bimirror interferometer [14] and a transient picosecond Ni-like Ag X-ray laser [15].
Fig. 5. Experimental set-up of the Fresnel bi-mirror X-ray interference microscopy.
The configuration of the experimental setup is shown in Figure 5. The X-ray laser illuminated the sample plasma and the bi-mirror separated the
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wave front after the plasma and produced an enlarged overlapped interference field. The diffraction-limited ellipsoidal imaging mirror gave a magnified image of the sample plasma onto the thinned backlighted CCD. The spatial resolution in the sample plasma plane was limited by the magnification and the pixel size to ~ 1.75 µm. The diagnosed plasma was formed by irradiating a 1 mm-long Al slab target with a 1 J, 1.2 ns IR (1053 nm) pulse. A line focus system produced a plasma column of ~ 100 µm in width and 6 mm in length (intensity within the line focus: 1.4×1011 Wcm-2). The X-ray laser probed the plasma along the column axis. The intense plasma self-emission was observed close to the target surface and mixed with the interference fringes. However this low frequency signal can be removed by using a Fourier filtering in order to let appear the interference field. The density map may be then easily deduced from the fringe pattern, as shown by figure 6, which describes the successive steps of the analysis leading from the raw data to the electron density map. For the plasma length of 1 mm, the electron density, ne, is related to the fringe shift as ne ≈1.583×1020 δfringe [cm-3]. Due to the limitation of the spatial resolution, the minimum detectable limit of the electron density is ~ 3×1019 cm-3.
Fig. 6. Main steps of results and analysis of laser-produced plasmas investigations. 1) Image of the sample plasma, reflected by the reference part of the bimirror, without X-ray laser. 2) Interference field with superimposed plasma image, recorded for the same shot. 3) Interference field after removing plasma emission by a Fourier treatment. 4) Electron density map deduced from 3.
Pictures of the figure 6 correspond to a delay of 1 ns between the plasma heating pulse and the X-ray laser. The peak electron density measured is 1020 cm−3 at the position comprised between 10 and 15 μm away from the target surface. In some zones of plasmas diagnosed later, typically 2 and 3 ns after the peak of the heating pulse, inverted fringe shifts were observed, leading to refraction index larger than 1. That means that the plasma is no more a classical dilute electron gas and that the refraction in-
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dex is not mainly governed by the electron density, but by free-bound and bound-bound transitions. Thus, these results will contribute to the validation of the 1D and 2D hydrodynamic codes and a better understanding of the physics of laserproduced plasma [16]. They could be performed in a near future using LASERIX facility.
6 Summary and perspectives. Thus, the LASERIX facility is now built. The laser driver is running and the choice of the Ti:Sa is experimentally successful confirmed. It will offer the possibility to highly increase the repetition rate of the X-ray lasers and then will be very useful for applications. A virtual (3D) of the experimental area is represented in Figure 7.
Fig. 7. 3D virtual view of the LASERIX facility. The main chamber producing TCE X-ray lasers is represented in the center of the room.
This laser facility will be located in a new building, available in November 2006, at the Laboratoire d’Optique Appliquée (Ecole Polytechnique, Palaiseau, France). Thus, the LASERIX facility will be installed during the first semester of 2007 and first applications investigations will be performed during the second semester of 2007. Among the different applications, we plane to purchase the density diagnostics of plasmas produced by the low-energy beam. The possibility to vary the duration of the IR beam producing the plasma, to vary the wavelength of the X-ray laser,
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and, above all, the large repetition rate (0.1 Hz) will be very useful to realize full-scale studies. That has been demonstrated at the 1st LASERIX Workshop [17], held in Orsay on 2-3 February 2006.
7 Acknowledgments LASERIX is an X-ray laser facility of the Université Paris-Sud. The financial support of the Conseil Général de l’Essonne and the Ministère de la Recherche under the Contrat de Plan Etat-Régions 2000-2006 is gratefully acknowledged. We are indebted to Patrick Georges (LCFIO), Pascal d’Oliveira (CEADRECAM) and Claude Rouyer (CEA-CESTA) for valuable discussions.
References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
D.L. Matthews et al, Phys. Rev. Lett. 54, 110, 1985 L.I. Gudzenko et al., Sov. Phys. Doklady 10, 147, 1965 R.C. Elton, Appl. Optics 14, 97, 1975 D. Ros et al, Laser ans Particle Beams Journal, 20, 23,.2002 B. Rus et al., Phys. Rev. A 55, 3858-73, (1997) S. Sebban et al., Phys. Rev. Letters, 86, 3004-7, (2001) P.V. Nickles et al., Phys. Rev. Lett. 78, 2748, 1997 A. Klisnick et al., J.O.S.A. B 17, 1093, 2000 G. Jamelot et al., in X-Ray Lasers 2004, IOP Conf Series N° 186, 677 (2005) P. Zeitoun et al., Nature 431, 426, (2004) D. Di Cicco et al., Opt. Lett. 17, 157, (1992). R.E. Burge, et al., Opt. Lett. 18, 66, (1993). D.H. Kalantar et al., Phys. Rev. Lett. 76, 3574, (1996). D. Joyeux et al., J. Phys IV France 11, Pr2, 511, (2001). A. Klisnick et al, J.O.S.A. B 17, 1093, (2000). H. Tang et al., Appl. Phys. B 78, 975, (2004). The CD ROM of contributions to the workshop is available : [email protected]
Seeding High Order Harmonic in a Transient X-Ray Laser Amplifier I. R. Al’Miev*, O. Larroche+, A. Klisnick*, C. Moller*, D. Benredjem*, S. Kazamias-Moucan*, O. Zabaydullin* and J. Dubau* *)
LIXAM, Laboratoire d’Interaction du rayonnement X Avec la Matiere, UMR 8624, Bat. 350, Universite Paris-Sud, 91405 Orsay, Cedex, France +) CEA-DIF, Boite postale 12, F-91680 Bruyeres-le-Chatel France
Summary. The seeding of high-order harmonic (HOH) radiation in a transient Xray laser amplifier was numerically investigated using the code COLAX. The code was recently modified to account (i) for the travelling-wave irradiation of a preformed plasma pumped in the transient regime, and (ii) for the injection of a HOH pulse at the X-ray laser wavelength, and at one boundary of the plasma amplifier. We show that the time-dependent description of the polarisation (TDP) leads to significantly different results in comparison to the widely used adiabatic description. Namely, with TDP, HOH produces a wake in the intensity distribution, which is not only amplified but lasts much longer than the HOH pulse. This could explain recent experimental observations in the spectral domain.
1 Context and motivation It is well known that a conventional optical laser exhibits few principal problems associated, firstly, with necessity of creating a high quality seed, secondly, with maintaining the quality over the amplification region, and, thirdly, with reducing the level of the self-emission of the amplifier. The area of X-ray lasers was investigated in a number of papers. Starting from the first successful demonstration of X-ray laser, the world has seen the lasing even at the wavelength 3.5 nm [2] that is just inside the waterwindow. One of new promising routes of the X-ray laser research is the amplification of HOH pulse inside the X-ray laser. The importance of this topic could be explained by the potential improvement of the properties of X-ray laser, for example, coherence. One of the first reports on the ampli-
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fication of the HOH was published by Ditmire et al [3]. In their work they reported an amplification of the 21st harmonic of neodymium chirpedpulse-amplification laser pulse in Ne-like Ga laser plasma. Substantial progress has been made by Ph.Zeitoun et al [4] in 2004 with successful demonstration of seeding HOH in Ni-like Kr OFI amplifier at a wavelength of 32.8 nm. The authors claimed an amplification of 25th harmonic from Ar gas by a factor of 103. We note that the work in similar area has been made by Japanese scientists Kawachi et al [5], and Hasegawa et al [6]. They made an attempt to produce shorter wavelength radiation using transient collisional excitation (TCE) scheme. If one would like to obtain larger energy output and reach shorter lasing wavelengths then, indeed, TCE X-ray lasers, based on the use of solid target, is a valuable medium for the potential amplification. Our goal is to simulate propagation of short high-order harmonic pulse within Ni-like Ag laser-produced plasma created by the traveling wave irradiation. We note that the HOH pulse differs from X-ray laser pulse in that the spectral width of HOH is much broader than that of the X-ray laser pulse. That is why we have used and upgraded the code COLAX that is appropriate to resolve numerically short-, of order of 10 fs, and long-duration, of order of 10 ps, electric field amplitudes. Conditions of the simulations match the experimental ones reported by Klisnick et al [7].
2 Simulated experiment To perform the simulations we considered such scheme where Ag target is initially irradiated by the pre-pulse of smaller intensity, creating a preplasma. Then, it is irradiated by the main pulse of larger intensity, creating conditions that are optimal for the population inversion. Main pulse takes the form of the travelling wave irradiation. The angle of the travelling wave (TW), that is related to the velocity of TW irradiation, can be varied in the present version of the code; for the particular calculations we fixed it as 45° that corresponds to the velocity of the TW, which is equal to the speed of the light in the vacuum. As soon as the amplified spontaneous emission is generated, the HOH pulse is injected. It interacts with the laser-plasma amplifier, and produces some radiation output. To simulate Nilike Ag laser-produced plasma we used the code EHYBRID [8]. The following parameters were used as an input into EHYBRID. Intensity of the pre-pulse was taken to be 1012 W cm-2; intensity of the main pulse was 1015 W cm-2; the duration of the pre-pulse was 600 ps; the duration of the main pulse was 400 fs; the time interval between the pre- and main pulses was
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250 ps. The HOH pulse has Gaussian temporal and spatial shape of 15 fs temporal and of 30 µm spatial widths. The time of the injection of HOH pulse is a parameter in the code – it can be varied. For the particular calculations we fixed it as 2 ps with respect to the start of the travelling wave irradiation.
3 The code COLAX: present status and upgrade The code COLAX was originally written by Larroche et al. and has been used to model X-ray laser signal build-up [1]. The evolution of the electric field is described by Maxwell equation, which is transformed into paraxial envelope form,
∂E ± ∂E ± ic ∂ 2 E ± iω + = + (ε R E ± + 4πP± ) , c ⋅ ∂t ∂y 2ω ∂x 2 2c
(1)
where E+ and E- are the complex, slowly varying amplitudes of waves propagating in the positive and reverse directions. The Eq.(1) is selfconsistently bound with the equation describing the evolution of the polarisation,
∂P± = −γP± − iωDE ± + Γ± , ∂t
(2)
where γ has a meaning of the dipole de-phasing factor, and D is the reduced, non-dimensional population inversion between the upper and the lower X-ray lasing levels,
D=
d2 1 ( ρu − ρl ) = γGλ , hω 8π 2ω
(3)
where d is the absolute value of the non-diagonal matrix element of the dipole operator, ρ u ( ρ l ) are the dimensional populations of the upper, and lower levels, respectively, and the gain G takes into account the effect of the saturation,
G=
G0 1+
I
,
(4)
I sat
with G0 describing the small-signal gain, I is the electric field intensity, and Isat is the saturation intensity. Noise term, Γ+ , in the Eq.2 effectively describes spontaneous emission. To perform simulations we have upgraded COLAX. Travelling wave irradiation was taken into account in the following way. Local conditions of
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plasma were determined by the angle of the travelling wave and EHYBRID time-history of plasma. EHYBRID is 1.5 dimensional code. It provided us with the cell position, electron density, electron and ion temperatures, populations of the upper and lower X-ray lasing levels, smallsignal gain, dipole de-phasing factor, and the saturation intensity as functions of the Lagrangian cell positions and time. By fixing plasma conditions along transverse axis at fixed y-coordinate, conditions at other ycoordinates are calculated, using space and time interpolation procedure, taking into account time delay of the front irradiation of the travelling wave. Then, such interpolated quantities are used as an input parameters in the code COLAX. To account for the HOH pulse injection boundary conditions as functions of time were modified.
4 Results Typical output of COLAX is shown in Fig.1. It shows the snapshot of intensity distribution as a function of the longitudinal, y, and transverse, x, distances at t = 8 ps. Longitudinal axis is the one, along which the X-ray radiation propagates. It has dimension of 3mm. The dimension of the
Fig. 1. Intensity distribution as a function of y- and x-coordinates at t = 8 ps with respect to the start of the travelling wave irradiation.
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transverse axis is 140 µm, while the initial position of the target surface is located at x = -70 µm . Intensity is given in log-scale. The narrow feature at y = 1.85 mm corresponds to the HOH pulse. The HOH pulse has a Gaussian spatial profile along the x-axis. The peak of the HOH profile is at x = -33 µm. The Fig.1 refers to the case when the electric field wave propagates towards the plasma output in “+”-direction, that is
I + = c E+
a)
2
/(8π ) , where c = 3 ⋅ 1010 cm ⋅ s −1 .
b)
Fig. 2. Intensity snapshots at a) t = 4.5 ps and b) t = 11.5 ps
This figure allows making important conclusions. Firstly, the HOH pulse is weakly amplified. Secondly, high-order harmonic induces the wake, or the tail, that is apparent behind the pulse. Fig.2 shows the evolution of the intensity at two successive times, as the electric field propagates towards the plasma output. It is clear, that the amplification of the intensity takes place behind the HOH pulse in the area with 10-20 µm transverse range where the gain has the maximum values. Secondly, the length of the amplified area is not conserved – it becomes longer as the pulse propagates further. To understand the nature of such distribution we ran COLAX including only the HOH pulse, while arbitrarily setting spontaneous emission to zero. Results are shown in Fig. 3a. One can see that, indeed, the HOH pulse induces the tail. In Fig 3b no HOH was injected, i.e. only spontaneous emission is amplified. Comparison of Fig.1 and Figs.3 shows that the
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a)
b)
Fig. 3. Intensity distribution that includes a) only the HOH pulse, and b) only amplified spontaneous radiation; t = 8 ps.
Fig. 4. Intensity distribution assuming adiabatic model of COLAX calculations; t = 8 ps.
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total contribution of the HOH and the ASE leads to the little increase of the intensity in the area where the intensity has a maximum. Present version of the code COLAX allows making the electric field, and, respectively, intensity calculations in the adiabatic approximation, where the left hand side of the Eq.(2) equals to zero, that is
∂P+ = 0 . In ∂t
such approximation the polarisation is proportional to the electric field, and to the population inversion, according to the following equation,
P+ =
χ ω E + = −i DE + , 4π γ
(5)
where ω is the X-ray laser frequency. Such an approximation is widely used, and in particular it is implicit in the numerical codes based on radiative transfer description. Running COLAX in the adiabatic approximation mode we obtained significantly different results, both qualitatively and quantitatively. Fig. 4 shows the intensity snapshot calculated using this model, that is to be compared to Fig. 1. Firstly, the high-order-harmonic pulse is much more amplified in comparison to the time-dependent case. This can be seen in the centre of the pulse – the HOH pulse wings in the transverse direction have larger intensity values than in the case of the TD description. Secondly, the adiabatic approximation does not predict the existence of the electric field wake. Thirdly, the overall shape of ASE area differs from that of time-dependent calculations. Fourthly, the region of the maximum intensity is situated in the ASE feature. It is 20 times larger than that of the time-dependent case.
5 Conclusion In conclusion, we incorporated the travelling-wave model into the code COLAX. High-order harmonic seed was included as time- and spacedependence of the boundary conditions. Calculations demonstrate that, firstly, it is important to include time-dependent treatment of the polarisation, secondly, the high-order harmonic pulse leads to the wake that is amplified in time, and, thirdly, the wake lasts much longer than the HOH pulse. That can explain the experimental observations [4] in the spectral domain: namely, that, contrary to common belief, the HOH pulse is not amplified as a short, broadband pulse, but rather triggers a long-lasting (and thus possibly narrow-band) wake where most of the XRL energy goes. This fact is the principal difference between time-dependent and adiabatic models. Optimisation of the injection of the high-order harmonic
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pulse and the extension of the population inversion calculations using time-dependent rate equations will be the asset in other paper.
References 1. Larroche, O., Ros, D., Klisnick, A., Sureau, A., Möller, C., Guennou, H., “Maxwell-Bloch modelling of x-ray-laser-signal buildup in single- and doublepass configurations”, Phys. Rev. A 62, 043815 (13 pages), 2000. 2. MacGowan, B.J., Maxon, S., Hagelstein, P.L., Keane, C.J., London, R.A., Matthews, D.L., Rosen, M.D., Scofield, J.H., Whelan, D.A., “Demonstration of soft x-ray amplification in nickel-like ions”, Phys. Rev. Lett. 59, 2157-2160, 1987. 3. Ditmire, T., Hutchinson, M.H.R., Key, M.H., Lewis, C.L.S., MacPhee, A ., Mercer, I., Neely, D., Perry, M.D., Smith, R.A., Wark, J.S., Zepf, M., “Amplification of xuv harmonic radiation in a gallium amplifier”, Phys. Rev. A 51, R4337-R4340, 1995. 4. Zeitoun, Ph., Falvre, G., Sebban, S., Mocek, T., Hallou, A., Fajardo, M., Aubert, D., Balcou, Ph., Burgy, F., Douillet, D., Kazamias, S., de Lacheze-Murel, G., Lefrou, T., le Pape, S., Mercere, P., Merdji, H., Morlens, A.S., Rousseau, J.P., Valentin, C., “A high-intensity highly coherent soft X-ray femtosecond laser seeded by a high harmonic beam”, Nature 431, 426-429, 2004. 5. Kawachi, T., Nagashima, K., Kishimoto, M., Hasegawa, N., Tanaka, M., Ochi, Y., Nishikino, M., Kawazome, H., Tai, R.Z., Namikawa, K., Kato, Y., “Recent Progress in X-ray Laser Research in JAERI”, Proc. of SPIE 5919, 59190L (11 pages), 2005. 6. Hasegawa, N., Kilpio, A.V., Nagashima, K., Kawachi, T., Kado, M., Tanaka, M., Namba, S., Takahashi, K., Sukegawa, K., Peixiang, L., Huajing, T., Kishimoto, M., Renzhong, T., Daido, H., Kato, Y., “Higher harmonics generation for the high coherent x-ray laser”, Proc. of SPIE, 4505, 204-210, 2001. 7. Klisnick, A., Guilbaud, O., Ros, D., Cassou, K., Kazamias, S., Jamelot, G., Lagron, J.-C., Joyeux, D., Phalippou, D., Lechantre, Y., Edwards, M., Mistry, P., Tallents, G., “Experimental study of the temporal coherence and spectral profile of the 13.9 nm transient X-ray laser”, JQSRT 370-380, 2006. 8. Pert, G.J., “Model calculations of XUV gain in rapidly expanding cylindrical plasmas”, J. Phys. B 9, 3301-3315, 1976.
Feasibility of 3.4 nm Laser Pumped by Ultraintense RBS Laser S. Suckewer, Y. Avitzour*, W. Cheng, J. Ren and S. Li Princeton University, Princeton, NJ, 08544, USA
Summary. Our presentation consisted of two parts. In the first part we presented main theoretical results on the plasma and pumping conditions required to generate gain at 3.4 nm in H-like CVI ions in transition from the first excited state to ground state. Transient population inversion is generated during the recombination process. It was shown that high gain (up to G ~200 cm-1) can be achieved using currently available compact lasers. In the second part we presented a new type of compact laser generating ultra-short and ultra-intensive pulses via Raman Backscattering (RBS) amplification and compression in plasma. We achieved large (up to 1000) “seed” amplification and its compression from ~1 psec down to 150 fsec in only 2 mm long plasma pumped with ~ 1014 W/cm2 pulses. We also presented very recent experiments on amplification in 2 passes setup. Such RBS amplifier and compressor is expected to provide in not too far future intensities ~1020 W/cm2 at high repetition rate in compact (university type) system, which would be ideal pump not only for 3.4 nm laser but even for shorter wavelength lasers.
1. Introduction Remarkable progress has been made in the development of soft x-ray lasers (SXLs) since their first demonstration in 1984 in so called collisional scheme [1] and recombination scheme [2]. Each of these schemes evolved into sub-schemes like transient gain generation (see e.g. [3 – 5], and very recently grazing incidence pumping [6, 7] in the collisional scheme, and generation gain in recombination scheme in transitions to ground states of ions pumped by very high intensity fsec-type of lasers [8 – 10]. Advances in their performance (wavelength range, gain and beam energy) have been achieved together with simplifications of the technology required to generate gain. These achievements have, in part, been stimulated by the first applications of soft x-ray lasers to soft x-ray microscopy, microholography, very high plasma density measurements and their potential applications to semiconductor surface studies, nano-lithography, dynami-
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cal response of semiconductors and biological cells, and a number of other applications. A key element here is the cost and availability of these
Fig. 1. Generic recombination soft x-ray laser scheme with lasing to the ground state.
devices, and intensive efforts are being made to develop compact soft xray lasers that are suitable and convenient for applications in academic and industrial research laboratories. Excellent examples of the progress in this direction are demonstrated by the achievement of lasing actions in the region 40–50 nm in ArIX in a capillary discharge[11] and in Xe IX with femtosecond laser [12]. However, right now, the most urging issue, in our opinion, is the development of compact soft X-ray laser, operating at repetition rate >1Hz and at much shorter wavelengths than collisional schemes offer.
Fig. 2. Scaling of the wavelengths versus ion charge Z- 1, of H-like ions for 32 and 2-1 lasing transitions
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In Fig. 2 is shown the scaling of the wavelengths versus ion charge (Z1) of H-like ions for 3–2 and 2–1 transitions in recombination scheme. One may see fast convergence to region of shorter wavelengths even for quite moderate Z. Especially attractive is scaling for 2 – 1 transitions with Z reaching wavelength ~ 1 nm already for the H-like NeX. Because fast decreasing the wavelength and high quantum efficiency for 2 – 1 transition in H-like ions it is possible to achieve lasing within the “water window” (2.3 – 4.4 nm) at quite high repetition rate using relatively compact lasers as pumps as is shown in Table 1 for CVI ions at 3.4 nm. (Description of the computer codes and results of calculations are discussed in the next sections). Consideration of plasma and pumping laser parameters for gain creation in transition to ground state of H-like ions Ultrashort laser pump pulses are crucial to realize lasing to the ground state of ions in the soft X-ray spectral region in order to provide the population inversion between the excited and ground states (see Fig. 1 for generic recombination scheme for generation population inversion to ground states and Fig.3 for transitions to ground state in C VI ions). Fig.1 illustrates the idea of the process of recombination to ground state. First, the ions are fully stripped from their electrons by an intense ultrashort laser pulse. Then, the ions are recombined by three-body recombination, The rate of such recombination is proportional to Ne2 and n4 (Ne is electron density, and n is the principal quantum number) Therefore the transition from Fast collisional recombinations 18.2 nm
H-like CVI ion
3.4 nm
Fig. 3. Recombination scheme for C VI ion
Lasing to ground state (with fsec pumping)
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C6+ to H-like CVI occurs primarily to the states with high n (Fig. 3). Collisional and radiative transitions to level n = 2 occurs faster than to ground level n = 1, creating population inversion between n = 2 and n = 1 (inversion is also created between levels n = 3 and n = 2, which lasts much longer than between levels n = 2 and n = 1). The ionization process has to be very fast. Rapid ionization generates minimal heating of the plasma, which is crucial for a recombination laser (in order for the recombination process to be dominated by collisional relaxation processes). In addition, the ultrashort pumping pulses are necessary because of the very short radiative life time, τ , of the first excited levels of ions and the decrease of this time with Z as Z-4. For example, τ = 26 psec for Li III and τ = 1.6 psec for C VI [13]. In fact, this time is significantly shorter because at high electron density, which is required for high gain, collisional life time is much shorter than radiative time. In addition, as will be discussed in the next section, short pumping time is required because high gain exist before Maxwellization of electron energy distribution takes place. Hence, only the powerful femtosecond-type laser makes it possible to realize transient recombination systems with lasing to the ground state in ions. Ions are initially totally stripped of all their electrons by optical-field-ionization (OFI). This process was predicted theoretically and calculations were performed based on Keldysh theory [1416]. The required power densities (intensities) and energies of fsec-type of laser for effective ionization of H-like CVI ions are shown in Table 1. Table 1. Required energies and intensities to reach C6+
Important result towards generating lasing action in “water window” by transitions to ground state of H-like ions was demonstration of the gain at 13.5 nm in H-like Li III ions in transition to ground state [8]. This experiment followed by demonstration the lasing action in the same transitions at 2 Hz repetition rate [9]. In [9] the lasing was generated with only a 50 mJ in 250 fsec, 0.25 μm KrF laser beam. This relatively high efficiency was achieved by longitudinal pumping and high quantum efficiency due to lasing to the ground state. Importance of these experiments was that they in principle “opened the road” to compact SXLs at much shorter wave-
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lengths using H-like ions with higher atomic number Z . Later, using ~1 μm , 300 fsec Nd/Glass laser and longer plasma column (14 mm instead of 5 mm) gain-length product was slightly increased to GL ≈ 7.2 from GL ≈ 6.5 for a 5 mm long plasma in an experiment with 0.25 μm indicating a tendency of decreasing gain G with an increasing wavelength of pumping beam. This result, which was confirmed in a similar experiment using 0.8 μm Ti/Sapphire laser [17], seems to imply higher Optical Field Ionization (OFI) efficiency at shorter wavelength, in contradiction to the theory of tunneling ionization. Only recently, based on computer modeling of the ionization (including tunneling, multiphoton and collisional ionizations) and recombination processes combined with calculation of electron distribution function from Fokker-Planck equation and radial motion of particles in plasmas (from MHD code) we were able to understand this phenomena and show that there is no contradiction. The reason for seemingly contradiction with the theory is higher deposition of above threshold ionization (ATI) energy to electrons when OFI laser is operating at longer wavelength. Such electron heating is decreasing rate of 3-body recombination of Li3+ to Li III hence, of course, has very negative effect on gain generation [18]. Even more puzzling was very large fluctuations of 13.5 nm output radiation intensity in all these experiments. We have attributed such fluctuations to gain G fluctuations due to some non-uniformity of the plasma column. Therefore we have dedicated a lot of effort to improve the uniformity of the plasma. However, we did not see any improvement in 13.5 nm intensity reproducibility with improvement of plasma uniformity. Again, only recent computer calculations has shown that all these problems were related to plasma heating during optical field ionization (primarily tunneling ionization) leading to too high electron temperature at the time of threebody recombination.
3. Computer modeling results for gain at 3.4 nm in CVI Recently, we have developed an elaborate numerical model to characterize recombination gain in the 2 - 1 transition of LiIII at 13.5 nm [18]. The model describes the effects of different experimental parameters on the gain. We were able to explain the gain observed in the earlier mentioned experiments [9, 10] and showed that it is possible to achieve high gain on this transition, especially when mixing the plasma with hydrogen. These calculations were extended into C VI at 3.4 nm [19,20].
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Recombination gain relies on having fully stripped ions in a relatively cold plasma. The ionization mechanism that is used to achieve this plasma is tunneling ionization by ultra-short and ultra-intense laser pulses (with pulse-duration of ≤ 100 fsec and intensities in the range of 1017 - 1019 W/cm2 depending on the element being used). Due to the short pulseduration, minimal heating is produced during the ionization. However, when calculating the average energy that is absorbed during the ionization process we find that the absorbed energy still corresponds to an electron temperature that would not allow for population inversion in the transition to ground state to be generated during the recombination process. But taking into account the actual phase-space distribution function of the plasma, including effects from both the non-Maxwellian nature of the distribution function and the spatial expansion and cooling of the plasma after ionization, we have shown that high gain is indeed feasible in the LiIII 2 - 1 transition [18]. In addition, we have shown very recently that the gain can be enhanced and become less stringently-dependent on exactly matching the required values of the experimental parameters, if hydrogen is mixed into the plasma [19,20]. The process of gain generation can be divided into three stages: (a) Ionization and heating, (b) Expansion and cooling and (c) Recombination and gain. We shall repeat briefly here the principles of our model (described in detail in [18]), and discuss more deeply the adjustments and enhancements that were required in order to apply the model to the C VI ion. (a) Ionization and heating: Ionization is achieved by OFI using an intense laser pulse. The ionization rate is calculated by the tunneling rate of an electron under the influence of the laser electric field treated in semiclassical approximation [16].The classical motion of the ionized electrons in the laser field after ionization yields the so-called residual energy that is absorbed by the electrons during the ionization process. This energy is due to the phase mismatch between the ionized electrons and the oscillating laser electric field. It is proportional to the quiver energy of the electrons, εq, at the time of ionization. Though the residual energy is in fact much smaller than the quiver energy, it would be high enough to prevent recombination gain to occur if the plasma were Maxwellian. However, the ionization process yields a plasma with a highly non-Maxwellian electron distribution function (EDF) as was shown in [18,19].Qualitatively, one can understand the properties of the OFI-EDF by realizing that most of the electrons are ionized at the peak of the laser oscillating electric field and continue to move in phase with it. Therefore, the vast majority of the electrons in the plasma absorb very little residual energy, and only a small fraction of the electrons are ionized off the peak of the laser electric field and absorb high energy. These highly energetic electrons contribute much
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to the overall electron average energy, but have a relatively low probability of participating in collisional processes. This effect gives rise to enhanced three-body recombination and electron-impact de-excitation rates. In other words, the non- Maxwellian nature of the distribution function causes the “effective recombination temperature" of the plasma to be much lower then the temperature of the corresponding Maxwellian plasma, given by 2/3 of the average energy. The “effective recombination temperature" can be defined by comparing the actual three-body recombination rate to the same rate in a Maxwellian plasma. The effective recombination temperature is always much lower for OFI-plasma than for a Maxwellian plasma with the same average energy. The ionization was simulated by the iPIC (Ionization Particle in Cell) code. For a sufficiently high electron density (Ne≥ 5 1019 cm-3), and a fixed electron temperature, gain is higher for higher Z ions. Therefore, we can expect to get better results for CVI (Z = 6) than for LiIII (Z = 3). However, the required intensity for the ionization of CVI ions is almost two orders of magnitude higher than the intensity required to ionize LiIII ions, and with it, the average energy of the electrons. The effects of the residual energy on the recombination gain are reduced significantly when taking into account the non-Maxwellian nature of the distribution function and by adding hydrogen to the plasma Adding hydrogen supplies cold electrons to the plasma since the hydrogen atoms are ionized by the front of the pump pulse (or by the pre-pulse) and absorb very little residual energy. These electrons then participate in the recombination process and enhance the gain. In the CVI case however, higher densities are required to achieve gain (about an order of magnitude higher than that required for LiIII), and collisions during the ionization process become more significant since the collision frequency scales linearly with the density. Unlike the residual heating, collisional heating affects the electrons ionized from carbon (Celectrons) and the electrons ionized from hydrogen (H-electrons) in the same way. One way to counter this effect is to use a shorter pulse for the ionization. The overall collisional heating is roughly proportional to the product νcolτ , where νcol is an average collision frequency, and τ is the pulse-duration. Therefore, increasing the density (and with it the collision frequency) by a factor of 5-10 and reducing the pulse-duration by the same factor should have very little net effect on the collisional heating. Using shorter pump pulses requires the use of a slightly higher intensity, since the ionization has to be completed in a shorter time, and full ionization is crucial to achieve high gain. However, even with the higher intensity the shorter pulses contain lower energy, which means that using shorter pulses would be more energy-efficient.
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(b) Expansion and cooling: The expansion and cooling (along with Maxwellization) process is simulated by numerically solving the FokkerPlanck (FP) equation for the distribution function that is calculated by the iPIC code with an implementation of the SPARK code [18]. Since the OFI-EDF was generated by the iPIC code in planar geometry and since the charge separation and space-charge oscillations may not have cylindrical symmetry (recall that the pump beam is linearly polarized), the straightforward conversion between planar and cylindrical was not appropriate here and the planar geometry option of the FP solver code was used. Finally, we note that due to the higher density and the short time scales at which gain occurs (usually less than 1 ps after ionization), the expansion cooling plays a less important role here since very little expansion can happen in these time scales. (The main importance of solving the FP equation is for calculating the Maxwellization process, which has to be taken into account to get realistic results.) Therefore, in contrast to the LiIII case, there is no need for a tight focus of the pump pulse in order to achieve gain (other than for achieving the required intensity). This property of the gain may make it easier to achieve longer gain channels for gain saturation.
Pump diameter: 10µm
Pump diameter: 30µm
C VI 3.4 nm
C VI 3.4 nm
b)
a) Plasma radius
b) Plasma
radius
Fig. 4. Gain coefficient (in cm-1) for CVI 2→1 transition with initial conditions of nC=1019cm -3 and nH=1020cm-3 for 2 different pumping beam(OFI) diameters, both with intensity I ~ 10!9 W/cm2
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(c) Recombination and gain: The recombination process was simulated by solving the rate equations governing the process, taking into account three-body recombination, electron-impact ionization, electronimpact excitation and de-excitation, radiative recombination and radiative relaxation (spontaneous emission). The plasma was assumed to be optically thin, hence no photoexcitation processes were considered. The values of the rate coefficients in the rate equations were obtained by integrating the cross-sections of the different interactions over the actual nonMaxwellian, time-dependent, electron distribution function that was obtained from the iPIC and FP codes. The small-signal gain coefficient G was then calculated from broadening for the cold ions (the ions are assumed to be fixed during the whole process hence the ions temperature was taken to be the initial plasma temperature, i.e., Ti ≈1 eV) and the Stark broadening estimated for the Lyman-α line by the lesser of the widths given by the quasi-static linear Stark effect (Holtsmark theory) and electron impact broadening. In Figs 4a,b, are shown results for gain G (in cm-1) calculations for CVI 2–1 transition at 3.4 nm for 2 different diameters of pumping laser beam (50 fsec, 1019 W/cm2 ) versus plasma channel diameters and time of gain evolution. The maximum gain is reaching very high values in range G ≈ 150 - 200 cm -1, which is very encouraging result.
4. Raman Backscattering (RBS) Amplification and Compression The second part of our presentation was devoted to a new type of ultrashort and ultra-intensive compact laser system based on Raman Backscattering (RBS) amplification and compression in a few millimeter long plasma. In that presentation we briefly described the research and recent results with emphasis on multi-passes approach for maximizing system efficiency. The principle of RBS amplification in counterpropagating geometry is shown in Fig.5. Moderately intense, but long, laser pulses can be scattered into short very intense counterpropagating pulses in a plasma through stimulated Raman backscattering (RBS). Raman amplification of ultrashort pulses in a plasma is based on the three-wave interaction between the counterpropagating “seed” and “pump” pulses and the plasma waves[21] as is shown schematically in Fig.6. The plasma waves, with frequency ωpe (ωpe2= 4πe2ne/me), are ponderomotively driven by the periodic intensity pattern produced by the
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Raman amplifier
ω pump
ω pump ω ω ω + ω pe = ω seed
“Pump”
“Seed”
“Seed”
ω seed
ωpe
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Fig. 5. Principle of Raman backscattering amplification.
interference between the pump pulse and the seed (subpicosecond) pulse. If the frequency detuning between the two pulses matches the plasma frequency ωpe, i.e., ωpe = ωpump - ωseed, then the seed pulse can be amplified through the RBS instability of the pump.
ω
S eed
P um p
pum p
ω
se e d
P la s m a w a v e
ω p e 2 = 4 π n e e 2 /m R e s o n a n t C o n d itio n s: ω pum p = ω se e d k
pum p
=
k
se e d
+ +
ω k
e
pe pe
Fig.6. Schematic of three waves mixing
The RBS amplification can be divided into linear and nonlinear regimes. In the linear regime, the pump depletion is negligible and the gain is inde pendent of the seed intensity. The seed pulse is amplified and the pulse duration is increased due to the narrow bandwidth of the linear amplification (which is approximately twice the growth rate). The nonlinear regime is characterized by significant pump depletion and simultaneous temporal compression of the amplified pulse, as illustrated in Fig. 7. The front of the pulse is amplified while the tail part interacts with a depleted pump and is not amplified as much as the front. In this regime the efficiency of energy transfer from the pump to the seed can reach ~ 90% when ωpump ≥ 10
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ωpe according to theoretical predictions [22] through the following relation η = 1 - ωpe/ωpump. This could happen when the pump pulse duration is
Pump
P
Depleted pump
Seed
S Amplified Ampliseed
Plas ma
Fig. 7. Resonant Raman non-linear regime (pump depletion)
sufficiently long to match the length of the plasma and obtain nearly full pump depletion. Operating in this nonlinear regime of RBS amplification in the plasma is of highest interest. In Fig. 8 is shown schematically experimental setup on which nonlinear regime was reached [23]. The pump entered the plasma at point A, and the seed at point B. The spatial overlap of the pump and the seed were guaranteed by imaging the two beams above the nozzle with a CCD camera. The temporal overlap was achieved by scanning of the optical delay between the pump and seed with precision better than ps. The output seed passed through a long wavelength (> 850 nm) band pass filter so that any reflected pump beam light was filtered out. A small part of the amplified seed pulse was directed to a spectrometer for spectral analysis. The rest of the beam was split by a 50% beam splitter. One part was directed to a power meter and the second part was directed to an autocorrelator. When the amplification entered the nonlinear regime, the increased bandwidth made the growth of the seed pulse more robust than thermal Raman in the nonuniform plasma. Pulse compression in the nonlinear regime is accompanied by bandwidth broadening. The pump (for pumping of both the Barium Nitrate crystal and the plasma) and the input seed had a bandwidth of about 12 nm. The bandwidth of the amplified seed was ~ 19 nm FWHM, which is an independent indication of reaching the nonlinear regime. With the high amplification of the seed pulse, we were able to perform a pulse duration measurement of the amplified seed using a standard autocorrelator (Positive Light Model SSA) at various plasma length. The pulse
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Fig.8. Schematic of the RBS amplifier & compressor experimental setup
was observed to lengthen to a maximum of ~ 800 fs when the amplification was below 10. The pulse duration began to decrease when the ampli fication approached 30. he trend that the pulse became shorter as the amplification became higher is clearly shown in Fig. 9. The shortest pulse we have observed so far had a FWHM of ~ 150 fs when the amplification was ~ 60. At this point, the power of the seed pulse increased more than 200 times, and its intensity increased ~ 1000 times when spatial beam narrowing was taken into account. The intensity of the amplified seed pulse at point A in Fig. 8 was 1.7 x 1015 W/cm2. The pump pulse diameter was about 50 μm FWHM at point A and had an intensity of ~ 1 x 1014 W/cm2, hence the intensity of the amplified seed exceeded the pump intensity by more than order of magnitude. Simulation results are also shown in Fig.9. Simulations were performed using the average 1D particle-in-cell code (aPIC). The seed and pump pulses were assumed to be initially Gaussian with FWHM given by the experimental values of 500 fs and 10 ps, respectively. The initial seed intensity was 1.6 x 1012 W/cm2 and pump intensity was 1 x 1014 W/cm2. The plasma density was chosen so that the plasma wave (including a thermal shift) was resonant with the beat frequency of the lasers. The electrons were assumed to be initially homogeneous with a Maxwellian velocity distribution of Te=50eV and the ions were assumed to be motionless over the short timescale of the simulation. The seed energy amplification (the final seed energy divided by the initial seed energy) and the FWHM of the seed pulse duration are plotted as a function of the amplification of the seed (function of interaction length ). The simulation clearly shows pulse
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Fig. 9. Pulse duration vs. output energy (amplification); amplified pulses: modeling (solid lines) and experiments (circles)
stretching of the seed during the initial amplification (until roughly 1mm, corresponding to an energy amplification of ~20 ), followed by pulse shortening to ~240 fs at an energy amplification of ~180 at the end of the 2 mm plasma. While the pulse duration evolution agreed quite well with the experimental measurements, we did not observe an energy gain factor as high as 180. This may be because the amplified seed pulse experienced energy loss due to heating and ionization induced diffraction of the plasma. The simulation results shown here are one-dimensional and are, in detail, sensitive to the initial value chosen for the temperature (which is not yet well known experimentally). Nevertheless, the qualitative features of the experiment are well-reproduced including pulse expansion followed by noticeable compression and amplification of the seed pulse after its intensity becomes larger than that of the pump.
5. Two-passes RBS amplification In Fig. 10 are presented recent results for amplification in two-passes set up. The system employed additional mirrors, and interferometeric filters in order for pump pulse, after amplifying seed pulse in plasma in the 1st pass, to be directed back to approximately the same plasma region and interact again with reflected back into the plasma amplified seed. This way in the second pass the seed was increased farther amplified by factor ~2.
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Amplified Seed Energy
This was just demonstration of possibility to amplification in second pass due to quite significant “left over” pump energy from the 1st pass. Such 2passes or even multi-pass systems could significantly improve efficiency of RBS amplifier/compressor. Single pass
(a) Pump delay (psec)
Double
(b) Pump delay (psec)
Fig. 10. Amplified seed energy in single pass (a) and in double pass (b) for input seed of 5 μJ and pumping energy ~ 62 mJ in the 1st pass and ~ 40 mJ in second pass *) Present address: The University of Texas at Austin
References
1. Matthews, D, Hagelstein, P, Rosen, M., et al.: ‘Demonstration of soft X-Ray Amplifier’, Phys. Rev. Lett., 54, 110, 1985. 2. Suckewer, S., Skinner, C.H., Milchberg, H., Keane, C., and Voorhees, D.: ‘Amplification of stimulated soft-x-ray emission in a confined plasma column’, Phys. Rev. Lett., 55, 1753, 1985; also Suckewer, S., Skinner, C.H., Kim, D., Valeo, E., Voorhees, D., and Wouters, Al, ‘Divergence measurements of soft-x-ray laser beam’, Phys. Rev. Lett., 57, 1004, 1986. 3. Dunn, J., Osterheld, A.L., Shepherd, R., White, W., Shlyaptsev, V.N., and Stewart, R.E., ‘Demonstration of x-ray amplification in transient gain nickellike palladium’, Phys. Rev. Lett., 80, 2825-2828, 1998; also Dunn, J., Li, Y., Osterheld, A.L., Nilsen, J., Hunter, J.R., and Shlyaptwev, V.N. ‘Gain satura-
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tion regime for laser driven tabletop transient Ni-like ion x-ray lasers’, Phys. Rev. Lett., 84, 4834-4837, 2000. 4. Nickles, P.V., Shlyaptsev, V.N., Kalachnikov, M., Schnurer, M., Will, I. Sandner, W., ‘Short pulse x-ray laser 32.6 nm based on transient gain in Ne-like titanium’, Phys. Rev. Lett., 78, 2748-2751, 1997. 5. Nilsen, J., MacGowan, B., DaSilva, L.B., and Moreno, J.C., ‘Prepulse technique for producing low-Z Ne-like x-ray lasers’, Phys. Rev. A, 48, 4682-4685, 1993. 6. Keenan, R., Dunn, J., Patel, P.K., Price, D.F., Smith, R.F., and Shlyaptsev, V.N., ‘High- repetition-rate grazing-incidence pumped x-ray laser operating at 18.9 nm’, Phys. Rev. Lett., 94, 103901, 2005. 7. Luther, B.M., Wang, Y. M., Larotonda, A., Alessi, D., Marconi, M.C., Rocca, J.J., and Shlyaptsev, V.N., ‘Saturated high repetition-rate 18.9-nm tabletop laser in nickel-like molybdenum’, Optics Lett., 30, 165-167, 2005. 8. Nagata, Y., Midorikowa, K., Obara, M., Tashiro, H., and Toyoda, K., Phys. Rev. Lett., 71, 3774, 1993. 9. Korobkin, D., Nam, C.H., Goltsov, A., and Suckewer, S., ‘Demonstration of soft x- ray lasing to ground state in Li III’, Phys. Rev. Lett,. 77, 5206-5209, 1996. 10. Goltsov, A., Morozov, A., Suckewer, S., Elton, R., Feldman, U., Krushelnick, K., Jones, T., Moore, C., Seely, J., Sprangle, P., Ting, A., and Zigler. A., ‘Is efficiency of gain generation in LiIII 13.5-nm laser with 0.25μm subpicosecond pulses the same as with 1 μm?’, IEEE J. Sel. Top. Quantum Electron., 5(6):1453–1459, 1999. 11. Rocca, J.J., Shlyaptsev, V.N., Tomasel, F.G., Cortazar, O.D., Harshorn, D., and Chilla, J.L., Phys. Rev. Lett., 73, 2192, 1994 ; also Benware, B.R., Macchietto, C.D., Moreno, C.H., and Rocca, J.J., ‘Demonstration of a high average power tabletop soft x-ray laser’, Phys. Rev. Lett., 81, 5804-5806, 1998 ; also Macchietto, C.D., Benware, B.R., Rocca, J.J., ‘Generation of millijoulelevel soft-x-ray laser pulses at a 4-Hz repetition rate in a highly saturated tabletop capillary discharge amplifier’, Opt. Lett., 24, 1115-1117, 1999. 12. Lemoff, B.E., Yin, G.Y., Gordon III, C.L., Barty, C.P., and Harris, S.E., ‘Demonstration of a 10-Hz Femtosecond-Pulse-Driven XUV laser at 41.8 nm in Xe IX’, Phys. Rev. Lett ,74, 1574-1577, 1995. 13. Attwood, D.T., Soft X-rays and extreme ultraviolet radiation, Cambridge University Press, 1999. 14. Keldysh, L.V., ‘Ionization in the field of strong electromagnetic wave’, Soviet Physics JETP, 20, 1307, 1965. 15. Perelomov, A.M., Popov, V.S., and Terent’ev, M.V., Soviet Physics JETP, 23, 924, 1965. 16. Burnett N.H., and Corkum, P.B., ‘Cold-plasma production for recombination extreme-ultraviolet lasers by optical-field-induced ionization’, JOSA B, 6, 1995, 1989.
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17. Ping, Y. Ph.D. Thesis ‘Soft X-ray Lasers and Raman Amplification in Plasmas’, Princeton University, 2002. 18. Avitzour, Y., Suckewer, S., and Valeo, E., ‘Numerical investigation of recombination gain in the LiIII transition to ground state’. Phys. Rev. E., 69, 046409, 2004. 19. Y. Avitzour Ph.D. Thesis “Numerical Modeling of Recombination X-Ray Lasers in Transition to Ground State”, Princeton University (2006). 20. Avitzour, Y., Suckewer, S., ‘The feasibility of achieving gain in transition to ground state of CVI at 3.4nm’, submitted for publication (August.2006) 21. Shvets, G., Fisch, N.J., Pukhov A., and Meyer-ter-Vehn, J., ‘Superradiant Amplification of an Ultrashort Laser Pulse in a Plasma by a Counterpropagating Pump’, Phys. Rev. Lett., 81, 4879, 1998; also Fisch, N.J., and Malkin, V.M., ‘Generation of Ultra-high Intensity Laser Pulses’, Physics of Plasma, 10, 2056-2063, 2003. 22. Malkin V. M., Shvets G. and Fisch N. J., ‘Fast compression of laser beams to highly overcritical powers’, Phys. Rev. Lett., 82, 4448, 1999;also Malkin V. M., Shvets G. and Fisch N. J., ‘Detuned Raman amplification of short laser pulses in plasma’, Phys. Rev. Lett,. 84, 1208, 2000. 23. Cheng, W., Avitzour, Y., Ping, Y., Suckewer, S., Fisch, N.J., Hur, M.S., and Wurtele, J.S., ‘Reaching Nonlinear Regime in Large Raman Amplification of Ultrashort Laser Pulses’, Physical Review Letters, 94, 2005.
Status and Prospects on Soft X-Ray Lasers Seeded by a High Harmonic Beam at LOA
S. Sebban1 , Ph. Zeitoun1, G. Faivre1, S. Hallou1, A. S. Morlens1, J.P. Goddet1 B. Cros2, G. Vieux2 and G Maynard2,T. Mocek4 and M. Kozlová4, J.P. Causmes5 and H. Merdji5 1
Laboratoire d’Optique Appliquée, chemin de la hunière, 91128 Palaiseau LPGP, Université Paris-Sud, 91405 Orsay, France 3 Institute of Physics, Department of X-Ray Lasers, Prague, Czech Republic 4 Service des Photons, Atomes et Molecules, CEA, 91191 Gif-surYvette,France 2
Summary. Thanks to the most recent works on x-ray laser and on high order harmonics (HHG), it is now possible to produce an energetic beam having at the same time the required optical properties. The solution consists in seeding the XRL amplifier medium with another beam (HHG). This experiment was successfully realized in LOA. We studied seeding of two x-ray laser transitions, 4d-4p at 32.8 nm in Kr8+ and 5d-5p 41.8 nm in Xe8+. The amplifying medium is generated by focussing a high energy circularly polarized, 35 fs 10 Hz Ti: sapphire laser system in a few mm cell filled with gas (xenon or krypton). We succeeded to increase from a factor 10 to 200 the HHG energy, without deteriorating their optical qualities. The resulting beam was polarized, coherent and we estimate the output energy to be about 0.5 µJ.
1 Introduction For decades, synchrotrons have been the acme of XUV sources, providing X-rays for biology, chemistry, physics applications and industrial developments, resulting in major scientific progress. But tomorrow’s most attractive applications (e.g. structural Biology) require pulses with much shorter duration (fs) and much higher energy (mJ) than delivered by synchrotrons. X-ray Free Electron lasers should fulfil these requirements by providing ultra-intense beams, but their limited number will stir tremendous beamtime pressure, slowing down the spreading of applications. Laser-driven XUV sources are comparatively inexpensive and widely avail-
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able, but they have reached a bottleneck in the race for ultra-high intensities. In this pioneer work, we have set up and characterised the first true XUV laser chain, overcoming these bottlenecks for the first time. By combining the high optical quality of high harmonics as a seed [1] , with a highly energetic x-ray laser plasma amplifier [2-3], we produced the first highly saturated, energetic, femtosecond, fully coherent and fully polarised tabletop x-ray laser operating at 10 Hz [4]. This technique, easily applicable on all existing laser-driven XUV facilities, opens the way to ultra-high intensities studies worldwide. Since some years x-ray laser community try to promote this source for applications. In this aim, it is necessary to offer an optically good beam to the users. Nevertheless most of x-ray laser (XRL) are using amplified spontaneous emission, i. e. laser has no cavity to select a spatial mode. Consequently the beam can not be polarized or spatially coherent and the wave front is not regular. Thanks to the most recent works on x-ray laser and on high order harmonics (HHG), it is now possible to produce an energetic beam (from 0.1 to 1mJ) having at the same time the required optical properties. The solution consists in seeding the XRL amplifier medium with another beam (HHG). This experiment was successfully realized in LOA. We studied seeding of two x-ray laser transitions, 32.8 nm (Kr8+) and 41.8 nm (Xe8+). We succeeded to increase from a factor 15 to 600 the HHG energy, without damaging their optical qualities. This structure seems to be the beginning of a new generation of XRL, with considerable improvements compare to the actual XRL. Furthermore this technique can help for the measurement of many plasma parameters.
2 Experimental setup The XUV amplifying laser chain was made of three parts: a high harmonics generation (HHG) seed, a focusing system, and an optical field ionized x-ray laser (XRL) amplifier medium. The seed beam was obtained by focusing a 20 mJ, 30 fs, infrared laser in a gas cell filled with argon or xenon .This seed was image relayed onto the entrance of the x-ray laser (XRL) amplifier (Kr or Xe gas longitudinally pumped by a 1 J, 30 fs laser) by means of a toroidal XUV mirror. This X-ray laser operates at 32.8 nm and 42.8 nm using Kr and Xe respectively. After amplification, the output beam was either analyzed by an XUV spectrometer or XUV CCD camera. The experiment has been performed in LOA with the multiterawatt, 30 fs, 10 Hz, Ti:sapphire laser emitting at 815 nm. The laser delivers two chirped beams having separate pulse compressor enabling to optimise in-
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dependently the XRL or the HHG drivers. One beam, lately called “pump”, contains most of the energy (about 1 J on target) and is used for creating the amplifying XRL medium. The second beam, called “probe”, has energy around 20 mJ on target and generates the HHG (Figure 1) Harmonics were produced by focusing the probe beam into a gas cell of variable pressure and length, filled with argon. The linearly polarised beam was focused with a f=1.5 m, aspherical lens. The focal spot has been 15 -2 measured to be about 150 µm leading to an intensity of about 10 W.cm . The harmonic flux was optimised by changing the conditions of laser interaction with the active medium, such as moving the focal spot position, changing the gas pressure, and the cell length. The highest HHG flux was obtained for a pressure of 25 mbar, 10 mm long cell, and focal plane situated 4 cm behind the gas cell. The main optimisation was the fine adjustment of the wavelength of one harmonic (25th) so as to coincide with the 8+ wavelength of Kr XRL (32.8 nm). This was done on a day-to-day basisby adjusting the chirp of the laser generating the HHG [5-6].
Fig. 1. Schematic description of the experimental set-up
The amplifying plasma was created by focusing the pump beam into another gas cell of variable length (from 0 to 6 mm) and pressure. The cell was filled with krypton or xenon held at uniform pressure. Fundamental radiation from the Ti:Sapphire laser was circularly polarised by a quarterwave plate and focused with an f=0.85 m, spherical on-axis mirror into the gas cell. Circular polarisation ensures the creation of energetic free electrons that collisionally pump the 4d-4p or 5d-5p lasing lasing transitions. The measured focal spot was around 50 µm in diameter leading to a net in17 -2 tensity of about 5×10 Wcm . The output of the harmonic source was re-imaged on the entrance of the amplifier plasma, using a 1:1 grazing incidence (4°) gold coated toroidal
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mirror. The theoretical reflectivity is around 80%. The focal spot of HHG has been measured to be around 150 µm. Special attention has been paid to the temporal and spatial overlapping between the harmonic and the X-ray laser beams. As the OFI XRL is longitudinally pumped, the position of the gain region coincides with the position of the IR driving laser. Since also the HHG are collinear with the IR beam, the superposition of the HHG and the XRL gain region has been done in IR. Temporal synchronisation of the HHG with the period of XRL amplification could not be done in such a simple way since the plasma starts to amplify after the interaction of the driving laser with the gas. Based on previous experiment, we may assume that the gain will appear around 5 ps after laser interaction and will last about 8 ps [7]. Since HHG are emitted only during the interaction of the IR laser with the gas, the synchronisation of the seed and the XRL period of amplification was done by adjusting the delay between the IR pump and probe beams. The XUV beams generated in this experiment were analysed by an onaxis XUV spectrometer and by making monochromatic images of the beam cross-section. These images were obtained by placing a removable 45°, XUV mirror in the beam path, redirecting the beam towards a cooled, thin, back-illuminated charge-coupled device (CCD). A 300 nm thick aluminium filter has been used to remove the IR beams. The interferential multilayer mirror has been designed to achieve a high reflectivity (estimated at 50%) and a strong polarisation at 45°. The XUV mirror is made of a stack of 30 Mo/B4C/Si tri-layers.
3 Results and discussion The delay between XRL plasma creation and HHG injection was variable to reach optimum amplification conditions, synchronizing HHG seeding with maximum gain. Four emission spectra are displayed in figure 2, corresponding to (a) high harmonics alone, (b) x-ray laser alone, (c) XRL and HHG seeded long after gain extinction, and (d) HHG synchronised with maximum XRL gain. The amplification period starts 5 ps after the interaction of the IR laser with the gas and lasts about 8 ps. Figure 2 (d) clearly shows that a strong amplification of the seed has been achieved. The HHG were seeded at about twice the intensity of the ASE x-ray laser, leading to an enhancement of the output signal by a factor of 13. Since the level of seeding may influence many laser parameters (intensity, pulse duration, ratio of the energies in the seeded beam to this in the ASE beam), it is crucial to understand how is the seeding level related to the saturation intensity.
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Fig. 2. Experimental spectra under conditions : (a) HHG only, (b) ASE XRL only, (c) both HHG and XRL in a non-amplifying timing, and (d) the amplified seeded XRL.
The amplification law (output intensity versus amplifier length) of the amplified spontaneous emission (ASE) XRL has been measured to clarify the level of seeding. The gas cell length ranged from 0 to 4 mm and the intensities have been fitted taking into account saturation effects [3]. A -1 small-signal gain coefficient of 80 cm has been inferred, reaching saturation above 1.7 mm plasma length. Clearly, the spectrum in Fig. 2(d) was obtained for an HHG seeding above saturation intensity (about 4.5 times higher). In the second part of the experiment, the seeding intensity was reduced down to 1/50th of the saturation intensity. The output signal was 38 times higher than the saturation intensity; the amplification factor became as large as 200 i.e. 15 times higher than for the amplification achieved with above-saturation-intensity seeding. The delay line has also allowed to measure the gain duration for several pressure. This measurement was done for both gas, krypton end xenon. For the Xe8+ at 41,8 nm (fig3a), the maximum gain was obtained for a pressure of 15 Torr and the duration of the gain was about 8ps. For Kr8+ at 32.8 nm (fig3b) the best pressure was 15 Torr, and for this pressure the gain duration was 4 ps. Using this method the temporal profile of the gain of the collisionally excited Xe8+ laser at 41.8 nm has been measured for various gas densities and compared to simulations of the atomic processes
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a)
b)
c) Fig. 3. (a) Measured amplification, (b) extracted average gain and (c) calculated gain coefficient as a function of function of the injection delay for Xe, and for 5 gas pressures
performed with a time-dependent collisional radiative code as shown in figure 3 [8]. The seeded XRL beam was also characterised in terms of optical parameters such as divergence, spatial coherence and polarisation. These parameters were directly inferred from images of the beam cross-section (fig. 5 and 6). Theoretically, the ratio of the mirror reflectivity for the 25th harmonic (32.8 nm) to the 23rd (35.65 nm) or to the 27th (30.37 nm) is about 10. Therefore only the 25th harmonic and/or the XRL might be reflected towards the detector. The seed divergence is imposed by both the geometry of the toroidal mirror and the HHG intrinsic divergence. The divergence of the seeded XRL was slightly lower than those of the seed. The brightest part of the image in Fig. 4 corresponds to the seeded XRL while the weak surrounding, circular signal is the ASE x-ray laser. The diver-
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gence of the seeded XRL was slightly lower than those of the seed. The brightest part of the image in Fig. 4 corresponds to the seeded XRL while the weak surrounding, circular signal is the ASE x-ray laser. The divergence of the ASE x-ray laser was found to be much larger (>12 mrad) than that of the seeded beam (1 mrad).
Fig. 4. 3D images (false color) of the seeded XRL cross-section as recorded by the XUV CCD detector after reflection on the monochromatic XUV mirror. The central strong signal (gray) belongs to the seeded XRL while the ASE XRL illuminating essentially the whole filter generated a circular signal (purple). The insert shows the seeding HHG signal recorded with the same set-up and displayed on the same scale as the main image.
The multilayer mirror has been designed to be highly polarising. The extinction ratio (intensity peak/lowest intensity) has been investigated by measuring the reflected signal versus the angle of polarisation of the HHG. Figure 5 displays the variation of both the HHG and the seeded XRL intensity versus the angle of polarisation The extinction ratio of the mirror is as high as 20. From these curves, it appears that the seeded XRL is polarised and follows well the initial polarisation of HHG. No sign of depolarisation has been observed. Inserts in Fig. 6 show the beam cross-section when the HHG were s- polarised (peak reflectivity) and p- polarised (minimum reflectivity). As expected, the ASE XRL alone is unpolarized. Also we have observed that the coherence of the seeded XRL beam can be dramatically improved, with the respect to seed HHG beam. In this aim, we have characterized the spatial profile and conducted a series of Young’s two-slit experiments to measure and systematically compare the
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Fig. 5. Variation of the HHG (open diamond) and seeded XRL (black square) intensities versus the angle of polarization.
Fig. 6. Fringe visibility of the HHG beam, the ASE emission and the amplified 32.8 nm pulse as a function of the slit separation.
spatial coherence of the seed HHG beam, the ASE amplifier emission and the seeded amplifier emission at 32.8 nm. Figure 6 shows the normalized complex degree of coherence ⎟µ12⎟ plotted for a gaussian profile. The coherent radius of the ASE emission is about 98 µm which is about 150 times smaller that the measured beam diameter. As the OFI XRL emission can be considered as spatial incoherent but temporally coherent, the equivalent incoherent source size which is here about 76 µm should closely correspond to transverse dimension of the plasma amplifier. For the seed HHG beam we estimate a coherent radius of 102 µm which corresponds to about a quarter of full beam diameter. When amplified by the population inverted plasma, the coherent radius build upto 232 µm which corresponds to about 60% of the central disc of the beam profile, showing the benefic action of spatial filtering on the improvement of the transverse coherence of the generated pulse.
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4 Conclusion Future work will be in a near future to seed in an OFI capillary (ASE x30 compare to OFI in a gas cell). With this kind of amplifier, the expected output energy is about 30 µJ). Later we plan to seed an XRL plasma created from a solid target such as to increase the output energy by at least three order of magnitudes (~ 1 mJ) thanks to the much higher density of XRL amplifying medium [9]. This rise in density and temperature will also lead to a spectral width broadening and consequently to even shorter pulse duration. As this technique matures, future compact XUV laser chains should achieve beams performances close to those of VUV Free-electron lasers [10].
References [1] Kazamias, S. et al, Global optimization of High Harmonic generation. Phys. Rev. Lett., 90, 193901 (2003) [2] Sebban, S., Demonstration of a Ni-Like Kr Optical-Field-Ionization at 32.8 nm. Phys. Rev. Lett., 89, 253901 (2002). [3] Sebban, S. et al, Saturated Amplification of a Collisionally Pumped OpticalField-Ionization Soft X-Ray Laser at 41.8 nm. Phys. Rev. Lett. 86, 3004 (2001). [4] Ph. Zeitoun. et al. , A high-intensity highly coherent soft X-ray femtosecond laser seeded by a high harmonic beam, Nature vol 431, 426-429 (2004) [5] Lee, D. G., Kim, J. H., Hong, K. H., Nam, C. H., Coherent Control of HighOrder Harmonics with Chirped Femtosecond Laser Pulses. Phys. Rev. Lett, 87, 24, 243902 (2001) [6] Reitze, D. H., Enhancement of high-order harmonic generation at tuned wavelengths through adaptative control. Opt. Lett., 29 1, p. 86 (2004) [7] T. Mocek et al, Characterization of collisionally pumped optical-fieldionization soft x-ray lasers. Appl. Phys. B, in press [8] T. Mocek, S. Sebban, G. Maynard, Ph. Zeitoun, G. Faivre, A. Hallou, M. Fajardo, S. Kazamias, B. Cros, D. Aubert, G. de Lachèze-Murel, J. P. Rousseau, and J. Dubau “Absolute Time-Resolved X-Ray Laser Gain Measurement”, Phys. Rev. Lett. 95, 173902 (2005) [9] Y. Wang et al. Phys. Rev. Lett 97 (2006) 12901 [10] Ayvazyan, A. et al, A new powerful source for coherent VUV radiation : Demonstration of exponential growth and saturation at the TTF free-electron laser. Eur. Phys. J. D, 20, 149 (2002)
Generation of Efficient Optical-Field-Ionization X-Ray Lasers in Cluster Jets M.-C. Chou, T.-S. Hung and J.-Y. Lin* Department of Physics, National Chung Cheng University, Chia-Yi 621, Taiwan P.-H. Lin, S.-Y. Chen and J. Wang Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan
Summary: We experimentally demonstrate the amplification of optical-fieldionization soft x-ray lasers in krypton cluster jets at pump energy of only 200 mJ. With the employment of small f-number optics, nature diffraction and ionizationinduced refraction in plasmas can be suppressed to enable the pump pulse producing a longer column of gains provided the focal position is optimized. A simple wave propagation code is developed to study and optimize the laser propagation in optical-field driven plasmas. Good agreements between experimental observations and simulations are found. The further enhancement of Kr x-ray laser output at 32.8 nm is achieved by guiding the pump beam in the optically preformed plasma waveguide. More than 4 times of x-ray photons are generated from pure Kr plasma waveguide at the same pump energy. Significant reductions of the pump energy make these pumping configurations favorable for practical high-repetitionrate operations.
1 Introduction Optical-field-ionization (OFI) has been considered as an efficient way for pumping tabletop, high-repetition-rate soft x-ray lasers through collisional excitation or recombination processes, because the electron energy distribution and the ionization balance in plasmas can be precisely controlled by the pump laser intensity and polarization [1-5]. A linearly polarized laser pulse can minimize the mean electron temperature in plasmas and promote strong recombination, whereas the hot electrons produced by a circularly polarized pulse can be used for collisional-excitation pumping. Moreover,
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the appearance intensity for various ion species in the OFI plasma is discrete and highly selective. These properties can be applied to enhance ion utilization, thereby achieve efficient lasing. Saturated lasing of collisional excitation OFI x-ray lasers was first demonstrated in Xe8+ ions for the 5d-5p transition at 41.8 nm by focusing an intense, circularly polarized laser pulse into a gas cell filled with pure xenon [6]. A similar result was later obtained in a xenon cluster jet operated at high backing pressures [7]. Strong amplification at 32.8 nm for the 4d– 4p transition of Ni-like krypton has also been demonstrated with a 760-mJ, 30-fs laser pulse [8]. Recently, enhancement of OFI x-ray lasing in preformed plasma waveguides driven by discharge was reported. The gain media were a capillary tube filled with xenon and buffer gas [9] or a multimode capillary waveguide [10]. By seeding an OFI x-ray laser amplifier with a pulse produced from high harmonic generation, a 20-fold increase in the x-ray output was achieved and sub-picosecond x-ray pulse was produced [11]. In this paper, we demonstrate low-threshold lasing of the 32.8-nm Kr8+ 4d–4p line by using tight-focusing pumping configurations. In the meantime, we use gas jets as the gain media to avoid accumulated optical damage. The combination of low pumping threshold and gas-jet media facilitates long-time high-repetition-rate operation, which is an important aspect for practical applications. We show that low-threshold OFI x-ray lasing can be achieved by tight focusing the pump laser at an optimal focal position. Both computer simulation and experimental diagnosis show that the balance between the converging power of the focusing optics, diffraction, and ionization defocusing can increase the gain length significantly as the spatial profile of the pump beam is well controlled at the optimal size. Near saturated lasing was observed at a pump energy of only 200 mJ, and the lasing threshold is only 70 mJ. In order to further improve the efficiency and beam quality of OFI x-ray lasers, a preformed plasma waveguide is developed to guide the intense pump pulse in OFI plasmas. The guided laser pulse can delivered a high pump intensity in a smaller diameter at a considerably low pulse energy. The interaction length and thus the gain-length product of x-ray lasers can also be extended significantly. We show that the plasma waveguide can be efficiently produced in a Kr/H2 cluster jet operated at a high backing pressure with axicon ignitor-heater scheme [12]. More than 70% of the pump energy in the vacuum focal spot is observed to transmit through the all optically preformed waveguide. The waveguide with buffer gas H2 can be used to develop recombination OFI x-ray lasers as electrons generated from high-density hydrogen are relatively cool [13]. On the other hand, strong amplifications of collisional excitation OFI Kr x-ray laser at 32.8
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nm is observed in pure Kr waveguide. The spectral brightness of Kr lasers amplified in waveguides is enhanced by a factor of > 100 compared to that obtained with tight focusing configuration.
2 Experimental Setup The experimental setup was similar to that described in Ref. 7, 12. A 10TW, 45-fs, 810-nm, and 10-Hz Ti:sapphire laser system (upgraded from the laser system in Ref. 14) based on the chirped-pulse amplification technique was used in this experiment. The pump pulse was focused by an offaxis parabolic mirror of 30-cm focal length onto a cluster jet. The focal spot size of the pump pulse was 7.5-µm diameter in full width at half maximum (FWHM) with 80% energy enclosed in a Gaussian-fit profile. A quarter-wave plate was used to change the pump polarization. The cluster jet was produced from a slit nozzle with a 5-mm×500-µm outlet and a round throat of 1.2-mm diameter. In the major axis of the outlet, the inner opening angle of the nozzle is 5.4°, and in the minor axis the inner width shrunk from 1.2 mm at the throat to 0.5 mm at the outlet. To produce a gas target with sharp boundaries, a rectangular aperture was mounted on the output of the cluster jet. So, the gas density profile had a flat-top region of 3.5 mm in length and a sharp boundary of 450 µm at both edges along the major axis. The average atom density increased linearly with the backing pressure and was measured to be 2.8×1017–3.2×1019 cm-3 for a backing pressure of 0.041–4.8 MPa. The preformed plasma waveguide was produced in pure krypton gases or the mixture of krypton and hydrogen gases with the axicon ignitor-heater scheme. The ignitor was a compressed 45 fs pulse, and the heater was the uncompressed beam with a pulse duration of 80 ps. They were focused by an axicon of 30° base angle to a line focus of ~8-mm length. The longitudinal intensity distribution of the line focus can be approximately controlled by a beam expander installed before the axicon. A relay-imaging system was used to measure the injection beam profile at the end of the plasma waveguide to verify the guiding of the injection beam. The on-axis diagnostic was a flat-field spectrometer (FFS) made of an aperiodic grazing-incidence grating with an average groove density of 1200/mm and a back-illuminated 16-bit soft x-ray CCD camera. A 0.5 µm-thick Al filter is used to block the pump beam and to attenuate x-ray emission. A dipole magnet was put in front of the spectrometer to deflect the electrons emitted from the interaction region, guarding against false signals from electrons in the x-ray CCD camera. Mach-Zehnder interferometry with a probe pulse passing transversely through the cluster jet
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Fig. 1. X-ray laser output as a function of the focal position at atom density of 1×1018 cm-3. The pump energy was 200 mJ and the pump polarization ellipticity was 0.55. The effective f-number of the focusing optics is 7. Inset: Kr x-ray laser spectrum at 32.8 nm.
was used to measure plasma density distribution 5 ps after the pump pulse. The propagation of the pump pulse in the cluster jet can be analyzed from the interferograms. By calibrating the grating reflectivity, the filter transmittance, and the CCD response, the absolute emission yield was obtained.
3 Experimental results and discussions 3.1 Low-threshold OFI Kr lasers with tight focusing pumping To create a uniform and elongated plasma column for x-ray amplification, we scan the focal position of the pump laser in vacuum relative to the entrance of the gas target along the laser propagation direction. At each position, the diameter and the wave front curvature of the pump beam at the front boundary of the gas target is different, so is the nonlinear evolution of the beam profile in the plasma. Fig. 1 shows the strong dependence of the lasing signal on the focal position. The inset shows the on-axis time integrated Kr x-ray laser spectrum for a pump polarization ellipticity of 0.55 at an atom density of 1×1018 cm-3 and a focal position of 2.2 mm behind the front edge of the gas target. When the laser pulse is focused at the front edge, the intensity is about 5.5×1018 W/cm2, which is much higher than needed for producing the correct ionization balance. Over-ionization depletes Kr8+ ions and shortens the gain length. In addition, overproduction
Generation of Efficient Optical-Field-Ionization X-Ray Lasers in Cluster Jets 239
Fig. 2. Dependence of the calculated gain length on the focal position for different focusing optics. The parameters used in the simulation are the same as in Fig. 1, except that the focal length of the pump laser is varied.
of free electrons promotes ionization defocusing which makes the laser beam diverge quickly. As the laser intensity drops below OFI threshold of Kr8+ ions, the lasing gain is also terminated at the rear portion of the gas jet. On the contrary, if the focal spot is moved to the rear edge of the gas jet, the beam diameter at the front edge becomes relatively large. The pump intensity becomes too low to generate lasing ions at the front portion of the gas jet. Consequently there exists an optimal focal position to achieve a good balance among beam convergence, diffraction, and ionization defocusing for the laser beam to maintain its intensity over a long distance. To study and optimize the pump beam propagation in OFI plasmas, a source dependent expansion method [15] is used to numerically solve three-dimensional nonlinear wave equations for the pump pulse. The computation takes account of photoionization, ionization energy depletions, and laser propagations in a plasma with spatially and temporally varying density. Since the lasing plasma is predominately generated by the laser pulse via optical-field ionization, the ion density, electron density, and photonionization rate in specific stages of ionization can be calculated using the Ammosov-Delone-Krainov formulas for a given field [16]. In turn, the spatiotemporal electron and ion density profile determine the propagation of the pump pulse. These two processes are described by a system of nonlinearly coupled equations which can be numerically integrated. Fig. 2 shows that the dependence of the calculated effective length of the gain re
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Fig. 3. X-ray lasing signal and calculated gain length as a function of pump energy. Solid square: lasing signal at 32.8 nm produced by a pump pulse with a polarization ellipticity of 0.55 at an atom density of 1×1018 cm-3. The focal position is at 2.2 mm behind the front edge of the gas target. Solid line: calculated gain length under the same condition.
gion on the focal position for various focusing configuration. All the parameters used in the simulation are the same as in Fig. 1, except that the focal length of the pump laser is varied. The result shows that the x-ray amplification length is increasingly more sensitive to the focal position as the f-number decreases. The length of the gain region is clearly enhanced by tight focusing at an optimal position. The dependence of the lasing output on the pump energy was measured to explore how OFI lasers work under low-energy pumping. As shown in Fig. 3, it was observed that the x-ray laser output was enhanced dramatically (up to factor of 1000) from pump energy of 70 mJ to 200 mJ. In the small signal region, the laser output is expected to increase exponentially with the length of the gain region. Simulations reveal that the effective amplification length increases monotonically with the pump energy when the pump beam is focused at the optimal position. The departure of simulation results from experimental data at large pump energy indicates that the laser gain may have started to saturate, as the saturation effect is not included in the simulation model. A small signal gain coefficient of 61±9 cm-1 is derived from the experimental and simulation data at the pump energy up to 130 mJ in Fig.3. A gain-length product of 15.9±1.3 is expected when the pump energy is 200 mJ. The absolute yield under 200-mJ pumping is estimated to be ~1×109 photons/pulse. This value is close to that of
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saturated Kr x-ray lasers reported in Ref. 8 with a 760-mJ, 30-fs pump pulse. It is interesting to note that in our experiments the optimal polarization ellipticity for maximum x-ray lasing was found to be in the range of 0.5– 0.6 regardless of the atom density. The result can be explained by the preionization of the clusters at the ionization front. If collisional heating and ionization at the ionization front can ionize Kr atoms to Kr3+ or Kr4+, these pre-ionized electrons may lose their energy via radiative cooling during the nanoplasma expansion and through collision with other colder electrons or surrounding neutral atoms during the uniform plasma expansion. As a result, upon the arrival of the main peak of the pump pulse, the energies of these pre-ionized electrons may fall below the threshold of collisional excitation and thus they cannot contribute to collisional excitation. This will greatly reduce the gain. A reduction of the polarization ellipticity toward linear polarization can shift the electron energy spectrum toward the lowenergy end for subsequent ionization stages from Kr3+ or Kr4+, thereby increases the collisional excitation rate. The observation suggests that by using time-domain polarization shaping [17], it may be possible to further optimize the electron energy spectrum in accordance with the ionization stages. This will further increase the gain and efficiency. 3.2 Generation of OFI Kr lasers in preformed plasma waveguide Figure 4(a) shows the interferogram at an ignitor-heater separation of 200 ps and a probe delay of 2.5 ns with respect to the heater in the 5-mm Kr/H cluster jet operated at 630-psi backing pressure. The ratio of Kr to H2 in the gas reservoir of the cluster jet was 1:11. The pulse energy for ignitor and heater were 43 mJ and 290 mJ, respectively. It was found that plasma waveguide cannot be generated if only the ignitor or the heater was used. Instead, a uniform plasma waveguide extended to ~4.4 mm was observed when both ignitor and heater were deployed. These results show that the plasma waveguide can be produced much more efficiently when the axicon scheme is used in conjunction with the ignitor-heater scheme. When only a short laser pulse is used, even though it has sufficient energy to ionize the gas, the pulse duration is too short to heat the plasma via inverse bremsstrahlung absorption. When only a long pulse is used, the laser intensity is too low to produce seed electrons so that there is no inverse bremsstrahlung absorption to drive the formation of plasma waveguide. In the ignitor-heater scheme, the short low-energy pulse first ionizes the gas to provide seed electrons by multi-photon ionization, so that the following long high-energy pulse can be absorbed efficiently to drive the expansion
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Fig. 4. Interferogram (a) and beam profile of the injected pump beam at ~ 5 mm after its focus (b) for various cases in the mixture gas of 1:11 Kr/H at a backing pressure of 630 psi. The ignitor-heater separation is 200 ps.
and the subsequent collisional ionization which makes the plasma density higher in the outer region than in the center of the beam. Guiding of the pump beam was verified from the beam profile imaging at the end of the plasma waveguide for an injection delay of 2.5 ns. As shown in Fig. 4(b), the pump pulse can not be guided at a small beam diameter without the presence of the plasma waveguide. The guided beam size was measured to be ~ 14 µm (FWHM) with more than 60% of the energy in the vacuum focal spot transmitting through the preformed waveguide. It is also noted that the guiding efficiency of the Kr/H plasma waveguide was enhanced to ~75% when the energy of the pump pulse increased from 15 mJ to 210 mJ. The pedestal of the high-energy pump pulse may induce pre-ionization and heating of plasmas to enlarge the density dip for a better guiding. Although high quality plasma waveguide can be generated in the mixture of Kr and H2 gases, it is believed that cold electrons produced during the ionization of hydrogen atoms can promote strong recombination in Kr8+ ions and thus reduce the lasing gain significantly. In our experiments, the energy of the pump pulse was varied systematically to obtain the optimal pump intensity for producing the correct ionization balance in the plasma waveguide. No lasing signal of Ni-like Kr 4d-4p line was observed. The effective gain-length product in plasma waveguide may become too small to produce a strong lasing output as the small signal gain coefficient is reduced dramatically.
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Fig. 5. Interferogram and beam profile of the injected pump beam at ~ 5 mm after its focus for various cases in pure Kr at a backing pressure of 200 psi. The ignitor-heater separation is 200 ps.
Without doping hydrogen as the buffer gas, the high efficiency plasma waveguide can not be generated in the pure Kr as shown in Fig.5. Only ~10% of the energy in the vacuum focal spot is observed to transmit through the preformed waveguide. For pump energy of 210 mJ. The laser intensity at the exit of the waveguide was estimated to be 1.5 × 1017 W/cm2 which is high enough to ionize Kr atoms to Ni-like ion state. Strong lasing signals from Kr8+ 4d–4p transition at 32.8 nm was detected by the on-axis x-ray flat-field spectrometer. Compared to the optimal lasing output with tight focusing pumping, more than 4 times of x-ray photons were generated in the Kr plasma waveguide with a small divergence angle of ~ 6 mrad. This indicates the brightness of Kr lasers can be enhanced by a factor of > 100 when the preformed plasma waveguide is presented.
4 Summary In summary, a low-threshold configuration of OFI x-ray laser in krypton cluster jets was demonstrated. The reduction of the pump energy is achieved by carefully balancing the focusing, diffraction, and ionization defocusing to maintain a high-intensity pump profile over an extended length. In contrary, an efficient method for generating extended plasma waveguides is developed by using the axicon lens in conjunction with the ignitor-heater scheme. High efficiency plasma waveguides in Kr/H mixed gas jets are generated with more than 70% of pump energy observed to transmit through a ~5-mm long waveguide channel. This high efficiency plasma waveguide is particularly suitable for producing recombination OFI x-ray lasers as the electron generated from hydrogen can be very cool to promote recombination. The generation of collisonal excitation Ni-like Kr x-ray lasers at 32.8 nm in a 5-mm pure Kr waveguide at a pump energy
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of only 210 mJ is also demonstrated. The brightness of Kr lasers amplified in waveguides is enhanced by more than 2 orders of magnitude compared to that obtained with free propagation, tight focusing pumping. In order to further increase the x-ray laser efficiency, the ratio between Kr and H2 has to be optimized to obtain a reasonable gain coefficient and guiding efficiency in the preformed plasma waveguide. Such that the gain-length product of x-ray lasers can be maximized while the pump energy can be kept at low value. With time-domain polarization shaping, it is possible to further reduce the threshold and increase the efficiency. We believe this is a promising direction toward the development of low-cost, high-repetitionrate soft x-ray lasers for practical applications.
References 1. Nagata, Y. et al., Phys. Rev. Lett. 71, 3774 (1993). 2. Lemoff, B.E. et al., Opt. Lett. 19, 569 (1994). 3. B.E. Lemoff B. E et a., Phys. Rev. Lett. 74, 1574 (1995). 4. Korobkin D.V. et al.,Phys. Rev. Lett. 77, 5206 (1996). 5. Hooker S.M., Epp P.T., and Yin G.Y., J. Opt. Soc. Am. B 10, 2735 (1997). 6. Sebban, S. et al., Phys. Rev. Lett. 86, 3004 (2001). 7. Chu H.-H. et al., Phys. Rev. A 71, 061804(R) (2005). 8. Sebban S. et al., Phys. Rev. Lett. 89, 253901 (2002). 9. Butler A. et al., Phys. Rev. Lett. 91, 205001 (2003). 10. Mocek T. et al., Phys. Rev. A 71, 013804 (2005). 11. Zeitoun Ph. et al., Nature 431, 426 (2004). 12. Xiao Y.-F. et al., Phys. Plasmas 11, L21 (2004). 13. Grout M.J. et al., Opt. Commun. 141, 213 (1997). 14. Chu H.-H. et al., Appl. Phys. B 79, 193 (2004). 15. Sprangle P., Penano J.R., and Hafizi. B., Phys. Rev. E 66, 046418 (2002). 16. Ammosov, M.V., Delone N.B., and Krainov V.B., Soviet Phys. JETP 64, 1191 (1986). 17. Brixner T. and Gerber G., Opt. Lett. 26, 557-559 (2001).
Experimental Investigation of the Parameter Space of Optical-Field-Ionization Collisional-Excitation X-Ray Lasers in a Cluster Jet M.-C. Chou1,2, P.-H. Lin1,3, T.-S. Hung1,2, J.-Y. Lin2, J. Wang1,3,4 and S.-Y. Chen1,4 1
Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan
2
Department of Physics, National Chung Cheng University, Chia-Yi 621, Taiwan
3
Department of Physics, National Taiwan University, Taipei 106, Taiwan
4
Department of Physics, National Central University, Chun-Li 320, Taiwan
Summary. Optical-field-ionization collisional-excitation soft x-ray lasers in clustered gas jets were experimentally investigated in detail. A tomographic measurement based on laser machining technique was used to resolve the growth of x-ray lasing intensity as a function of position in a cluster jet, exploring the origins of the dependences of x-ray lasing intensity on atom density and laser polarization. The presence of optimal atom density was found to be a result of ionizationinduced refraction. An unexpected observation is that circular polarization appears to be not the optimal polarization ellipticity, which may be a manifestation of effects of pre-ionization at the laser-cluster ionization front.
1 Introduction The first saturated operation of collisional-excitation optical-fieldionization (OFI) x-ray laser was demonstrated with 5d-5p transition at 41.8 nm of Pd-like Xe in a xenon gas cell [1]. A similar result was later achieved in a Xe clustered gas jet [2]. Strong amplification at 32.8 nm for 4d-4p transition of Ni-like Kr has also been demonstrated with a 760 mJ, 30 fs laser pulse [3]. Recently, enhancement of OFI x-ray lasing in a preformed plasma waveguide driven by discharge in a capillary tube filled with xenon and buffer gas [4] and that in a multi-mode capillary waveguide [5] were reported. In addition, by seeding an OFI x-ray laser
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amplifier with a pulse produced from high harmonic generation, enhancement of the x-ray laser intensity and quality was achieved [6]. Here we report the investigation of the parameter space of OFI collisional-excitation x-ray lasers in a clustered gas jet for Pd-like Xe at 41.8 nm and Ni-like Kr at 32.8 nm. A tight focusing configuration was used to explore how the lasers work under low-energy pumping. A tomographic measurement technique based on laser machining was used to resolve the growth and decay of the x-ray lasing intensity as a function of position in the cluster jet. Maximum x-ray lasing was found to appear at a pump polarization ellipticity other than circular polarization. This may be ascribed to the effect of pre-ionization during the laser-cluster interaction at the ionization front.
2 Experimental setup A 10-TW, 45-fs, 810-nm, and 10-Hz Ti:sapphire laser system based on chirped-pulse amplification technique (upgraded from the laser system in Ref. 7) was used in this experiment. A 210-mJ, 45-fs pump pulse was used for preparation of the lasing ionization stages and above-thresholdionization (ATI) heating of electrons, and a 30-mJ, 45-fs pulse set to be 6 ns earlier than the pump pulse was used as the machining pulse for the tomographic measurement to be described below. The pump pulse was focused with an off-axis parabolic mirror of 30-cm focal length onto a cluster jet and the focal spot size was 10-μm in diameter. The cluster slit-jet has a 3.5 mm flat-top region with 750-μm slopes at both edges. Propagating perpendicularly to the pump pulse, the machining pulse was imaged from the location of a knife edge onto the interaction region by a spherical lens of 20-cm focal length with a demagnification factor of 3. In the meantime it was focused in the vertical direction to a width of 20 μm by this spherical lens in combination with a cylindrical concave lens of 75-cm focal length. Based on the laser machining technique as that in Ref. 8, by scanning the knife-edge position the end of the region in which the pump pulse interacts with clusters was varied and the growth of x-ray lasing intensity with pump-pulse propagation in the cluster jet was resolved tomographically. The primary diagnostics for x-ray was a flat-field grazingincidence x-ray spectrometer consisting of an aperiodically ruled grating and a 16-bit x-ray charge-coupled device (CCD) camera. The spectrometer was used to measure the x-ray lasing spectrum and the lasing divergence angle in the direction of pump laser propagation. Aluminum filters of 0.5 μm thickness were used to block transmitted pump laser pulses and attenu-
Experimental Investigation of the Parameter Space of Optical-Field
247
ate x-ray emission. By calibrating the grating reflectivity, the filter transmittance, and the CCD response, the absolute emission yield was obtained.
3 Dependence on atom density The inset in Fig. 1(a) shows the Xe x-ray spectrum. The photon number of the 41.8 nm lasing line reached about 109 photons and the divergence angle was 13 mrad. The dependence of number of photons for Pd-like Xe on atom density is shown in Fig. 1(a). It was observed that an optimal atom density for maximum lasing is present at 7.4×1017 cm-3, which agrees with the number found in previous experiments using a gas cell [1]. It is expected that increase of atom density should result in a larger gain and thus a larger lasing photon number. However, if the atom density is increased beyond an optimal value, the lasing photon number is expected to drop as a result of ionization-induced refraction [1]. The ionization-induced refraction refers to the defocusing of a laser beam caused by the plasma with a higher on-axis density than that at the radially outer region produced by optical-field ionization. Similar results for 32.8 nm x-ray lasing were observed. The inset in Fig. 1(b) shows the Kr x-ray spectrum. The photon number of the 32.8-nm lasing line reached about 109 photons and the divergence angle was 14 mrad. The dependence of number of photons for Ni-like Kr lasing at 32.8-nm on atom density is shown in Fig. 1(b). The optimal atom density was 1.2×1018 cm-3.
Fig. 1. Number of photons of Pd-like Xe lasing at 41.8 nm, (a), and Ni-like Kr lasing at 32.8 nm, (b), as functions of atom density. Insets in (a) and (b) show the x-ray lasing spectrum at atom densities of 7.4×1017 cm-3 for Xe and 1.2×1018 cm-3 for Kr. The pump polarization ellipticity were 0.65 for Xe and 0.55 for Kr. The energy of the pump pulse was 210 mJ and the focal position of the pump pulse was 2500 μm after the entrance of the cluster jet both for Xe and Kr.
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To gain further insight on the decrease of lasing photon number at higher atom densities, we used the tomographic technique to measure the lasing photon number of Pd-like Xe at 41.8 nm as a function of position in the cluster jet at various atom densities, as shown in Fig.2. The results reveal that the decreased lasing photon number at an atom density higher than the optimal value comes not only from the decrease of gain length and increase of length of absorption as a result of ionization-induced refraction, but also from a reduction of gain. Aside from ionization-induced refraction, line-width broadening due to increased ion momentum obtained during dissociation of larger clusters and/or increased rate of collisional deexcitation of the upper level may also contribute to the reduction of gain.
Fig. 2. Number of photons of Pd-like Xe lasing at 41.8 nm as a function of position in the cluster jet for various atom densities. The energies of the pump pulse and the machining pulse were 210 mJ and 30 mJ, respectively. The pump polarization ellipticity was 0.65 and the focal position of the pump pulse was 2500 μm after the entrance of the cluster jet. The temporal separation between the machining pulse and the pump pulse was 6 ns.
4 Dependence on polarization ellipticity Figure 3 shows the number of photons of Pd-like Xe lasing at 41.8 nm and Ni-like Kr lasing at 32.8 nm as a function of pump polarization for various atom densities. The optimal polarization ellipticity for maximum x-ray lasing was found to be in the range of 0.6-0.7 for Xe and 0.55 for Kr regardless of the atom density. This shows that the effects of atom density
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Experimental Investigation of the Parameter Space of Optical-Field
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and polarization ellipticity are decoupled. We observed unexpectedly that the optimal pump polarization ellipticity for maximum x-ray lasing is not the circular polarization.
Fig. 3. Number of photons of Pd-like Xe lasing at 41.8 nm, (a), and Ni-like Kr lasing at 32.8 nm, (b), as a function of pump polarization for various atom densities. The energy of the pump pulse was 210 mJ and its focal position was 2500 μm after the entrance of the cluster jet.
To further examine the x-ray amplification process under different polarization ellipticities of the pump pulse, the photon number of Pd-like Xe lasing at 41.8 nm as functions of position in the cluster jet were measured using the tomographic method, as shown in Fig. 4. This result indicates that a mechanism that changes the electron energy spectrum produced by ATI heating was present and resulted in a decreased collisional-excitation rate when the polarization ellipticity was larger than the optimal value. One possible explanation is the effects from pre-ionization of the clusters at the ionization front. If the collisional heating and ionization in the lasercluster interaction at the ionization front can ionize Xe atoms to Xe3+ or Xe4+, these pre-ionized electrons may lose their energy via radiative cooling during the nanoplasma expansion and through collision with other colder electrons or surrounding neutral atoms during the uniform plasma expansion. As a result, upon the arrival of the main peak of the pump pulse at roughly 2 ns later [2] the energies of these pre-ionized electrons may fall below the threshold of collisional excitation and thus they cannot contribute to collisional excitation. This will greatly reduce the lasing photon number. However, under this circumstance, if the ATI energies of the electrons produced from the subsequent ionization stages by the main peak of the pump pulse are lowered to fall in the region above and near the excitation threshold, in which the collisional-excitation cross section is larger, the gain can be raised. This can be achieved by shifting the polarization ellipticity of the pump pulse away from the circular polarization, resulting in
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Fig. 4. Number of photons of Pd-like Xe lasing at 41.8 nm as functions of position in the cluster jet for 7.4×1017 cm-3 atom density and various pump polarization ellipticities. The energies of the pump pulse and the machining pulse were 210 mJ and 30 mJ, respectively. The focal position of the pump pulse was 2500 μm after the entrance of the cluster jet. The temporal separation between the machining pulse and the pump pulse was 6 ns.
the observed optimal polarization ellipticity at less than 1. This also explains the decoupling of optimal atom density and optimal polarization ellipticity, because by the time the main peak of the pump pulse arrives to heat up the plasma again, the cluster structure has already disintegrated. Also note that in Fig. 4 the position of maximum lasing photon number does not shift with variation of laser polarization ellipticity. This is reasonable since the ionization fraction is not very different for varying polarization ellipticity when the laser intensity is well above the ionization intensity threshold.
References 1. 2. 3. 4. 5. 6. 7. 8.
S. Sebban et al., Phys. Rev. Lett. 86, 3004 (2001) H.-H. Chu et al., Phys. Rev. A 71, 061804(R) (2005) S. Sebban et al., Phys. Rev. Lett. 89, 253901 (2002) A. Bulter et al., Phys. Rev. Lett. 91, 205001 (2003) T. Mocek et al., Phys. Rev. A 71, 013804 (2005) Ph. Zeitoun et al., Nature 431, 426 (2004) H.-H. Chu et al., Appl. Phys. B 79, 193 (2004) C.-H. Pai et al., Phys. Plasmas 12, 070707 (2005)
Collisionally Pumped X-Ray Lasers for Shorter Wavelengths G.J. Pert Department of Physics, University of York, York, YO105DD, U.K.
Summary. The scaling of the pumping requirements for X-ray lasers in the range 50-100Å is investigated using analytic models for the interaction of the laser with solid targets. It is found that due to the rapid increase of the electron temperature required to establish Ni-like ionisation that the irradiance needed in the pre-pulse to generate the plasma increases rapidly with atomic number. In particular the mass of the heated plasma is dominated by upstream thermal conduction. In contrast due to the high temperatures achieved in the pre-pulse relatively little energy is required to further heat the plasma to generate strong gain. The large mass of upstream plasma at wavelengths ~50Å is comparable with that in freestanding foils, and suggests the use of the latter for targets at shorter wavelengths. The validity of these models is confirmed by simulation.
1 Introduction Soft X-ray lasers using grazing incidence pumping and nickel-like ions are now established as efficient sources of radiation in the super-100Å waveband [1]. Underlying this approach is the separation of the ionisation and excitation phases of the laser, and matching the operating density to the optimum for pumping the population inversion [2]. The first ionisation pulse (or pre-pulse) tends to be long and the second excitation (or main pulse) short. In this paper we examine whether these ideas can be applied to sub-100Å systems. We find two problems arise: firstly the optimum pumping density is at or above the critical density of the fundamental of the pumping laser, and secondly that the scaling of the electron temperature required to generate the Ni-like ionisation stage scales adversely with atomic number. The laser irradiation conditions required to achieve the necessary background plasma are identified by using appropriate analytic models of laser-plasma interaction developed many years ago. We find that, at the temperatures necessary for Ni-like ionisation, thermal conduction plays an important role, dominating the energy transfer upstream rather than
252G.J. Pert
downstream into the expanding plasma plume. This has the advantage that the plasma at densities in excess of that of the absorption layer will be hotter than predicted directly from the standard expansion models, and will allow more rapid ionisation and a higher pumping density. Using simulation applied to a variety of representative atomic systems suitable for generating laser action at these wavelengths, we identify a strategy which offers a possible route to achieving these aims reasonably efficiently. This is based on a pre-pulse comprising both fundamental and harmonic radiation generated from the pump laser, and a normally incident fundamental main pulse. However we find that the pump laser energy required scales very adversely with the atomic number and therefore wavelength to the extent that typically about 100J/cm for a target of width 100µm is required in the pre-pulse to ionise the shortest wavelength systems such as tantalum or ytterbium lasing at 45Å or 50Å respectively. In practice these values which neglect any transverse heat losses are probably an underestimate of those needed in an experiment. At these high pre-pulse energies a relatively small main pulse of only a few 10sJ/cm is needed to generate the gain. Energies typically of a few 10s of µJ are generated from these designs.
2 Analytic Models Simple one dimensional analytic models for the interaction of laser on solid targets were developed many years ago. These differ only in the nature of the absorption process and the role of thermal conduction. 2.1 Deflagration Model In this regime [3] the plasma flow is assumed steady state with localised absorption at the critical density, c, by unspecified mechanisms. The upstream flow, and downstream isothermal rarefaction are both supported by thermal conduction from the absorption layer. The flow is therefore a classical Chapman-Jouget deflagration flow, with heat input given by the irradiance. The electron temperature is given by
Collisionally Pumped X-Ray Lasers for Shorter Wavelengths253
Te 0.397
1 2 3 c 2 3 Z R g
where Z is the ionisation,
(1)
R g the gas constant per unit mass and
= 1 + Ti Z Te . The above equation neglects the energy required for ionisation and that held in the conduction zone, hence the effective irradiance is significantly less than that actually required. 2.2 Self-regulating Model In this case absorption is global by inverse bremsstrahlung absorption, and thermal conduction is neglected [4]. Since the plasma grows in time, the model is not steady state [5].
Te 0.423
1 b 1 4 1 2 1 4 Z R g
(2)
where is the pulse length and b the appropriate inverse bremsstrahlung constant. The characteristic absorption density at the isothermal sonic point
a 0.784 b 3 8 1 4 3 8
(3)
This model is closely related to that above when the time dependency and the different absorption density are taken into account 2.3 Thermal Conduction Zone Upstream of the absorption layer in either model, thermal conduction will be important if the temperature is high. This gives rise to layers of hot plasma, which over long times will pass through the absorption zone. However if the pulse is short (as is the case here) the upstream plasma will have a substantial heat content at the end of the pulse which must be included in the overall energy balance. The length, mass and energy of this zone may be expressed in terms of the characteristic length [6]
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254G.J. Pert
2ac 4 L= a
c2 =
Z kTe M
(4)
determined by the values at the absorption layer. For a flux limiting factor of 0.1, the length, mass and energy of the layer take the values: Length 0.0629L : Mass 0.1767a L : Energy 0.1089ac2L
(5)
where a is the characteristic constant for electronic thermal conduction.
3 Ionisation We may estimate the minimum temperature needed to achieve the Ni-like ionisation stage in the plasma at the conclusion of the laser pulse from that needed for equilibrium at the appropriate ionisation stage. Using the screened hydrogenic model for the ionisation and excited state energy levels, we find that the ionisation temperature scales only weakly with electron density over the density range of interest, but strongly with atomic number Z:
Te Aion Z 5.5
(6)
where the constant Aion varies with ionisation stage and density. For the Nilike ion and electron density 1021 cm-3 we find Aion 5.8710-8 eV. Using this temperature (6) we may use equations(1), (2) and (5) to calculate the minimum irradiance needed to achieve the Cu-like ionisation , since this has a sufficient population of Ni-like ions to generate gain. As a set of scaling relations we find for the irradiance
Ade Z 8.25 Ace Z 13.4 e 10 + Asr Z
(7)
and for the mass ablation rate
A m Z 3 A m Z 9 µ& dm 4.5 + c Asr Z
(8)
Collisionally Pumped X-Ray Lasers for Shorter Wavelengths255
where Ade , Asre and Ace , and Adm , Asrm and Acm refer to the empirical coefficients from the deflagration, self-regulating and thermal conduction models respectively. The self-regulating/deflagration transition is determined by the absorption density, namely if a < c the flow is selfregulating and vica versa. 3.1 Ionisation Time Thus far we have assumed that the ionisation takes place over times short compared to the pulse duration. To check this assumption is valid we show in fig. 1 the time taken to reach the Cu-like ionisation stage at the Ni-like equilibrium temperature. It can be seen that this time is nearly linearly proportional to the electron density. Furthermore we note that at an electron density of 1021 cm-3 the time is about 200ps. for Z=70 and increases rapidly thereafter. We therefore conclude that we require prepulse durations of at least 100ps. 1.5 20
-3
Ionization time (ns.)
5 × 10 cm 21 -3 1 × 10 cm 21 -3 4 × 10 cm 22 -3 1 × 10 cm 1
0.5
0 40
50
70 60 Atomic number
80
90
Fig. 1. Plot of the time required to achieve the Cu-like ionisation at the equilibrium temperature of the Ni-like ion as a function of the atomic number
4. Optimum Pumping Density It can be shown that there are electron densities at which the population inversion density and the gain are maximised. Fig.2 shows the variation of the fractional inversion density and a parameter measuring gain defined below in dysprosium over a range of electron densities and temperatures.
256G.J. Pert
Population inversion fraction = 1 q 2 q1 q0 g 2 g1
Gain parameter = Population inversion fraction 1020 ne
(9)
It is clear from Fig.1 and Fig.2 that typical conditions after the final heating require an electron density of about 1021 cm-3 to achieve both ionisation with a pulse length of about 100ps, and high gain. This is the critical density for the fundamental of Nd-glass laser radiation at 1.06µm. However since the absorption in these systems is dominated by inverse bremsstrahlung absorption, this suggests that we need to use the harmonic radiation at 0.53µm as the pre-pulse to generate the ionisation and create a suitable density profile. 10 500eV 1000eV 2000eV 3000eV
1
Gain
er
met
para
Population fraction
-1
10
-2
10
Inversion fraction -3
10
-4
10
-5
10
19
10
20
10
21
10 -3 Electron density (cm )
22
10
23
10
Fig. 2. Plots of the inversion density and gain parameter in dysprosium as functions of the electron density for different temperatures.
Unfortunately, harmonic generation is typically only about 50% efficient, the remaining 50% remaining in the fundamental. To obtain maximum efficiency therefore it is advantageous to focus both harmonic and fundamental on to the plasma, if a suitable focusing arrangement can be designed. We will assume this can be done. From equation (6) we see that for dysprosium, the temperature required for ionisation is about 500eV. From fig.2 it is clear that significant gain can be developed by the pre-pulse alone. Furthermore it can be seen that
Collisionally Pumped X-Ray Lasers for Shorter Wavelengths257
an increase in temperature of a further 500eV, which is achieved without additional ionisation or hydrodynamic effects is all that is required from the main pulse. The energy needed by the main pulse is therefore substantially less than that in the pre-pulse.
4 Examples from Simulation The analytic modelling presented above has been entirely one dimensional, appropriate for a plasma width of 100µm. We will use the 1_d code EHYBRID to simulate such plasmas, where the hydrodynamics are essentially 1 dimensional. The pre-pulse will be assumed to have a constant irradiance over the full pulse length of 100 or 200ps and the main pulse a Gaussian temporal profile of 2ps half-width. The ionisation is calculated using screened hydrogenic energy levels for all ions except the lasing Ni-like stage. 4.1 Dysprosium (Z=66) Fig.3 shows the gain and electron density spatial profiles along the plasma axis at increasing times measured from the onset of the main pulse. It can be seen that the maximum gain increases with time until about 10ps and decreases slowly thereafter. However we note that increasing gain is associated with a shift to higher density. This is due to thermal conduction heating plasma at densities greater than the absorption density, with consequent higher gain as reflected in fig.2. However we also note that this move to higher density is accompanied by an increase in the gradient of the electron density, leading to progressive deterioration of the output due to refraction. We note that at the electron density of 1021 cm-3, the gain decreases slowly as the plasma cools. Fig.4 shows output from plasma similar to that shown in fig.3. It will be noted that although the magnitude of the outputs differ by a factor of 10, their temporal profiles are similar, indicating that the temporal profile is controlled by the spatial profile of the expansion resulting from the prepulse. The peak power occurring at 7.5ps is significantly earlier than gain maximum, reflecting the limitation imposed by the density gradient as the gain moves to higher density. The relatively large change in output from a small change in main pulse energy should be noted, cosequent to increased temperature and stronger pumping, consistent with fig.2.
258G.J. Pert
4.2 Ytterbium (Z=70) Ni-like ytterbium lases at 50Å. Fig.5 shows the gain and electron density profile in this case. It is immediately apparent that the pre-pulse energy is greatly increased over that needed for dysprosium (by a factor 4) despite the relatively small increase in the atomic number. This is larger than our
1e+23
80 70
−1
Gain (cm )
50
1e+22 −3
1e+21
40
Electron density (cm )
2 ps 6 ps 10ps 14ps 18ps
60
30 1e+20
20 10 0 −0.001
0
0.001 0.002 Distance (cm)
0.003
1e+19 0.004
Fig. 3. Plots of the gain at 59 Å and electron density for dysprosium pumped by a pre-pulse of mixed harmonic and fundamental of 23.75 J/cm in 200 ps and a fundamental main pulse of 8.8 J/cm in 2 ps all at normal incidence.
model predictions (factor 2), even when account is taken of the reduction in inverse bremsstrahlung absorption due to the higher temperature. The additional energy is required to meet the increasing demands of radiation escaping from the hot plasma. It can be seen that reasonable gain is generated over quite a large plasma body with a small density gradient lasting quite long times ~25ps. We therefore expect to obtain a relatively long output pulse at quite low power, but with significant total energy. Fig.6 confirms this expectation.
5 Foils at Shorter Wavelengths Referring to equation (8) we see that the mass scales rapidly with atomic number. Fig.7 illustrates this behaviour and shows that for Z > 67 the mass ablated exceeds 100µg. This suggests that we may limit the mass of ionised plasma by using thin foils, which are uniformly heated by thermal
Collisionally Pumped X-Ray Lasers for Shorter Wavelengths259
conduction – exploding foils. The analysis of this system can be carried out reasonably easily and shows that the ratio of kinetic to thermal energies is about unity for a foil expansion. This is significantly larger than for slabs, where much of the mass is in the slowly moving conduction zone. Consequently the energy balance is in favour of slabs up to atomic numbers of about 73. 250 Power
Power (MW)
8.8J/cm 5.4J/cm (×10)
10
200
150
100
Energy
Energy (µJ)
Energy
20
Power 50
0
0
5
10 Time (ps)
0 20
15
Fig. 4. Plots of the output power and energy at 59 Å generated from a 1 cm. length of dysprosium plasma by pre-pulse irradiation with a pure harmonic beam of 23.75 J/cm in 200ps and a main pulse irradiation by normally incident fundamental beams of 5.4 J/cm and 8.8J/cm Note that in the 5.4 J/cm case the power and energy are both multiplied by a factor of 10.
23
60
Gain(cm
-1)
40
22
10
30
21
20
10
-3
2.5ps 5.0ps 7.5ps 10.0ps 12.5ps 15.0ps 17.5ps
50
Electron density (cm )
10
10
0
20
0
0.001
0.002 Distance (cm)
0.003
10 0.004
Fig. 5. Plots of the gain and electron density from ytterbium at 50 Å pumped by a combination harmonic/fundamental pre-pulse of energy 97 J/cm in 200 ps and a fundamental main pulse of 23 J/cm
260G.J. Pert
10
80 70
8
50
Power Energy
6
40 4
Energy (µJ)
Power (MW)
60
30 20
2 10 0
0
10
5
15 Time (ps)
20
0 30
25
Fig. 6. Plot of the output power and energy at 50 Å from a 1cm plasma length of ytterbium heated by a pre-pulse of 97 J/cm in 200ps and main pulse 23 J/cm in 2 ps. 20000
Foil Slab
-2
-2
Mass (µg/cm )
Energy
10000 200 Mass
0 60
65
70 Atomic number
Total energy (J/cm )
400
75
0 80
Fig. 7. Comparison of the mass and energy required to achieve Cu-like ionisation in slabs and 100 µ g foils with a laser pulse of 100 ps duration at 0.5 µ m wavelength.
However foils have two further advantages. Firstly the density gradient at peak density is zero due to their symmetry. Secondly it is possible to use
Collisionally Pumped X-Ray Lasers for Shorter Wavelengths261
them at high density by adjusting the pulse length so that the main pulse is applied before much expansion has occurred. This requires a short pulse and one must take care to ensure that thermal conduction has burnt through the plasma and that the ionisation is completed. With care operation at electron densities ~1022 cm-3 can be achieved.
6. Conclusions Simple analytic models have been used to identify the conditions necessary to pump Ni-like ions to generate laser action in the range 5070Å. It is found that ionisation is a limiting factor, both in respect of the pre-pulse input energy and the time required. Since the densities required both for ionisation and inversion are high > 1021 cm-3, harmonic radiation at 0.53 µm is needed, and grazing incidence pumping does not offer any advantage. At the high temperatures needed thermal conduction, even when flux limited, plays a key role. Although greatly increasing the energy demands, it does allow a mixture of the fundamental and harmonic wavelengths to be used, provided that the practical difficulties can be overcome. Since the temperature is high at the conclusion of the main pulse, a relatively small additional energy is required from the main pulse, which being short is not affected by hydrodynamic or conduction losses. The main pulse energy required is therefore only about _ of that in the prepulse. For shorter wavelengths it is suggested that foils with limited mass may allow a reduction in the pump energy, and improve the density and gradients in the plasma.
References 1. Y.Wang et.al. Phys. Rev. A 72, 053807, 2005 2. G.J.Pert Phys. Rev. A, 73, 033809, 2005 3 C.Fauquignon and F.Floux Phys. Fluids 13, 386, 1970 4 I.V.Afanas’ev et.al. Appl. Maths. Mech. 30, 1218, 1966 5 G.J.Pert J Plasma Phys. 36, 415, 1986 6 G.J.Pert J Plasma Phys. 29, 415, 1983
Inner Shell Lasing In Titanium via Electron Collisional Ionization E. F. Spracklen and G. J. Pert Department of Physics, University of York, York, YO10 5DD, UK
Summary. The possibility of generating gain in the x-ray region of the spectrum through the technique of electron collisional ionization is studied in titanium . As in previous work transient inversions of moderate size are seen to be produced on the L2 – M1 and L3 – M1 transitions provided that the collisional effects of the secondary and Auger electrons are ignored. Inclusion of these effects is seen to significantly decrease both the magnitude and duration of the gain obtained.
1 Introduction Inner-shell x-ray laser schemes present the possibility of generating gain at wavelengths of several angstroms in small scale devices. Conventionally such techniques have involved using x-ray photo-pumping to generate the inner-shell transitions as originally discussed by Duguay [1]. Widespread implementation of such devices has however been curtailed due to the difficulty of generating x-ray pulses with durations of the order of the inversion lifetimes. An alternative approach, outlined by Barty et al [2], is to use fs electron pulses to generate the inversion. However, although such pulses can be relatively easily produced via laser-plasma interactions, atomic electron impact cross-sections favor outer shell over inner shell ionization. Such techniques therefore cannot produce gain directly and instead rely upon Auger transitions to generate transient inversions. Initial studies into the possibility of generating gain in such a manner identified Ti as the most favorable candidate for lasing and predicted gains of up to 30 cm-1 [3]. The work in question however assumed mono-energetic electron pulses and ignored the collisional effects of the secondary and Auger electrons produced. Further simulations carried out using more realistic electron
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fluxes predicted gains of only around 10-3 cm-1 [4]. Yet again however this work ignored the secondary electron effects. This paper investigates the possibility of generating gain on the L2 - M1 and L3 - M1 transitions in Ti using physically realistic electron pulses and taking full account of the collisional effects of secondary and Auger electrons.
2 Method The production of a hot electron flux via a laser-plasma interaction is simulated using a 2-D PIC code. The superthermal electrons produced are followed using Monte-Carlo methods with the titanium level populations obtained by numerical solutions of the relevant rate equations. Within this atomic code the secondary electron energies are calculated using the symmetrized binary encounter theory of Burgess and Percival [5]. In all the simulations performed the titanium lasing media is assumed to be initially un-ionised and at solid density.
3 Results Simulations performed using a variety of laser and plasma parameters predict larger gains upon the L3 – M1 transition in contradiction of the work of Barty et al [3] – figure 1. However, in Barty’s work the L2 and L3 levels are treated as having identical transition rates and electron impact cross-sections. The larger degeneracy of the L3 level therefore leads to smaller gains being generated upon the L3 – M1 transition. Treating the L2 and L3 levels separately it can be shown that L2 states possess faster filling rates and smaller impact cross-sections [6,7] explaining the larger L3 – M1 gains observed. Asides from this discrepancy it can be seen that the gains obtained are in the region of those predicted by Barty et al rather than those forecast by Upcraft [4]. Examining the spectra in more detail it is seen that the gain in the initial titanium regions is not consistent with that obtained at larger depths. This feature arises as the initial gain is produced by thermal electrons obtained in the PIC simulation before the hot electrons are generated. The gain in the deeper regions meanwhile is produced by the hot electron flux with the gain fall-off obtained with increasing depth a consequence of the small number of hot electrons produced in typical laser plasma interactions.
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Inner Shell Lasing In Titanium via Electron Collisional Ionization265
The thermal electron effects can be negated by allowing the plasma electron flux to pass through a thin atomic filter – figure 2. It can be seen that, provided the filters are thick enough, the anomalous behaviour of the gain at small penetration depths disappears. However as the filter thickness is increased the gain produced is seen to decrease as a result of the increasing numbers of electrons being removed from the flux. 12
8
Gain (cm**-1)
6
9
4
6
2
3
0
0
0.2
0.4
0.8 1 0.6 Penetration Distance (microns)
1.2
0
0.2
0.4
0.8 1 0.6 Penetration Distance (microns)
1.2
Gain Duration (fs)
L3-M1 L2-M1
L3-M1 L2-M1
0
Fig. 1. Titanium gain characteristics obtained from electron fluxes produced in the interaction of a 10 fs, I2 = 1018 W cm-2 µm2 laser with a 1 keV plasma. 12
8
9
4
6
2
3
0
0
0.2
0.4
0.8 1 0.6 Penetration Distance (microns)
1.2
0
0.2
0.4
0.8 1 0.6 Penetration Distance (microns)
1.2
Gain Duration (fs)
6
Gain (cm**-1)
X=0 X = 0.1 X = 0.3 X = 0.5
X=0 X = 0.1 X = 0.3 X = 0.5
0
Fig. 2. L3-M1 gain characteristics for electron fluxes produced in the interaction of a 10 fs, I 2 = 1018 W cm-2 µm2 laser with a 1 keV plasma filtered by aluminum filters of thickness X µm.
Allowing for different irradiance beams it is seen that all the gain spectra exhibit the same behaviour at shallow penetration depths due to the thermal plasma electrons – figure 3. For deeper regions however larger but
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shorter lived gains are obtained for the more intense beams. This feature can be attributed to the increasing number of hot electrons generated by the higher intensity pulses. These electrons are capable of penetrating further into the titanium and thus produce a more significant inversion in the deeper segments. The increasing electron number however causes more rapid over-ionisation leading to the afore-mentioned decrease in gain duration. 30
X = 16 X = 17 X = 18 X = 19
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Fig. 3. L3-M1 gain characteristics for electron fluxes produced by the interaction of 10 fs, I2 = 10X W cm-2 µm2 lasers with 1 keV plasmas.
Allowing for the collisional effects of the secondary and Auger electrons generated during the interaction is seen to significantly decrease both the gain magnitude and duration – figure 4. This decrease arises as a result of the fact that the secondary electrons are overwhelmingly produced at low energies [5] and thus act to destroy any inversion. 4
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Fig. 4. L3-M1 gain characteristics for electron fluxes produced by the interaction of 10 fs, I2 = 10X W cm-2 µm2 lasers with 1 keV plasmas allowing for secondary and Auger electrons.
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Similar effects are also seen in simulations of photo-ionised inner-shell devices. In such schemes it is possible to somewhat alleviate the effects of the secondary electrons by doping the lasing material with hydrogen [8]. Such an approach cannot however be adopted in electron collisional devices due to the similar electron impact cross-sections of hydrogen and titanium at intermediate to high energies.
4 Conclusions The gain and population dynamics of the L23 – M1 transitions in titanium have been investigated in the case of electron collisional ionization. Moderate gains of fs duration are predicted when the collisional effects of the Auger and secondary electrons are ignored. Inclusion of these effects is seen to significantly decrease both the magnitude and duration of the gains obtained.
References 1. Duguay, M. A. and Rentzepis, P. M., Appl. Phys. Lett., 10, 350 (1967) 2. Barty, C. P. J., Guo, T., Le Blanc, C., Raksi, F., Rose-Petruck, C., Squier, J., Walker, B. C., Wilson, K. R., Yakovlev, V. V. and Yamakawa, K., X-ray Lasers IOP Conference Series, 151, 282 (1996) 3. Kim, D., Toth, C. and Barty, C. P. J., Phys. Rev. A., 59, 4129 (1999) 4. Upcraft, L. M., X-ray Lasers 2002: 8th International Conference on X-Ray Lasers, 349 (2002) 5 Burgess, A. and Percival, I. C., Adv. At. Mol. Phys., 34, 109 (1968) 6. Deutsch, H., Margreiter, D. and Mark, T. D., Z. Phys. D., 29, 31 (1994) 7 Chen, M. H. and Crasemann, B., At. Data Nucl. Data Tables, 24, 13 (1979) 8. Kapteyn, H. C., Appl. Opt., 31 4931 (1992)
Gain Generation in the Critical Density Region of a TCE XRL D. Ursescu1, D. Zimmer1,2, T. Kühl1,2, B. Zielbauer1,2,3 and G.J. Pert4 1
Gesellschaft für Schwerionenforschung mbH, Darmstadt, Germany; Johannes Gutenberg Universität, Mainz, Germany; 3 Max Born Institute, Berlin, Germany; 4 University of York, United Kingdom
2
Summary. Significant reduction of the total pumping energy for a transient collisionally excited (TCE) x-ray laser (XRL) was made possible by using nonnormal main pulse pumping. In the attempt to scale to shorter XRL wavelengths, it is described here a theoretical investigation of the influence of the pumping pulse parameters on the gain generation in a Ni-like Ag x-ray laser (XRL). The possibility of gain generation closer to the critical density is shown by the EHYBRID code for a set of optimized parameters, corresponding to a possible setup at the PHELIX laser facility.
1 Introduction The advance of the TCE XRL in the last few years was marked by the introduction of a non-normal incidence focusing system (see e.g. [1]) and of the grazing incidence angle pumping (GRIP) technique for the main pumping pulse (MP) [2]. At the introduction of GRIP technique it was largely believed that the optimal angle is determined by the density where the gain appears, in the range of 1020 cm-3. A number of experiments were then investigating the effect of the MP non-normal incidence angle on the XRL output [3,4,5], with the results that slightly smaller incidence angles on target are beneficial to the output of the XRL. Also on the theoretical side, a study concerning Ag and Sm [6] has shown that the incidence angle for Sm of 45° at 1054 nm would reduce the pumping needs of the XRL a factor of three. In the present paper the same modeling program is used as in [6] and the influence of the incidence angle is investigated for Ni-like Ag XRL. It is found that the incidence angle of the main pulse has
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different effects depending on the pumping conditions. With parameters typical for the PHELIX preamplifier [7], the optimal MP incidence angle is found to be 45° (see section 2). Moreover a simple plasma shaping technique is implemented to control the density profile of the pre-plasma, by a variation of the incidence angle of the pre-pulse (PP). It is found that for large PP incidence angles on target, the XRL output improves, due to a better interplay of the electron temperature and the electron density in the gain region.
2 Influence of the MP incidence angle The parameters used for the modelling of the Ag Ni-like XRL were selected to fit a possible experiment with the PHELIX preamplifier. Two pulses are used, a long one to create the pre-plasma, and the short pulse which produces the strong excitation needed for lasing. The PP duration is 800 ps with a total energy of 4 J in a line focus of 10 mm length and 50 μm width and it is followed at it's conclusion by a MP with 2 ps duration and 2 J energy, with the same line focus length. In this evaluation the PP incidence angle on target is 0° while the MP incidence angle is varied from 0° to 75°. The EHYBRID code was used employing detailed level information of the Ni-like Ag ions, in order to obtain good description of the main lasing line, at 13.9 nm wavelength. The local XRL signal is defined as the product of the density normalized to critical density with the exponential of the gain g multiplied with the length of the target l, for a small target length (l=0.1 mm).
sl =
ne ⋅ (e gl − 1) nc
The results for the local XRL signal are shown in fig.1 for MP incidence angles from 0° to 75° on a logarithmic scale at the moment when the highest local signal is obtained, relative to the arrival of the main pulse. For the 75° incidence angle the MP energy is deposited in a quite diluted plasma region (0.5 1020 cm-3) and the local signal is less than unity. The highest local signal obtained is for 45° incidence angle, and corresponds to a density close to critical density which is 1.1 1021 cm-3 in this case. The gain appears after the MP is gone, when the heated plasma region reaches the Ni-like state. However, due to ionization and plasma expansion, the electron density at that given distance from the target increases so that the local signal is enhanced.
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When the MP incidence angle is 0°, the energy is deposited close to the critical density so the heated mass is much larger and the heat conductivity is large, so the temperature reached at the end of the MP is about 500 eV.
Fig. 1. Local signal as a function of the position relative to the target for several main pulse incidence angles
Increasing the angle, the maximum temperature increases to a value of 2150 eV in the case of 45° and the cooling of the plasma takes longer time. This time is needed to build up the Ni-like charge state which, as a consequence, will see higher temperatures of the electrons. For larger MP angles, the maximum electron temperature further increases but the ionization process is becoming slower and the Ni-like charge state appears at a much later time when the plasma cooled again; in this case also the electron density does not increase any more in a significant way. In conclusion, the balance of the ionization dynamics and temperature dynamics determines the optimal angle for MP. In the optimal case, the local gain is enhanced by the increase of the electron density in the gain region.
3 Influence of the PP incidence angle Further optimization was performed by variation of the PP incidence angle. This is a simple plasma shaping technique which allows controlling the density profile together with the temperature and the charge state of the plasma generated by the PP. With this technique, the plasma is heated at a given density region determined by the chosen incidence angle in the same way as in the MP case.
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The highest local signal is obtained in the case of a large incidence angle of 75° for a 30° MP incidence angle as shown in fig. 2. For comparison the maximum local signal for PP incidence angles from 0° to 75° are also represented.
Fig. 2. Local signal as a function of the position relative to the target for several prepulse incidence angles
The local XRL signal builds up in a region close to the target surface and in the simulation is a factor of 6 higher than the one obtained in the best case of the 0° PP angle (shown in fig. 1). In the cases presented in fig. 2, the electron density region has densities above the critical density of the pumping laser, being placed at 1.5 to 1.9 1021 cm-3 electron density. In conclusion, here we presented a systematic modelling study of the influence of the incidence angles for the PP and MP for a Ag XRL. It is found that strong local signal appears for MP angles around 45° in the case of normal PP incidence. When varying the PP angle, the optimal angle is found 75° for PP using an MP incidence angle of 30°. In this last case a factor of 6 in the local XRL signal is expected. The results correspond to a possible setup at the PHELIX laser facility. Furthermore they open new perspective for scaling TCE XRL towards sub-10 nm wavelengths [7].
References 1. Neumayer, P.; Alvarez, J.; Mos, B.B.; Borneis, S.; Brück, K.; Gaul, E.W.; Häfner, C.; Janulewicz, K.A.; Kuehl, T.; Marx, D.; Reinhard, I.; Tomaselli, M.; Nickles, P.V.; Sandner, W.; Seelig, W.: 'X-ray laser spectroscopy on
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lithium-like ions', Soft X-Ray Lasers and Applications IV, SPIE, 4505, 236242, 2001 2. Keenan, R.; Dunn, J.; Patel, P.K.; Price, D.F.; Smith, R.F. & Shlyaptsev, V.N.: 'High-Repetition-Rate Grazing-Incidence Pumped X-Ray Laser Operating at 18.9 nm', Phys. Rev. Lett., 94, 103901, 2005 3. Neumayer, P.; Seelig, W.; Cassou, K.; Klisnick, A.; Ros, D.; Ursescu, D.; Kuehl, T.; Borneis, S.; Gaul, E.; Geithner, W.; Haefner, C. & Wiewior, P. 'Transient collisionally excited X-ray laser in nickel-like zirconium pumped with the PHELIX laser facility', Appl. Phys. B, 78, 957-959, 2004 4. Kazamias, S.; Cassou, K.; Ros, D.; Plé, F.; Jamelot, G.; Klisnick, A.; Lundh, O.; Lindau, F.; Persson, A.; Wahlström, C. G.; de Rossi, S.; Joyeux, D.; Zielbauer, B.; Ursescu, D.; Kühl, Th.: 'A 10 Hz, 3 µJ transient X-ray laser pumped in grazing incidence geometry', these proceedings 5. Luther, B.M.; Wang, Y.; Larotonda, M.A.; Aless, D.; Berrill, M.; Marconi, M.C.; Rocca, J.J. & Shlyaptsev, V.N.: 'Saturated high-repetition-rate 18.9-nm tabletop laser in nickellike molybdenum', Opt. Lett., 30, 165, 2005 6. Pert, G.J.: 'Optimizing the performance of nickel-like collisionally pumped xray lasers', Phys. Rev. A, 73, 033809, 2006 7. Kühl, Th.; Ursescu, D.; Bagnoud, V.; Javorkova, D.; Rosmej, O.; Zimmer, D.; Ros, D.; Cassou, K.; Kazamias, S.; Klisnick, A.; Zielbauer, B.; Janulewicz, K.; Nickles, P.; Pert, G.; Neumayer, P.; Dunn, J.: 'A Non-Normal Incidence Pumped Ni-like Zr XRL for Spectroscopy of Li-like Heavy Ions at GSI/FAIR', these proceedings
2-D Hydrodynamic Simulation of Laser Plasma Generation For Transiently Pumped Soft X-Ray Amplifier K. Cassou, S. Kazamias, A. Klisnick and D.Ros LIXAM– Université Paris XI 91400 Orsay – France
Ph. Zeitoun Laboratoire d’optique Appliquée – ENSTA, Ecole Polytechnique - 91620 Palaiseau France
E. Oliva, P. Velarde, C. Garcia and F. Ogando Institute de Fusion Nuclear (DENIM), Universidad Politecnica de Madrid Madrid Spain
Summary. A soft x-ray laser amplifier based on solid target plasma is numerically investigated using a 2-D hydrodynamic code ARWEN with radiative transport solved by multigroup method based on adaptive mesh refinement. The code has been used to describe the spatial and temporal plasma evolution and, ultimately, to understand how to generate an ideal preformed plasma in the transient collisional pumping scheme. Firstly, we examine the influence of the laser driver spatial profile on the characteristics of the preformed plasma. We show that using a super Gaussian, instead of gaussian, spatial transverse profile leads to a substantial reduction of the transverse refraction by two orders of magnitude and to an enlargement of the gain zone surface by about a factor of 2. Secondly, we perform a study on the pre-pulse significance in the transient collisional scheme, as it was done several years ago for the J=0-1 Ne-like line in the quasi-steady-state pumping. All above studies were carried out for an iron target with gain on the J = 0- 1 neon like transition at λ= 25.5nm
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1 Introduction These In recent years, worldwide soft-x-ray laser research has progressed to the point where many laboratories have routinely been able to produce stimulated emission over a wide range of wavelengths. Demonstration of multi-millijoule soft-x-ray laser has been achieved in the quasisteady-state (QSS) collisional pumping scheme [1]. Significant progress has also been made in the past few years to push the soft-x-ray lasers toward higher intensity, shorter pulse duration, shorter wavelength, and particularly much higher repetition rate with much less pumping laser energy. These accomplishments were made by the use of high-repetition-rate laser system, and the implementation of the transient-collisional-excitation (TCE) x-ray laser scheme [2,3] TheTCE scheme is often poorly homogeneous exhibiting many large- and small-scale structures. Since the beam homogeneity is a key parameter for focusing applications or imaging experiments, the problem has to be overcome. These structures originate from two separate phenomena. First, speckle-like pattern is generated from the interferences of several incoherent sub-pupils [4]. This effect may be easily alleviated by seeding the amplifier with a nearly fully coherent source such as high harmonic generation [5]. This has been achieved recently [6] and opens the route to a new generation of soft-x-ray lasers [7]. The second phenomenon is the beam degradation because of its propagation along the plasma amplifier that is non-homogeneous. Control and improvement of the plasma homogeneity remains one of the key studies for the increase of soft-x-ray laser performance. More precisely, the non-uniformity of the plasma density induces a spatial fluctuation of the index of refraction that in turn refracts the soft-x-ray laser beam. Although soft-x-ray laser beam degradation was observed on other pumping schemes, it was not as crucial as now with the transient scheme. Deleterious effects of refraction associated to the transient scheme consist in beam degradation but also in the reduction of the output soft-x-ray laser energy by refracting the beam out of the gain region before reaching the end of the amplifier [8]. All the previous works related to the refraction underwent by soft-x-ray laser has shown that the refraction impacts the beam propagation in not only horizontal but also in vertical directions (Fig. 1). It has been demonstrated that the use of bent target and pre- or double-pulse pumping compensate for horizontal refraction of the soft-x-ray beams in the plasma [9, 10]. The hydrodynamic of soft-x-ray plasma amplifier is a bidimensional problem. Up to now, vertical refraction has been treated only with phenomenological modeling using 1.5D hydrocode post-
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processed by ray-tracing code but assuming ab initio plasma vertical profiles [11]. This approach prevents one from a realistic description of plasma structure along the vertical direction. As it will be pointed out in this paper, the two dimensional (2D) effects are strongly impacting the plasma shape, requiring a full 2D hydrocode for approaching a realistic description. Furthermore, the bidimensional modeling pointed out a large overestimation of the vertical size of the gain zone calculated with 1.5D hydrocode. In this conference, we report numerical modeling of the impact of the spatial shaping of the driving laser beam in order to improve the soft-x-ray laser amplifier quality by reducing the vertical refraction combined with a broadening of the amplification surface, in the transient collisional schme. We demonstrate by numerical modeling that refraction might be dramatically reduced by using (n=10) super-Gaussian laser (SGL) spatial profile instead of the classical Gaussian laser (GL) spatial profile [12]. We also observed that for (n=10) super-Gaussian, the gain region size might be increased by a factor of 2 as compared to the Gaussian spatial profile case, doubling the soft-x-ray laser (SXRL) output energy. This additional unexpected result enhances the interest of SGL spatial profile. We show that even with low prepulse energy before the long pulse, the effect reminds for optimal pre-plasma formation.
2 ARWEN code and modelling To model the laser deposition influence and the following hydrodynamic plasma evolution we used the bidimensional (2D) hydrocode ARWEN. The ARWEN [13] code is based on adaptive mesh refinement (AMR) fluid dynamic and radiation transport calculations. The radiation intensity is calculated with a discrete energy multigroup scheme [14] coupled to the adaptive algorithm. To our knowledge this is the first time that an AMR code is used to model SXRL plasmas. As compared to older 2D hydrocodes, AMR technique is much faster enabling to run a full, highly resolved hydrodynamic case in a reasonable CPU time (8h) as required to achieve a complete case. Simulations are realized with a base cell grid of 128×64 cells and two refinement levels. The radiation transport is initialized with 16 angles. The simulation window is defined by a 240 µm×120µm square side with a slab target of 10 µm. The vacuum in front of the target is set at a baking pressure of 10−3 mbar. The goal of hydrodynamic modeling of the
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Fig. 1. Schematic view of modeling geometry
laser-produced plasma is to find optimum laser drive spatial conditions for the long laser pulse to obtain the largest possible gain region associated with negligible vertical density gradients (Fig. 1).For the sake of clarity we define the axis along which the soft-x-ray laser propagates as z, the vertical direction y as the axis perpendicular to the driving laser incidence, x direction. For all the simulations of interest, the target is illuminated by a λ=800 nm laser having a Gaussian pulse duration of 400ps full width at half maximum (FWHM) and 1 J energy corresponding to the typically
Fig. 2. Transverse vertical spatial laser profiles for different n-value
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uncompressed chirped pulse of Ti:Sa laser system. 100ps after the peak of the long pulse, a second short 5ps (FWHM) duration pulse of 2 J heats preformed plasma with temporal and spatial shape identical to the long laser pulse. The spatial deposition profile of the laser pulse energy on the target, modeled by: 2n
⎛ y ⎞ ⎟ −⎜ ⎜ 2σ y ⎟ ⎝ ⎠
I ( y) = I0e
is Gaussian for n=1 or super-Gaussian for n greater than 1. Our study has been performed considering the cases of n=2, 5, and n=10. For all Gaussian or super-Gaussian lasers, the widths at half maximum are set at 100 µm (Fig. 2). The target length is set at 5 mm. We assume a homogeneous deposition along the z direction. The SGL spatial profile can be realized experimentally by using diffractive optics or by coupling a standard combination of a cylindrical and spherical lens to an adaptive mirror [15]. With this scheme the line focus is achieved thanks to the use of the lenses while the adaptive optic [16] serves to shape the transverse (vertical) profile of the line focus. The longitudinal line shape is normally sufficiently homogeneous to prevent any correction. We consider that both the long and short pulses are focused with the same optics meaning that the gain region properties of interest (ions density, electron density gradient, sizes) are given by the energy deposition of the long pulse while electronic temperature profile is given by the short laser pulse.
3 Vertical shaping of the pre-plasma It is fairly justified to expect that the preforming process (i. e. long laser pulse or combination of prepulse and long pulse) is very important for SXRL operating in transient collisional scheme and more especially for SXRL pumped in the GRIP geometry [17,18]. As not only the state of the plasma column but also the pump pulse propagation are affected by the plasma preforming process. We concentrated our interest on the plasma density shape and temperature. The ionization is not illustrated because in the LTE assumption it follows the electron temperature. On the other hand the parameters of the heating pulse decide about the final plasma temperature.
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3.1 Influence of transverse spatial profile (n) Figures Fig. 3 and Fig. 4 displayed respectively 2D maps of the electron densities and temperatures for n=1 (left side) and n=10 (right side) for a delay of 100ps after the peak of the long laser pulse. During the early times of the laser-target interaction, the laser pulse shapes strongly imprint Gaussian or super-Gaussian density profiles. However, later during the plasma evolution, at delay Δt=100ps, when we choose to fire the short pulse to heat up the plasma, the density and temperature profiles do not reproduce so precisely the laser shapes (Figs. 3a,b). On both plasmas created by Gaussian and super-Gaussian lasers the edges looks perturbed. For n =10 SGL, at 100 ps after the peak of the long pulse, plasma jets appear clearly around y=40 µm and 190 µm while the central part of the plasma is homogeneous in terms of electron density and temperature. For both GL and SGL generated plasmas cases, the plasma centers are expanding with the highest velocities because most of the laser energy is laid down there, while the sides are cooler and less dense leading to lower lateral velocities.
a)
b)
Fig. 3. Electron density map,
These results in the plasma inhomogeneities observed on the edges. For plasma created by SGL profile (Fig. 3b) there is no cold dense plasma on each side formed by the feet of the Gaussian laser pulse that increase the cooling of the plasma by thermal conduction, as compared with plasmas created by GL profile pulse. This is even reinforced by the lateral expansion for the case of plasmas created by super-Gaussian beam which creates jets containing the expansion in the x-axis. Besides, the density profiles follow somehow the laser deposition profile, creating a kind of
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plateau on the electron density with sizes increasing with n. For n=1, the plateau is about 25% of the laser full width while it rises 40% for n=5 to 60 % for n=10 SGL profile. On other and, we can notice in Fig. 4a,b the electron temperature is more homogeneous in the dense part of the plasma for the SGL spatial profile. The homogeneous region, in terms of temperature follows the size of the density plateau. During the plasma expansion, the edge of the plasma in the case of SGL profile, the temperature decrease rapidly but the center part remind homogeneous. We can observe cold plasma region on each side of the main plasma in the case of SGL spatial profile, where there is no laser energy lay down. These plasmas are created by the x-ray coming from the main plasma which produced dense and cold plasma. The direct consequence of this enlargement of the hottest and densest parts of the plasmas, is that neonlike ions, i.e., lasing ions, are found in regions with boundaries at ±25 µm from the plasma centre for GL pulse, increasing to ±40 µm for n=5 SGL pulse up to ±50 µm for n=10. Note that for all GL or SGL cases, lasing ions are found from x=20→40 µm. This means that the potentially amplifying surface, and then the maximum output energy of the SXRL, is multiplied by a factor of 2 for n=10 SGL vertical profile as compared to GL.
Fig. 4. Electron temperature distribution for a) GL profile, n=1 b) SGL profile, n10 for a delay Δt=100ps after the peak of the long pulse.
As previously discussed, the electron density gradients, particularly along the y direction, may dramatically reduce the net SXRL amplification and destroy the beam homogeneity. Comparison of figures (Fig. 3a) and
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(Fig. 3b) shows an impressive reduction by three orders of magnitude of the vertical density gradient in the region of peak gain localization for n=10 SGL ∇yNe~1.1×1021 cm−4 as compared to n=1 case ∇yNe~6.0×1024 cm−4. Following the calculation in the paraxial approximation propagation of soft-x-ray beam, this shows that the refraction is negligible for n=10 SGL profile [19]. Note that electron density gradients along the x direction are equivalent for any GL- or SGL-produced plasmas (n=2, 5 and 10). 3.2 Prepulse influence on the vertical plasma shape As we show, the electron density and temperature mainly follow the laser energy deposition. We investigate now the effect on the imprint of the laser energy deposition when the long pulse irradiated the plasma formed by low energy prepulse.
Fig. 5. Pre-plasma formed by combination of prepulse and long pulse for a delay of 100 ps after the peak of the long pulse: a) GL laser spatial profile b) SGL spatial profile
We add a prepulse 2.3 ns before the peak of the long pulse containing 0.1% of its energy. This leads to laser intensity on the target of 2 1010 W.cm-2 and 5 1011 W.cm-2. The prepulse spatial profile width and shape are the same as the long pulse, considering they are often focused by the same optical system. To decrease the computation time we cut the simulation window in half in the y direction using the x-axial symmetry. We Show in Fig. 5 that the density distribution (logarithm scale) is still more homogeneous in the case of SGL spatial profile in the vicinity of the critical surface. If we compare with the Fig.3 where there is no pre-pulse,
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the electron density gradient fall by 2 orders of magnitude on the x-axis [20, 21]. In the case of SGL profile, the density is higher for a same x coordinate compared to GL profile case. This could be explained by the difference in the velocity distribution and particularly, the difference of the ratio of (vx/vy) which is closer to one in the case of SGL profile. Finally, we can notice, the beginning of a jet formation in y=60µm generated by the long pulse and the second one expanding to the top of the figure from y=75µm to y=120µm. These structures are not generate in the case of a perfect GL spatial profile.
4 Plasma heating and gain estimation Thus at high electron density Ne~1020–1021 cm−3, where the second pulse is absorbed, the GL generated plasma has a temperature of about Te~470 eV at its center y=120 µm dropping to Te~ 200 eV at y=75 µm and y=175 µm. For SGL profile pulse, the peak temperature is nearly the same, however on the edges y=75 µm and y=175 µm a much higher temperature of Te ~320 eV is achieved. Besides, the density profiles follow somehow the laser deposition profile, creating a kind of plateau on the electron density with sizes increasing with n. For n=1, the plateau is about 25% of the laser full width while it rises 40% for n=5 to 60 % for n =10 SGL profile. This means that the potentially amplifying surface, and then the maximum output energy of the SXRL, is multiplied by a factor of 2 for n=10 SGL vertical profile as compared to GL.
Fig. 6. Gain map a) Super Gaussian profile, n=10 b) Gaussian profile, n=1.
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To achieve 2D gain maps, we postprocessed the outputs of ARWEN with a simplified three-level atomic model. Such a calculation is known to slightly overestimate the gain [20]. We assumed that the fundamental level 1s22s22p6 is much more populated than the other levels. The upper lasing level (1s22s22p53p,J=0) is linked to the fundamental level by a forbidden transition and following the conclusions of Goldstein et al. [22], we assume that is mainly populated by direct collisional excitations. The lower lasing level (1s22s22p53s,J=1) is populated and depopulated through both collisional and radiative transitions. Collisional and radiative rates have been obtained from previous works on neon-like iron [23]. Spectral width is calculated assuming both homogeneous and inhomogeneous broadening based on ARWEN output. The electron density is given by ARWEN at the instant of firing the second pulse. From Figs.6a and 6b we can observe in the 2D gain maps that the shapes of the gain regions follow the energy deposition profiles. Close maximum gain, around 136 cm−1, is found for all profiles. Yet, it is interesting to note that the peak gain zone is two times larger over the y direction for the n=10 SGL 80 µm as compared to GL case 40 µm.
5 Conclusion This study underlines the need of complete bidimensional hydrodynamic code to achieve realistic soft-x-ray plasma amplifier description. Indeed, we show that lateral thermal conduction reduces the gain zone to a third of laser width when Gaussian laser shape is considered. By using a 2D hydrocode, we have numerically demonstrated that n=10 SGL spatial profile reduces the vertical refraction to an insignificant level. Consequently, an amplified soft-x-ray beam of high homogeneity would be achievable. Another beneficial phenomenon observed is an enlargement of the gain region surface by a factor of 2 while using super- Gaussian spatial profile as compared to classical Gaussian laser profile. Broadening of effective amplification surface would lead to doubling of the output energy while keeping driving laser energy constant. These two points allow a better output soft-x-ray laser energy extraction ensuring to double the output energy without increasing the driving laser energy.
2-D Hydrodynamic Simulation of Laser Plasma Generation
References 1. B. Rus et al., Phys. Rev. A 66, 063806 (2002). 2. P. V. Nickles et al., Phys. Rev. Lett. 78, 2748 (1997). 3. J. Dunn et al., Phys. Rev. Lett. 84, 4834 (2000). 4. O. Guilbaud et al., Europhys. Lett. 74, 823, (2006). 5. R. Bartels, Nature 406, 164 (2000). 6. Ph. Zeitoun et al., Nature 431, 427 (2004). 7. Y. Wang et al. Phys. Rev. Lett. 97, 123901 (2006) 8. S. Le Pape and Ph. Zeitoun, Opt. Commun. 219, 323 (2003). 9. J. G. Lunney, Appl. Phys. Lett. 48, 891 (1986). 10. R. Kodama et al., Phys. Rev. Lett. 73, 3215 (1994). 11. J. A. Plowes, Opt. Commun. 116, 260 (1995). 12. K. Cassou et al. Phys. Rev. A, 76, 1 (2006) 13. F. Ogando and P. Velarde, J. Quant. Spectrosc. Radiat. Transf. 71, 541 (2001). 14. L. H. Howell et al., Numer. Heat Transfer, Part B 35, 47 (1999). 15. G.-Y. Yoon et al., Appl. Opt. 36, 847 (1997). 16. T. A. Planchon et al., Opt. Commun. 216, 25 (2003). 17. K. Cassou et al. Optics Letters, to be published. 18. S. Kazamias et al, in this proceedings 19. E. Fill, J. Opt. Soc. Am. B 14, 1505 (1997). 20. J. Nilsen et al., Phys. Rev. A, 48, 4682 (1993) 21. Y. Li, G. P. Preztler et al., Phys. Plasmas 4, 164 (1997). 22. W. H. Goldstein et al., Phys. Rev. A 36, 3607 (1987). 23. M. Cornille et al., At. Data Nucl. Data Tables 58, 1 (1994).
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2D Hydrodynamic Simulation of Focus-Line Plasma in Ni-Like Ag X-Ray Laser Research W. Zheng and G. Zhang (Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088,China)
Summary. In the research of X-ray laser (XRL) driven by line focused laser, because focus-line had very large aspect ratio with narrow width (100μm), the jet of plasma showed clear 2D structure, and all sorts of peculiar 2D distributions of near-field and far-field XRL intensity were already observed in experiments, such as “bow-like” field image of XRL on ShengGuang-II facility. In order to understand and simulate this phenomenon, we developed a 2D non-equilibrium radiation hydrodynamics code named XRL2D, which was introduced in this paper briefly. The hydrodynamics behavior of Ni-like Ag XRL had been simulated by XRL2D code, simulation results were also presented in this paper. Similar to the QSS XRL experiments on ShengGuang-II, a slab Ag target was irradiated by a 1ω laser beam (85J) with 100μm×1.8cm focus-line, drive laser included a pre-pulse (2.55J) and a main pulse(82.45J), both with width of 100ps, and the interval of two pulses was 3ns. The abundance distribution of Ni-like ion appeared bow-like structure. The 2D gain calculation was our future work.
1. Introduction In the study of X-ray laser (XRL) driven by laser, line-focus beam were used popularly. Because focus line had a long length and a narrow width (100μm), the plasma expanded two dimensionally, in addition to the nonuniform of drive beam, hydrodynamic behavior of plasma and gain distribution of XRL can’t been described by 1D code. For this 2D characteristic of plasma expansion, many peculiar distributions of near and far field XRL intensity have been observed in many experiments [1-4]. In the experiments conducted on ShengGuang-II facility, the near- and farfield intensity distribution of Quasi-Steady-State (QSS) Ni-like Ag 13.9nm XRL presented a bow-like shape, which were showed in fig.1. This XRL were produced by irradiating Ag slab target (1.6cm long) with 100μm×1.8cm line focused beam (1ω/100ps/100J) at an intensity of 4~6×1013W/cm2, drive laser beam included two pulses, energy rate of pre-
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pulse and main-pulse was 3~5%, main-pulse delayed by ~3ns. There were two reasons to explain this bow-like shape. First, the gradient of electron density of plasma made XRL refracted out of the center area. Second, the gain of XRL maybe have this bow-like profile. In order to understand physical processes in it exactly and to study 2D effects of interaction between laser and plasma, we developed a non-equilibrium radiation hydrodynamics 2D code (XRL2D). The brief introduction of this code was presented in this paper, as well as the hydrodynamic simulation result of QSS Ni-like Ag XRL.
Fig. 1. The intensity distribution of Ni-like Ag 13.9nm XRL (experiments on ShengGuang-II facility). (a) Near-field image of two opposite coupling targets, and (b) far-field image of single target. x was the normal direction of target surface, y was the tangent direction of target surface. θ was the refraction angle
2. Introduction of XRL2D code Inverse bremsstrahlung absorption and resonant absorption of drive laser were considered, and geometric optic approximation was used. Flux-limit heat-conduct approximation and flux-limit multi-group diffusion approximation (~100 groups) were adopted. Average atomic model only considering principal quantum number was used in code. Considered micro-processes included bremsstrahlung and its inverse process, electron collisional ionization and three-body recombination, photo ionization and photo recombination, electron collisional excitation and de-excitation, line emission and line absorption, di-electron recombination and self ionization. In the view of Lagrange, equations of irradiation hydrodynamics employed by code were listed below, v du 1 ≈ − ∇( pe + pi + pr + q ) dt ρ
(1)
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v d (CveTe + V ) 1 d ⎛1⎞ ≈ − ∇ ⋅ Fe − pe ⎜⎜ ⎟⎟ + Wie + Wl − Wr ρ dt dt ⎝ ρ ⎠
(2)
v d (CviTi ) 1 d ⎛1⎞ ≈ − ∇ ⋅ Fi − pi ⎜⎜ ⎟⎟ − Wie ρ dt dt ⎝ ρ ⎠
(3)
v ρν ∂fν ∂ ⎛ 1 ⎞ ∂fν = −∇ ⋅ Fr + ⎜ ⎟ + Dν − Cν fν ∂t 3 ∂ν ∂t ⎜⎝ ρ ⎟⎠
(4)
v
In which, u was the hydrodynamic velocity, ρ was the matter density, pe, pi and pr were the pressures of electron respectively, ion and irradiation, q was the Von-Neumann viscosity, CveTe and CviTi were the electron and ion internal energy per unit mass, fv was the photo number of unit quantum state, v was the frequency of photo. V was combine energy of ion, Wie was the term of energy exchange between electron and ion, Wl was the term of laser energy deposit, Wr was the term of energy exchange between matter and irradiation. Dv, Cv were the emission and absorption coefficients of photo. Fe, Fi and Fr were flux of electron, ion and irradiation respectively. r Fe = FDe ⋅ f e FLe
and
F
( Fr
De
were
Le v FLe = N e kTe kTe / me
+ f e FLe
), where, f
diffusion
e
flux
v
was electron flux-limitv factor, FDe
and
direct
flux,
FDe = − K e ∇Te
,
, so as well as flux of ion and irradiation. ALE method adopted by code included three steps. First was Lagrange step. Differential scheme of momentum equation was IGA scheme. In order to decrease calculation amount, split scheme was used, diffusion processes of electron, ion and irradiation were separated from local processes such as atomic processes, energy exchange between electron and ion, temperature increase induced by energy deposit of laser, and local photo-absorption and irradiation et al. using implicit scheme, local processes were all coupled. Second step was rezone, mesh were rezoned every time-step. Last step was remap, 2-order precision remap scheme were adopted.
3. Hydrodynamic simulation of QSS XRL The calculation model was according to the experiments of Ni-like Ag XRL on ShengGuang-II described above. Drive laser (1ω) irradiated Ag slab target with 100 μm×1.8 cm line focused at a intensity of 4.7×1013 W/cm2, laser beam included pre-pulse (2.55 J) and a main-pulse (82.45 J)
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delayed 3ns. Both were Gaussian pulse in time with a width of 100ps, and flat-top pulse in space. Electronic flux-limit factor (fe) of 0.03 was applied. The incidence direction of drive beam was reverse to x axis,
Fig. 2. Electron temperature and density distribution before the main-pulse. Meshes were also plotted.
Fig. 3. Electron temperature and density distribution 20ps after main-pulse peak time.
initial target surface was located at x=0, the target thickness was 30μm. The tota l mesh number was 150×100. At the beginning, area out of target surface was filled with rareness gas (Ag) with a density of 10-6g/cm3. In calculation, meshes were kept perpendicularly always by rezoning, see in fig.2-3. For the symmetric of problem, only half physical area was calculated. Fig.2 showed the simulation results before main-pulse. Pre-pulse only prepared a pre-plasma. After expanding for 3ns, Pre-plasma cooled down
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no more than 20 eV, and while approaching target surface, electron temperature decreased more and more. Simulation results 20 ps after main pulse peak time showed in fig.3, when gain of XRL would appear (the result from 1D simulation of JB19 code). According to our simulation, in the
Fig. 4. At center of focus line, electron temperature Te, radiation temperature Tr, electron density Ne, abundance of Ni-like ion PNi_like and laser energy deposit WL distribution along normal direction of target surface, 20ps after main-pulse peak time.
period of incidence of main pulse, plasma moved a little because the width of main pulse was short enough. With the arrival of main-pulse, plasma at laser energy deposit area was heated and ionized dramatically. At this area, for rapid electron collisional ionization, Ni-like ion dominated at lower electron temperature (1 because the preplasma is not transparent for the pedestal pulse. The solutions are
Similarity Model of Longitudinally Pumped X-Ray Laser
329
4/3 8/9
T = a1 t 3/ 4
3/ 4
(1 − t m t 17 / 9
−17 / 9
Tm t m
+
t
L = b1 t
3/2
)
3/ 4
, here a
1
a1
(1 − t m t 17 / 9
−17 / 9
Lm t
+
−1
= 28.45 I m 1 L A
2/3
−17 / 9
2
1/ 2
−17 / 9
10 / 9
)
1/ 2
, here b
1
b1 t m
= 17.81 × 10
−1
−4
I m1 L
(3) 1/ 4
c1 t
n0 = (1 − t m t 17 / 9
−17 / 9
−5 / 4
, here c
1
c1
+
28 / 9
4
t
−17 / 9
)
20
= (5.69 × 10 )
4
−1
I
−2
5
m1 L A
1/ 4
nm t m
b) During the time of t2trans ≤ t ≤ t2L
The plasma changes to be transparent for the pedestal pulse again with the laser heating. Considering the physics meaning of the t2trans we get
t 2 trans = 0.51 I
−7 /15
23 / 15
m1 L A
−2 / 3
Λ
8 /15
λ
16 /15
(4)
Also 5/ 2
T = a2 (1 − t 2 trans t 2/5
5/3
−5 / 3
L = b2 t [1 − t 2 trans t 4 / 15
5/3
+
−5 / 3
5/3
T2 trans t 2 trans t +
−5 / 3
a2 15 / 4 −5 / 3 L2 trans t 25 / 12
2/5
]
b2 t 2 trans
4 / 15
t[1 − t 2 trans t 5/3
−5 / 3
+
(8.08 × 10 )
20 15 / 2
c2
c2 t 15 / 2
, here c2 =
−5 / 3 35 / 6
]
2 / 15
2
, here b2 = (1.29 × 10 −2 )15 / 4 a2 A
2 / 15
n0 =
−1
) , here a2 = 19.46 I m1 L λ Λ
a2 A
−5 / 4
15 / 2
m1 L
5/2
n2 trans t 2 trans (5)
c) During the time of t2L≤ t ≤ t3L
The main pulse is so short that the plasma is not transparent for the laser and there is not enough time to change the state of ion charge. At time t2L
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the solutions can be obtained by considering the initial conditions before t2L: 2/3
5 / 3 −5 / 3
T = a 3 t (1 − t 2 L t
+
T2 L t 2 L
t
−5 / 3
−1
), here a 3 = 23.12 keV I 2 m AZ
−1
a3 2
1/ 2 3 / 2
L = b3 t
n0 = c3 t 1/ 2
5 / 3 −5 / 3
(1 − t 2 L t
−3 / 2
L2 L
+
t
4/3
−5 / 3 1 / 2
)
b3 t 2 L −5 / 3 −5 / 3
(1 − t 2 L t
2
−1
3
c3
+
, here b3 = (5.16 × 10 −2 ) 2 I 2 m
4/3
t
−5 / 3
n2 L t 2 L
)
−1 / 2
, here c3 = (3.16 × 10 ) 20
2
m Z 1
2 2
I2 A (6)
d) During the time of t3L≤ t
After the time t3L the main pulse is turned off and the plasma continues to expand adiabatically. The solutions can be obtained using the condition before t3L: 2/3
T = T3 L t 3 L t
−2 / 3
−5 / 9
L = L3 L t3 L t
5/9
7/9
n0 = n3 L t 3 L t
−7 / 9
(7)
here T3L L3L and n3L are the temperature scale length and density at the t3L respectively.
3 Results and Discussion We firstly calculate the experiment results of T.Ozaki et al. under the same condition to demonstrate the credibility of the model. Then we investigate the hydrodynamic of longitudinally pumped x-ray laser plasma using the model. 3.1 Credibility of the model
We calculate the longitudinally pumped nickel-like molybdenum slab xray lasers under the same experimental conditions of T.Ozaki’s. The calculation results indicate that the average ionization state only reach to 10 not 14 required by nickel-like molybdenum at the pre-pulse laser intensity of 1.5×1011 W/cm2 and the duration of 300ps which is a bit bigger than 9 from T.Ozaki et al. But the pedestal of main pulse with the intensity
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3.0×1011 W/cm2 and the duration 300ps heat the electron to 88.1 eV which is quite similar to Ozaki’s results. The ionization is 14.04 and the electron density reach to 1.01×1020 cm-3 according with Ozaki’s results. The comparison shows successfully that the results from this simplified model well match the calculation by Ozaki. 3.2 Affection of the pedestal of main pulse on the ionization
In order to realize the affection of the pedestal to x-ray laser we calculate the affection on the ionization of pulse pedestal with different duration and intensity respectively as shown in Fig 1. 14.15
Z (Average ionization)
(a) 14.10 14.05 14.00 13.95 13.90
0.1
0.2
0.3
0.4
0.5
0.6
7
8
t2L (ns)
(b)
Z (Average ionization)
16.0 15.5 15.0 14.5 14.0 3
4
5
6 11
2
Intensity (10 W/cm )
Fig. 1. The average ionization vs the duration (a) and the intensity (b) of the pedestal of the main pulse.
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Fig.1 shows that the ionization just decreases from 14.12 to 13.93 (stay Ni-like) with the increase of the duration of main pulse pedestal from 100 ps to 600 ps under the condition that the intensity is invariable (3.0×1011 W/cm2). While the ionization increases rapidly from 14.03 to 15.96 (over Ni-like state) with the increase of intensity of pulse pedestal from 3.0×1011 W/cm2 to 8.0×1011 W/cm2 when the duration of main pulse pedestal (300 ps) is invariable. It is clear that the variety of the ionization is sensitive to the intensity of pulse pedestal. 3.3 The hydrodynamic of the longitudinally pumped x-ray laser
We know that people always pay more attention to the variety of temperature scale and density of plasma with different value of z along propagation of pumped laser (z axis) in longitudinally pumped scheme due to its direct affection if the plasma can form the uniform population inversion and if x-ray laser can be amplified effectively instead of being absorbed. In order to investigate the above problems particularly we calculate the electron temperature the ionization state and the variety of density respectively with the different value of z under the same experimental conditions of T.Ozaki’s as shown in Fig.2. We firstly calculate different value of z dependent electron temperature before the ending of the main pulse pedestal as shown in Fig.2 (a). It should be noted that the temperature rapidly decreases from 90 eV to 5.9 eV before 600 μm and then approaches to 5.6 eV after 600 μm which is the same to the electron
temperature without main pulse pedestal indicating that the pumped laser intensity has approached to 0 after 600 μm. The different value of z dependent electron temperature in Fig.2 (b) has also demonstrated the above conclusion: the ionization decreases from 14.03 to 5.69 with the variety of z from 0 to 600 μm and then approaches to 5.6. At last we calculate the variety of the electron density with the different value of z (shown in Fig.2 (c)). The electron density varies from 1.01×1020 cm-3 to 1.84×1020 cm-3 and then approaches to 1.95×1020 cm-3 after 600 μm. Therefore we can conclude that the intensity of pumping laser decreases rapidly along propagation in the plasma due to the absorption and refraction. When the value of z exceeds a definite value the proportion of Ni-like ion is much little because of the low temperature. Here the x-ray laser will be absorbed instead of being enhanced by plasma. So it is important to choose the appropriate slab length. We also calculate the different value of z dependent electron temperature at the end of pulse pedestal with different electron density as shown in Fig.2(d) due to the condition that we can vary different incident
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100
14
Z (Average ionization)
(a)
80
T (eV)
60 40 20 0 0.00
0.05
0.10
0.15
(b)
12 10 8 6 4
0.20
0.00
0.05
0.10
0.15
0.20
z (cm)
z(cm)
100
2.0
(c) 80
(d)
1.4
T (eV)
-3
1.6
20
n0 (10 cm )
1.8 60 40 20
1.2
0
1.0 0.00
0.05
0.10
z (cm)
0.15
0.20
0
500
1000
1500
2000
-3
z (10 mm)
Fig. 2. The curve of the temperature (a) ionization (b) and electron density (c) with z axis along the longitudinal direction before the main pulse arrive. The delay time is 4ns other conditions are same as fig.1. (d) The curve of the temperature with different density along z axis at the end time of the main pulse. Here the solid line is for n0=1.0×1019 cm-3 the dash line is for n0=4.0×1019 cm-3 the dot line is for n0=8.0×1019 cm-3 the dash-dot line is for n0=1.2×1020 cm-3 the dot-dot line is for n0=4.0×1020 cm-3 the short dash line is for n0=8.0×1020 cm-3.
density through choosing different longitudinally incident position in the experiment. It is noted that the electron temperature changes obviously with z in different electron density. It also shows that the electron temperature varies only from 88.11 eV to 83.62 eV when the density is lower 1.0×1019 cm-3 for instance while the electron temperature decreases rapidly to the initial value of 5.37 eV in the 8.0×1020 cm-3. Therefore it is more effective method to choose the proper element of which the requirement of the density in the gain region is lower.
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4 Conclusions A similarity model is developed for the longitudinally pumping x-ray lasers. The results are in agreement with the experimental results. The hydrodynamics of the scheme are investigated using the model. The results show that (1) The pedestal of the longitudinal pumping pulse play an important role in the Ni-like ionization state (2) The absorption of longitudinally pumping laser in the plasma result in the asymmetry of the temperature and the density in the laser propagation direction so that the gain length is limited. (3) It is an effective method to choose the proper element of which the required density is low in the gain region.
References 1. P. V. Nickles et al. Phys. Rev. Lett 78 2748 1997. 2. R. Li et al. Phys. Rev. E 57 7093 1998. 3. T. Ozaki et al. Phys. Rev. Lett 89 253902 2002. 4. Y. J. Li et al. 9th International conference of x-ray lasers page 333 Beijing May 24-28 2004. 5. Y. J. Li et.al. Phys. Rev. E 63 036410 2001.
Numerical Analysis of Plasma Medium of a Fully Coherent X-Ray Laser N. Ohnishi1, M. Nishikino2 and A. Sasaki2 1
Department of Aerospace Engineering Tohoku University 6-6-01 Aramaki-Aza-Aoba Aoba-ku Sendai 980-8579 Japan 2 Kansai Photon Science Institute Japan Atomic Energy Agency 8-1 Umemidai Kizu Souraku Kyoto 619-0215 Japan
Summary. Two-dimensional (2D) radiation hydrodynamics simulations have been performed to investigate the generation and the refraction influence in the plasma medium of a fully coherent x-ray laser at 13.9 nm by the double-target configuration. The local energy deposition of the main laser pulse generates a blast wave near the critical density surface and the density dip structure is gradually formed behind the blast wave. The size of the density dip structure is about 10 μm after 50 ps of the main pulse. The three-dimension (3D) ray-trace calculation using the result of the 2D simulation shows the x-rays pass through the density dip with less refraction. The size and the position of the density dip area are similar to the light source of the fully coherent x-ray laser.
1 Introduction The development of the brilliant x-ray source has been progressed for the material science and the biological science and the soft x-ray free-electron lasers (XFELs) [1 2] will open up possibilities of the new scientific area. The laser-driven x-ray lasers (XRLs) [3–9] with highly spatial and temporal coherence are applicable light sources as a scientific tool for the purpose of the practical application of the XFEL. Since the first demonstration of the laser-driven soft XRL [10] the improvements of the beam properties have been demonstrated by a number of the groups [11– 15]. The significantly improvement of the beam quality such as spatial and temporal coherence is the important issue for the practical applications. Recently soft-XRLs with small divergence and highly spatial coherence have been demonstrated by the double-target amplification [16–18] and the longitudinal pumping [19]. In contrast to the transient-collisionalexcitation (TCE) XRL [20 21] the highly spatial coherent XRL is
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developed with discharged capillary plasma [22] and the amplification of the high-order harmonic generation [23]. A fully coherent XRL has firstly demonstrated at a wavelength of 13.9 nm by the double-target amplification [16–18]. In the double-target amplification the XRL from the first target is used as a seeding light and a coherent portion of the seeding XRL is amplified in the gain medium of the second target. Since the spatial coherence of the TCE XRL is limited by the short length of the gain medium the amplifier of the second target was separated from the first target by a sufficient distance with the condition of the Fresnel number N < 1. When the delay time between two pumping pulse is optimum condition the highly directional XRL is generated. The total gain of the amplification of the second target is about 1000 with the gain coefficient of about 8 cm−1 and the output energy is achieved about 1 μJ [24 25]. In this configuration the gain medium of the second target works as an active spatial filter. From the first experimental result and the simple analysis the spatial position of the gain medium of the second target is generated in a lower density area for avoiding the influence of the x-ray refraction. Then the position of the gain medium is about 100 μm from the target surface. However the gain region is about 20 μm distance from the target surface and the source size of the gain medium is about 20 μm in the 2D imaging experiment [26]. It turns out that there is a difference between the simple estimation and the experimental result. Therefore we have performed the 2D radiation hydrodynamics simulation to investigate the generation and the refraction influence of the gain medium plasma. In this paper we present the numerical analysis of the gain medium plasma of the fully coherent XRL using a 2D radiation hydrodynamics code and the 3D ray-tracing of x-ray laser has been conducted with arranging flow-fields of the 2D simulation result. We have carried out the comparison of the gain medium between the experimental result and the simulation one. The effects of hydrodynamic properties of the gain medium plasma have been investigated for finding the optimal pumping laser condition.
2 Numerical Methods and Conditions The computational code for plasma medium of x-ray laser should be able to properly reproduce high-temperature dense plasma. In the preset paper we have developed a 2D radiation hydrodynamics code based on the RAICHO code [27] which was originally developed for inertial fusion
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plasmas with some modifications for including the effects of thermal nonequilibrium realistic equation of state and laser refraction. The governing equations consist of inviscid compressible hydrodynamic equations with the additional terms due to electron/ion thermal conduction x-ray radiation and laser absorption in energy equation. Also radiative transfer equation is simultaneously solved to estimate the radiation source term. Numerical fluxes due to inviscid compressible flow are estimated by AUSM-DV approximate Riemann solver [28] with second-order spatial accuracy. The radiative transfer equation is approximated by the multigroup diffusion with variable Eddington factor. Non-LTE (CRE) emissivity and opacity is tabulated before the simulation based on the averaged ion model [29]. The electron and ion thermal conductions are modeled with the assumption of the flux-limited diffusion with classical conductivities. The flux-limiter was set to be 0.1 in the present simulation. In our code two-temperatures for electrons and ions are adopted with the relaxation term because they must be in thermally non-equilibrium in a corona. The laser absorption of inverse-bremsstrahlung is calculated by the ray-tracing manner including the refraction due to the electron density gradient [30].
Fig. 1. Simulation conditions for plasma medium of the second target.
The computations are conducted to investigate the density effect of the plasma medium of the second target in the oscillator-amplifier configuration. Figure 1-(a) shows the simulation area of the second target. The simulation domain with 50 _m long and 150 _m wide is calculated on the center of the target with 301 x 51 computational grids. This number of grids is sufficient for capturing the plasma features. The target material is silver. The laser wavelength is 1.06 _m. Input laser pulses consist of the Gaussian shaped pulses shown in Fig. 1-(b) which are pico-sec prepulse 100-ps prepulse and pico-sec main pulse. The pulse widths are 12 ps 100 ps and 12 ps at FWHM respectively. The pulse energies are 1J, 3 J and 12 J respectively. Since the pedestal of the laser pulse affects the plasma condition [7] we performed the calculation including the pedestal with 1012
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W/cm2. The timing of t = 0 ps is the peak of the main pulse. The silver target is irradiated from right hand side of Fig. 1-(b) by the line focused laser whose spatial width is 20 μm (10 μm in the computational domain) at the focal position. In the present study the spatial distribution of the laser intensity is uniform in that width. The laser is divided into 100 computational rays and the rays are parallel to each other without divergence.
3 Results and Discussion Electron temperature is rapidly increased by the main pulse near the critical densisy and exceeds 2 keV in the preformed plasma. Then pressure becomes very high while density gradient is relatively gradual. This leads the formation of a blast wave. The blast wave formation depends on the geometrical condition. Figure 2 shows the typical profiles of electron number density and electron temperature with different dimensions at 50 ps after the main pulse. In 1D (planar) geometry we cannot find the formation of the blast wave. However the propagation of the shock wave towards the corona region and the low density dip (circled region in Fig. 2(b)) can be found with 2D simulation. This density dip may affect on the refraction of the incident x-ray laser from the first target.
Fig. 2. Profiles of electron number density and electron temperature by (a) 1D planar simulation and (b) 2D simulation (in axis of symmetry) at 50 ps after the main pulse.
In order to confirm this density dip effect we have performed 3D raytracing of injected x-ray laser in the variable flowfield along the incident direction. The flowfield felt by the injected rays was constructed with arranging the time series of 2D simulation. Figure 3-(c) shows the contours of electron number density at 50 ps after the main pulse. The rays in the
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density dip around X = 20–30 μm and Y = 0–10 μm meander though the dip while the other rays are refracted to the expansion direction. Figure 3-(b) shows the ray positions at the cross section of the second target (6 mm from the incidence). In the present study a gain length for each ray is defined by the light path integrated over the assumed gain region where 1020 < ne < 1021 cm−3 and 0.25 < Te < 1.0 keV. The length for the rays in the density dip can be longer than that for the other rays because that dip is in the condition of the gain region. In this timing the length is about 5 mm. The size of the ray passed through the density dip is about 10 and 20 μm for the horizontal and vertical direction respectively. The non-refracted rays are located at X = 20–30 μm. Figure 3-(a) shows the near-field pattern (NFP) of the second target of the double-target amplified XRL in the case of the gain length of about 6 mm. The NFP was measured using a near-field imaging system with magnification of 8.5[26]. The size and the position of transmitted rays where the non-refracted rays are found are similar to those of intense area of the NFP.
Fig. 3. (a) The NFP of the 6-mm length second target of the double-target amplified XRL. (b) The ray positions in the cross section of the second target at 6 mm from the incidence. (c) The contours of electron number density at 50 ps after the main pulse.
4 Conclusion We have performed 2D radiation hydrodynamics simulations and 3D raytracing for investigating the plasma medium of the fully coherent x-ray
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N. Ohnishi, M. Nishikino and A. Sasaki
laser. The results suggest that the density dip behind the blast wave near the critical density suppresses the refraction of the injected x-ray laser from the first taget. We are planning the coupling computation with unsteady atomic process for detailed analysis of the fully coherent x-ray laser.
References [1] J. Arthur Rev. Sci. Instrum. 73 1393 (2002). [2] V. Ayvazyan et al. Phys. Rev. Lett. 88 104802 (2002). [3] M. Kalachnikov et al. Phys. Rev. A 57 4778 (1998). [4] A. Klisnick et al. J. Opt. Soc. Am. B 17 1093 (2000). [5] J. Dunn et al. Phys. Rev. Lett. 84 4834 (2000). [6] R. Tommasini J. Nilsen and E. Fill Proc. SPIE 4505 85 (2001). [7] T. Kawachi et al. Phys. Rev. A 66 033815 (2002). [8] S. Sebban et al. Phys. Rev. Lett. 89 253901 (2002). [9] B. M. Luther et al. Opt. Lett. 30 165 (2005). [10]D. L. Matthews et al. Phys. Rev. Lett. 54 110 (1985). [11]C. L. S. Lewis et al. Opt. Commun. 91 71 (1992). [12]R. E. Burge et al. J. Opt. Soc. Am. B 14 2742 (1997). [13]H. Daido et al. J. Opt. Soc. Am. B 16 2295 (1999). [14]G. Cairns et al. Appl. Phys. B 58 51 (1994). [15]R. Kodama et al. Phys. Rev. Lett. 73 3215 (1994). [16]M. Tanaka et al. Opt. Lett. 28 1680 (2003). [17]M. Nishikino et al. Phys. Rev. A 68 061802(R) (2003). [18]M. Nishikino et al. IEEE Journal of Selected topics in quantum electronics 10 1382 (2004). [19]T. Ozaki et al. Phys. Rev. Lett. 89 253902 (2002). [20]P. V. Nickles et al. Phys. Rev. Lett. 78 2748 (1997). [21]J. Dunn et al. Phys. Rev. Lett. 80 2825 (1998). [22]Y. Liu et al. Phys. Rev. A 63 033802 (2001). [23]Ph. Zeitoun et al. Nature 431 426 (2004). [24]T. Kawachi et al. Proc. SPIE 5919 1 (2005). [25]M. Nishikino et al. AIP Conf. Proc. 827 499 (2006). [26]M. Tanaka et al. Surface Rev. Lett. 9 641 (2002). [27]N. Ohnishi et al. J. Quant. Spectrosc. Radiat. Transf. 71 551 (2001). [28]Y. Wada and M. S. Liou AIAA Paper 94-0083 (1994). [30]H. Takabe and T. Nishikawa J. Quant. Spectrosc. Radiat. Transf. 51 379 (1994). [31] A. L. Edwards and J. A. Fleck Jr. J. Appl. Phys. 50 4307 (1979).
Longitudinally Pumped Ne-Like Titanium X-Ray Laser Simulation with a Post-Processor Code Coupled to EHYBRID A. Demir, E. Akman, S. Bilikmen*, P. Demir*, S. İnce*, E. Kacar, E. Yurdanur* and S. Yaltkaya** University of Kocaeli Laser Technologies Research and Application Center Aslanbey Campus Kocaeli / Turkiye * Middle East Technical University Department of Physics Ankara / Turkiye ** Akdeniz University Department of Physics Antalya / Turkiye
Summary. Longitudinal pumping with a grazing incidence scheme of Ne-like Ti has been modeled by using the EHYBRID and a post-processor code. The atomic data that are required in the simulation are obtained by using the Cowan code. The variation of the Ne-like Ti x-ray laser gain at 32.6 nm is calculated for a fixed delay time with a variation in the incidence angle and a fixed incidence angle with a variation in the delay time. The post processor code has been used to simulate the x-ray resonance lines between 17 and 29 Å.
1 Introduction The first x-ray laser was put into practice in the LLNL Novette laser facility in 1984 [1]. In this first demonstration kilo joule scale optical pump energy with a transverse scheme was used to ionize Ne-like Se thin foils and the output wavelength was seen at 20 nm. Since then numerous amount of experiments have been held throughout by using Li-like Ne-like Ni-like targets [2-5] with different pumping schemes [6-9]. Besides these the progress in the area has also been due to the technological improvements achieved in the laser technology. The general aim in these researches has always been to increase the gain efficiency and the repetition rate of the x-ray lasers with a shorter wavelength output and make them compact for their further usage in science and technology. In the grazing incidence pumping scheme a double irradiation is used for lasing output. The first long duration and low intensity transversely
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pumped pulse is used to ionize the target and form a plasma column. After a delay a second higher intensity shorter duration pulse irradiates the plasma column at grazing incidence. The angle of incidence is chosen so that at a preferential electron density the pulse is refracted into the gain region. In this way the beam will pass through the same density region and the absorption and therefore the efficiency will be increased. 2 Method of Calculation
During this study the modelling of Ne-like Ti has been done by using a modified version of the original EHYBRID code [10]. This modification allowed the spontaneous transition rates to be calculated from the absorption oscillator strengths which are used in the evaluation of the ionisation balance. Besides this the line intensities are calculated with a post-processor code that is coupled to EHYBRID by simulating the excited level population densities. The required atomic data are obtained by using the Cowan code [11]. 112 Ne-like 1s22s22p6 - 1s22s22p5 nl and 214 F-like 1s22s22p5 - 1s22s22p4 nl resonance line intensities have been calculated for the simulation of the spectral emission from the titanium plasma. 3 Results and Discussion
In the simulations firstly a 4 mm slab target is irradiated by a pre-pulse of 70 mJ energy and 200 ps pulse duration to form a plasma column. Afterwards a main pulse of 80 mJ energy and 1.2 ps duration has been sent with a grazing incidence for observing x-ray lasing (Fig.1.). The pulses have a 800 nm wavelength. The optimum delay time between the pulses and the incidence angle are searched for.
Fig. 1. Grazing Incidence Pumping Scheme
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The variation of the gain of the 32.6 nm Ne-like Ti laser line as a function of the incidence angle of the main pulse to the normal of the target surface for a 500 ps delay time is shown in Fig.2. Maximum gain is obtained around 10o of incidence angle. 32.6 nm Ne-like Ti Lasing Line
50
-1
Gain( cm )
40
30
20
10
0 0
10
20
30
40
50
60
70
80
90
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Fig. 2. Variation of the gain of the 32.6 nm Ne-like Ti laser line as a function of the incidence angle of the main pulse to the normal of the target surface. Data was obtained using a 70 mJ 200 ps duration pre-pulse followed by an 80 mJ 1.2 ps duration grazing incidence short pulse separated by a 500 ps time delay.
Simulation is performed to determine optimum delay time between the two pulses. Pre heating pulse has 70 mJ energy and 200 ps pulse duration in the simulation. The main pulse has 1.2 ps pulse duration and 80 mJ of energy. Fig.3. shows the variation of the gain as a function of the time delay with a grazing incidence angle of 10o. 70 32.6 nm Ne-like Ti Lasing Line 60
Gain (cm-1)
50
40
30
20
10
0 200
250
300
350
400
450
500
550
600
650
700
Delay Time (ps)
Fig. 3. Variation of the gain of the 32.6 nm Ne-like Ti laser beam as a function of the delay time between the two pulses. Data was obtained using a 70 mJ 200 ps duration pre-pulse followed by a 80 mJ 1.2 ps duration grazing incidence shot at 10o to the normal.
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Fig.4. shows the simulated time integrated Ne-like and F-like Ti resonance line spectrum for total pulse energy of 150 mJ. The Ne-like resonance lines are more intense than the F-like resonance lines. Ne-like 3d-2p
3.0E+15
Ne-like 3s-2p
F-like 3s-2p
F-like 3s-2p
1.0E+15
F-like 4s-2p
Ne-like 4s-2p
2.0E+15
F-like 3d-2p
Intensity (photons/Å)
4.0E+15
0.0E+00 17
19
21
23 Wavelength Å
25
27
29
Fig. 4. The time integrated Ne-like and F-like resonance line spectrum emitted from Ti plasma.
Fig.5. shows the Ne-like plus F-like resonance line intensity and gain of the Ne-like Ti lasing lines at 32.6 nm as a function of time. The FWHM of the gain is ~64 ps for 32.6 nm. 45
1.4E+22
40
1.2E+22
30 8.0E+21
25
6.0E+21
20
Gain (cm-1)
Intensity (photons/Å)
35 1.0E+22
15 4.0E+21 10 2.0E+21
0.0E+00 710
Ne-like and F-like Resonance Line 32.6 nm Gain Line
720
730
740
750
760 770 Time (ps)
780
790
800
5 0 810
Fig. 5. Variation of the gain and the intensity of the 32.6 nm Ne-like Ti laser beam as a function of time. Data was obtained using a 70 mJ 200 ps duration prepulse followed by a 80 mJ 1.2 ps duration grazing incidence shot at 10o to the normal. The time delay between the two pulses is 500 ps.
Longitudinally Pumped Ne-Like Titanium X-Ray Laser Simulation
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Ti(I) 3d 4s4p-3d 4s5s
3
2
430
480
530 580 Wavelength (nm)
Ti(III) 3p 3d5d-3p 3d5f
6
6
630
6
6
3
750
0 380
Ti(III) 3p 3d5s-3p 3d5p
3
Ti(I) 3d 4p-3d 4d
3
Ti(I) 3d 4s4p-3d 4s5s
2
3
3
Ti(I) 3d 4s-3d 4p
2 2 2 3
3
1500
Ti(I) 3d 4s -3d 4s4p
6 6
Ti(II) 3d -3d 4p
6
2250
6
Intensity (Au)
3000
Ti(III) 3p 3d4f-3p 3d5g 3 3 + Ti(I) 3d 4s-3d 4p
6
3750
Ti(III) 3p 3d5p-3p 3d5d 3 3 + Ti(I) 3d 4s-3d 4p
6
4500
Ti(II) + Ti (III) 3p 3d4f-3p 3d5g 3 3 + Ti(I) 3d 4s-3d 4p
Fig.6. shows the visible line spectrum emitted from Titanium preplasma created using pre-pulse laser conditions. The energy of the laser pulse is 200 mJ and the pulse duration is approximately 6 ns. The pre-pulse has created low ionized plasma and the main pulse interacts with the preformed plasma to create lasing action. The focus width is 100 μm.
680
730
Fig. 6. Experimentally observed visible spectrum of Titanium under pre-pulse condition.
4 Conclusions
During the simulations firstly the optimum incidence angle corresponding to the irradiation of a Ti target with a 70 mJ 200 ps pre-pulse which is followed by a 80 mJ 1.2 ps main pulse after 500 ps of time delay has been investigated and the optimum incidence angle is found at 10o. The pulses have an 800 nm wavelength. After this at 10o the optimum time delay is searched between 200-700 ps for the data given above and it is seen that 500 ps is near to the optimum case. The FWHM of the gain and the resonance lines between 17 and 29 Å for these optimum cases have been investigated.
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Acknowledgements This project has been supported by DPT under the contract number K120710.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
Matthews D.L. et al.: Phys. Rev. Let. 54 110 1985 Nickles P.V. et al.: Phys. Rev. Let. 78 2748 1997 Zhang J. et al.: Phys. Rev. A 53 3640 1996 Zhang J. et al.: Phys. Rev. Let. 78 3857 1997 Zhizhan Xu et al.: App. Phys. Let. 63 1023 1993 Kolacek K.: Proc. National Laser Symposium Indore India 2001 Sebban S. et al.: Phys. Rev. Let. 86 3004 2001 Ruxin Li et al.: Phys. Rev. E 57 7093 1998 Keenan R. et al. : Phys. Rev. Let. 94 103901-1 2005 Pert G.: J. Fluid. Mech. 131 401 1983 Cowan R.D.: J. Opt. Soc. Am. 58 808 1968
Simulation of Longitudinally Pumped Ni-Like Molybdenum X-Ray Laser Medium Using PostProcessor Code Coupled to EHYBRID E. Kacar, P. Demir, P. Demir*, A. Demir and S. Yaltkaya** Laser Technologies Research and Application Center University of Kocaeli Aslanbey Campus Kocaeli / TURKEY * Department of Physics METU Ankara/TURKEY ** Department of Physics University of Akdeniz Antalya/TURKEY
Summary. Longitudinally pumped Ni-like Mo x-ray laser media is modeled using EHYBRID and a post-processor code. The required atomic data are obtained using the Cowan code. In this study the pre-formed plasma is pumped on longitudinal direction with a grazing angle. Variation of the x-ray laser gain of the 18.9 nm and 18.2 nm Ni-like Mo lines according to the incidence angle of the main heating pulse normal to the target surface is calculated for different main pulse energies. X-ray resonance lines between 26 and 37 Å emitted from molybdenum plasma have been simulated using post-processor coupled with EHYBRID.
1 Introduction A longitudinal Ni-like Mo x-ray laser at 18.9 nm was proposed in 1998 [1] and it was demonstrated by using a short pulse which pumps the inversion along a pre-formed plasma column [2-5]. The pump energy required to produce a saturated Ni-like Mo x-ray laser can be reduced by pumping preplasma column from a longitudinal direction. An 18.9 nm Ni-like Mo x-ray laser operating close to saturation at 10 Hz repetition rate have been reported to be produced by pumping with 14° grazing incidence angle and 150 mJ of total pumping energy [3]. A plasma column is preformed by irradiating a slab target transversely with a long pulse. Then the short pulse is sent with a grazing angle to the target surface through the laser-produced plasma after a delay and refracted back into the gain region from a predetermined electron density. Refraction of the short pulse in the plasma depends on the incidence angle of the short pulse relative to the target surface. Path length and absorption of the short pulse is increased by
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refraction [3]. In experimental investigations dependencies of the longitudinally pumped Ni-like Mo x-ray laser intensity on parameters such as delay time heating pulses’ energy ratio intensity of the main pulse have been observed and the optimal conditions have been obtained [6]. In this paper longitudinally pumped Ni-like Mo x-ray laser is modelled by using EHYBRID code [7]. The modelling was performed for different parameters such as delay time between pulses heating pulses’ energy incidence angle of the main pulse.
2 Method of Grazing Incidence Pumping Simulations Longitudinally pumped Ni-like Mo x-ray laser is modelled using EHYBRID code [7]. Line intensities are calculated in a post-processor coupled with the EHYBRID using the simulated excited level population densities. The orginal EHYBRID code was modified to calculate the spontaneous transition rates from the absorption oscillator strengths used in the evaluation of the ionisation balance. The required atomic data are obtained using the Cowan code [8]. 128 Ni-like 1s22s22p63s23p63d10 1s22s22p63s23p63d9 nl and 230 Co-like 1s22s22p63s23p63d9 1s22s22p63s23p63d8 nl resonance line intensities have been calculated for the simulation of the spectral emission from the molibdenium plasma. In our simulations laser pulses of 0.8 µm wavelength focused on 4 mm target have been simulated. Molibdenium has been pumped with a prepulse and a short pulse. The pre-pulse has 70 mJ energy and 200 ps pulse duration and the following short pulse has 80 mJ energy and 1.2 ps pulse duration. The pre-pulse and the main pulse are separetad by 300 ps.
3 Results and Discussion
A plasma column is preformed by irradiating a slab target transversely with a long pulse. Then the short pulse is sent with a grazing angle to the target surface through the laser-produced plasma after a delay and refracted back into the gain region from a predetermined electron density. Refraction of the short pulse in the plasma depends on the incidence angle of the short pulse relative to the target surface. Variation of the gain of the 18.9 nm and 18.2 nm Ni-like Mo laser lines as a function of the incidence angle of the main heating pulse normal to the target surface is shown in Fig. 1. Maximum gain is obtained around 20° of incidence angle. And also
Simulation of Longitudinally Pumped Ni-Like Molybdenum X-Ray Laser
349
Fig. 1 shows the plasma gain widths for each incidence angle of the main pulse . Gain for 18.9 nm Gain for 18.2 nm
400
Gain width
10
350
-1
Gain (cm )
250 6 200 4
150
Gain width (µm)
8
300
100 2 50 0
0 0
10
20
30
40
50
60
70
80
Incidence Angle
Fig. 1. Variation of the gain of the 18.9 nm and 18.2 nm Ni-like Mo laser lines as a function of the incidence angle of the main heating pulse normal to the target surface. Data was obtained using a 70 mJ 200 ps duration prepulse followed by a 80 mJ 1.2 ps duration grazing incidence short pulse separated by a 300 ps.
90 -1
18.2 nm 18.9 nm
350
80
300 70 250
60
200
50 40
150
30 100 20 50
10
0
Gain of 18.9 mn Ni-like Mo line (cm )
-1
Gain of 18.2 mn Ni-like Mo line (cm )
Simulation is performed to determine optimum energy level of pumping in the range of 18.9 nm and 18.2 nm. Pre heating pulse has 70 mJ energy and 200 ps pulse duration in the simulation. Delay time between the pre-pulse and the short pulse is 300 ps and the main pulse duration is 1.2ps. Fig. 2. shows the variation of gain as a function of the main pulse energy at 20° of incidence angle.
0 0
30
60
90
120
150
180
210
240
Main pulse energy (mJ)
Fig. 2. Variation of the gain of the 18.9 nm and 18.2 nm Ni-like Mo laser beam as a function of the main heating pulse energy at 20o of incidence angle. Data was obtained using a 70 mJ 200 ps duration prepulse followed by a 1.2 ps duration grazing incidence short pulse separated by a 300 ps.
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Fig. 3. shows the simulated time-integrated Ni-like and Co-like Mo resonance line spectrum for total pulse energy 150 mJ. The Co-like resonance lines are more intense than the Ni-like resonance lines. Co-like 4f - 3d
5.0E+15
Ni-like 4p - 3d
Ni-like 4f - 3d
Ni-like 5f - 3d
1.0E+16
Co-like 4p - 3d
1.5E+16 Co-like 5f - 3d
Intensity (photons/Å)
2.0E+16
0.0E+00 26
28
30
32
34
36
38
Wavelength (Å)
Fig. 3. The time integrated Ni-like and Co-like resonance line spectrum emitted from Mo plasma.
Fig.4. shows the Ni-like plus Co-like resonance line intensity and gain coefficient of the Ni-like Mo lasing lines at 18.9 nm and 18.2 nm as a function of time from the start of the short pulse interaction time. The FWHM of the gain coefficient duration is ∼ 23 ps for 18.9 nm and for 18.2 nm. Ni-like and Co like resonance line
4.0E+19
300
18.9 nm Gain line 250
200 -1
Gain (cm )
Intensity (photons/Å)
18.2 nm Gain line 3.0E+19
150
2.0E+19
100 1.0E+19 50
0.0E+00 495
0 515
535
555
575
595
Time (ps)
Fig. 4. The time variation of the resonance lines for Ni-like plus Co-like lasing lines and gain coefficient for 18.9 nm and 18.2 nm Ni-like Mo lasing lines.
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4 Conclusion Longidutinally pumped Ni-like Mo x-ray laser medium is modelled to determine optimum grazing incidence angle of the main heating pulse normal to the target surface and optimum main heating pulse energy. Optimum grazing incidence angle of the main pulse is found around ∼ 20° under the explained simulation conditions in the text. X-ray laser output at 18.2 nm and 18.9 nm and intensity of resonance lines between 26 Å and 37 Å emitted from molibdenium plasma has been simulated using the EHYBRID. Acknowledgements
This project is supported by DPT under the contract number K120710.
References 1. 2. 3. 4. 5.
Li R. et al. Phys.Rev.A 66 047402 2002. Ozaki T. et al. Phys.Rev.A 66 047402 2002. Keenan R.et al. Phys.Rev.Lett. 94 103901 2005. Tümmler J. et al. Phys.Rev.E 72 037401 2005. Larotondo M.A. et al. IEEE J. of Selected Topics in Quant. Electronics 10 6 1363 2006. 6. Kuroda H. et al. 29th EPS Conf. On Plasma Phys. And Contr.Fusion Monterux ECA 26B D-5.005 2002. 7. Pert G.J. Fluid. Mech. 131 401 1983. 8. Cowan R.D. J.Opt.Soc.Am. 58 808 1968
X-Ray Laser at 10–15 nm in Pd-like Ions Er XXIII – Re XXX. E.P. Ivanova, A.L. Ivanov and T.E. Pakhomova Institute of Spectroscopy of Russian Academy of Sciences
Summary. The intensive output radiation at 10-15 nm is possible by the use of the Pd-like scheme of X-ray laser. We have performed the calculations of spectroscopic constants kinetics of level populations in plasmas and gains for eight Pd-like ions ErXXIII – ReXXX. The laser action proved to be efficient at the optically self-pumping transition 4d95f 1P1 – 4d95d 1D1 and at the conventional transition 4d95d 1S0 – 4d95p 3P1. The optimum plasma parameters for lasing and time evolution of gain are calculated. The experimental scheme is implied which use an ultra-short laser pulse pumping.
1 Introduction. The first observations of the Pd-like X-ray laser [1-2] have proved that it is most efficient in compare with the Ne-like either Ni-like schemes. The first reason: the ionization of the electron shells with n=6 occurs at relatively smaller electron energy; thus smaller energy of pumping source is necessary. The second: the optimal electron density (ne=neopt) for X-ray lasing is relatively smaller (ne ~3·1018 - 4·1020 cm-3 for Pd-like ions with Z=54 - 75); hence the recombination and bremstraulung radiation plasma losses are negligible. In [3] we have interpreted the results of experiments [1-2] and suggested the improvements for the pumping and target parameters in order to increase the X-ray radiation yield. During last decade the spectra of Pd-like ions with Z = 52-60 were carefully analyzed (see [4] and references herein) however the spectroscopic data for the heavy ions (Z > 65) are known from the only work [5]. Recently in several independent experiments investigating the interaction between the optical field of intense laser pulse and a xenon cluster beam an anomalously high quantum yield in the plasma radiation in the range 10-15 nm was recorded [6-7]. In our work [8] the nature of this phenomenon was interpreted high conversion efficiency is shown to be possible when producing plasma with optimum parameters for the
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amplification of spontaneous radiation on the definite transitions in Xe XXVII. At present nanowires grow by electro-deposition using nonporous template have attracted much attention due to the simplicity of this technique for preparing nano-scaled materials. For instance a standard way to fabricate lead or tin nanowires arrays is suggested in [9]. The production of nanowires arrays of other heavy elements is quite possible. In the present work we imply the experimental scheme similar to that described in [6-7] but nanowires (or dust) array of heavy element (Z = 68-75) is used instead of Xe clusters. Recently the method of relativistic perturbation theory with model potential of zero approximation (RPTMP) was used for the calculation of energy levels of Ag- Rh- and Pd- like ions with Z≤86 [10]. The results of [10] are used here for the calculation of the spectroscopic constants and gains of the Pd-like ions Er XXIII – Re XXX. Optimal plasma parameters for the X-ray lasing at 10-15 nm are determined. The method of gain calculation may be found elsewhere ([8] see the references herein).
2. X-ray laser in Pd-like ions. There are two principal X-ray laser transitions in Pd-like ions; i) 4d3/25d3/2 [J=0]–4d3/25p1/2 [J=1] (5d-5p 0-1); the amplification of this line emission was observed in [1-2]; ii) 4d3/25f5/2 [J=1] – 4d3/25d3/2 [J=0] (5f–5d 1-1). The amplification on the 5f-5d 1-1 optically self-pumping transition is weak in the light Pd-like ions and was not observed experimentally yet. However the amplification grows significantly along the sequence. The kinetics of level population is calculated here with the following assumptions: i) Plasma is produced in the shape of cylinder with diameter d = 100 μm and length L. ii) The pumping pulse parameters are such that plasma with initial temperature Te (at the moment τ = 0) in which the Pdlike ions constitute 90% of the plasma and are in the ground state is produced immediately after the interaction of the optical field laser with array of nanowires or dust). iii) Plasma parameters: electron density (ne) temperature (Te) and diameter (d) are not varying with time. iv) The electron and ion energy distribution are Maxwellian and the shape of the distribution plays no significant role in calculating the rates of the transitions induced by electron-ion collisions. v) The ion temperature Ti = Te/10. For each ion Er XXIII – Re XXX we calculate the gain g(neTed|τ) with unchanged d = 100 μm. For each transition at given Te the optimal value
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X-Ray Laser at 10–15 nm in Pd-like Ions Er XXIII – Re XXX.
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ne= neopt is determined by the condition that the time averaged ĝ = g(neoptTed|τ) is maximum value. Figure 1 shows the time dependences of the gains for the 5d-5p 0-1 (a λ = 107.8 Å) and 5f-5d 1-1 (b λ = 139.5Å) transitions in W XXIX. The decay of the gain of the 5d-5p 0-1 transition is conditioned predominantly by ionization of the W XXIX into higher stages while the decay for 5f-5d 1-1 transition is due to collisional mixing of level populations ⎯ as a result the gain disappears on a shorter time interval than it does on the 5d-5p 0-1 transition. The gain is presented for three values of Te and ne = 1020 cm-1 for the 5d-5p 0-1 transition (Fig.1a) ne = 3·1020 cm-3 for the 5f-5d 1-1 transition (Fig.1b). 120
100
a) g (cm-
80
60 40
20 0 0.01
0.1
1
τ
10
100
1
τ
10
100
300
b) g (cm250 200
150 100
50 0 0,01
0,1
Fig. 1. Time evolution of the gain (g) in W XXIX for two transitions at Te = 0.5 (open circles) 1 (black circles) 1.5 (triangles) keV; d = 100 μm; a) 5d-5p 0-1 transition (λ = 10.78 nm); ne = 1020 cm-3; b) 5f-5d 1-1 transition (λ = 13.95 nm) ne = 3·1020 cm-3.
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a)
b)
λ [Å] Fig. 2. Model W XXIX spectra calculated with accounting for theamplification at Te=1.5 keV d=100 μm λ = 100 Å - 160 Å a) ne = 1020 cm-3 L=0.4 cm b) ne = 3·1020 cm-3 L=0.15 cm.
The model spectra in the region 10 – 16 nm with accounting for the amplification are shown in Fig.2 ab. One can see also the second strong 5d-5p 0-1 laser transition at 12.08 nm and the second strong 5f-5d 1-1 transition at 14.48 nm. We used the time-averaged values of g(τ)=ĝ to compute the spectra. In Fig.2 the plasma length L corresponds to the saturation of the amplification. At relatively low Te≤ 700 eV amplification saturation is conditioned by the time duration of lasing. At high Te ≥ 1000 eV time-averaged ĝ is more than 100 cm-1 in this case the saturation is
X-Ray Laser at 10–15 nm in Pd-like Ions Er XXIII – Re XXX.
357
caused by too high inversion value. In this case Lsat determination should be based on the model that accounts for the interaction between X-ray laser field and Pd-like ions. Table 1. Characteristics of X-ray laser on the transition 5d-5p 0-1 in the Pd-like ions.
Z λ [nm] Aul· 1010 Al0· 1011 neopt 1019 R· 10-10 Δν· 1012 I0· 1029 g0 cm-1
68
69
70
71
72
73
74
75
14.61
13.84
13.15
12.49
11.88
11.32
10.78
10.29
4.70
5.52
6.44
7.45
8.57
9.80
11.2
12.7
2.69
3.30
3.94
4.65
5.44
6.31
7.26
8.29
4.0
4.0
5.0
5.0
6.0
6.0
7.0
7.0
9.18
8.75
8.00
7.09
6.56
6.06
5.65
5.02
1.4
1.4
1.4
2.2
1.7
2.0
2.1
2.3
0.8
0.9
1.0
1.2
1.7
2.0
2.6
2.1
32.0
30.4
40.1
17.4
42.9
35.9
44.4
24.6
To make an estimate of Lsat the condition ĝ·Lsat ≈ 15-16 might be used. The results of spectroscopic constants and gain calculations for Er XXIII – Re XXX are summarized in the Tables 1 and Tables 2. For all Pd-like ions the calculations have been performed with the same values Te = 1000 eV d = 100 μm. In the table 1 time-averaging for g(τ) I0(τ) is performed on the interval 0 - 21 ps in the table 2 - on the interval 0 – 5.2 ps. One can see that radiative and collisional transition probabilities as well as time averaged emissive power I0 change gradually along this piece of the sequence. However ĝ value exhibits abrupt jumps along Z what is meant by the inversion sensitivity to a mixing of level populations due to the multitude of transitions induced by electron collision.
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Table 2. Characteristics of X-ray laser on the transition with a short-lived inversion 5f-5d 1-1 in Pd-like ions.
Z λ [nm] Aul · 1010 Au0· 1012 neopt 1020 R· 10-11 Δν· 1012 I0· 1030 Ĝ cm-1
68
69
70
71
72
73
74
75
17.64
16.92
16.24
15.61
15.02
14.47
13.95
13.47
7.41
7.92
8.43
8.96
9.50
1.00
1.06
1.12
1.06
1.33
1.64
2.00
2.39
2.83
3.31
3.85
1.4
1.8
2.2
2.6
3.0
3.2
3.6
3.9
2.74
2.71
2.68
2.63
2.57
2.56
2.57
2.28
2.2
2.8
3.1
3.7
3.4
4.1
3.8
5.2
0.3
0.4
0.5
0.5
0.7
0.9
1.0
1.1
186.0
120.8
115.9
76.9
116.3
104.9
125.3
68.5
Note: Wavelengths λ (nm) radiative transition probabilities (RTP) from upper to low active level Aul(s-1). RTP from the low active level 4d3/25p1/2 [J=1] to the ground level Al0(s-1) RTP from the upper active level 4d3/25f5/2 to the ground level Au0(s-1). The rates of level excitation by electron collision from the ground state per unit volume R(cm--3s-1) the Voight line width Δν(s-1) the time-averaged transition emissive power (without accounting for an amplification) I0(eV/cm3s) and the time-averaged gain ĝ (cm--1) were calculated at ne=neopt Te=1000 eV d=100μm.
3. Conclusion This investigation allows drawing the following principal conclusions: a. In all ions ĝL ≥ 14 is possible at Te ≥ 800 eV. b. The time it takes for the gain decay (τlas) reduces at larger ne.τlas = 30 – 60 ps for the 5d-5p 0-1 transition; τlas = 6 – 10 ps for the 5f – 5d 1-1 transition. In each ion the value neopt for the transition 5d-5p 0-1 is few times smaller than for the optically self-pumping transition 5f-5d 1-1. c. Amplifications on the 5f-5d 1-1 transitions with a short-lived inversion are possible only with the use of an high intensity ultra
X-Ray Laser at 10–15 nm in Pd-like Ions Er XXIII – Re XXX.
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short laser pulse pumping. Amplifications on the 5d-5p0-1 transitions are possible with either ultra short or long lasting laser pulse pumping. This investigation confirmed beyond any reasonable doubt that the Pd-like X-ray laser scheme is promising to attain the most efficiency as compared to the Ne-like either Ni-like scheme. The other models of an X-ray laser derived from the Pd-like scheme are under development.
References 1. Lemoff B.E. Barty C.P.J. Harris S.E.: Opt. Let. 19 569-572 1994. 2. Sebban S. et.al. : Phys. Rev. Lett. 86 3004-3007 2001. 3. Ivanova E.P. Ivanov A.L.: ‘Theoretical search for optimal pump parameters for observing spontaneous radiation amplification on the λ=41.8 nm transition of Xe IX in plasma’ Quantum Electronics 34 1013-1017 2004. 4. Churilov S.S. et al: ‘Analysis of the spectra of Pd-like Praseodymium and Neodymium’ Physica Scripta 71 589-598 2005. 5. Sugar J. Kaufman V. Rowan W.: ‘Observation of Pd-like resonance lines through Pt32+ and Zn-like resonance lines of Er38+ and Hf42+’ J. Opt. Soc. Am. 10 799-801 1993. 6. Ter-Avetisyan S. Schnürer M. Stiel H. et.al. ‘Absolute extreme ultraviolet yield from femtosecond-laser excited Xe clusters’ Phys. Rev. E 64 0364041-8 2001. 7. Mori M. et. al. ‘Extreme ultraviolet emission from Xe clusters excited by high- intensity lasers’ J. Applied Physics 60 3595-3601 2001. 8. Ivanova E.P. Ivanov A.L. ‘A Superpower Source of Far-Ultraviolet Monochromatic Radiation’ J. Exp. Theor. Phys. 100 844-856 2005. 9. Michotte S. ‘Standard manufacture and properties of arrays of Pb and Sn nanowires’ Int. J. of Modern Physics B 17 4601-4618 2003. 10. Ivanova E.P. ‘Energy levels of the ions of the isoelectronic sequences Silver and Rhodium’ Optics and Spectroscopy (Russian)
Temporal Characterization of Attosecond Harmonic Pulses C. H. Nam and K. T. Kim Department of Physics and Coherent X-ray Research Center, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, Korea
Summary. Techniques to characterize attosecond harmonic pulses based on the cross-correlation between harmonic and IR laser pulses are presented. The selfcompression of an attosecond harmonic pulse in the harmonic generation itself has been demonstrated, obtaining near transform-limited attosecond harmonic pulses.
1. Introduction High harmonic x-ray sources possess unique features suitable for attosecond physics and science [1,2]. High harmonics from atoms driven by intense femtosecond laser pulse can form an attosecond pulse train or a single attosecond pulse when properly controlled and selected. For proper understanding of the interactions between attosecond pulses with matter, the temporal structure of attosecond pulses should first be well characterized. Since efficient nonlinear material for two photon processes is difficult to realize in the xuv wavelength region, autocorrelation techniques, normally used for the characterization of femtosecond pulses, can be applied only to limited cases of low-order harmonic pulses. Cross correlation techniques based on the photoionization of atoms by high harmonic and femtosecond laser pulses, acting simultaneously, are thus useful for the characterization of attosecond pulses. As a realization of the cross correlation technique, the reconstruction of attosecond beating by interference of two-photon transition (RABITT) method was demonstrated by Paul et al. [3]. An attosecond pulse train with 250-as duration was measured, and attosecond intrinsic chirp structure was revealed as theoretically predicted [4,5]. For complete characterization of attosecond pulses, the frequency resolved optical gating method for the complete reconstruction of attosecond bursts (FROG CRAB) was proposed by Mairesse et al. [6]. The demon-
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stration of FROG-CRAB would provide the detailed temporal structure of attosecond harmonic pulses. Here we present techniques to characterize attosecond harmonic pulses, especially the FROG-CRAB method, and the self-compression of an attosecond harmonic pulse to generate near transform-limited attosecond harmonic pulses.
2. Temporal characterization of attosecond harmonic pulses Attosecond pulses obtained from high harmonic generation contain a complex chirp structure. In single atom calculations, each single pulse in an attosecond pulse train is positively chirped [5], while each harmonic is negatively chirped [7]. For rigorous temporal characterization of such complex attosecond harmonic pulses, one needs to precisely determine the spectral phase and amplitude of the attosecond pulses. In the RABITT method, photoionization of atoms by attosecond harmonic pulse and IR laser pulse is used for the temporal reconstruction of the attosecond pulse. The photoelectron spectrum shows sidebands due to the interference between photoelectrons with same energy but generated through different two-photon transitions. The sideband is modulated as the time delay between the harmonic and IR probe pulses changes. The phase information of the attosecond pulses can then be found in the side band modulation as A cos ( 2ω0τ + Δϕq ) .
Here, A is the amplitude of the modulation, ω0 is the laser frequency, τ is the time delay between harmonic and laser pulses, and Δϕ0 is the phase difference between (q+1)th and (q-1)th harmonics. The spectral amplitude can be obtained from the photoelectron spectrum obtained only with the harmonic pulse. The reconstruction of the attosecond harmonic pulse is possible from those phase and amplitude information. However, this technique has some drawbacks because the attosecond harmonic pulses are assumed to be the sum of the discrete harmonics, separated by 2ω0. It cannot be used for the reconstruction of a single attosecond pulse having continuum spectrum. Furthermore, the reconstruction result is always an attosecond train with identical individual pulses which is the average of the real pulse train. The chirp information on individual pulses is not available. The FROG CRAB method can provide the complete information on attosecond pulses. In this technique, the photoelectron spectra obtained with harmonic and laser pulses with time delay τ can be represented by
Temporal Characterization of Attosecond Harmonic Pulses S ( ω ,τ ) =
∫
+∞
−∞
2
dt G ( t ) E X ( t − τ ) eiωt .
363
(1)
Here E X ( t ) is the harmonic electric field to be measured and G(t) is the phase gate function defined by +∞ G ( t ) = exp ⎡i ∫ dt ′ { v ⋅ A ( t ′ ) + A 2 ( t ′ ) / 2}⎤ , ⎣⎢ t ⎦⎥
(2)
where v is electron velocity and A(t) is the vector potential of IR laser pulse. Since Eq. (1) is the spectrogram expressed in frequency and time delay, a conventional FROG inversion algorithm, such as the principal component generalized projection algorithm (PCGPA), may be used to reconstruct the attosecond harmonic pulse [6]. However, slight modification is necessary to overcome the problem that the gate function does not have same values at both ends. Consequently, one can retrieve the harmonic electric field containing the detailed information of the attosecond harmonic pulse.
3. Experiment setup The schematic of the experimental setup is shown in Fig. 1. A 1-kHz Ti:sapphire laser, generating pulses of 30-fs duration, was used to obtain high harmonics. The laser beam was split into two parts by a beam splitter; the first beam was focused into a gas cell for high harmonic generation. The second beam was used as a probe laser beam. After harmonic generation, the transmitted laser beam was blocked by a 200-nm aluminum filter
Fig. 1. Schematics of the experiment setup.
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to completely eliminate the laser light. The harmonic and the probe beams were combined using a mirror having a hole in the center, and both beams were then focused together, using a gold-coated toroidal mirror, into an effusive atomic beam and generated photoelectrons were measured with a time-of-flight photoelectron spectrometer.
4. Results
Intensity (arb. units)
First, applying the RABITT technique, we achieved the generation of selfcompressed attosecond harmonic pulses. A 30-fs laser pulse with intensity of 2.5×1014 W/cm2 was applied to an argon gas cell with length of 12 mm. Photoelectron spectra were obtained for harmonics from 17th to 41st orders. As the argon pressure was increased from 15 torr to 40 torr, the harmonics below 25th order were severely absorbed, and the intrinsic positive chirp was compensated by the negative group delay dispersion of argon itself. The reconstructed temporal profile of the attosecond harmonic pulse is shown in Fig. 2. The measured pulse width of 206 as is slightly longer than the transform-limited width of 200 as. 1.0 0.8 0.6 0.4 0.2 0.0 -600
-400
-200
0
200
Time (as)
400
600
Fig. 2. Self-compressed attosecond harmonic pulse measured using RABITT.
Second, FROG CRAB measurements were carried out using the same experiment setup, but with different harmonic conditions due to the poor energy resolution of the spectrometer at high photoelectron energy. Attosecond harmonic pulses, consisting of harmonics up to 31st order, were generated with a 6-mm-long 25-torr argon gas cell. Photoelectron spectra obtained by changing the time delay between the harmonic and IR laser pulses is shown in Fig. 3 (a). The temporal reconstruction of the harmonic pulses was carried out using a modified principal component generalized
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a)
b) Fig. 3. (a) Photoelectron spectra obtained by applying harmonic pulse with IR laser pulse with time delay. (b) Temporal profile of an attosecond harmonic pulse reconstructed using the FROG CRAB technique.
projections algorithm (PCGPA). Figure 3(b) shows the temporal reconstruction of the attosecond harmonic pulse. The envelope width of the pulse train is 11 fs and the width of the single attosecond pulse at the center of the train is 230 as. In this case, the intrinsic attosecond chirp at the center of the train and the harmonic chirp of the 17th order are estimated to be 1.4×10-32 s2 and -2.3×10-28 s2, respectively. Since the modified PCGPA
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is a blind FROG technique, the FROG CRAB measurement provides the information on both harmonic pulse and laser pulse.
5. Conclusion We have demonstrated the temporal characterization of attosecond harmonic pulses using both RABITT and FROG CRAB techniques. The 206as self-compressed attosecond pulses was reconstructed using RABITT. And the FROG CRAB technique has been applied for the complete reconstruction of attosecond harmonic pulses, obtaining an attosecond pulse train of 11-fs envelope width and 230-as width at the pulse peak.
References [1] M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, Nature 414, 509 (2001). [2] M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, F. Krausz, Nature 419, 803 (2002). [3] P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001). [4] Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovacev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, Science 302, 1540 (2003). [5] K. T. Kim, C. M. Kim, M.–G. Baik, G. Umesh, and C. H. Nam, Phys. Rev. A 69, 051805(R) (2004). [6] Y. Mairesse and F. Quéré, Phys. Rev. A 71, 011401(R) (2005) [7] J.-H. Kim and C. H. Nam, Phys. Rev. A 65, 033801 (2002).
Nonlinear Interaction of Intense Attosecond XUV Pulses with Atoms and Molecules K. Midorikawa, T. Shimizu and Y. Nabekawa Laser Technology Laboratory, RIKEN
Summary. We have observed nonlinear optical processes such as two-photon double ionization and above threshold ionization of rare gases in the xuv region with intense high-order harmonics. Using two-photon double ionization in He, the pulse width of the 27th (42 eV) harmonic was measured by an autocorrelation technique, and found it to be 8 ns. A train of attosecond pulses was also characterized directly by the energy-resolved autocorrelation of the above threshold ionized electrons.
1 Introduction The progress of chirped pulse amplification and femtosecond Ti:sapphire laser enables the study of the interaction of strong optical fields with atoms and molecules. A variety of interesting phenomena, including highharmonic generation, high energy radiation/particles emission, and Coulomb explosion of molecules, have been investigated intensively. The underlying physics of these extremely nonlinear optical phenomena have been explored through the interaction with low-frequency radiations such as infrared or visible light; however, little has been understood concerning the interaction of intense high-frequency radiation. Great interest has been aroused recently in the interaction of intense high-frequency radiation with matters. Yet no one could observe it because of the lack of an intense coherent light source in this spectral region. The induced phenomena are expected to be much different from those caused by low frequency radiation because the electron quiver energy—the cycle averaged electron energy in the optical field—is proportional to a square of the wavelength. In this paper, we report on the generation of intense soft X-ray pulses and its application to nonlinear multiphoton processes. Using such nonlinear processes, the temporal width of the 42-eV soft x-ray pulse was meas-
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ured directly by an autocorrelation technique. A train of attosecond pulses was also characterized by frequency-resolved autocorrelation. Intense high harmonics produced by the phase-matching technique enable the observation of these nonlinear optical processes.
2 High-Power High Harmonic Generation For application of high harmonics to nonlinear optics in the XUV region, high focused intensity is crucial because the cross section of nonlinear processes in atoms or molecules tends to decrease rapidly with decrease of the pump wavelength. To increase high harmonic energy by improving conversion efficiency from the pump energy, phase matching is essential. It is, however, not easy to satisfy the phase matching condition along the interaction length, because in contrast to low-order harmonic generation in the perturbative regime, the atomic dipole phase is dependent on the driving laser intensity [1]. This means that the atomic phase varies rapidly around the focus when the pump pulse is tightly focused in the nonlinear medium. Furthermore, in addition to the medium’s dispersion, nonlinear phenomena such as self-focusing and plasma defocusing accompanied by a high-intensity pump pulse also make the experimental achievement of the phase matching quite difficult. Overcoming such difficulties, the energy scaling of high-order harmonics under the phase-matched condition has been achieved using a long interaction length and a loosely focused pumping geometry [2]. This method shows a linear increase in harmonic energy with respect to the geometrical focusing area of the pump pulse, while keeping an almost perfect spatial profile of the harmonic output. Peak powers of 130 MW at 62.3 nm in Xe [3], 10 MW at 29.6 nm in Ar [2], and 1 MW at 13.5 nm in Ne [4] are obtained with femtosecond, high-power Ti:sapphire laser pulses.
3 Focusing Property of High Harmonics Although the advent of high harmonics having excellent beam quality and spatial coherence, together with high output energy, opens up the possibility of focusing XUV beams as intensity sufficient for inducing nonlinear optical processes, a technique for focusing an intense, coherent soft x-ray beam and its characterization should be established before the observation of nonlinear phenomena. Figure 1(a) shows the 1/e2 beam spot size of the 27th harmonic beam as a function of distance from the off-axis parabolic
Nonlinear Interaction of Intense Attosecond XUV Pulses with Atoms
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mirror. In this measurement, the 27th harmonic wave was selected and focused to a Ce:YAG scintillator by an off-axis parabolic mirror with a SiC/Mg multilayer coating having 40% reflectivity. A set of image relay optics transferred the visible light image onto an image-intensified chargecoupled device (CCD) camera. The red circles and blue squares correspond to the horizontal and vertical spot sizes, respectively. There is little difference between the horizontal and vertical diameters, showing that circularity is maintained during focusing. The best-fit curve provided a figure of M2 = 1.4, indicating nearly perfect spatial beam quality [5]. The focusing property was also investigated by an ablation pattern produced on a gold-coated mirror placed at the focal position. Figure 1(b) shows the atomic force microscope image of the ablation pattern. Note that the pattern was produced by a single shot irradiation of the focused 27th harmonic pulse. The diameter of the circular hole is approximately 2 μm, which agrees well with the scintillator experiment. Because the high-order harmonics have excellent spatial coherence and beam quality, the focusability might be dominated by the performance of the mirror. The focused intensity of the 27th harmonic wave was estimated from those experimental results of the energy, spot size, and pulse width. Assuming that the pulse width of the 27th harmonic wave was the same as the fundamental pulse, the maximum focused intensities of 1.0 x 1014 W/cm2 were obtained. 20 Horiz. Vert. 15 μm
p o
0 .5
10
0 - 0 .5 - 10
5
-5
0
5 μm 60
60.5
0
61
61.5
62
5 1 0 μm
Distance from focusing mirror [mm]
(a)
(b)
Fig. 1. Focusing property of the 27th harmonic pulse: (a) spot size as a function of middor distance and (b) ablation pattern produced on a gold coated mirror surface by a single-shot irradiation.
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4 Two-Photon Double Ionization in He at 42 eV As the first step in investigating the interaction of intense high-frequency radiation with matter, the He atom has been selected as a target. At the very high frequency and low intensity limit, double ionization by single photon absorption has been investigated in detail using synchrotron radiation; this process has been understood as “shake off.” On the other hand, in the low-frequency and high-intensity regime realized by femtosecond high intensity Ti:sapphire lasers, the occurrence of double ionization has also been reported and the process was explained by a rescattering model. Between these two extreme experimental conditions, the occurrence of twophoton double ionization by intense XUV lights was theoretically predicted about 20 years ago. Particularly, two-photon double ionization in He has attracted much interest and has been studied theoretically in a number of papers because it provides insight into the electron-electron interaction (that is, electron correlation) and paves the way for unexplored aspects of the three-body problem [6, 7]. Figure 2(a) shows the ion spectrum produced by the interaction between the focused 27th harmonic pulses and 3 He. The production of 3He2+ results dominantly from the one-photon absorption of 3He. The strongest peak of 1.8 μs can be assigned to 3He2+. The signal of 3He2+ clearly appears between the H+ signal and H2+ signal. The generation of doubly charged He2+ confirms the observation of a nonlinear optical process (two-photon absorption) in the soft x-ray region. To further confirm that the He2+ ions are produced via the two-photon process, the 27th harmonic intensity dependence of the He2+ yield was investigated. As shown in Fig. 2(b), the result clearly showed the slope of two, giving more evidence of the occurrence of the two-photon double ionization. This is the first observation of a nonlinear optical process in the soft x-ray region [8, 9]. The XUV nonlinear optical process is not only interesting in the field of atomic or molecular physics, it is also of importance for the direct measurement of the pulse width by autocorrelation method in the ultrafast optics field. With the two-photon double ionization in He, the pulse duration of the 42-eV soft x-ray pulse was measured by means of autocorrelation. For the autocorrelation measurement, an autocorrelator splits a measured pulse equally into two pulses and spatially overlaps the separated delayed pulses at the focus point. The construction of the autocorrelator for the XUV light is, however, not straightforward because no beam splitter or high reflectance-/transmittance optics are available. Therefore, a novel autocorrelator using a split beam separator was designed [10]. The delayed pair of harmonic pulses is produced by spatially dividing the harmonic
Nonlinear Interaction of Intense Attosecond XUV Pulses with Atoms
371
8 6
3
He2+
(a)
3
H2
H+
He+
+
He2+ yield
4
(b)
2
0.01
8 6
Slope = 2
4 2
0.001 1.0
1.2
1.4
1.6
1.8
2.0
Time of flight ( μs)
2.2
2.4
2
3
4
5 6 7 8 9
1
2
+ He yield Harmonic Intensity
Fig. 2. (a) The time of flight ion spectrum and (b) doubly charged helium ion yield as a function of the 27th harmonic intensity.
beam with two beam separators of SiC substrates. One of the divided pulses is delayed or advanced to another pulse by moving one of the separators placed on a translation stage with a piezo-actuator. The measurement principle using this split beam separator is the same as an allreflective interferometric autocorrelator. With this autocorrelator and twophoton double ionization in He, a pulse width of the 42-eV soft X-ray radiation was measured for the first time and it was determined to be 8 fs [8].
5 Temporal Characterization of XUV Attosecond Pulse Train by Autocorrelation Although the temporal width of the soft X-ray pulse was measured directly by an intensity autocorrelation technique, the pulse width is limited by the bandwidth of the 27th harmonic wave. The narrow bandwidth of a SiC/Mg multilayer mirror has high reflectivity only for the 27th harmonic wavelength. If several harmonics are simultaneously focused with a broadband mirror, a train of extremely short pulses would be observed. As is well known, Fourier synthesis of harmonic wave fields exhibits a train of ultrashort pulses. The pulse width decreases in inverse proportion to the number of harmonics. The optical field in the XUV region generated as high order harmonics of a femtosecond laser pulse is one of the most significant examples of the Fourier synthesis because it can serve an attosecond pulse train. For characterization of an attosecond pulse train, several harmonics should be simultaneously measured and the information of individual harmonic phase should be determined. But the phase information can hardly
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be obtained from ion signals. Therefore, a new method to reconstruct an attosecond pulse train was proposed [11]. This method uses electrons produced by the above threshold ionization (ATI) process, another type of nonlinear mutlitphoton process. In the ATI process, an ejected electron absorbs the photons in excess of the minimum required for ionization. The ejected electrons carry the information of the phase of the XUV pulse used for ionization.
Fig. 3. Mode-resolved autocorrelation trace of two-photon above threshold ionization in Ar and the reconstrcuted train of attosecond pulses.
In the experiment, the electron energy spectra produced by the two-photon ATI process in Ar are utilized as mode-resolved signals of the autocorrelation measurement for the pulse train and its envelope [11, 12]. To simplify the analysis of the ATI electron spectra, only three harmonics from 11th to 15th were selected by passing through a Sn thin-foil filter.
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When these three harmonics are simultaneously focused to Ar gas, five peaks form the lowest-order mode at 22nd (11th + 11th) to the highest order mode at 30th (15th + 15th) are expected to appear in the photo-electron spectrum. Among these five processes, the 24th (11th + 13th) and the 28th (13th + 15th) processes show beating due to interference of two harmonics, while only the 26th (13th + 13th, 11th + 15th) process contains the phase information between the three harmonics. The three-dimensional image of the mode-resolved autocorrelation with two-photon ionization electrons is shown in Fig. 3. From the spectral analysis, the chirp among the three harmonic fields was specified and it was found that a pulse duration should be shorter than 450 as, which is the first determination of the chirp in the attosecond pulse train with an autocorrelation technique [11]. Conforming to the custom that a method characterizing ultrashort pulses is named after creatures like FROG (frequency resolved optical gating) or RABITT (resolution of attosecond beating by interference of two-photon transitions) in the ultrafast optics field, this method is called PANTHER (photoelectron analysis of nonresonant two-photon ionization for harmonic electric-field reconstruction). PANTHER will open the way to full characterization of an attosecond pulse train.
Acknowledgment The authors wish to thank Drs. K. Yamanouchi, H. Hasegawa, K. Furusawa, K. Ishikawa, E. Takahashi, T. Okino, A. Suda, and H. Mashiko for their experimental contribution and helpful discussions.
References 1. P. Saliéres, A. L'Huillier, M. Lewenstein: Phys. Rev. Lett. 74, 3776–3779, 1995. 2. E. Takahashi, Y. Nabekawa, T. Otsuka, M. Obara, K. Midorikawa: Phys. Rev. A 66, 021802(R), 2002. 3. E. Takahashi, Y. Nabekawa, K. Midorikawa: Opt. Lett. 27, 1920 –1922, 2002. 4. E. J. Takahashi, Y.NabekawA, K. Midorikawa: Appl. Phys. Lett. 84, 4-6, 2002. 5. H. Mashiko, A. Suda. K. Midorikawa: Opt. Lett. 29, 1927-1929, 2004. 6. H. Bachau, P. Lambropoulus: Phys. Rev. A 44, R9-R12, 1991. 7. P. Lambropoulos, L. A. A. Nikolopoulos, M. G. Makris: Phys. Rev. A 72, 013410, 2005.
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8. Y. Nabekawa, H. Hasegawa, E. J. Takahashi, K. Midorikawa: Phys. Rev. Lett. 94, 043001, 2005. 9. H. Hasegawa, E. J. Takahashi, Y. Nabekawa, K. L. Ishikawa, K. Midorikawa: Phys. Rev. A 71, 023407, 2005. 10. H. Hasegawa, E. J. Takahashi, Y. Nabekawa, K. Midorikawa: Laser Phys. 15, 812-820, 2005. 11. Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamnouchi, K. Midorikawa: Phys. Rev. Lett. 96, 083901, 2006. 12. K. Furusawa, T. Okino, T. Shimizu, H. Hasegawa, Y. Nabekawa, K. Yamanouchi, and K. Midorikawa: Appl. Phys. B 83, 203-211, 2006.
Anomalous Enhancement of Single High-Order Harmonic Generation at 61 nm and 47 nm by Indium and Tin Due to Strong Resonance M. Suzuki, M. Baba, R. A. Ganeev and H. Kuroda Institute for Solid State Physics, University of Tokyo T. Ozaki Institut national de la recherché, Universite du Quebec
Summary. We have successfully demonstrated the intensity enhancement of single high-order harmonic at a wavelength of 61.26 and 46.76 nm using low ionized indium and tin ions in laser ablation plume as the nonlinear medium. The ablation plume was produced by irradiating of solid tin target with 10 mJ energy picosecond laser pulse. Using the indium target, the 13th harmonic at the wavelength of 61.26 nm was obtained with conversion efficiency of 8x10-5. Using the tin target, the 17th harmonic at a wavelength of 46.76 nm was observed with conversion efficiency of about 10-4. We attribute the strong enhancement of single high-order harmonic to multiphoton resonance with a strong radiative transition of the In and Sn II ions.
1 Introduction High-order harmonic generation (HHG) is a very attractive radiation source in the extreme ultraviolet (XUV) and soft x-ray region, with good spatial quality and femtosecond resolution. One of the most important subjects of HHG research is the enhancement of conversion efficiency. In the past, such conversion efficiency enhancement has been pursued by controlling the phase matching condition in the gas filled capillary or gas cell. The strongest output energy of harmonics were 7 μJ for the 11th harmonic at a wavelength of 72.7 nm, 4.7μJ for 13th harmonic at a wavelength of 62.3 nm, and 1μJ for 15th harmonic at a wavelength of 54 nm using xenon gas-cell.1 Very recent results have reported an enhancement of high-order harmonic conversion efficiency when a two-color (fundamental and sec-
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ond harmonic field) orthogonally polarized driving field is used.2 Using the helium from the gas-jet, the conversion efficiency of the 38th harmonic at a wavelength of 21.6 nm was 5x10-5. An alternative approach is the resonance enhancement of HHG, which has been proposed by theoretical calculations.3 Experimentally, the resonance enhancement of the 13th and the 15th order harmonics generation using the argon gas medium has been observed.4 However the enhancement in these works were a factor of two to three, and the harmonic spectrum consisted of multiple harmonics. In this proceeding, we report the first observation of the single highorder harmonic enhancement in the XUV region. In this experiments, the nonlinear medium was indium and tin ablation plumes, produced by a lowenergy laser pulse, instead of the conventional gas medium. Using the tin target, the intensity of the 17th order harmonic at the wavelength of 46.76 nm was 20 times higher than its neighbor harmonics. The output energy of only this harmonic is measured to be about 1.1 μJ. Such output energy that was obtained the maximum output energy in the XUV region. Using the indium target, the conversion efficiency of the 13th harmonic at a wavelength of 61 nm was about 10-4, which was two orders of magnitude higher than its neighboring harmonics. The output energy of the 13th harmonic was measured to be 0.8 μJ.5 The origin of these enhancements is attributed to resonance with strong radiative transitions, produced within the laserablated plume.
2 Experiments The schematic of experimental setup was described in another proceeding.6 The pump laser was a commercial, chirped pulse amplification laser system (Spectra Physics: TAS-10F), whose output was further amplified using a homemade three-pass amplifier operating at a 10 Hz repetition rate. A pre-pulse was split from the amplified laser beam by a beam splitter before a pulse compressor. The pre-pulse energy is 10 mJ with pulse duration of 210 ps. A main pump pulse output at a center wavelength of 795 nm has energy of 10 mJ with pulse duration of 150 fs. A cylindrical lens focuses the pre-pulse onto a solid tin target placed within a vacuum chamber, which generates a laser ablation plume that contains low-charged ions. The size of the line focus on the target surface was 600 μm width and 1mm long, and the intensity of the pre-pulse was varied between 1010-1011Wcm2. The main pulse is focused onto the ablation plume by a spherical lens (focus length of 200 mm), 100 ns after pre-pulse irradiation. The intensity of the main pulse at the plasma plume is 1014Wcm-2. The spectrum of the
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generated high-order harmonics was measured by grazing incidence spectrometer with a gold-coated Hitachi 1200 grooves/mm flat-field grating. A gold-coated grazing incidence cylindrical mirror was used to image the target harmonics at the ablation plume onto detector plane. The XUV spectrum was detected using a micro-channel plate (MCP) with a phosphor screen read-out (Hamamatsu, model F2813-22P), and the optical output from the phosphor screen was recorded using a CCD camera (Hamamatsu model C4880). The detail of an absolute calibration of the spectrometer was described in elsewhere6.
3 Results and discussions Figure 1 shows the spectra of HHG from tin and vanadium laser-ablated plume pumped by femtosecond laser pulse. The plateau and cut-off of the harmonics have observed in these experiments. The second ionization potential of tin and vanadium are 14.63 eV and 14.65 eV, respectively. Therefore, the cut-off order for both targets should be the same, since the cut-off order has been shown to depend on the ionization potential. Though the signal is weak, high-order harmonics up to the 23rd (wavelength: 34.56 nm) order was observed in these experiments with both tin and vanadium. However, a strong 17th order harmonic at a wavelength of 46.76 nm was observed using tin laser ablation plume, as shown in Fig. 1(a). The intensity of the 17th harmonics was 20 times higher than those of its neighbors. The conversion efficiency of the 17th harmonic was measured to be about 1.1x10-4, and this output energy of 1.1 μJ was obtained from the pump laser energy of 10 mJ. For vanadium ablation plume, the strong single HHG was not observed, as can be seen in Fig. 1(b). To confirm the nature of this strong emission at the wavelength of 46.76 nm, we investigated the effect of pump laser polarization on HHG. Figure 2 shows the intensity of the 46.76 nm line as a function of the laser polarization ellipticity. A quarter-wave plate was installed after the focusing lens to change the pump laser polarization from the linear to circular. The line intensities shown in Fig. 2 are normalized to that generated using linearly polarized pump laser, corresponding to the zero position. The intensity of emission at the wavelength of 46.76 nm decreased after 10-degree rotation of the quarter-wave plate, which completely disappeared after 50-degree rotation of the quarter-wave plate. This tendency is consistent with that of HHG, which leads us to conclude that the strong emission at 46.76 nm should be generated by HHG.
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Fig. 2.. The 17th order harmonic at the wavelength of 46.76 nm as a function of the quarter wave-plate rotation. The position of linear polarization is zero. By changing the rotation, the laser polarization changes the linear to circular.
To investigate the mechanism of enhancement for the 17th harmonic, the central wavelength of the pump laser pulse was changed from 795 nm to 778 nm. Figure 3 shows the HHG spectra from the laser-ablated tin laser with three different laser wavelengths of 795 nm, 782nm, and 775 nm. In Fig. 3(a), one sees that the intensity of the 17th harmonic using 795 nm wavelength pump dominates the harmonic spectrum. The intensity of the 17th harmonic is 20 times higher than that of other harmonics. However, in Fig 3(b), the intensity of the 17th harmonic using 782 nm wavelength pump is decreased, and is almost same as that of other harmonics. In Fig. 3(c),
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the intensity of the 17th harmonic with 775 nm wavelength pump is further decreased. In the case, the 17th harmonic intensity is weaker than that of the 13th and 11th harmonics. The above results show that the intensity of the 17th harmonic gradually decreased as the wavelength of the pump laser become shorter. In the past work, the strong Sn II ion has been shown to posses a strong transition of the 4d105s 25p2P3/2-4d95s25p2 (1D) 2D5/2 at the wavelength of 47.256 nm.7 The gf-value of this transition has been calculated to be 1.52 and this value is 5 times larger than other transition from ground state of Sn II. Therefore, the enhancement of the 17th harmonic with 795 nm wavelength laser pulse can be explained be due to resonance with this transition driven by AC-Stark shift. By changing the pumping laser wavelength from 795 nm to 778 nm, the wavelength of the 17th harmonic is changed from 46.76 nm to 45.76 nm. Therefore, the wavelength of 17th harmonic pumped by laser wavelength of 775 nm is farther away from the 4d105s 25p2P3/2-4d95s25p2 (1D) 2D5/2 transition, at the wavelength of 47.256 nm. As a result, the resonance condition of the 17th order harmonic is weaker when pumped by a 778 nm, compared with the case for 795 nm pump.
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Fig. 4. HHG spectra from indium laser ablation for pump laser with central wavelength of (a) 795 nm, (b) 782 nm. The intensity of the 13th harmonic is two orders of magnitude higher than its neighboring harmonics.
Figure 4 shows the typical spectra of HHG from the laser ablation indium plume. For indium, the 4d105s2 1S0-4d95s25p (2D) 1P1 transition of In II, which have an absorption oscillator strength (gf–value) of 1.11,8 can be driven into resonance with the 13th order harmonic by AC-Shark shift. The intensity of 13th harmonic for indium is attributed to such resonance of the harmonic wavelength with that of a strong radiative transition. By changing the laser wavelength from 796 nm to 782 nm, the 15th harmonic at the wavelength of 52.13 nm increased, and the intensity of 13th harmonic decreased at the same time. The reason of 15th harmonic enhancement is due to resonance with the 4d105s5p 3P2-4d95s5p2 (2P) 3F3 transition of In II, which has a gf-value of 0.30. The enhancement of 15th order harmonic intensity is lower than that of 13th harmonic because the gf-value of 4d105s5p 3 P2-4d95s5p2 (2P) 3F3 transition is lower than that of the 4d105s2 1S04d95s25p (2D) 1P1 transition. Furthermore the central wavelength of the 13th harmonic was driven away from resonance with the 4d105s2 1S0-4d95s25p (2D) 1P1 transition when using 782 nm wavelength laser, thereby decreasing the 13th order harmonics.
4 Conclusions We have observed the strong resonance enhancement of the single highorder harmonic generation at the wavelengths of 46.76 nm and 61.26 nm using tin and indium laser ablation plumes irradiated by femtosecond laser pulse. Conversion efficiencies of these harmonics were about 10-4 in the
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XUV region. We attribute the strong harmonic intensity to resonance with a strong oscillator strength transitions of Sn and In.
References 1. 2.
3. 4. 5. 6. 7. 8.
Takahashi, E., Nabekawa, Y., Midorikawa, K.: 'Generation of 10-μJ coherent extreme-ultraviolet light by use of high-order harmonics', Opt. Lett., 27, 1920-1922, 2002. Kim, I.J., Kim, C. M., Kim. H. T., Lee, G. H., Lee, Y. S., Park, J. Y., Cho, D. J.,Nam, C. H.:'Highly Efficient High-Harmonic Generation in an Orthogonally Polarized Two-Color Laser Field ' Phys. Rev. Lett. 94, 243901 2005. Gaarde, M B., Schafer. K. J.: 'Enhancement of many harmonics via a single multiphoton resonance ' Phys.Rev. A 64, 013820 2003. Toma, E. S., Antoine, Ph., Bohan, A. de., Huller, H. G.: 'Resonanceenhancement high-harmonic generation ' J. Phys. B 32, 5843-5852 1999. Ganeev. R. A., Suzuki. M., Baba, M., Kuroda, H., Ozaki, T.: 'Strong resonance enhancement of a single harmonic generated in the extreme ultraviolet range' Opt. Lett. 31, 1699-1701 2006. Ganeev, R. A., Baba, M., Suzuki, M., Kuroda: 'High-order harmonic generation from silver plasma', Phys. Lett. A, 339, 103-109, 2005. Duffy, G., Kampen, P. van.,Dunne, P: ' 4d-5p transitions in the extreme ultraviolet photoabsorption spectra of Sn II and Sn II' J. Phys. B 34, 3171-3178 2001. Duffy,G.,Dunne, P.: ' The photoabsorption spectrum of an indium laser produced plasma ' J. Phys. B34, L173-L178 2001.
Enhanced High Harmonic Generation from Ions Using a Capillary Discharge Plasma
M. Grishama, D. M. Gaudiosib, B. Reagana, T. Popmintchevb, M. Berrilla, O. Cohenb, B. C. Walkerc, M. M. Murnaneb, H. C. Kapteynb and J. J. Roccaa
NSF ERC for Extreme Ultraviolet Science and Technology a Electrical and Computer Engineering Department, Colorado State University, Fort Collins, CO b JILA and Physics Department, University of Colorado at Boulder c Department Physics and Astronomy, University of Delaware.
Summary. We demonstrate a significant extension of the high harmonic cutoff observed in xenon, up to 150 eV, by generating harmonics from ions in a capillary discharge plasma. The pre-ionized plasma generated by the capillary discharge dramatically reduces ionization-induced defocusing and energy loss of the driving laser due to ionization, allowing higher photon energies to be generated from xenon ions. We also demonstrate enhancement of the harmonic flux of nearly two orders of magnitude at photon energies around 90 eV when the capillary discharge is used to ionize xenon, compared with harmonic generation in a hollow waveguide. The use of a capillary discharge plasma as a medium for high harmonic generation shows great promise for extending efficient harmonic generation to much shorter wavelengths.
The extension of high harmonic generation (HHG) to higher photon energies from neutral atoms is not limited by the laser intensity, but is rather limited by the intensity at which all the neutral atoms are ionized. Ionization of the gas by the driving laser pulse leads to ionization-induced defocusing and beam attenuation, therefore limiting the peak intensity and cutoff photon energy. Generation from ions removes this limitation by reducing ionization-induced defocusing and beam attenuation and allows for extension of the cutoff harmonic [1]. A preformed plasma waveguide has been suggested as an advantageous media in which to generate efficient high harmonics [2,3]. Capillary discharges can conveniently produced elongated plasma waveguides suitable for guiding high intensity
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light pulses [3,4]. In this work, we demonstrate a significant extension of the high harmonic cutoff observed in xenon using a capillary discharge plasma waveguide. We have extended the cutoff by 60 eV, and have enhanced the harmonic flux at 90 eV photon energy by an order of magnitude.
Fig. 1. Schematic of the experimental setup for generating high-order harmonics from a capillary discharge created plasma
The experiment (fig. 1) made use of a 10-Hz, two stage Ti:sapphire laser system capable of generating 12 mJ pulses with a 28 fs duration. The laser pulses were focused into the entrance of a 175 um diameter, 5 cm long capillary discharge plasma. The capillary was filled with 2-4 Torr of xenon and simmered with a small DC current of ~10 mA. A main current pulse with a peak amplitude of ~5A and duration of ~5 µs generates a plasma with a density profile that is minimum on-axis, constituting in an index waveguide. The discharge was operated at 10 Hz matching the repetition rate of the laser used in this experiment. The high harmonic spectrum was measured using a flat field EUV spectrometer with an X-ray CCD camera.
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Fig. 2. Harmonic spectrum observed through thin Al-coated Zr filters. The solid line shows harmonics when the discharge is on, while the dotted line corresponds to generation in a hollow core fiber with the discharge on.
A comparison of typical spectra obtained in the capillary dicharge and in a hollow-core fiber is shown in figure 2. In both situations 5 mJ, 28 fs laser pulses were focused into the waveguides filled with 2.8 Torr of xenon. The laser pulses were injected into the discharge 2 μs after the intiation of the current pulse. The use of the discharge clearly extends the highest observable harmonic from 90 eV to ~ 150 eV. Above photon energies of 75 eV the discharge enhances the HHG signal. Harmonics around 85 eV are enhanced by an order of magnitude. Both the flux enhancement and cutoff extension are due to a reduction in the losses in the waveguide by the discharge plasma. The reduction of laser induced-ionization by the discharge also results in spectra with more distinct harmonic peaks as shown in Fig. 3. This is due to a reduction of the severe SPM broadening of the driving laser resulting from the rapid ionization of neutral Xenon. Time-resolved visible spectroscopy of the discharge plasma shows that the plasma is completely ionized at the time delay that corresponds to the observation of the highest harmonics. At this time, the spectrum is dominated by Xe II and Xe III lines, with Xe I lines (dominant before the onset
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of the discharge pulse) practically unobservable. The temporal evolution of typical lines of each species is shown in Fig. 4. These spectra confirm 4
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the results of hydrodynamic / atomic physics simulations of the capillary discharge plasma which predict that the plasma is fully ionized. This is also in agreement with ADK ionization rate calculations that show harmonics greater than 80 eV could only be generated at an intensity where the plasma is fully ionized. For a particular photon energy of 120 ev, figure 4 shows delays between the rise of the current pulse and injection of the laser as well as a complete current profile. Before the current pulse there is no signal at this photon energy. The flux then rises to a peak 2 μs after the initiation of the current pulse and then slowly returns to zero. This clearly demonstrates the advantages of HHG in a capillary discharge created plasma. Spectroscopy measurements of the plasma show that at the time of maximum high harmonic emission the plasma is completely ionized. It is possible that the delay of the maximum HHG signal is due to the presence of plasma nonuniformities caused by the fast rise time of the current pulse.
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Fig. 4. (a) Time evolution of the harmonic signal at 120 eV in Xe (diamonds). The current pulse is shown for reference (solid). (b) time evolution of the visible emission lines from Xe I (823.16 nm) (dotted), Xe II (418.01 nm) (dashed), and Xe III (410.92 nm) (solid).
In conclusion, we have demonstrated that a capillary discharge plasma waveguide can be used to extend high harmonic generation to shorter wavelengths. We have obtained high harmonic generation from Xenon to a photon energy of 150 eV. This is an increase of more than 70 eV over the highest previously published cutoff observed in xenon. Preliminary experiments in krypton and argon show similar enhancement. The capillary discharge overcomes the limitations imposed by ionization-induced defocusing, allowing for much higher laser intensities and harmonic generation at shorter wavelengths. This technique combined with quasi-phase matching methods promises to achieve efficient high harmonic generation at high photon energies.
Acknowledgement Work supported by the U.S. Department of Energy, Chemical Sciences, Geosciences, Biosciences Division of the Office of Basic Energy Sciences and by the NSF ERC for Extreme Ultraviolet Science and Technology under NSF Award No. 0310717. BCW acknowledges support from the JILA Visiting Fellows Program.
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References 1. EA Gibson et al., “High-Order Harmonic Generation up to 250 eV from Highly Ionized Argon”, Phys. Rev. Lett. 92, 033001 (2004) 2. H. M. Milchberg, C. G. Durfee III, and T. J. McIlrath, “High-Order Frequency Conversion in the Plasma Waveguide”, Phys. Rev. Lett. 75, 2494–2497 (1995) 3. A Butler, DJ Spence, and SM Hooker, “Guiding of High-Intensity Laser Pulses with a Hydrogen-Filled Capillary Discharge Waveguide”, Phys. Rev. Lett. 89, 185003 (2002) 4. Y. Wang, et al., “Capillary discharge-driven metal vapor plasma waveguides”, Phys Rev. E 72, 026413 (2005)
Generation of High-Order Harmonic Continuum Supporting Single Attosecond Pulse in Argon Driven by Intense 7 fs Laser Pulse Y. H. Zheng 1, H. Xiong 1, Y. Peng 2, H. Xu 2, X. Yang 2, Z. N. Zeng 1, X. W. Chen 1, R. X. Li 1, H. P. Zeng 2 and Z. Z. Xu 1 1
State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
2
Key Laboratory of Optical and Magnetic Resonance Spectroscopy of Ministry of Education, Department of Physics, East China Normal University, Shanghai 200062, China
Summary. High-order harmonic continuum in the cutoff is demonstrated with an argon gas cell driven by 0.4 mJ/7 fs (FWHM) ultrashort intense laser pulse. We find that the spectral structure, the modulation depth and the continuum bandwidth of the high-order harmonic spectra vary when the carrier-envelope phase (CEP) of driving laser pulse is stabilized at different values. At some CEP values, a continuous spectrum of 0.08 J/cm2, and the exothermic reaction of silicide formation starts. Main degradation mechanisms of MLs are discussed. The results of this study can be used for development of advanced multilayer mirrors capable handling the intense radiation conditions of new generation coherent X-ray sources.
1 Introduction Multilayer (ML) X-ray mirrors are widely used as optical components in the regions of UV and soft X-rays (1-50 nm) due to their high efficiency and flexibility in the parameters and forms. Under aggressive environment (heating, ion irradiation and exposure to high-power laser radiation) they can degrade as a result of the structural nonequilibrium conditions [1-4]. Growing power of new generation coherent X-ray sources (tabletop laser [5], FEL [6] and others) makes the stability of ML optical properties even more critical. The Sc/Si MLs developed for the wavelength range 35-50 nm have been successfully used in many applications with the capillary-discharge laser generating at the wavelength λ=46.9 nm [7]. Knowledge of radiationinduced degradation mechanisms in the Sc/Si structures will help finding high-end edges of the application and the ways to enhance their stability.
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On the other hand, the very laser radiation represents a specific interest for the surface processing [8]. Diffusion mixing of the layers and formation of the chemical compounds at moderate temperatures indicate the excessive free energy of the MLs. Moreover, the energy released in the mixing process can trigger self-sustained reaction observed in multilayer nanofoils [9]. In this work we discuss features of a single-shot laser influence onto Sc/Si ML degradation process related to the nonequilibrium of the layered structure.
2 Experimental Sc/Si MLs with the period of ~27 nm were deposited onto silicon and float glass substrates by the method of DC magnetron sputtering. Part of Sccontaining layer in the period was ~0.5. Number of the periods was 10 (Sc/Si/10) on glass substrate and 33 (Sc/Si/33) on Si. MLs deposited onto both type of substrates were exposed to the focused laser radiation operating at λ=46.9 nm. The energy of the pulsed (1.2 ns) laser beam was ~ 0.13 mJ. To vary the fluence value (F) we translated ML sample with respect to the beam focus. Each laser shot stroke the sample surface in a new ML region at normal incidence. Scanning electron microscope JSM-820 was used to get the information on surface morphology and chemical composition of Sc/Si MLs. Crosssectional images were produced with the help of transmission electron microscope PEM-U (SELMI, Ukraine) at accelerating voltage of 100 kV.
3 Results and discussions
3.1 Scanning electron microscopy study We investigated different laser imprints (LIs) obtained with the change of irradiated area on the Sc/Si ML surface, which corresponded to a set of the fluences in the range of 0.04-5.00 J/cm2. We observed traces of a ML melting at the fluence values starting from F~0.08 J/cm2. This fluence corresponds to the melting threshold predicted using the thermal diffusion model [10] for the MLs with average thermal characteristics being between Sc and Si.
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An incidental change in the morphology of the molten surface was observed at the fluences up to F~0.3 J/cm2 (fig. 1a) in the irradiated areas of Sc/Si/33 ML deposited on Si substrate. Note that the rectangular undamaged area in the center of LI is a shadow of the ML sample inherited from the irradiation scheme [11]. Further growth of the fluence resulted in the melt cracking structures. Cracks advent is an evidence of deep ML melting; better contrast SEM images obtained with the reflected electrons (penetration depth up to ~1 μm) have denoted this fact. First signs of evaporation were revealed at F~0.9 J/cm2 (fig. 1b) in the form of small micron-sized pits (visible in fig. 1b as black dots inside the LI center) indicating a melt boiling. Simultaneously a “crown” was formed as a result of pressing out the melt to the LI rim by excessive vapor pressure. The thermal diffusion model gives the lower threshold fluence for evaporation to be F~0.2 J/cm2. Perhaps, the evaporation process would start before the cracks appearing at the surface, but to define the threshold value more precisely one need to use more accurate and sensitive instruments (for example, probe beam deflection technique [12]). At F~2.2 J/cm2 the active evaporation or ablation of Sc/Si/33 ML becomes visible. The specific features of this stage are a crater formation in the LI center (fig. 1c) and appearing solidified drops around the LI. According to electron microanalysis there is no Sc within the crater of evaporated region, i.e. ML is completely absent in this region. The crater as a rule occupies less than a half the LI area. Presence of the drops means the ML being removed from the center in liquid phase as well. So, the mechanism of a combined ablation is characteristic for the Sc/Si ML: an ejection of the melt and vaporization; it is similar to that for metals [13].
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Despite the fact that ~97% of absorbed energy is concentrated in top 10 periods, melting and ablation in Sc/Si/10 ML deposited on the glass goes
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in completely different way as compared to Sc/Si/33 ML. Melting as a rule is accompanied by cracking and flaking the ML practically up to F~0.5 J/cm2 (fig. 2a). An ablation processes in some LI areas begins at F~0.6 J/cm2 (fig. 2b) that is considerably less than that for Sc/Si/33 (2.2 J/cm2). Fig. 2c shows SEM picture for LI at 1.4 J/cm2 with ML removed from the most LIs. Judging from the presence of the drops the ablation mechanism here didn’t change. The rest of laser energy (~3%) is concentrated within the substrate surface because of high absorption [14] and low heat conductivity of the glass [15] compared to Si and Sc [16]. However this energy is insufficient to reduce the observed threshold of the ablation for Sc/Si/10 ML at least to one-third. Taking into account the strong absorption of practically all incident energy in the ML material we expected the similar behavior of MLs with 10 and 33 periods under the irradiation. We believe the difference of heat conductivity in glass and the ML material is the reason of observed distinction.
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According to our calculation, at F~0.4 J/cm2 the laser radiation can ablate the Sc/Si/10 ML material completely. However, it looks like it doesn’t take place (see fig. 2a). Our estimations show that even at F~0.6 J/cm2 (fig. 2b) the bottom two periods cannot be melted by the absorbed laser energy directly. Complete ablation can occur at F≥1.4 J/cm2, with all the layers being melted under the laser irradiation. 3.2 Transmission electron microscopy study Fig. 2 shows cross-sectional image of the Sc/Si/33 ML after irradiation by the laser beam at F~0.13 J/cm2 (laser source is on the left). The most of
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ML has been molten, and according to electron diffraction analysis the alloy composition corresponds to Sc3Si5 silicide. Only 7 periods of 33 survived at the substrate (on the right). This ratio of molten and survived volumes indicates the fluence approaching the full structure melting threshold for the Sc/Si/33 ML. The estimations, however, show that only 4 periods can be molten at that fluency, i.e. only one-sixth of the value observed in the experiment. Such a discrepancy can be explained by the suggestion that the formation of the Sc3Si5 silicide results in a release of up to 570 kJ/mol [17]. This energy is enough to heat and melt the material. For the short laser pulse duration (~1.2 ns) no efficient diffusion process can occur, therefore that melting is believed to be the main mechanism of ML degradation.
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Fig. 3. Cross-sectional TEM image of Sc/Si/33 ML after irradiation at fluence of 0.13 J/cm2. Laser beam falls from the left. Substrate (S) is on the right.
So, we see that melting of the Sc/Si ML by the laser beam initiates the exothermic reaction, which, from one hand, facilitates the ML ablation (for F≥1.4 J/cm2) and, from the other hand, enlarges the molten region at low fluences (F10-4.Thus, it is very attractive to use relativistic harmonics for the attosecond pulse generation. The theory of the attosecond pulse generation [3,27] in the framework of the sliding mirror model
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[24] has been developed. As was demonstrated by the PIC simulations [23,24], when a few-cycle relativistic-irradiance laser pulse interacts with a thin foil target as shown in Fig. 6, the ions remain at rest, while the electrons move as a whole. We consider the case when the electron motion in the direction perpendicular to the foil is negligible, so they move ("slide") mainly along the foil. Perpendicular electron motion can be neglected in two cases. First, when it is suppressed by the strong electric charge separation field Ech = 2πenl, which is of the order of the laser field amplitude E0 or more in this case; here e is the electron charge, n and l are the foil density and thickness. Second, when the thin foil target is irradiated by two identical laser pulses from both sides. We consider a p-polarized incident pulse obliquely incident on the thin foil. The problem was solved using the plane wave approximation in the boosted reference frame moving along the foil with the velocity V = c sinθ, where c is the velocity of light and θ is the incidence angle; in this reference frame, the incidence is normal [26]. Under the above assumptions, calculation has been performed. Both reflected and transmitted pulses contain harmonics of the incident laser radiation as shown in Fig. 7; furthermore, the spectral phase varies little at high harmonic orders. After spectral filtering, these harmonics form isolated attosecond pulses, like in the case of harmonics generated in gases for few-cycle driver pulses. Using spectral filtering, it is possible to obtain extreme ultraviolet pulses with the duration of few hundred attoseconds and the conversion efficiency of 10-8 – 10-5 [3, 27]. In order to obtain high conversion efficiency, we should not use spectral filtering technique. We found new regime of attosecond pulse generation in transmission, where the conversion efficiency can be as high as several percent. Example of the transmitted attosecond pulse is shown in Fig. 9 (a). Driver laser pulse has the duration of 6.3 fs and the dimensionless amplitude a0 = eE0/(mcω0) = 16 (I0 = 5.5×1020 W/cm2 for λ0 = 800 nm). Normalized aerial foil density is ε0 = 13.6, which corresponds, for example, to a fully-ionized 10-nm carbon foil. Duration of the transmitted attosecond pulse is τFWHM = 0.44/ω0 (190 as for λ0 = 800 nm), the energy conversion efficiency into the main pulse is 0.033. For the 5-µm focal spot this corresponds to 12 mJ, 60 TW attosecond pulse, which is at least six orders of magnitude larger than can be generated in gases. We take advantage of the analytic theory to establish the optimum parameters for the attosecond pulse generation in this regime. We obtain that the dimensionless pulse amplitude should be approximately equal to the normalized aerial foil density: a0 ≈ ε0, which can be cast into the form I0 ≈ 1.1×1019 W/cm2× (n/1024cm-3)2(l/nm)2. If a0 ε0, the pulse is transmitted through the foil almost without change; thus, only small part of the laser energy is transformed to higher frequencies, so the interaction is not efficient, and the transmitted pulse remains femtosecond. Dependencies of attosecond pulse duration and conversion efficiency on a0 under the optimum conditions are shown in Fig. 8 (b). The established relation a0 ≈ ε0 is rather general. It represents the condition of strongest coupling between a laser and a thin foil, so it holds not only for the attosecond pulse generation, but also for harmonic generation [3], ion acceleration [28-30] and so on. Experimental implementation of the sliding mirror technique requires clean femtosecond pulses with extremely low ASE(amplified spontaneous emission) level so the thin foil is not destroyed before the arrival of the main pulse. We will employ techniques to dramatically reduce the ASE level.
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6 Summary The high intensity femtosecond laser driven quantum beams such as x-ray, electron, proton, THz radiation and their combinations for fruitful applications such as various pump-probe technique are described. A well defined thin plasma layer in a thin foil target created by a clean femtosecond pulse opens collective relativistic phenomena which may bring a lot of fruitful applications.
References [1] M. Borghesi et al., Fusion Science and Technol. 49 April (2006). [2] K. W. Ledingham et al., Phys. Rev. Lett.84, 899(2000). [3] A. Pirozhkov et al., Phys. Plasmas 13, 13107(2006) [4] Hamster et al., Phys. Rev. Lett.71, 2725(1993). [5] T. Tajima and J. M. Dawson, Phys. Rev. Lett.43, 267(1979). [6] L. Willingale et al., Phys. Rev. Lett.96, 245002(2006). [7] T. Detmire et al., Phys. Rev. Lett. 78, 3121(1997). [8] M. Mori et al., Laser Physics 16, 1092(2006). [9] T. Fujii et al., Appl. Phys. Lett. 83, 1524(2003). [10] D-K Ko and J. Lee, Abstracts of ICUIL 2006 Ref:ICUIL067-Session1 “Recent progress on APRI PW Project and related high field physics researches”, pp. 49-50. [11] H. Shwoerer et al., Phys. Rev. Lett. 86, 2317(2001). [12] A. Rousse et al., Rev. Mod. Phys. 73, 17(2001). [13] C. Reich et al., Phys. Rev. Lett. 84, 4846 (2000). [14] K. Ta Phuoc et al., Phys. Rev. Lett. 91, 195001(2003). [15] A. Rousse et al., Phys. Rev. Lett.93, 135005(2004). [16] A. Sagisaka et al., Appl. Phys. B84, 415(2006) [17] M. Nishiuchi et al., Phys. Lett. A357, 339(2006). [18] Borghesi et al., Phys. Rev. Lett. 92,55003(2004). [19] M. Nishiuchi et al., Repetitive highly collimated intense proton beam with sub-MeV energy range driven by a compact few tera-watt femto-second laser, submitted for publication. [20] S. Nashima et al., IEEE Proc. 2004 Conf. Optelectronics and Microelectronics materials and Devices(COMMAD 2004), Brisbane, Australia, 8-10 December 2004, (2004) p.303 [21] M. Mori et al., Phys. Lett. A356, 146(2006) [22] Kando, Proc. APRC symposium 2006 ; H. Schwoerer et al., Phys. Rev. Lett. 96, 014802 (2006). [23] S. V. Bulanov et al., Phys. Plasmas 1, 745 (1994). [24] V. A. Vshivkov et al., Phys. Plasmas 5, 2727 (1998).
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[25] M. Zepf et al., Phys. Rev. E 58, R5253 (1998); A. Tarasevitch et al., Phys. Rev. A 62, 023816 (2000); I. Watts et al., Phys. Rev. Lett. 88, 155001 (2002); I. Watts et al., Phys. Rev. E 66, 036409 (2002); U. Teubner et al., Phys. Rev. A 67, 013816 (2003). [26] U. Teubner et al., Phys. Rev. Lett. 92, 185001 (2004). [27] A. Pirozhkov et al., Phys. Lett. A.349, 256(2006) [28] K. Matsukado et al., Phys. Rev. Lett. 91, 215001 (2003). [29] T. Esirkepov et al. Phys. Rev. Lett. 89,175003(2002) [30] T. Esirkepov et al. Phys. Rev. Lett. 92, 175003(2004)
Radiative Properties and Hydrodynamics of LaserProduced Tin Plasma for Efficient Extreme Ultraviolet Light Source S. Fujioka1, H. Nishimura1, K. Nishihara1, Y. Tao1, T. Aota1, T. Ando1, K. Nagai1, T. Norimatsu1, N. Miyanaga1, Y. Izawa1, K. Mima1, H. Tanuma2, H. Ohnishi2, A. Sunahara3, Y. Shimada3 and A. Sasaki4 1) Institute of Laser Engineering, Osaka University, 2) Department of Physics Tokyo Metropolitan University, 3) Institute for Laser Technology, 4) Japan Atomic Energy Agency.
Summary. A laser-produced tin (Sn) plasma is an attractive extreme-ultraviolet (EUV) light source for the next generation lithography in terms of its brightness and compactness. Radiative properties and hydrodynamics of the laser-produced Sn plasmas are quite important for investigating the optimum conditions for EUV generation. Several experiments have been performed to clarify the above issues; (i) EUV spectra emitted from isolated Snq+ (5 < q < 15) ions and opacity spectrum of a 30-eV Sn plasma have been measured as fundamental data for accurate modeling radiation energy transport in plasmas, (ii) electron density profile in 13.5 nm emission dominant region of a laser-produced Sn plasma was measured with a laser interferometer for understanding hydrodynamics of an EUV source plasma. (iii) benchmarking one-dimensional (1D) radiation-hydrodynamic simulation code with multiple laser beam irradiated spherical 1D Sn plasma. Based on the experimental results and calculations, it was found that optically thinner plasma emits 13.5 nm light more efficiently. Optical depth of Sn plasma is actively controlled with changing laser pulse duration and the use of low-density porous target.
1. Introduction Laser-produced high-Z plasma is a typical example of radiationhydrodynamics, in which the radiative properties of a plasma are tightly coupled with hydrodynamic motion via energy transport. A clear understanding of radiation-hydrodynamics is important for the fields of inertial fusion energy, astro- and planetary physics, and x-ray source applications.Extreme ultraviolet (EUV) light sources for microlithography are receiving much attention as an application of laser-produced high-Z plasma. EUV lithography (EUVL) is a promising technology for volume produc-
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tion of next-generation microprocessors whose node size is less than 40 nm [1]. A commercial EUVL system requires > 300 W of output EUV power into a solid angle of 2π sr. from a plasma source of 13.5 nm wavelength within a 2% bandwidth (BW). Laser produced tin (Sn) plasma has a highly intense emission peak at 13.5 nm of wavelength, thus much effort is devoted to the development of the Sn-based EUV light source [2].
2. Radiation properties of laser-produced Sn plasma
2.1 Absolute opacity of 30-eV Sn plasma The opacity, as well as the emissivity, of laser-produced Sn plasma is so high for 13.5-nm light that the light emitted from deep within the Sn plasma is absorbed strongly during propagation through surrounding plasma as it expands. To obtain high conversion efficiency (CE) from incident laser energy to output EUV energy, the plasma size should be controlled to attain an appropriate optical depth, i.e., the product of the mass absorption coefficient and area density of the plasma for 13.5-nm light. The opacity of Sn plasma in the dominant EUV emission region is a critical parameter for investigating the optimum conditions for EUV generation, however no reliable experimental data has been available. The electron temperature and ion density of the dominant EUV emission region are in the ranges from 20 to 80 eV and from 1017 to 1020 cm-3, respectively [3]. Opacity measurements of Sn plasma were performed on the Gekko-XII laser facility [4]. Figure1 (a) shows the experimental set up for opacity measurement. A radiation-confining gold cavity, called the "dog-bone (DB)" [5], was used to uniformly heat an opacity sample. The opacity sample consisted of a thin Sn layer sandwiched between two 100-nm-thick CH tampers mounted on an observation window (200 μm x 200 μm) of the DB. The CH tamper was used to minimize the density gradient of the Sn plasma. The area density of the Sn layer in the sample was 2.04 +/- 0.18 x 10-5 g/cm2, which was analyzed with an inductively coupled plasma (ICP) device. Six beams of the Gekko-XII laser [6] (1.053 μm wavelength, 500 ps pulse duration) were focused through two inlet holes of 500 μm diameter onto the inner surface of x-ray generation sections set at both end of the DB. X-ray radiation from the sections propagated diffusively toward the central cavity for thermal radiation confinement.
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The radiatively heated sample was backlit with broadband EUV light from another Sn plasma generated with a laser pulse of 1.053 mm wavelength and 500 ps duration at 1 x 1013 W/cm2. The backlight source was set 2 mm away from the DB and backlight x-rays were shone at 1.0 ns after the peak of the heating x-ray. The transmitted EUV spectrum through the sample was measured by a grazing incidence spectrograph (GIS) coupled with an x-ray streak camera (XSC). The Sn sample was heated by a TR = 50 eV thermal radiation pulse with a Gaussian shape (500-ps FWHM). Radiation hydrodynamic simulation (ILESTA-1D) [7] predicts an averaged temperature and density of the heated Sn sample of 30 eV and 0.01 g/cm3 at 1 ns after the peak of the heating x-ray pulse. Since the spectrum inevitably includes self-emission from the Sn and CH plasmas, we separately measured the self-emission spectra from the sandwiched Sn sample and from the CH tamper alone.
Fig.1 (a) Schematic of opacity measurement, (b) transmission of 30 eV Sn plasma for EUV light.
The dots in Fig. 1 (b) represent the raw measured spectrum of the transmission, while the solid line in Fig. 1 (b) is the smoothed measured spectrum in consideration of the spectral resolution of the GIS-XSC. The dash-dotted, dashed, and dotted lines represent the spectra calculated by an atomic code HULLAC [8] with electron temperatures of 20.9, 31.0, and 40.3 eV, respectively. The configuration interaction between the 4dn, 4dn1 4f, 4dn-15p, 4dn-15f, and 4p54dn configurations were taken into account, since the configuration interaction changes the wavelength and strength of emission lines considerably [9]. The population of the ionization state was calculated under the collisional radiative equilibrium condition. Strong absorption is seen around 13.5 nm, arising mainly due to the 4p-4d and 4d-4f transitions of Sn8+ to Sn13+
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The transmission at 13.5 nm, the most interesting wavelength, shows quite good agreement between the measurement and calculation, demonstrating that the HULLAC calculation is useful for calculating 13.5 nm light generation. The measured mass absorption coefficient of the Sn plasma at 13.5 nm is 0.96 +/- 0.18 x 105 cm2/g. 2.2 Identification of transition energies of multiply charged ions For accurate modeling of atomic process in plasma, spectroscopic data of Sn ions is necessary. However, the available spectroscopic information on multiply charged Sn ions is fairly limited at present. Even though much spectroscopic data has been reported, the energy levels of multiply charged Sn ions have not been established yet, because of the complexity of their electric structures attributed to the strong electron correlation among the large number of active electron. Photon-emission spectroscopy, in which the line intensities of the photon emissions are measured following the charge-transfer reaction in collisions of multiply charged ions with neutral target gases, is a very powerful experimental technique to investigate the transition energies and energy levels of multiply charged ions [10]. The multiply charged Sn ions were produced in a 14.25 GHz ECR (electron cyclotron resonance) ion source at Tokyo Metropolitan University. The Snq+ (5 < q < 15) ions were extracted with an electric potential of 20 kV and select by a double-focusing dipole magnet according to their massto-charge ratio. The ion beam was directed into a collision chamber, where the ion beam interacts a target gas jet ejected from a capillary plate. The background pressure in the collision chamber was 6 x 10-6 Pa and the target gas pressure in the chamber was held at about 1 x 10-3 Pa during the measurement. The target gas pressure was low enough to maintain the single-collision conditions. The EUV emission from the collision center was observed at 90 deg. to the ion beam direction with a GIS spectrometer equipped with a toroidaltype conversing mirror. As a photon detector, a liquid nitrogen cooled CCD camera was attached to the EUV spectrometer and an emission spectrum in the wavelength range of 6 – 24 nm was accumulated simultaneously. Spectral resolution of the spectrometer is about 0.1 nm. Wavelength calibration was performed using the established EUV emission lines of oxygen ions. From comparison between the measured spectrum and calculation, photon wavelength calculated by the HULLAC code is systematically different by 0.5 nm from the measured one for 4d-4f transitions. Therefore calculated wavelength of 4d-4f transition is manually adjusted to match the
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experimental results for coupling with radiation-hydrodynamic simulation. Furthermore, the measurement reveals transitions corresponding to the dip observed in the opacity spectrum, i.e. the characteristic absorption peaks at 11, 12, 16 and 18 nm are caused by 4d-5f of Sn9+, 4d-5f of Sn8+ 4d-5p of Sn10+ and 4d-5p of Sn9+, respectively.
3. Hydrodynamics of 13.5 nm emission dominant region in laser-produced Sn plasma
3.1 Dynamic imaging of 13.5 nm emission from laser-produced Sn plasmas EUV emission from a laser-produced Sn plasma was imaged on an XSC using a monochromatic EUV Schwarzschild microscope. The microscope employed two concentric spherical mirrors with Mo/Si multilayer coating, operating at 13.5 nm in 4% BW [11]. A 0.4 µm Zr filter over coated on a 0.5 µm CH foil was placed in front of the mirrors to block visible light and particles from the plasma. In the present experiment, spatial and temporal resolutions of the microscope were checked to be better than 15 m and 1.5 ns, respectively. The microscope was installed in the plane of laser incidence and parallel with the target. A 10 ns laser pulse at 1064 nm with energy up to 2 J was illuminated onto the target. The laser beam was focused by an F/4 lens onto the target surface at normal incidence. The focal spot size was measured with both an optical imaging system and a monochromatic EUV pinhole camera. The diameter defined by FWHM was 220 μm and the width defined at 10% of the peak intensity was 450 μm. Targets used in the experiment consists of a strip Sn foil with a width of 200 μm and a thickness of 15 μm. It was placed on a 1 μm-thick CH film. Since CH plasma has much less average mass, CH plasma expands faster than Sn plasma, and CH plasma acts as a tamper to prevent lateral expansion of Sn plasma. Figure 2 shows temporal evolution of the EUV emission profiles at laser intensity of 1 x 1011 W/cm2, which is appropriate for efficient EUV generation [12]. Zero time represents the peak of the laser pulse. The EUV emission region expands with time and the peak of the EUV emission moves away from the target surface. At the peak of the laser pulse, the peak of the EUV emission locates 200 μm away from the target surface.
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Fig. 2 Temporal evolution of EUV emission observed from the side direction.
3.2 Density profile of 13.5-nm dominant emission region in laserproduced Sn plasma The electron density profile of laser-produced Sn plasma was investigated using two interferometers: a Mach-Zehnder interferometer using a probing beam of 266 nm UV light and a Michelson interferometer using 532 nm green light [13]. A small amount of laser energy, split from the heating beam, was used as a probe beam. The wavelength of the probe beam was converted to 532 and 266 nm. High temporal resolution was achieved by using a visible framing camera (HAMAMATSU C7400), which was synchronized with the laser pulse with a jitter less than 1 ns. The gate interval was set to 1 ns. The temporal resolution was less than 1.5 ns. The spatial resolution limited by the camera was 15 µm. For the both the green and UV interferometers, an interferometer data evaluation algorithm was used to calculate the Abel inversion to extract the density map from the phase shift map. Density profiles along the center of the plasma are plotted in Fig. 3. The circles an triangles represent the data from the green and UV interferometers, respectively. The error bars arise from the Abel inversion process, due to the irregular phase profiles. The solid line is an exponential decay fit to the experimental points with two typical scale length of 70 and 120 μm. Electron density of the EUV emission dominant region (EDR) is in range from 1019 to 1020 cm-3, those are much lower than the critical density for 1.064 μm light.
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The measured density profile was compared with that predicted by onedimensional (1D) code (STAR-1D) [15]. It can be seen in Fig. 3 that there is a considerable discrepancy in their absolute values. A possible reason for this discrepancy arises from three dimensional plasma expansion. Because of the finite size of the focal spot, a lateral plasma expansion occurs as well as a longitude expansion. It is noted that the plasma scale length and the diameter of the focal spot are comparable, so multi-dimensional expansion becomes to have significant effects on plasma structure. As is expected, two-dimensional radiation hydrodynamic code reproduces the density reduction caused by the multi-dimensional expansion.
Fig. 3 Comparison of electron density profile between measurement and simulation. Dashed and solid lines are calculated by 1D and 2D code.
4. Benchmarking radiation-hydrodynamic simulation code with one-dimensional spherical plasmas Radiation-hydrodynamic simulation code is a powerful tool to investigate the optimum conditions for the EUV generation. Its reliability is proven only by experimental data, however a plasma produced from a planar target irradiated by single laser beam shows the multi-dimensional effects. The multi-dimensional plasma expansion make it difficult to compare the experimental results with 1D simulation. For eliminating these problems, spherical targets were irradiated uniformly with a multiple laser beam [14] on Gekko-XII laser facility [6]. Spherical plastic targets coated with a 1 μm-thick tin layer, were used in the experiment. The target diameter was varied from 300 to 750 μm. A 1.2 ns Gaussian pulse of 1.05 μm wavelength and 0.5 – 15 J in total energy
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was focused with an F/3 lens and the focal point was displaced based on the target diameter such that the target was illuminated uniformly. The laser intensity on the target was varied from 2 x 1010 to 1 x 1012 W/cm2 by adjusting the laser energy and the target diameter. The radiation-hydrodynamic code (STAR-1D) [15] describes radiation transport with a multi-group diffusion approximation, in which photon from 0.5 to 1500 eV is divided into 1500 groups. Electron thermal conduction is treated with a flux-limited Spitzer-Harm model, and laser absorption is calculated using a ray-tracing method. Tabulated emissivities and opacities calculated by the HULLAC code under the collisional radiative equilibrium condition are coupled with the radiation-hydrodynamic code.
Fig. 4 EUV spectra emitted from multiple laser beams irradiated spherical target. (a) experiment, (b) calculated by 1D code.
Figure 4 shows the comparison of spectra between experiment [14] and calculation at the laser intensity of 9 x 1011 W/cm2. The EUV spectrum was measured with a transmission-grating spectrometer coupled with a CCD camera. Its spectral resolution is better than 0.42 nm. The simulation spectrum is smoothed with taking into account of the instrument spectral resolution. The calculated spectrum shows quite good agreement with the experimental results. The agreement is observed in the wide range of the laser intensity from 1010 to 1012 W/cm2. The atomic process and energy transport included in the simulation code are proven to be appropriate for the EUV source modeling. The conversion efficiencies (CEs) from incident laser energy to output 13.5 nm 2 % BW energy were measured with a calibrated energy-meter called E-mon. Figure shows the CE dependence as a function of laser intensity. The highest CE of 3% was attained at an intensity of 0.5 – 1 x 1011 W/cm2. The calculated CEs are almost consistent with, but somehow higher than, the experimental values, because 20 % of intensity non-
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uniformity still remains on a spherical target irradiated by finite (twelve) laser beams.
5. Active control of the laser produced Sn plasma for efficient EUV generation
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Dependence of EUV-CEs on laser pulse duration
Optical depth of a produced Sn plasma is a key parameter to obtain efficient EUV light [4]. The optical depth can be controlled by changing the laser pulse duration. We investigated dependence of optical depth on the laser pulse duration. Pulse duration, which makes the optical depth unity, is calculated to be 3.7 ns at 1 x 1011 W/cm2 of 1.064 µm laser [16]. Experiments were carried out using a Q-switched Nd:YAG laser of 1.064 μm in wavelength. Pulse duration was changed from 2 to 9 ns using a pockels cell pulse slicer, and from 1 to 2 ns using a stimulated-Brillouinscattering pulse compressor. The laser was focused onto Sn plates with an F/30 lens from the target normal direction. Spot size was changed from 300 to 900 μm to obtain laser intensity in the range from 1 x 1010 to 1 x 1012 W/cm2. A 100-nm thick Sn layer coated on a plastic plate was used as a target to minimize influence of oxidation layer formed at the target surface on EUV conversion. Absolute 13.5 nm light energy was measured with the E-mon installed at 45 deg. with respect to the target normal. The spectral response of the E-MON, the measured spectral shape and measured angular distribution of the EUV emission were taken into account for the CE evaluation. Figure 5 shows dependence of EUV CEs on the incident laser intensities for various pulse durations. The optimum laser intensities are in the range from 5.0 x 1010 W/cm2 to 1.0 x 1011 W/cm2 for all the pulse durations. The maximum CE of 2.2 % was attained with the pulse duration of 2.3 ns at 5.0 x 1010 W/cm2. The CEs increase with shortening laser pulse duration for longer than 2.3 ns, however, the peak CE which obtained with 1.2 ns pulse is lower than that with 2.3 ns pulse. This result implies that the optimum pulse duration is determined not only by the optical depth but also by a fraction of laser energy absorbed in the EUV-EDR. The fraction of laser energy absorbed in the EDR were calculated to be, respectively, 25, 42, 73 and 85 % in 1.2, 2.3, 5.6 and 8.5 ns pulse produced plasmas. Therefore , for shorter pulse produced plasma, incident laser energy is not directly ab-
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sorbed in the EDR, but in higher dense region. Optimum laser pulse should have enough duration to absorb sufficient laser energy in the EDR.
Fig. 5 Dependence of EUV-CEs on laser pulse duration.
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Low-density porous target for efficient EUV generation
The other method to change plasma properties is the use of low density porous target [17]. Experiments were carried out using a Q-switched Nd:YAG laser (1.064 m in wavelength and 10 ns in pulse duration) focused with an F/30 lens at the target normal. The focal spot size was optically measured to be 500 µm, and was unchanged within this experiment. Three kinds of planar targets were used. The first target is a solid-density Sn foil, whose initial density is 7.28 g/cm3. The second and third ones are low-density SnO2 foils, whose initial densities are respectively 23 % (1.62 g/cm3) and 7 % (0.49 g/cm3) of the solid SnO2 density. The low-density targets were fabricated using monodispersed polystyrene nanoparticles and liquid Sn chloride [18]. After calcination process of the chloride, the lowdensity SnO2 targets have porous structures whose cell size is about 1 µm. Dependence of the EUV-CEs on the laser intensity is shown in Fig. 6. In the case of the solid-density targets, the EUV-CEs depend weakly on the laser intensity, and almost constant CE of 1.2 % is obtained. On the other hand, the EUV-CEs from the low-density targets show relatively strong dependence on the laser intensity, this trend is similar to those for the shorter laser pulse (1.2 ns and 2.2 ns) produced -- optically thinner -- Sn plasmas. The highest CE of 2.2 % was obtained at the optimum intensity of 5 x 1010 W/cm2 for the 7% low-density SnO2 targets. The peak CE for
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the 7 % low-density SnO2 targets is 1.7 times higher than that for the soliddensity Sn targets.
Fig. 6 Dependence of EUV-CEs on initial target density.
Acknowledgement This work was performed under the auspices of a Leading Project promoted by MEXT (Japanese Ministry of Education, Culture, Sports, Science and Technology).
References [1] Silfvast W. T. et al., Appl. Opt. 32, 6895 (1993). [2] Jin F. et al., Appl. Opt. 34, 5750 1994); Spitzer R. C. et al., J. Appl. Phys. 79, 2251 (1996); Shimoura A. et al., Appl. Phys. Lett. 75, 2026 (1999); Choi I. W. et al., J. Opt. Soc. Am. B 17, 1616 (2000); Aota T. et al., Phys. Rev. Lett. 94, 015004 (2005). [3] Nishihara K. et al., in “EUV sources for Lithography” (SPIE, Bellingham, WA, 2006), Vol. PM149, Chap. 11, p. 339. [4] Fujioka S. et al., Phys. Rev. Lett. 95 235004 (2005). [5] Eidmann K. et al., Phys. Rev. E 52, 6703 (1995). [6] Yamanaka C. et al., IEEE J. Quantum Electron. 17, 1639 (1981). [7] Takabe H. et al., Phys. Fluids 31, 2884 (1988).
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[8] Bar-Shalom A. et al., Phys. Rev. E 56, R70 (1997). [9] Svendsen W. et al., Phys. Rev. A 50, 3710 (1994). [10] Tanuma H. et al., Nucl. Instrum. Meth. Phys. Res. B 235, 331 (2005). [11] Tao Y. et al., Rev. Sci. Instrum. 75, 5173 (2004). [12] Tao Y. et al., Appl. Phys. Lett. 87, 241502 (2005). [13] Tao Y. et al., Appl. Phys. Lett. 86, 201501 (2005). [14] Shimada Y. et al., Appl. Phys. Lett. 86, 051501 (2005). [15] Sunaharra A. et al., “Proceedings of the 3rd International EUVL Symposium”, Miyazaki, Japan, 2004. [16] Ando T. et al., to be published in Appl. Phys. Lett. [17] Okuno T. et al., Appl. Phys. Lett. 88, 161501 (2006). [18] Gu Q. et al., Chem. Mater. 17, 1115 (2005).
Laser Physics Research Relevant to Laser-Electron X-Ray Generator A.V. Vinogradov, M.V. Gorbunkov, Yu.Ya. Maslova and Yu.V. Shabalin P.N. Lebedev Physical Institute, Moscow, Russia Summary. A prototype of laser unit for Laser Electron X-Ray Generator is constructed on the basis of the optoelectronic control. The laser system in which an optoelectronic negative feedback is realized by means of a signal reflected from an intracavity Pockels cell polarizer is proposed and tested. The design provides flexible control over pulse train time structure.
1 Introduction Laser produced plasma proved to be a convenient and flexible source of incoherent and coherent soft X-rays probably including water window in the near future [1]. However the scaling of laboratory X-ray lasers and laser plasma X-ray sources to photon energies higher than 5 keV is questionable. Laser plasma based hard X-rays sources are still uncompetitive with conventional X-ray tubes, synchrotrons and free electron lasers. Meanwhile a dramatic (several orders of magnitude) gap exists between Xray tubes and accelerator based X-rays sources in respect of average power, brightness, sizes, cost, monochromaticity, tunability etc. The filling in of this gap would be beneficial for various scientific and commercial applications. In other words a new X-ray source that could bring together the compactness of X-ray tubes and X-ray beam manipulation ability of synchrotron radiation (SR) beamlines without the substantial rise of cost and loss of average power is highly desirable. The applications are biological and medical imaging, material structure and chemical analysis, protein crystallography, microscopy and microtomography for life sciences, medical diagnostics, industrial online X-ray inspection, security and custom control in ports and border terminals. A promising candidate to fill in the gap between conventional and SR sources is laser-electron X-ray generator (LEXG) based on Thomson scattering [2]. The idea to use Thomson scattering of laser radiation by relativistic electrons to extend the output energy spectrum down to hard X-ray of several tens keV range was n [3] and attracted last decade several research groups [4-12]
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Pulse picker
. Fig. 1. The near analogue of the LEXG laser system [13].
A project of LEXG developed jointly by Moscow State University and proposed in Institute of Quantum Radiophysics of Lebedev Physical Institute is aimed at the system containing pulsed synchrotron and a repetitive picosecond laser [11, 12]. Electron bunch is circulating in a storage ring and appears in the interaction chamber (IC) with the period 10-20 ns. Original laser beam time structure is a millisecond train of pulses separated by microsecond-scale interval. Thanks to multiplication in optical circulator the period of laser signal is transformed from microsecond-scale interval into 10-20 ns inside the IC that provides the most efficient coupling of laser and electron beams. Since the microsecond interval is far above a master oscillator’s resonator round-trip (generally about 10 ns), one has to use pulse picking by means of an electrooptical modulator (see Fig. 1). A well-known method to obtain highly stable trains of picosecond pulses is to apply a system of feedback loops, which proved to be efficient in hundred microsecond range [14, 15]. Furthermore, feedbacks allow not only to stabilize the pulse amplitude, but also to obtain regular pulsations with controlled period far exceeding a resonator round trip time Tr [16]. In this case a laser radiation looks like microgroups of picosecond pulses separated by microsecond interval. It is important to note that such mode has an attractive advantage. In fact, after single pulses at 0.5 MHz are picked from a train of pulses at 100 MHz, only 0.5% of average power is utilized. The mode of regular pulsations with 2-microsecond (0.5 MHz) period is
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more favorable, since it provides increase in intensity for the pulses picked in pulsation peaks.
2 Two Feedback Loops-Controlled Laser To investigate the dynamics of a picosecond laser controlled by feedbacks we use the approach describing a mode-locked laser as an object with discontinuous control [16, 17]. In the simplest case of system with one negative feedback (NFB) loop delayed by a resonator round trip the control can be described by means of the so-called logistic mapping
xn +1 = rxn (1 − xn )
(1)
where xn stands for a normalized energy at the n-th pass (a pass corresponds to a laser cavity round trip), r is an overall gain including active medium gain and passive losses, and the term in brackets represents the one-pass delayed feedback loop action. The maximum acceptable gain for steady operation is rmax = 3 [16]. When r exceeds the threshold value rmax, the logistic mapping demonstrates a well-known nonlinear dynamics [18].
Fig. 2. Calculated log of pulsation period T(rmax) over relative feedback sensitivity: curves are in close agreement in the region of negative argument. The upper curve is an approximation.
Another dynamics can be observed in a system controlled by two feedback loops (delayed by one and two round trips) described by the equation
xn +1 = rxn (1 − α xn − xn −1 )
(2)
where α is relative feedback sensitivity, its negative value denotes that feedback loop delayed by a resonator round trip is positive (PFB). The
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analysis shows that if −1 < α < 1 a nonlinear dynamics displayed by (2) differs fundamentally from that of the logistic mapping (1): regular pulsation with period above three round-trips appears. The pulsation period T (rmax) at r = rmax (α) calculated by means of the mapping stationary point stability analysis and the approach based on differential equations (approximation) is presented in Fig. 2. For negative α (i.e. positive and negative feedback combination control) at r = rmax (α) the pulsation is harmonic and the period can be expressed as
T ( rmax (α ) ) =
2π α +1
(3)
Formula (3) implies that regular dynamics with large periods (tens and hundreds of round-trips) can be observed at α close to - 1 (see Fig. 2).
3 Optoelectronic Feedback Designed for Pulsation Mode The above discussion showed that pulsations with period far exceeding a resonator round trip time are expected in a laser controlled by a combination of feedbacks where a negative feedback loop is delayed by one resonator round trip with regard to the positive one. With this aim in mind we designed a laser system in which an optoelectronic negative feedback is realized by means of a signal reflected from an intracavity Pockels cell polarizer. Self-mode-locking [19] in the negative feedback-controlled laser is a known technique for stable ultrashort pulses generation. The laser modelocked by a fast time-shifted negative optoelectronic feedback loop [20] is a very simple and reliable source of light pulses with about hundred picosecond duration. In such a laser the losses caused by an intracavity Pockels cell look like a periodic asymmetric "saw" with a long front and short tail. The tail is forming due to fast charge of the Pockels cell capacity by photocurrent generated in optoelectronic element under ultrashort light pulse. The long front is formed by slow discharge of intracavity cell capacity through the control system resistor. Stable self-mode-locking occurs with temporal delay in feedback control system corresponding to light pulse passage through the Pockels cell at the moment of low intracavity losses. Discharge time should be [20, 21] about several cavity round trip time Tr. Optimal delay for short pulse generation is approximately Tr. Usually the optical control signal is taken at the moment after passage of intracavity Pockels cell polarizer. The control proved to be efficient in laser output stabilization [16, 17].
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The laser dynamics changes dramatically if an optoelectronic feedback is realized by means of a signal reflected from an intracavity Pockels cell polarizer. The diagram of discontinuous control in the laser is shown in Fig. 3. When the laser pulse length varies slightly from pass to pass, the (n+1)-th pulse energy in the cavity En+1 is related to En as En +1 = En G 2 RPn , where G is a gain in a round-trip and R is an output mirror reflectivity (see Fig. 3). Similarly to [5], we use the Pockels cell transmission Pn = P0 (1 − Bn ) where Bn is control signal, and P0 is the initial Pockels cell transmission when feedback is off. In the proposed laser design Bn is the difference between incident light flux on the polarizer and transmitted flux. G2REn-1 - En NFB
Output mirror, R
→G2REn-1
→En
Polarizer, P
Gain medium, G
Fig. 3. The diagram of discontinuous control in a laser with NFB: the control signal is getting from Pockels cell polarizer.
As a result for the recurrence relation we have
(
En +1 = EnG 2 RP0 1 − ( En −1G 2 R − En ) Using r = G 2 RP0 and En = xn
)
(4)
P0 leads to r
P ⎞ ⎛ xn +1 = xn r ⎜1 − xn −1 + 0 xn ⎟ r ⎠ ⎝
(5)
Applying (3) and taking into account the Pockels cell transmission
⎛ U π⎞ P (U ) = cos 2 ⎜ ⎜ U λ 2 2 ⎟⎟ ⎝ ⎠
(6)
where U is a static bias voltage and U λ 2 is a cell half-wave voltage, we estimate the nonlinear dynamics development threshold gain rmax(U) and oscillation period T(U) in two limits.
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When U is far less than U λ 2
T (U ) = 2
2π U λ 2 U
, rmax (U ) = 1 +
π2 ⎛ U ⎞
2
⎜ ⎟ 4 ⎜⎝ U λ 2 ⎟⎠
When U → U λ 2 , T (U ) → 2π , rmax (U ) → 2 . Thus, we conclude that in the laser system controlled by optoelectronic NFB with the control signal getting from the Pockels cell a large period regular pulsation can be obtained. The period increases and the nonlinear dynamics development threshold decreases when the Pockels cell bias voltage U decrease.
4 Laser Dynamics Simulation Results To complete our demonstration of the laser, where the optoelectronic control signal is taken from an intracavity Pockels cell polarizer, however, we still have to show that the regime of pulsations can be reproduced qualitatively by extending the mapping (4) to take into account the laser output radiation fine time structure evolution as well as Pockels cell voltage variation at the time scale of Tr depending on the feedback delay time, Pockels cell capacity discharge time, active medium gain, and the cell bias voltage Ust following the same approach as in our previous works [16,21] The goal is to investigate self mode locking in pulsation regime with corresponding significant control voltage and time-dependent Pockels cell transmission variation. The main question was about the possibility to obtain a single short pulse circulating in a laser cavity. In the numerical simulation spontaneous emission noise was placed in the laser cavity and subsequently transformed by time-dependent transmission P(t) of the Pockels cell. On the other hand P(t) is calculated from the feedback signal proportional to the laser intensity I(t) reflected from the intracavity polarizer. The simulation proved that the discussed laser system allows not only to obtain stable mode-locking in quasi CW mode, but also to generate short pulses microgroups with controlled period far exceeding a resonator round trip time. To show gain sensitivity of microgroup envelope, the trains at gain r = 1.03 and 1.09 are shown in Fig. 4 (in both cases Ust = 0.05 U λ 2 ).
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a
b
Fig. 4. Simulated trains: r = 1.03 (a) and 1.09 (b).
Experiment The experiments were performed using a flash-lamp pumped Nd:YAG laser (∅6.3×60 mm rod was used). A PC-controlled laser pumping based on the incomplete discharge of large capacity allowed us to vary pump duration
Fig. 5. Millisecond lamp pumped YAG-Nd laser designed for mcs scale pulsations. AM active laser medium; M1, M2 cavity mirrors; P polarizer; IA iris aperture; MT – mirror telescope; Pockels cell DKDP electrooptical crystal ; CC feedback control circuits.
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up to 3.9 milliseconds. Laser cavity was made by flat wedge-shaped reflectors of 0.98 and 0.35 reflection coefficient respectively. We introduced an intracavity mirror telescope 3:1 to enlarge a laser mode volume in the active media and thus to raise the laser output. Total cavity length was 150 cm. Iris aperture was used for mode selection. Two-pass Pockels cell was based on a multilayer polarizer (Brewster angle) and 8×8×11 mm3 DKDP a
b
Fig. 6. Traces for a lasing power (a) and a pump lamp running (b), discharge time is 3,9 ms obtained with C8-14 scope; time scale 0.5 ms/div.
(Uλ/2= 3.9 kV) crystal with antireflection faces placed close to the laser mirror. Crystal was installed directly on the control circuit plate. Static bias voltage Ust applied to the Pockels cell was varied in a range 0÷2 kV. A high voltage silicon mesa-structure was used as a control element of an optoelectronic system. Discharge time of intracavity Pockels cell ca pacity was set to 20 ns (2Tr). The control signal was taken from an intracavity Pockels cell polarizer (Fig. 5). Pin-diode and C8-14 storage (low resolution) and digital TDS-3052 (5 GS/s, 500 MHz) oscilloscopes were used for laser emission registration. Control voltage vs time was registered by using of specially made HF voltage divider and fast oscilloscope C7-19 (5 GHz frequency bond). Fine time structure of the laser light was investigated using streak-camera AGAT SF-3M (time resolution < 2 ps) synchronized with laser pulses with specially-made electronic delay system. Pumping pulse shape is shown in Fig. 6, b. Setting an optimal diameter of intracavity iris aperture we obtained a picosecond pulse train of stable amplitude with total number of pulses up to 350000 (Fig. 6, а). By varying Ust and fine angular DKPD crystal tuning we obtained modes of regular pulsations having periods 0.5, 1, 1.3, and 2 microseconds. The experiments showed that despite of significant control
Laser Physics Research Relevant to Laser-Electron X-Ray Generator Fine time structure, 50 ns/div.
gain increase
Pulsations, 2 mcs/div.
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Overview trace, 0.5 ms/div.
Fig. 7. The development of regular microsecond pulsations and a microgroup fine time structure in millisecond laser. Pulsation period is 200 round trips (2 mcs). The dynamics is shown in three time scales: millisecond, microsecond and nanosecond.
voltage and corresponding time-dependent Pockels cell transmission variation a single pulse is circulating in the laser cavity for all modes. An example of 2 microsecond period pulsation development is shown in Fig. 7. Millisecond oscilloscope traces (see Fig. 8) show that the peak pulsation power (feedback is on) is several times higher than a steady-state power level in free-running lasing (feedback is off, all other conditions being equal).
a
b
Fig. 8. Overview oscilloscope traces: a – feedback is switched off, b – feedback is switched on (time scale 0.5 ms/div). Vertical scales are equal.
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We are grateful to N. A. Borisevich, V. G. Tunkin and V. A. Petukhov for fruitful discussions and to A. M. Chekmarev for help in work. The work was partially supported by the Program of Fundamental Research of RAS, subprogram “Laser systems” and RFBR grant 05-02-17448a.
References 1. R. Toth, J.C. Kieffer, A. Krol, et al.: 'Phase contrast micro-CT with an ultrafast laser-based hard x-ray source', Proc. SPIE, p. 591813-1 – 591813-8, 2005. 2. P. Sprangle, A. Ting, E. Esarey, and A. Fisher: 'Tunable, short pulse hard xrays from a compact laser synchrotron source', J. Appl. Phys. 72, p. 5032, 1992. 3. A. Luccio and A.B. Brik: 'Methods and Apparatus for Producing X-rays', US Patent 4,598,415 July 1 1986, European Patent 0,05032 24.08.1988. 4. Z. Huang and R.D. Ruth: 'Laser-Electron Storage Ring', Rhys. Rev. Letters, Vol. 80, No. 5, p. 976, 1998. 5. R.J. Loewen: SLAC-R-632, June 2003, Ph.D. thesis, Stanford University, Stanford CA. 6. A. Agafonov, V. Androsov, J.I.M. Botman et al.: 'Status of Kharkov x-ray generator NESTOR', Proc. SPIE, 5917, p. 97, 2005. 7. F.E. Carroll: 'Tunable Monochromatic X Rays: A New Paradigm in Medicine', AJR 179, p. 583, 2002. 8. W.J. Brown, S.G. Anderson, S.P.J. Barty et al.: 'Experimental characterization of an ultrafast Thomson scattering x-ray source with three-dimensional time and frequency-domain analysis', Physical Review Special Topics – Accelerators and Beams, 7, 060702, p. 1, 2004. 9. K. Dobashi, A. Fukasawa, M. Uesaka et al.: 'Design of Compact Monochromatic Tunable Hard X-Ray Source Based on X-band Linac', Japanese Journal of Applied Physics, Vol. 44, No.4A, p. 1999, 2005. 10. T. Yanagida, T. Nakajyo, S. Ito et al.: 'Development of high-brightness hard x-ray source by Laser-Compton scattering', Proc. SPIE, Vol. 5918, p. 231, 2005. 11. M.V. Gorbunkov, V.G. Tunkin, E.G. Bessonov et al.: 'Proposal of a Compact Repetitive Dichromatic X-ray Generator with Millisecond Duty Cycle for Medical Applications', Proc. SPIE, 5919, OU1-OU6, 2005. 12. I.A. Artyukov, E.G. Bessonov, A.V. Vinogradov et al.: 'Laser-electron X-ray Generator', Preprint INP MSU 2006-7/806. 13. S. Schreiber, I. Will, D. Sertore et al.: 'Running experience with the laser system for the RF gun based injector at the TESLA Test Facility linac', Nuclear Instruments and Methods in Physics Research A 445, 427-431, 2000. 14. M.V. Gorbunkov, Yu.Ya. Maslova, A.M. Chekmarev et al.: 'Pulse generation of a large number of picosecond pulses microtrains in Nd:YAG laser controlled by negative feedback loop', Proc. of MIPT, Moscow, p. 50, 2005.
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15. M.V. Gorbunkov, A.V. Konyashkin, P.V. Kostryukov et al. 'Pulsed-diodepumped, all-solid-state, electro-optically controlled picosecond Nd:YAG lasers', RUS Quantum Electronics 35 (1), p.2, 2005. 16. I.M. Bayanov, V.M. Gordienko, M.G. Zvereva, S.A. Magnitski, A.P. Tarasevich. A High-Stable Negative-Feedback Picosecond YAG:Nd3+ Laser. RUS Quantum Electronics, 16 (8), p. 1545, 1989. 17. M.V. Gorbunkov, Yu.V. Shabalin: 'Two-Loop Feedback Controlled Laser: New Possibilities For Ultrashort Pulses Generation And High-Level Stabilization', Proc. SPIE, Vol. 4751, p. 463, 2002. 18. H.G. Schuster: Deterministic Chaos. An Introduction, Physik-Verlag, Weinheim, 1984. 19. V.K. Makukha, V.M. Semibalamut, V.S. Smirnov: 'Simulated Emission of Ultrashort Pulses from a Negative Feedback Laser', Sov. Quantum Electronics 4, No.5, p.1023-1027, 1977. 20. D.B. Vorchik, M.V. Gorbunkov: 'Self Mode-Locked Nd-YAG Laser Under Fast Delayed Negative Feedback by Means of High-Voltage Assemblies of Inversely-Shifted Silicon p-n Junctions', Physical Foundations of Electronic Laser Engineering, Proceedings of MIPT, Moscow, p. 4 - 11, 1995. 21. M.V. Gorbunkov, Yu.V. Shabalin: 'Picosecond YAG:Nd3+ Laser with SelfExcitation of HF Oscillations in Optoelectronic Negative Feedback System', Bulletin of the LPI 8, p.38-50, 1998
Laser Electron Generator of the X-Ray Radiation I. A. Artyukov, E. G. Bessonov, A. V. Vinogradov, M. V. Gorbunkov, Yu. Ya. Maslova, N. L. Popov, A. A. Postnov, Yu. A. Uspenski, R. M. Feshchenko and Yu.V. Shabalin P.N. Lebedev Physical Institute of RAS 19991 53 Leninski Pr, Moscow, Russia
Yu. L. Slovokhotov and Ya.V. Zubavichus Institute of elemental organic compounds of RAS, 119991 28 Vavilov st, Moscow, Russia
B.S. Ishanov, A.V. Poseryaev and V.I. Shvedunov Institute of Nuclear Physics of MSU
P. V. Kostrukov and V. G. Tunkin International Laser Center of MSU
Summary. The possibility of the creation and the application prospects of the laser-electron X-ray generator based on the Thompson scattering of the laser radiation on a bunch of relativistic electrons are considered. Such a generator fills the existing gap between X-ray tubes and synchrotron sources, which is several orders of magnitude in terms of the brightness, average intensity, size and also in the construction and exploitation costs. The layout of beam-lines and experimental stations intended for the applications of the X-ray laser-electron generator to the investigation of the elemental composition and material structure and biological objects is discussed.
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1 Introduction The development of the technologies connected to the generation and utilization of the X-ray radiation is an important part of the scientific and technical progress in lots of fields of the industry including metallurgy, chemical and pharmaceutical industry and also in such areas of the human experience as medicine, whole agricultural and food trade, ecological monitoring, social security, work of the custom and boarder terminals etc. For the introduction of many scientific developments in areas the investigators need constant access to X-ray sources. The modern generators of X-radiation can be divided into two main classes. X-ray tubes (with a fixed or rotating anode) and boosters of electrons: synchrotrons and storage rings. The X-ray tubes are used in overwhelming majority of production devices and apparatuses. The tubes with a fixed anode are reliable enough, compact, and simple to service and rather inexpensive - from hundreds up to several thousand dollars. The modern tubes with a rotated anode give in 10-100 times higher emission power, however they cost tens and hundred thousand dollars and is much more complex in exploitation. Common faults of this class of X-ray sources are absence of directivity of X-ray radiation, broad and, at a given material of the anode practically not variable spectrum, rather a small emission power and impossibility of generating bright monochromatic xray radiation. As compared to X-ray tubes, synchrotron accelerators and the storage rings are large power-intensive research installations with a closed path of the electron beam of tens and hundreds meters length. All over the world there are about hundred accelerators intended for deriving of X-ray synchrotron radiation (SR). This radiation has high luminosity, directedness and wide spectrum, with possibility of obtaining tunable monochromatic radiation. However size and cost - tens and hundred millions USD – of the modern synchrotron sources seriously restrict their applications, which do not satisfy the needs of the science and practice. Thus, now there is objective need for a new source of X-rays, which would fill in the gap existing between X-ray tubes and synchrotron centers. An X-ray source adequate to the formulated requirements, can be built on the basis of complex systems, which combine a compact high-current electron accelerator and laser emitting intensive light pulses. X-rays are in this case generated at head on collision of electronic and laser bunches; in other words, the photons of high energies bear as a result of diversion of the electron beam from the linear trajectory in the field of an intensive light wave. The relevant elementary process is well investigated and wears a title Thomson or Compton scattering (depending on quantity of parameter
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EħωL/(mc2)2, determining the size of the quantum contributions, E - energy of an electron, ħωL - energy of the laser photon). From the end of 70th years of XX century the Compton scattering on bunches of relativistic electrons serves as an effective method of deriving γ - photons (down to energies ~ 2 GeV), used in photonuclear reactions. However in generation of photons of lower energies (~ 10 - 100 keV), which have the greatest interest for the applications, the X-ray tubes and synchrotron radiation until recently remained beyond the competition. Now new active solid-state mediums using pumping by laser diodes, diode bars and matrixes, allow to generate and enhance trains of picosecond light pulses in compact devices and with a high efficiency. On the other hand, the modern electron accelerators allow to generate bunches with high luminosity, which can be focused in a spot with the size about 10 microns, and the modern accelerating structures can supply rate of acceleration up to 50 MeV/m, that allows to build installations of the small sizes. The integration of lasers and accelerators in one device enables to create rather a cheap compact source of intensive X-rays for the scientific and applied purposes.
2 Thompson scattering by relativistic electrons The research on deriving gamma and X-rays by the scattering of laser pulses on relativistic electrons has been carried on for more than 40 years [1-7]. In this section we shall give an estimate of intensity and luminosity of the laser-electronic generator and compare it by the last parameter to Xray tubes and sources of SR. For the electrons with energies Ee = γmc2 ~ 25 – 50 MeV and laser photons ħωL ≤ 2 eV, which provide X-ray generation in the range 5-50 kev interesting for us, the inequality holds:
2γ hω L 99.9% t T = 2 μs τ
< 40 ps
R>99.9% Pockels cell 1
P 1 R>99.9% Pockels cell 2
T c = 10 ns
1 ms
40eV
Wp
N 0 g0
)3
N 2 g2
A21 N 1 g1 Wg
Fig. 2. Simplified 4 level scheme
37.2 nm -
e -collisions
5
2p 3s
2
3
P
3
P1 Na +
1
2p6 1 S0
0
2p 6 3s
Na
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Rate equations dN 0 dt
= − N 0W p (t ) − N 0W g (t ) − N 0 N el C
dN el dt
= N 0W p (t ) + N 0Wg (t ) + N 0 N el C
dN1 dt
= N 0Wg (t ) + N 2 A21 + N 0 N el C
dN 2 dt
= 14 N 0W p (t ) − N 2 A21
dN 3 dt
= 34 N 0W p (t )
In these 5 equations, N0 is the density of sodium atoms in the ground state (2p63s), N1 and N2 are the population densities of the lower (2p6 1S0) and upper (2p53s 1P1) laser levels and N3 is the population density of the 2p53s 3 P level manifold, which however does not contribute to the laser process itself. Wp describes the total pump rate to the excited 2p53s states of the sodium ion and Wg the corresponding pump rate for the lower laser level (sodium ion ground state). According to the level degeneracies, only ¼ of the pump rate Wp is used for the upper laser level. The pump rates Wp,g are given by Wp,g = Ip/hνp* σp,g, where Ip is the intensity of the x-ray pump laser (hνp: photon energy) and σp.g are the photoionization cross sections for extraction of an inner p-electron, leading to the population of the upper laser level, and of an outer s-electron, leading to the population of the Na+ ground state. According to Fig. 1 and the data of Ref. 3, σp is about 8 Mb at the pump wavelength of 21.2 nm and σg is about a factor of 200 smaller. With the ionization of sodium atoms electrons are produced, which may then populate ionic levels by collisional excitation of sodium atoms. Of special importance thereby is the population of the lower laser level, leading to a reduction of the population inversion. This population of the lower laser level is described by the rate NelC, where Nel is the electron density. The collisional coupling rate C is estimated as 10-7 cm3/s (Ref. 7). From the equations, the inversion density ΔN = N2 – g2/g1*N1 can be calculated, where g2 and g1 are the degeneracy factors of the levels, with g2= 3 and g1 =1. With the inversion ΔN the gain coefficient g is then given as g = σstim*ΔN, with the stimulated emission cross section σstim. Assuming a Doppler broadened linewidth at a temperature of about 400 oC and a lifetime τ of the upper laser level of 400 ps (A21 = 2.5x109 s-1), σstim amounts to 5x10-14 cm-2. At a temperature of 400 oC the sodium density is about 1016 cm-3. For numerical calculations of the gain, the intensity, duration (pulse shape) and spatial change of the pump pulse (depending on the focussing) have to be chosen. Also the starting density N0 may change in pump beam
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direction and perpendicular to it, which depends on the used sodium oven. In the following, calculations of the inversion density and gain coefficient for specific scenarios (assuming constant intensity and density) will be presented and discussed. Assuming pulses with a sech2 pulse form and different peak intensities, a pulse duration (FWHM) of 100 ps and a starting sodium density of 1016 cm-3, the time development of the relative inversion density ΔN/N0 shown in Fig.3 is obtained. Population inversion is achieved in a certain time window, first at an intensity of about 109 Wcm-2 just around the maximum of the pulse. With increasing intensity this window shifts to earlier times and the inversion density finally saturates due to the depletion of the sodium density N0. The inversion density at the maximum intensity of 1013 Wcm-2 corresponds to a gain coefficient of about 28 cm-1.
Fig. 3. Time behaviour of the relative inversion density ΔN/N0 in units of τ (1/A21 = 400 ps)
To achieve a larger gain for the given density of 1016 cm-3, pulses with shorter pulse duration have to be used, as can be seen from Fig.4. For a pulse duration of 50 ps a gain coefficient of 65 cm-1 can already be obtained at a pump intensity of 5x1011 Wcm-2. To reduce the saturation at higher pump intensities, which is due to the depletion of the sodium density, the initial particle density has to be increased further, as can be seen from Fig. 5. For a given pump intensity and pulse duration an optimum density exists, which for the 50 ps pulse duration and intensity of 5x1011 Wcm-2 is around 2.5x1016 cm-3, leading to a gain coefficient of more than 100 cm-1
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Fig. 4. Gain versus pump intensity for different pulse durations (sech2 pulse) at a sodium density of 1016cm-3
Fig. 5. Gain versus sodium density for different pulse durations (sech2 pulse) at an intensity of 5x1011Wcm-2
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3 Planned experiment In the planned experiment, the x-ray laser radiation will be focussed with an off axis paraboloid into the sodium vapour which is generated in an
Fig. 6: Time dependent gain (in unit of τ = 400 ps) for the measured Zn-x-ray laser pulses (pulses superimposed at maximum intensity)
oven. The vapour streams out of a nozzle head, which has 800 µm holes on both sides and a length which can be varied between 5-15 mm. The oven is located in a vacuum chamber, which can be attached to the target chamber of the x-ray laser. The x-ray laser delivers pulses with energies between 1 mJ - 10 mJ and pulse durations of 150ps (single pass) and 250 ps (double pass) (Fig.6), with the larger energies for the double pass geometry. Assuming a pulse energy at the sodium target of 0.25 mJ/1 mJ for the 150 ps/250 ps pulses and a focus radius of 50 μm, the 150 ps/250 ps pulses deliver peak intensities of 0.75x1011cm-2 and 2.2x1011Wcm-2. For a sodium density of 1016 cm-3 these pulses then yield maximum gain coefficients of 52 cm-1 and 62 cm-1 (Fig.6). The large gain is due to the steep raising of the pulses and comparable to the gain for a 75 ps sech2 pulse (Fig.4). For interaction lengths of about 5mm-10mm and assuming constant pump intensity, saturated amplification should be possible.
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4 Conclusions The presented calculations yield high gain in a wide parameter range. Planned more detailed calculations will include changes of the pump intensity within the vapour due to the focussing and absorption, and also changes of the vapour density especially at the nozzle exit. These effects may slightly reduce the gain. But as the x-ray laser data are assumed conservative and further improvements expected, good chances for realization of the innershell x-ray laser in sodium exist.
References 1. 2. 3. 4. 5. 6. 7.
M.A. Duguay and P.M. Rentzipis; Appl. Phys. Lett. 10,350 (1967) W.T. Silfvast and O.R. Wood II; J. Opt. Soc. Am. B4, 609 (1987) J.J. Yeh and I. Lindau; Atomic Data and Nuclear Data Tables 32, 1 (1985) S. Meyer et al.; Inst. Phys. Conf. Ser. No 151, 173 (1996) S. Meyer et al.; Inst. Phys. Conf. Ser. No 159, 313 (1998) B. Rus et al.; Phys. Rev. A 66, 063806 – 12 (2002) W. Lotz; Z. Physik 216, 241 (1968)
310 Angstroms X-Ray Lasing Under Beta-Decay of Tritium M. Yu. Romanovsky1 and V. K. Bityukov2 1 2
A.M.Prokhorov General Physics Institute of RAS Moscow State Institute for Radiotechnics, Electronics, and Automatics
Summary. The beta-decay of atomic tritium produces the ion 3He+ at the first exited state 2s with the probability of 25%. This state can irradiate two photons (two-photon lifetime is about 0.01 ms) or one photon (the lifetime is 173 s). The stimulated emission of one-photon may depress the two-photon decay. This is a soft X-ray laser with the wavelength 310 angstroms (40.8 eV). The first problem of two-photon decay depression is solved by largereflectivity mirrors for 310 A. The periodic array of non-dispersive, periodically positioned, quasi-dielectric cylinders in vacuum oriented along the axis of X-ray emission has narrow-band reflection of about 100% for wavelength closed to the distance between dielectric cylinders. Such array with quasi-dielectric cylinders periodically located at about 300 angstroms chess table can be realized by forthcoming lithography methods. Two such mirrors shape the proper resonator for generated emission and form good divergency of (coherent) X-ray beam. The second problem of 310 A radiation absorption by tritium atoms in bounded-free electron transitions may be solved by application of (strong) permanent magnetic field to the tritium sample. The magnetic field produces the spectrum of permitted free electron energy in one direction (of X-ray propagation). While the energy of possible free electron 27.2 eV is out of this spectrum, the bounded-free transition is forbidden, and the absorption of stimulated emission is depressed by several orders and becomes negligible small. The theoretical limit of X-ray continuous laser power is 0.15 mW per cubic cm of liquid atomic tritium. The required magnetic field is about 300 kGs.
1 Introduction: irradiation of tritium under the beta-decay. The beta-decay of any nucleus provides the nucleus with the additive charge +e. After the small time of the beta-decay (it is about the flight time of decayed electron through the atom), the electron system of the atom becomes in a non-stationary state. All electrons have some additional energy with respect to new stationary states. The deepest K- and L- electrons have the energy
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E
− K ,L
Z 2e2 = 2rB (n − δ − ) 2
before the beta-decay, and the energy
E
+ K ,L
( Z + 1) 2 e 2 = 2rB ( n − δ + ) 2
after the beta-decay, where Ze is the charge of initial parent nucleus, n is the principal quantum number (n = 1 for K-electrons and n = 2 for Lelectrons), rB is the Bohr radius, δ- and δ+ are quantum defects of atomic states of initial and product nuclei. To obtain a population inversion, the L states of the product nuclei should have less energy that K state of the parent one. It means that
( Z + 1) 2 e 2 Z 2e2 ΔE = E − E = − + ≤0 2rB (2 − δ + ) 2 2rB (1 − δ − ) 2 + L
− K
Since δ- ~ δ+ ~ δ < 1, this inequality does not fulfill for any pair of nuclei, taken place in beta-decay, except one. Auger-processes start in any nuclei (except one) immediately after the beta-decay [1], and normally do not accompany by any X-rays since the effective “width” of state in an atom with product nucleus (of “product” ion) is very large. There is one atom where radiation processes permitted not only by energy, but due to the fact the electron in a product atom appears in some stationary state. This is atomic tritium. The product ion is 3He+ is produced by beta-decay of tritium. Indeed, the energy of the ground state of tritium (Z = 1, δ- = δ+ = 0) E1T = - e2/2rB while the energy of the first excited state of + 2 2 2 3He (Z = 2, n = 2) ion is E2He = - 2 ·e /2rB·2 = E1T. The probability to appear at this state is about 25% [2]. The process is fast due to the absence of large transformation of a wave-function. At the same time, there are no mechanisms of an energy transfer for transitions to the ground state (the probability is about 70%, see, for example, [2]) as well as to other excited states (total probability 5%). It means, looks, that these lasts transitions occur while some body (nearest atom) collides with the decayed tritium (3He+ ion) and rates of these transitions are (very) slow. Thus, there is a long-life temporal population inversion on the transition 2s – 1s in 3He+ ion. Indeed, the beta-decay of atomic tritium leads to an appearance of the part (denote this part as α) of ions 3He+ at the meta-stable state 2s. There
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are 3 possible decays of this state: two-photon decay to 1s state, and the cascade transition to 1s state via Lamb transition to 2p state. The last process is very slow and can be neglected. The third possible decay is the forbidden one-photon M1 transition to 1s state (the electro-dipole and electroquadropole transitions are forbidden) [3]. Thus the radiation of tritium can be calculated easily. The two-photon component is very wide: from zeros for 0 eV and 40.8 eV quanta energy to the maximum of quanta with the 20.4 eV energy. The one-photon component with quanta energy 40.8 eV (wavelength λ = 310 A) is narrow (its natural width is about 19 orders less than the width of the two-photon component), but the maximum is 12 orders larger (the total ratio of 7 orders is the ratio of lifetimes of one-photon transition τ1 ~ 175 s and twophoton transition τ2 ~ 0.92·10-5 s). The spectrum of tritium radiation (it is, in fact, the radiation spectrum of an ion 3He+) is presented on Fig.1. The total rate of tritium emission under the beta-decay (the radiation of ions 3He+) is
v = αΛ -9
where Λ = ln2/T= 1.78·10 s, T is the period of tritium half-decay. The rate of two-component decay is
v2 = αΛ
τ1 ≈v τ1 + τ 2
while the rate of one-photon decay is τ2/τ1 ~ 0.5·10-7 times less.
Fig. 1. The radiation spectrum of tritium under the beta-decay in arbitrary units: the radiation spectrum of an ion 3He+. The width of one-photon radiation is 19 orders less than the width of two-photon radiation (the scale along X-axis is not kept).
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The total power of quantum radiation of ℏ ω1 = 40.8 eV is
P1 = αΛhω1 N 0
τ2 τ1
where N0 is the total number of (tritium) atoms. The one cubic cm of liquid atomic tritium (N0 = 5·1022) irradiates P1 ~ 3α·10-11 W spontaneously, the total power of this two-photon is about one mW. Note that the total power of beta-decay of atomic tritium is
Pβ = ΛN 0
Emax
∫ f ( E )dE 0
where f(E) is the energy spectrum of decayed electrons. The value Pβ ~ 0.15 W for one cubic cm of liquid atomic tritium, i.e. Pβ is two orders larger than the total radiation power. The radiation of tritium is isotropic. To create X-ray laser with the beta-decayed tritium as active medium, several problems have to be solved. The first problem is to get atomic tritium with high enough density. It is in most technical. The second problem is to depress two-photon radiation. It is solved through a creation of conditions for one-photon stimulated radiation with the wavelength λ = 310 A. Such conditions achieve due to good reflectivity resonator (high reflectivity mirrors) for λ = 310 A. This problem is solved [4]. At least, losses of stimulated one-photon radiation (per one pass of resonator) should be less than the gain (per one pass of resonator), i.e. these losses should be depressed specially.
2 High-reflectivity mirrors for λ = 310 A. The first problem of two-photon decay depression is solved by largereflectivity mirrors for 310 A. The periodic array of non-dispersive, periodically positioned, dielectric cylinders in vacuum oriented along the axis of X-ray emission has narrow-band reflection of 100% for wavelength closed to the distance between dielectric cylinders [4]. Such array with dielectric cylinders periodically located at about 300 angstroms chess table can be realized by usual lithography methods. Two such mirrors shape the proper resonator for generated emission and form good divergency of (coherent) X-ray beam.
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In Fig. 2, the reflection coefficient is shown as a function of the wavelength expressed in units of array step Dg. The solid-blue and dashed-red curves correspond, respectively, to dielectric constants ε = 2 and ε = 4. As one can see the array becomes a perfect reflector within a fairly narrow wavelength range centered at the resonant wavelength that is slightly larger than the period Dg. Similar results have been obtained for dielectric grating structures. The resonant pattern is associated with the so-called Wood anomalies [5], and can be explained by the existence of trapped modes or guided wave resonances [6].
Fig. 2. Calculated zero-order reflection coefficient for a periodic array of dielectric cylinders in vacuum described in the text. Results are presented as a function of the wavelength of the incident radiation measured in units of the period Dg. The solid blue and dashed red curves correspond, respectively, to the array of cylinders with dielectric constants ε = 2 and ε = 4.
Of course, all medium (of cylinders) can not be considered as dielectrics for X-ray radiation: such radiation excites currents in cylinders (heads). Nevertheless, the volume of such currents is very small due to the cylinders radius, and losses may be considered as negligibly small. Indeed, the cylinders mirror can be compared with the metal grating mirror [4]. The reflection coefficient from “dense” silver grating is about 85% with zero transmission (losses are about 15%) while the grating holes square is about 3%. The square of cylinders head is about 0.7%, therefore total losses are much less than 1%, which is quite enough for the proposed X-ray laser. The good (theoretically, very closed to one) reflectivity for λ = 310 A plays the role in a solutions of damp losses. As well, this perfect reflectiv-
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ity leads to the stimulated emission of λ = 310 A with a sharp space diagram and to the depression of two-photon radiation. Thus, the periodic array of non-dispersive, periodically positioned, dielectric cylinders in vacuum oriented along the axis of X-ray emission solves two problem of Xray laser by tritium: the depression of two-photon radiation (all energy will be forwarded to the one-photon stimulated emission) and increase of final power output of X-ray laser. Moreover, the sharp space diagram of stimulated emission permits to solve the problem of radiation losses.
3 Damping of radiation losses inside an active medium. The third problem of 310 A stimulated emission is the (large) radiation absorption. There are two types of absorption: by bounded electron transitions in 3He+ ions which transited to ground state, and by bounded-free electron transitions in by tritium atoms. Since the concentration of 3He+ ions is small, this type ob absorption can be neglected. The absorption of 40.8 eV quanta radiation in tritium is much more larger. The cross-section of this process can be estimated by well-known Kramers formula 3
σ vn = 7.9 × 10 −18
n ⎛ ωn ⎞ ⎜ ⎟ cm 2 2 Z ⎝ω ⎠
where ωn is the minimal frequency needed for an ionization of hydrogen atom from the n state. For tritium Z = 1, n = 1, and σ1n = 2.9·10-19 cm2. The bound-free absorption coefficient in tritium is proportional to the density, and for liquid tritium (density n0 = 5·1022 cm-3) is equal 14600 cm-1. Even for moderate (gaseous) tritium n ~ 1019 cm-3, this absorption coefficient remains large enough to prevent any stimulated emission (the gain is not so large). How to solve this problem? It is necessary to transform the spectrum of free electrons, appeared due to an absorption of stimulated radiation with λ = 310 A. This spectrum should have the forbidden energy band near the 27.2 eV. It is impossible to realize uniformly in space, but possible for free electrons propagated in the definite direction. Indeed, the magnetic field produces the discrete spectrum of particles, moving at the direction perpendicular to the field direction. Classical motion of charged particles in this case goes along circles, radiuses of these circles depend on particles energy continuously. Quantum effect is the change of the continuous radi-
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uses spectrum (in one direction!) to a linear spectrum. The differences between two nearest values of possible energy ΔE is
ΔE =
ehH = hωL mc
where H is an amplitude of (permanent) magnetic field, e is an electron charge, m is an electron mass, ωL is the Larmor frequency (see, for example, [7]. This energy difference should be larger than the energy difference of stimulated emission arises by line broadening ℏ Δω, i.e.
ωL > Δω If the permanent magnetic field provides this inequality, the energy value of 27.2 eV becomes forbidden for free electrons, moving along the axis of stimulated radiation. Since only these electrons can absorb quanta of stimulated radiation due to the momentum conservation law, the absorption coefficient along the X-ray axis becomes depressed strongly. Experimentally, this fine depression can be achieved by tuning of the magnetic field amplitude.
4 Estimates. Since the total radiation of tritium under the beta-decay in good resonator goes at the wavelength of 310 A, the output power of stimulated emission may reach the value
P1s = αΛhω1 N 0 Thus the theoretical limit of X-ray continuous laser power is 0.15 mW per cubic cm of liquid atomic tritium, α = 0.25. Of course, an experimental preparation of liquid atomic tritium is doubt: atomic tritium with gas densities is much more achievable. The gas atomic tritium has to be prepared specially. The gas with room temperature and normal pressure, the expected output laser power is about 0.1 μW per cubic cm. The broadening of 310 A X-ray laser radiation in above normal gas conditions has the non-uniform character (collision broadening is small). The recoil linewidth ΔωR ≈ 4·1012 s-1, the Doppler linewidth ΔωD ≈ 0.4·1012
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s-1, thus the total non-uniform linewidth Δω = ΔωR + ΔωD ≈ 4.4·1012 sThis limits the magnetic field above the value
1
H > mcΔω / e
or, for normal gas atomic tritium, H > 2.2·105 CGS. Such magnetic field can support the existence of tritium in form of atomic gas.
Fig. 3. The possible experimental scheme of atomic tritium X-ray laser. The gaseous atomic tritium is contained in the tube. Cylinder array mirrors are located in vacuum near the side windows of the tube.
The possible experimental scheme of 310 A X-ray laser based on the beta-decay of atomic tritium can be the following (Fig.3). The tritium tube can have the volume up to 102 – 103 cm3, therefore the expected X-ray laser power output may be up to 1 mW while α = 0.25. Thus, the combination of three devices: the tube with gaseous atomic tritium, high reflectivity mirrors (cylinders array), and strong magnetic field may provide X-ray lasing of λ = 310 A with output power up to 1 mW.
References 1. K.Siegbahn. Beta-and Gamma-rays Spectroscopy. Amsterdam (1955). 2. P.V.Elyutin, V.D.Krivchenkov. Quantum mechanics. Moscow: Science (1976) [in Russian]. 3. Berestetskii V. B., Landau L. D., Lifshitz E.M., Pitaevskii L. P. Quantum Electrodynamics. Oxford, UK: Pergamon Press (1982). 4. A.G.Borisov, S.V.Shabanov. J. Comp.Phys., 209, 643 (2005). 5. R.W. Wood, Phys. Rev. 48, 928 (1935) 6. R. Magnusson and S.S. Wang, Appl. Phys. Lett. 61, 1022 (1992);
310 Angstroms X-Ray Lasing Under Beta-Decay of Tritium 7. 8. 9. 10. 11.
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S. Peng, G.M. Morris, Opt. Lett. 21, 549 (1996); T. Peter, R. Br¨auer, O. Bryngdahl, Optics Communications 139, 177 (1997); K. Koshino, Phys. Rev. B 67, 165213 (2003); L. Pilozzi, A. D’Andera, R. Del Sole, Phys. Rev. B 54, 10763 (1996). L.D.Landau, E.M.Lifshitz. Quantum mechanics: non-relativistic theory. 3rd ed., Oxford, UK: Pergamon Press (1991).
Capillary Discharge Soft X-Ray Laser at University of L’Aquila: Laboratory Survey A. Ritucci, G. Tomassetti, A. Reale and P. Zuppella Physics Department of University of L’Aquila, gc LNGS-INFN, via Vetoio 67010 Coppito L’Aquila, Italy
Summary. We report on different experimental investigations regarding the use of the 0.3 mJ, 0.3 Hz, 1.7 ns, 46.9 nm Ar laser developed at the University of L’Aquila. Firstly, we have investigated the potentiality of the EUV laser in the ablation of hard dielectrics such as CaF2 and LiF crystals, which are largely transparent to the visible and to the ultraviolet laser light. We determined the ablation thresholds and the ablation rates for these two crystals and compared the results with the values obtained with other kinds of visible-ultraviolet laser systems. Secondly, we investigated a method to manipulate the intense soft X-ray laser beam based on the use of hollow waveguides. We used monocapillary tubes in a multireflection regime to achieve a substantial modification of the intensity distribution of the beam. These results can be of great interest for several applications of these soft X-ray laser sources.
1 Introduction Among the variety of soft X-ray lasers, which are recently under fast development in several laboratories worldwide, the capillary discharge soft X-ray Ar laser operating at 46.9 nm remains, to now, the most reliable one [1-2]. This laser is the most suitable for a large number of laboratory investigations for its simplicity of use, its compactness and the relatively large output energy per pulse. Many of such investigations may be of relevance in the field of applied science and the basic physics [3-4]. Moreover they can represent a valuable starting point in view of the applications of the new, high rep-rate, tabletop EUV lasers in laser-produced-plasmas having shorter wavelengths and smaller pulse durations [5]. The aim of this paper is to report some experimental investigations, which have been performed by the use of the 46.9 nm Ar laser, recently developed at the University of L’Aquila [2]. The laser under consideration operates at the reprate of 0.3 Hz, with 0.3 mJ/pulse and 1.7 ns pulse duration.
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2 EUV Laser Ablation Today, laser ablation has a significant role in the field of applied science for the processing of different kinds of materials and/or for their characterization. From the general point of view, laser ablation depends on different experimental parameters such as the pulse laser energy and duration, the energy fluence and strongly on the penetration depth of the laser light through the material. In this work we have focused our attention to hard dielectrics, such as CaF2, LiF, BaF2 or SiO2, which have relevant interest for several applications such as for miniaturized optical devices. These crystals are characterized by very large band gap (e.g. Eg ≈12.0, 13.6-14.5 or 9.1 eV for CaF2, LiF and BaF2 respectively [6]), so that they are largely transparent from the infrared up to the vacuum ultraviolet (where hν <Eg). In order to improve the ablation quality, several experimental investigations on these materials have been typically performed employing ns vacuum ultraviolet excimer lasers (see for example refs. [7] and references therein) or ultra-intense optical picosecond- and femtosecond-laser pulses [7]. As a larger absorption of the radiation by the material generally leads to an improved quality of the ablated region, significant improvement should be expected by the use an EUV laser. Another considerable advantage in the use of the EUV is the high spatial resolution of the processing. In fact, using a corrected optical system one can expect an ablation spot diameter lower than 1-2 µm [8]. In this section we present a description of the laser ablation of CaF2 and LiF crystals by focusing our 46.9 nm, 1.7 ns Ar laser and analyzed the ablated surfaces using Scanning Electron Microscopy (SEM) and a vertical profilometer. We experimentally determined the etch rates of these crystals and the ablation thresholds and compared the assessed values with those found in literature using lasers with a longer wavelength. 2.1 Experimental setup The irradiations were performed by focusing the laser on the samples by a 12 cm-focal-length spherical Ir mirror, located 2 m far from the capillary output with an incidence angle of 5° (reflectivity ~15%) (see, fig. 1). The fluence was varied by changing the position of the sample along the optical axis of the mirror. The simplicity of this focusing system had several limitations due to the strong optical aberrations of the beam spot on the target. The coma due to the 5° incidence angle produced an elongated shape of the beam, an irregular illumination of the sample and a non-planar wavefront of the radiation. The spherical aberration limited the beam fo-
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cusability to only a few tens of micrometers. Moreover, it should be noticed that by moving the sample along the optical axis of the mirror, we have changed not only the fluence, but also the curvature of the wavefront. This last effect was neglected because of the small numerical aperture (NA=0.05) of the focusing mirror. The values of the fluence were determined by measuring the beam energy and the area of ablated craters with an estimated accuracy of about 20%.
Fig. 1. Scheme of the experimental setup used for the laser ablation and an AFM image of a typical ablated structure.
Despite the poor focusing resolution, we reached a maximum laser fluence of 3 J/cm2, which is well above the ablation thresholds. In these measurements, we operated in a multi-shot irradiation mode using 25 shots for each ablation. The CaF2 samples consisted of 2-mm thick plates optically polished on both sides, while the LiF samples consisted of 1-mm thick plates polished on one side. The samples were placed in an evacuated environment at the pressure of 10-4 Torr. The ablation was studied analyzing the craters produced on the surfaces through a vertical profilometer (TENCOR) and an Atomic Force Microscope (AFM). Scanning Electron Microscopy (SEM) was used as a complementary experimental technique, for the inspection of the ablated surface. 2.2 Results and discussion The behavior of the ablation rates versus the fluence is shown in figs. 2 and 3 for LiF and CaF2, rispectively. The experimental points have a threshold behavior for both materials, which can be fitted by the standard expression [9]: L = d·ln(F/Fth), where L is the ablation rate, F and Fth are the irradiation fluence and the fluence threshold respectively, and d is a
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Fig. 2 Experimental (points) ablation rate vs the fluence for LiF. The line is a theoretical fitting.
Fig. 3 Experimental (points) ablation rate vs the fluence for LiF. The line is a theoretical fitting.
characteristic ablation depth, related to the effective absorption length of the radiation in the material. The results of figs. 2-3 present several interesting aspects. Firstly, we find very low ablation thresholds: 0.11 J/cm2 for LiF and 0.06 J/cm2 for CaF2, while with the nanosecond 248 nm laser beam the typical values are in the range of 20-40 J/cm [10]. Secondly, the best fit of the experimental data provides for d the values of 20 and 14 nm for LiF and CaF2, respectively. These values, which are in agreement with the optical penetration depths (α-1 ~14 nm and ~10 nm) assessed for λ = 46.9 nm from Ref. [11], are about five orders of magnitude smaller than in the deep UV. This is due to the large photon energy (hν = 26.4 eV) of our laser, which can induce efficient excitations of electrons from the valence band into the vacuum level of the crystal. This strong interaction introduces new ablation conditions for these large band gap dielectrics, which could be of significant interest for the fine processing of these materials. The topography of the ablated areas depends strongly on the laser fluence. At the lower fluence, the inhomogeneous distribution of the laser intensity produces an inhomogeneous heating of the surface and an irregular profile of the crater. By contrast, at values >1 J/cm2, the fluence is sufficiently high to produce evaporation of material over the whole beam cross section. The ablated crater has, in this case, a conical shape with regular vertical profile and deepness >1-1.5 µm. The analysis performed at the AFM (Fig. 1) for the large fluence confirms the regularity and the deepness of the ablated region. This behavior in the vertical profile of the craters is found both in the case of LiF and CaF2. Figures 4 (a) – (b) show the SEM images of LiF irradiated with the fluence of 0.8 J/cm2 (a) and 3 J/ cm2 ((b). Irregular reliefs on the ablated region can be reasonably attributed to the irregular distribution of the laser fluence due to the diffraction of the beam and not to liquid waves formed by the melting of the surface. This analysis shows also that the ablation processes at 46.9 nm is accompanied by the formation of micro-sized cracks inside the irradiated area.
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These cracks are due to the strong thermoelastic stress on the surface and to the brittleness of the materials. An interesting behavior is that the cracks are observed already very close to
Fig. 4 SEM image of an ablated region of LiF with fluence of (a) 0.8 J/cm2 and (b) 3 J/cm2.
6 µm
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Fig. 5 Ablated spot on LiF with fluence > 3 J/cm2 and using an improved optical configuration.
the ablation threshold at very low irradiation fluences and increase with the number of pulses. These cracks stand along preferential directions, which should correspond to the cleavage planes of the crystal. The higher density of short microcracks at the periphery (see Fig. 4 (a)-(b)) of the craters can be attributed to the different thermoelastic forces acting inside and at the edge of the laser spot. As the fluence is increased from the threshold, the evaporation of material is more efficient, cracks become less evident and a cleaner condition of ablation is found. Fractures on CaF2 samples are typically less evident and of smaller dimensions. They present irregular shape homogeneously distributed through the irradiated area. Approaching 3
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J/cm2, the mechanical stress of the surface becomes so large (see fig. 5) to detach away from the surface macroscopic pieces of material and the quality of ablation is lost. The presence of cracks even close to the ablation threshold is in contrast to what is generally expected by the shortening of the laser wavelength and suggests the necessity for the modeling and a better understanding of the ablation processes induced by EUV and soft Xrays. Concerning the resolution fig. 5 show an ablated spot obtained at a large fluence (>3 J/cm2) using an improved focusing system. The central hole has diameter of only 6 µm. The fluence in this case is so large to destroy substantially the crystal in proximity of the hole.
3 Capillary waveguides in the EUV Soft X-ray lasers are generally obtained without any optical cavity by the single pass amplification of a lasing line through elongated hot plasma columns. Unfortunately, the amplifying plasmas are often characterized by large density gradients where the laser emission can experience large refraction effects. As a consequence, the intensity distribution of a soft X-ray laser can have unusual and not uniform profiles, which are quite difficult to control. As an example, our laser is characterized by an annular shape with the divergence of 4.5 mrad. This beam profile may be inconvenient for several kinds of applications. The need for the manipulation of the beam of such a kind of coherent soft X-ray radiation pushes the need for testing different kinds of optical elements. In this section we have investigated the possibility to use hollow glass capillary waveguides to modify the intensity distribution of the soft X-ray laser beam. The soft X-ray propagation in different kinds of capillary optics (both in the form of mono- and poli-capillary structures) has been well studied for several years and it has been successfully employed on different kind of sources: synchrotrons, incoherent plasma sources (laser plasmas and z-pinches) and x-ray tubes (see for example refs. [12-13]) at wavelengths typically
