ɆɂɇɂɋɌȿɊɋɌȼɈ ɈȻɊȺɁɈȼȺɇɂə ɊɈɋɋɂɃɋɄɈɃ ɎȿȾȿɊȺɐɂɂ ɆɈɋɄɈȼɋɄɂɃ ȽɈɋɍȾȺɊɋɌȼȿɇɇɕɃ ɂɇɀȿɇȿɊɇɈ-ɎɂɁɂɑȿɋɄɂɃ ɂɇɋɌɂɌɍɌ (ɌȿɏɇɂɑȿɋɄɂɃ ɍɇɂȼ...
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ɆɂɇɂɋɌȿɊɋɌȼɈ ɈȻɊȺɁɈȼȺɇɂə ɊɈɋɋɂɃɋɄɈɃ ɎȿȾȿɊȺɐɂɂ ɆɈɋɄɈȼɋɄɂɃ ȽɈɋɍȾȺɊɋɌȼȿɇɇɕɃ ɂɇɀȿɇȿɊɇɈ-ɎɂɁɂɑȿɋɄɂɃ ɂɇɋɌɂɌɍɌ (ɌȿɏɇɂɑȿɋɄɂɃ ɍɇɂȼȿɊɋɂɌȿɌ)
ɋ.Ʉ. ɀɞɚɧɨɜ ȼ.Ⱥ. Ʉɭɪɧɚɟɜ Ɇ.Ʉ. Ɋɨɦɚɧɨɜɫɤɢɣ ɂ.ȼ. ɐɜɟɬɤɨɜ
ɈɋɇɈȼɕ ɎɂɁɂɑȿɋɄɂɏ ɉɊɈɐȿɋɋɈȼ ȼ ɉɅȺɁɆȿ ɂ ɉɅȺɁɆȿɇɇɕɏ ɍɋɌȺɇɈȼɄȺɏ
ɍɑȿȻɇɈȿ ɉɈɋɈȻɂȿ
Ɇɨɫɤɜɚ 2000
ɍȾɄ 533.9 (075) ȻȻɄ 22.333 ɀ42
ɀɞɚɧɨɜ ɋ.Ʉ., Ʉɭɪɧɚɟɜ ȼ.Ⱥ., Ɋɨɦɚɧɨɜɫɤɢɣ Ɇ.Ʉ, ɐɜɟɬɤɨɜ ɂ.ȼ. ɈɋɇɈȼɕ ɎɂɁɂɑȿɋɄɂɏ ɉɊɈɐȿɋɋɈȼ ȼ ɉɅȺɁɆȿ ɂ ɉɅȺɁɆȿɇɇɕɏ ɍɋɌȺɇɈȼɄȺɏ. Ɇ: ɆɂɎɂ, 2000
ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɫɨɞɟɪɠɢɬ ɢɡɥɨɠɟɧɢɟ ɨɫɧɨɜ ɮɢɡɢɤɢ ɩɥɚɡɦɵ ɢ ɩɪɨɰɟɫɫɨɜ, ɩɪɨɢɫɯɨɞɹɳɢɯ ɜ ɩɪɢɛɨɪɚɯ ɢ ɭɫɬɚɧɨɜɤɚɯ, ɩɪɟɞɧɚɡɧɚɱɟɧɧɵɯ ɞɥɹ ɫɨɡɞɚɧɢɹ ɢ ɩɪɚɤɬɢɱɟɫɤɨɝɨ ɩɪɢɦɟɧɟɧɢɹ ɩɥɚɡɦɵ, ɚ ɬɚɤɠɟ ɫɜɟɞɟɧɢɹ ɨɛ ɷɦɢɫɫɢɨɧɧɵɯ ɹɜɥɟɧɢɹɯ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɩɪɢ ɝɟɧɟɪɚɰɢɢ ɩɥɚɡɦɵ, ɫɜɟɞɟɧɢɹ ɨɛ ɷɥɟɦɟɧɬɚɯ ɢɨɧɧɨɣ ɢ ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɢ, ɨ ɮɢɡɢɤɟ ɨɫɧɨɜɧɵɯ ɜɢɞɨɜ ɝɚɡɨɜɵɯ ɪɚɡɪɹɞɨɜ. ȼ ɨɫɧɨɜɭ ɩɨɫɨɛɢɹ ɩɨɥɨɠɟɧɵ ɤɭɪɫɵ «Ɏɢɡɢɤɚ ɩɥɚɡɦɵ», «ȼɜɟɞɟɧɢɟ ɜ ɮɢɡɢɤɭ ɩɥɚɡɦɵ» ɢ «ɇɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɚɹ ɩɥɚɡɦɚ», ɱɢɬɚɟɦɵɟ ɜ ɆɂɎɂ ɫɬɭɞɟɧɬɚɦ ɮɚɤɭɥɶɬɟɬɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɢ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɮɢɡɢɤɢ, ɫɩɟɰɢɚɥɶɧɨɝɨ ɮɚɤɭɥɶɬɟɬɚ ɮɢɡɢɤɢ ɢ ɮɚɤɭɥɶɬɟɬɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɢɛɨɪɨɜ ɢ ɭɫɬɚɧɨɜɨɤ. Ȼɚɡɨɜɵɣ ɯɚɪɚɤɬɟɪ ɩɨɫɨɛɢɹ ɢ ɫɨɱɟɬɚɧɢɟ ɜ ɨɞɧɨɦ ɩɨɫɨɛɢɢ ɫɜɟɞɟɧɢɣ ɨ ɮɢɡɢɤɟ ɩɥɚɡɦɵ, ɨ ɮɢɡɢɱɟɫɤɨɣ ɷɥɟɤɬɪɨɧɢɤɟ ɢ ɨ ɮɢɡɢɤɟ ɝɚɡɨɜɨɝɨ ɪɚɡɪɹɞɚ ɞɟɥɚɟɬ ɟɝɨ ɭɧɢɜɟɪɫɚɥɶɧɵɦ ɢ ɩɨɥɟɡɧɵɦ ɞɥɹ ɫɬɭɞɟɧɬɨɜ, ɛɭɞɭɳɢɯ ɢɧɠɟɧɟɪɨɜ-ɮɢɡɢɤɨɜ, ɢ ɚɫɩɢɪɚɧɬɨɜ, ɫɩɟɰɢɚɥɢɡɢɪɭɸɳɢɯɫɹ ɤɚɤ ɜ ɮɢɡɢɤɟ ɝɨɪɹɱɟɣ ɩɥɚɡɦɵ, ɬɟɯɧɨɥɨɝɢɢ ɬɟɪɦɨɹɞɟɪɧɨɝɨ ɫɢɧɬɟɡɚ, ɬɚɤ ɢ ɜ ɞɪɭɝɢɯ ɨɛɥɚɫɬɹɯ, ɫɜɹɡɚɧɧɵɯ ɫ ɩɪɢɦɟɧɟɧɢɟɦ ɩɥɚɡɦɵ ɢ ɩɨɬɨɤɨɜ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɝɟɧɟɪɚɬɨɪɚɯ ɢ ɜ ɭɫɤɨɪɢɬɟɥɹɯ ɱɚɫɬɢɰ ɜ ɩɥɚɡɦɟɧɧɨ-ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɭɫɬɚɧɨɜɤɚɯ, ɜ ɩɥɚɡɦɟɧɧɵɯ ɢ ɢɨɧɧɵɯ ɞɜɢɠɢɬɟɥɹɯ ɢ ɜɨ ɦɧɨɝɢɯ ɞɪɭɝɢɯ ɨɛɥɚɫɬɹɯ.
Ɋɟɰɟɧɡɟɧɬ ɩɪɨɮɟɫɫɨɪ, ɞ.ɮ-ɦ.ɧ. ȿ.ȿ. Ʌɨɜɟɰɤɢɣ Ɋɟɤɨɦɟɧɞɨɜɚɧɨ ɪɟɞɫɨɜɟɬɨɦ ɆɂɎɂ ɜ ɤɚɱɟɫɬɜɟ ɭɱɟɛɧɨɝɨ ɩɨɫɨɛɢɹ ɋ.Ʉ. ɀɞɚɧɨɜ, ȼ.Ⱥ. Ʉɭɪɧɚɟɜ, Ɇ.Ʉ. Ɋɨɦɚɧɨɜɫɤɢɣ, ɂ.ȼ. ɐɜɟɬɤɨɜ, 2000. Ɇɨɫɤɨɜɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ ɢɧɠɟɧɟɪɧɨ-ɮɢɡɢɱɟɫɤɢɣ ɢɧɫɬɢɬɭɬ, 2000.
ɈȽɅȺȼɅȿɇɂȿ ɉɊȿȾɂɋɅɈȼɂȿ ȼȼȿȾȿɇɂȿ ȽɅȺȼȺ 1. ɈɋɇɈȼɇɕȿ ɉɈɇəɌɂə ɂ ɋȼɈɃɋɌȼȺ ɉɅȺɁɆɕ §1. Ɉɛɪɚɡɨɜɚɧɢɟ ɩɥɚɡɦɵ §2. Ʉɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɶ, ɩɥɚɡɦɟɧɧɚɹ ɱɚɫɬɨɬɚ § 3. Ⱦɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ, ɞɟɛɚɟɜɫɤɢɣ ɫɥɨɣ § 4. ɂɞɟɚɥɶɧɨɫɬɶ ɩɥɚɡɦɵ § 5. ɉɪɹɦɵɟ ɢ ɨɛɪɚɬɧɵɟ ɩɪɨɰɟɫɫɵ ɜ ɩɥɚɡɦɟ § 6. ɍɩɪɭɝɨɟ ɪɚɫɫɟɹɧɢɟ § 7. Ɋɚɜɧɨɜɟɫɢɹ ɜ ɩɥɚɡɦɟ § 8. ɇɟɪɚɜɧɨɜɟɫɧɨɫɬɶ ɩɥɚɡɦɟɧɧɵɯ ɫɢɫɬɟɦ § 9. ɉɪɨɰɟɫɫɵ ɪɟɥɚɤɫɚɰɢɢ ɜ ɩɥɚɡɦɟ § 10. ɉɪɨɰɟɫɫɵ ɩɟɪɟɧɨɫɚ ɜ ɩɥɚɡɦɟ § 11. Ⱦɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɥɚɡɦɵ ȽɅȺȼA 2. ɉɅȺɁɆȺ ȼ ɆȺȽɇɂɌɇɈɆ ɉɈɅȿ § 12. Ɉɞɧɨɱɚɫɬɢɱɧɨɟ ɪɚɫɫɦɨɬɪɟɧɢɟ § 13. Ⱦɜɢɠɟɧɢɟ ɜ ɩɨɫɬɨɹɧɧɨɦ ɢ ɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ § 14. Ⱦɜɢɠɟɧɢɟ ɜ ɫɢɥɶɧɨɦ ɦɟɞɥɟɧɧɨ ɦɟɧɹɸɳɟɦɫɹ ɩɨɥɟ. Ⱦɪɟɣɮɨɜɨɟ ɩɪɢɛɥɢɠɟɧɢɟ § 15. Ⱦɜɢɠɟɧɢɟ ɱɚɫɬɢɰɵ ɜ ɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɩɨɫɬɨɹɧɧɨɣ ɫɢɥɵ § 16. Ⱦɪɟɣɮ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜɞɨɥɶ ɩɥɨɫɤɨɫɬɢ ɫɤɚɱɤɚ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ §17. ȼɚɠɧɟɣɲɢɟ ɬɢɩɵ ɞɪɟɣɮɨɜɵɯ ɞɜɢɠɟɧɢɣ ɱɚɫɬɢɰ ɜ ɩɥɚɡɦɟ § 18. Ⱥɞɢɚɛɚɬɢɱɟɫɤɢɟ ɢɧɜɚɪɢɚɧɬɵ § 19. ɉɪɢɦɟɧɟɧɢɟ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɢ ɞɪɟɣɮɨɜɨɝɨ ɩɪɢɛɥɢɠɟɧɢɣ § 20. əɜɥɟɧɢɹ ɩɟɪɟɧɨɫɚ ɜ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɟ ȽɅȺȼȺ 3. ɆȺȽɇɂɌɈȽɂȾɊɈȾɂɇȺɆɂɑȿɋɄɂɃ ɆȿɌɈȾ ɈɉɂɋȺɇɂə ɉɅȺɁɆɕ § 21. ɂɞɟɚɥɶɧɚɹ ɨɞɧɨɠɢɞɤɨɫɬɧɚɹ ɝɢɞɪɨɞɢɧɚɦɢɤɚ ɩɥɚɡɦɵ. ɍɫɥɨɜɢɹ ɩɪɢɦɟɧɢɦɨɫɬɢ § 22. Ɉɫɧɨɜɧɵɟ ɭɪɚɜɧɟɧɢɹ § 23. Ɇɚɝɧɢɬɧɨɟ ɞɚɜɥɟɧɢɟ § 24. Ɋɚɜɧɨɜɟɫɢɟ ɩɥɚɡɦɵ ɜ ɦɚɝɧɢɬɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɟ
§ 25. Ȼɵɫɬɪɵɟ ɩɪɨɰɟɫɫɵ § 26. ȼɡɚɢɦɧɨɟ ɩɪɨɧɢɤɧɨɜɟɧɢɟ ɩɥɚɡɦɵ ɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ȽɅȺȼȺ 4. ɄɈɅȿȻȺɇɂə ɂ ȼɈɅɇɕ ȼ ɉɅȺɁɆȿ. ɇȿɍɋɌɈɃɑɂȼɈɋɌɂ ɉɅȺɁɆɕ § 27. Ⱦɢɫɩɟɪɫɢɨɧɧɵɟ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɩɪɨɞɨɥɶɧɵɯ ɢ ɩɨɩɟɪɟɱɧɵɯ ɜɨɥɧ ɦɚɥɨɣ ɚɦɩɥɢɬɭɞɵ § 28. Ɇɟɬɨɞ ɦɚɥɵɯ ɤɨɥɟɛɚɧɢɣ. Ⱦɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɧɟɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɵ § 29. ɉɨɩɟɪɟɱɧɵɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɜɨɥɧɵ ɜ ɧɟɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɟ § 30. əɜɥɟɧɢɟ ɨɬɫɟɱɤɢ ɧɢɡɤɨɱɚɫɬɨɬɧɨɣ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ § 31. Ʌɟɧɝɦɸɪɨɜɫɤɢɟ ɤɨɥɟɛɚɧɢɹ ɢ ɜɨɥɧɵ ɜ ɩɥɚɡɦɟ. ɉɥɚɡɦɨɧɵ § 32. ɂɨɧɧɵɟ ɥɟɧɝɦɸɪɨɜɫɤɢɟ ɜɨɥɧɵ. ɂɨɧɧɨ-ɡɜɭɤɨɜɵɟ ɜɨɥɧɵ ɜ ɩɥɚɡɦɟ. § 33. Ȼɟɫɫɬɨɥɤɧɨɜɢɬɟɥɶɧɨɟ ɡɚɬɭɯɚɧɢɟ ɜɨɥɧ ɜ ɩɥɚɡɦɟ § 34. Ⱦɢɷɥɟɤɬɪɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɦɚɝɧɢɬɨɚɤɬɢɜɧɨɣ ɩɥɚɡɦɵ § 35. ȼɨɥɧɵ ɜ ɦɚɝɧɢɬɨɚɤɬɢɜɧɨɣ ɩɥɚɡɦɟ § 36. ɇɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɥɚɡɦɵ § 37. Ʉɢɧɟɬɢɱɟɫɤɢɟ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɥɚɡɦɵ ȽɅȺȼȺ 5. ɗɅȿɄɌɊɈɇɇȺə ɂ ɂɈɇɇȺə ɈɉɌɂɄȺ § 38. Ⱥɧɚɥɨɝɢɹ ɫɜɟɬɨɜɨɣ ɢ ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɢ § 39. ɗɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɢɟ ɥɢɧɡɵ § 40. Ɇɚɝɧɢɬɧɵɟ ɥɢɧɡɵ § 41. Ɉɬɤɥɨɧɹɸɳɢɟ ɢ ɮɨɤɭɫɢɪɭɸɳɢɟ ɷɥɟɬɪɨɧɧɨ-ɨɩɬɢɱɟɫɤɢɟ ɫɢɫɬɟɦɵ ȽɅȺȼȺ 6. ȼɅɂəɇɂȿ ɉɊɈɋɌɊȺɇɋɌȼȿɇɇɈȽɈ ɁȺɊəȾȺ ɗɅȿɄɌɊɈɇɇɕɏ ɂ ɂɈɇɇɕɏ ɉɍɑɄɈȼ § 42. Ɉɝɪɚɧɢɱɟɧɢɟ ɬɨɤɚ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɦ ɡɚɪɹɞɨɦ ɜ ɞɢɨɞɟ § 43. ɉɪɟɞɟɥɶɧɚɹ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ ɩɭɱɤɚ ɱɚɫɬɢɰ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɜ ɜɚɤɭɭɦɟ ȽɅȺȼȺ 7. ɗɆɂɋɋɂɈɇɇȺə ɗɅȿɄɌɊɈɇɂɄȺ § 44. Ɍɟɪɦɨɷɦɢɫɫɢɨɧɧɚɹ ɷɥɟɤɬɪɨɧɢɤɚ § 45. Ⱥɜɬɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ § 46. ɂɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɷɦɢɬɬɟɪɚ ɩɪɢ ɬɟɪɦɨ ɢ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ § 47. Ɏɨɬɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ § 48. ȼɬɨɪɢɱɧɚɹ ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ȽɅȺȼȺ 8. ɗɅȿɄɌɊɂɑȿɋɄɂɃ ɌɈɄ ȼ ȽȺɁȺɏ ɂ ȽȺɁɈȼɕɃ ɊȺɁɊəȾ § 49. ɗɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ ɜ ɝɚɡɚɯ § 50. Ɍɟɨɪɢɹ ɷɥɟɤɬɪɨɧɧɵɯ ɥɚɜɢɧ
§ 51. Ɍɥɟɸɳɢɣ ɪɚɡɪɹɞ § 52. Ⱦɭɝɨɜɵɟ ɪɚɡɪɹɞɵ § 53. ɂɫɤɪɨɜɨɣ ɢ ɤɨɪɨɧɧɵɣ, ȼɑ ɢ ɋȼɑ ɪɚɡɪɹɞɵ ɋɩɢɫɨɤ ɢɫɩɨɥɶɡɨɜɚɧɧɨɣ ɢ ɪɟɤɨɦɟɧɞɭɟɦɨɣ ɥɢɬɟɪɚɬɭɪɵ
ɉɊȿȾɂɋɅɈȼɂȿ ȼ ɞɚɧɧɨɦ ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ ɢɡɥɚɝɚɸɬɫɹ ɨɫɧɨɜɵ ɮɢɡɢɤɢ ɩɥɚɡɦɵ ɢ ɩɪɨɰɟɫɫɨɜ, ɩɪɨɢɫɯɨɞɹɳɢɯ ɜ ɭɫɬɚɧɨɜɤɚɯ ɢ ɩɪɢɛɨɪɚɯ, ɩɪɟɞɧɚɡɧɚɱɟɧɧɵɯ ɞɥɹ ɫɨɡɞɚɧɢɹ ɢ ɩɪɚɤɬɢɱɟɫɤɨɝɨ ɩɪɢɦɟɧɟɧɢɹ ɩɥɚɡɦɵ. ɉɨɷɬɨɦɭ, ɧɚɪɹɞɭ ɫ «ɤɥɚɫɫɢɱɟɫɤɢɦ» ɢɡɥɨɠɟɧɢɟɦ ɨɫɧɨɜɧɵɯ ɩɨɧɹɬɢɣ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɯ ɩɥɚɡɦɭ ɢ ɩɥɚɡɦɨɩɨɞɨɛɧɵɟ ɫɪɟɞɵ, ɚ ɬɚɤɠɟ ɫɩɟɰɢɮɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɩɥɚɡɦɵ ɢ ɩɪɨɬɟɤɚɸɳɢɯ ɜ ɧɟɣ ɹɜɥɟɧɢɣ, ɜ ɩɨɫɨɛɢɢ ɩɪɢɜɟɞɟɧɵ ɫɜɟɞɟɧɢɹ ɨɛ ɷɦɢɫɫɢɨɧɧɵɯ ɹɜɥɟɧɢɹɯ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɩɪɢ ɝɟɧɟɪɚɰɢɢ ɩɥɚɡɦɵ, ɷɥɟɦɟɧɬɚɯ ɢɨɧɧɨɣ ɢ ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɢ ɢ ɨ ɮɢɡɢɤɟ ɧɟɤɨɬɨɪɵɯ ɨɫɧɨɜɧɵɯ ɜɢɞɨɜ ɝɚɡɨɜɵɯ ɪɚɡɪɹɞɨɜ. Ɍɚɤɨɟ ɫɨɱɟɬɚɧɢɟ ɜ ɨɞɧɨɦ ɩɨɫɨɛɢɢ ɫɜɟɞɟɧɢɣ ɨ ɮɢɡɢɤɟ ɩɥɚɡɦɵ, ɨ ɮɢɡɢɱɟɫɤɨɣ ɷɥɟɤɬɪɨɧɢɤɟ ɢ ɨ ɮɢɡɢɤɟ ɝɚɡɨɜɨɝɨ ɪɚɡɪɹɞɚ ɞɟɥɚɟɬ ɷɬɨ ɩɨɫɨɛɢɟ ɛɨɥɟɟ ɭɧɢɜɟɪɫɚɥɶɧɵɦ ɞɥɹ ɫɬɭɞɟɧɬɨɜ, ɛɭɞɭɳɢɯ ɢɧɠɟɧɟɪɨɜ-ɮɢɡɢɤɨɜ, ɢ ɚɫɩɢɪɚɧɬɨɜ, ɤɨɬɨɪɵɦ ɩɪɢɞɟɬɫɹ ɢɦɟɬɶ ɞɟɥɨ ɫ ɫɨɡɞɚɧɢɟɦ ɢ ɩɪɢɦɟɧɟɧɢɟɦ ɩɥɚɡɦɟɧɧɵɯ ɭɫɬɚɧɨɜɨɤ ɢ ɭɫɬɪɨɣɫɬɜ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɢ ɩɥɚɡɦɵ, ɢ ɩɭɱɤɨɜ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɪɚɡɥɢɱɧɵɯ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɢɯ ɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɡɚɞɚɱɚɯ. ȼ ɨɫɧɨɜɭ ɩɨɫɨɛɢɹ ɩɨɥɨɠɟɧɵ ɤɭɪɫɵ «Ɏɢɡɢɤɚ ɩɥɚɡɦɵ», «ȼɜɟɞɟɧɢɟ ɜ ɮɢɡɢɤɭ ɩɥɚɡɦɵ» ɢ «ɇɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɚɹ ɩɥɚɡɦɚ», ɱɢɬɚɟɦɵɯ ɜ ɆɂɎɂ ɫɬɭɞɟɧɬɚɦ ɮɚɤɭɥɶɬɟɬɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɢ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɮɢɡɢɤɢ, ɫɩɟɰɢɚɥɶɧɨɝɨ ɮɚɤɭɥɶɬɟɬɚ ɮɢɡɢɤɢ ɢ ɮɚɤɭɥɶɬɟɬɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɢɛɨɪɨɜ ɢ ɭɫɬɚɧɨɜɨɤ. Ȼɚɡɨɜɵɣ ɯɚɪɚɤɬɟɪ ɷɬɨɝɨ ɩɨɫɨɛɢɹ, ɜ ɤɨɬɨɪɨɦ ɢɡɥɚɝɚɸɬɫɹ ɨɫɧɨɜɵ ɮɢɡɢɱɟɫɤɢɯ ɹɜɥɟɧɢɣ ɤɚɤ ɜ ɫɚɦɨɣ ɩɥɚɡɦɟ ɩɪɢ ɟɟ ɨɛɪɚɡɨɜɚɧɢɢ ɜ ɩɥɚɡɦɟɧɧɵɯ ɭɫɬɚɧɨɜɤɚɯ, ɬɚɤ ɢ ɩɪɢ ɝɟɧɟɪɚɰɢɢ ɫ ɟɟ ɩɨɦɨɳɶɸ ɢɨɧɧɵɯ ɢ ɷɥɟɤɬɪɨɧɧɵɯ ɩɭɱɤɨɜ, ɞɟɥɚɟɬ ɟɝɨ ɩɨɥɟɡɧɵɦ ɞɥɹ ɫɬɭɞɟɧɬɨɜ, ɫɩɟɰɢɚɥɢɡɢɪɭɸɳɢɯɫɹ ɢ ɜ ɮɢɡɢɤɟ ɝɨɪɹɱɟɣ ɩɥɚɡɦɵ, ɬɟɯɧɨɥɨɝɢɢ ɬɟɪɦɨɹɞɟɪɧɨɝɨ ɫɢɧɬɟɡɚ, ɢ ɜ ɞɪɭɝɢɯ ɨɛɥɚɫɬɹɯ, ɫɜɹɡɚɧɧɵɯ ɫ ɩɪɢɦɟɧɟɧɢɟɦ ɩɥɚɡɦɵ ɢ ɩɨɬɨɤɨɜ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɝɟɧɟɪɚɬɨɪɚɯ ɢ ɜ ɭɫɤɨɪɢɬɟɥɹɯ ɱɚɫɬɢɰ ɜ ɩɥɚɡɦɟɧɧɨ-ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɭɫɬɚɧɨɜɤɚɯ, ɜ ɩɥɚɡɦɟɧɧɵɯ ɢ ɢɨɧɧɵɯ ɞɜɢɠɢɬɟɥɹɯ ɢ ɜɨ ɦɧɨɝɢɯ ɞɪɭɝɢɯ ɨɛɥɚɫɬɹɯ. ɇɟɫɤɨɥɶɤɨ ɫɥɨɜ ɨ ɫɬɪɭɤɬɭɪɟ ɤɧɢɝɢ. ɇɚɦɟɱɟɧɧɚɹ ɜɵɲɟ ɰɟɥɶ ɨɩɪɟɞɟɥɢɥɚ ɨɬɛɨɪ ɦɚɬɟɪɢɚɥɚ ɢ ɩɪɢɧɹɬɭɸ ɧɚɦɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɟɝɨ ɢɡɥɨɠɟɧɢɹ. Ƚɥɚɜɚ 1 ɩɨɫɜɹɳɟɧɚ ɤɪɚɬɤɨɦɭ ɨɛɫɭɠɞɟɧɢɸ ɨɫɧɨɜɧɵɯ ɩɨɧɹɬɢɣ, ɭɩɨɬɪɟɛɢɬɟɥɶɧɵɯ ɜ ɨɩɢɫɚɧɢɢ ɩɥɚɡɦɟɧɧɵɯ ɹɜɥɟɧɢɣ ɢ, ɩɨ ɫɭɬɢ ɞɟɥɚ, ɫɨɫɬɚɜɥɹɸɳɢɯ ɨɫɧɨɜɭ ɮɢɡɢɤɢ ɩɥɚɡɦɵ ɤɚɤ ɫɨɫɬɨɹɧɢɹ ɜɟɳɟɫɬɜɚ. ȼ ɝɥɚɜɟ 2 ɨɛɫɭɠɞɚɸɬɫɹ ɧɚɢɛɨɥɟɟ ɯɚɪɚɤɬɟɪɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɩɨɜɟɞɟɧɢɹ ɩɥɚɡɦɵ, ɩɨɦɟɳɟɧɧɨɣ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ. ȼ ɝɥɚɜɟ 3 ɢɡɥɚɝɚɸɬɫɹ ɨɫɧɨɜɵ ɦɚɝɧɢɬɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɢ ɩɥɚɡɦɵ ɢ ɞɚɧɵ ɩɪɨɫɬɟɣɲɢɟ ɟɟ ɩɪɢɥɨɠɟɧɢɹ ɞɥɹ ɨɩɢɫɚɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɩɥɚɡɦɵ ɢ ɞɢɧɚɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɜ ɧɟɣ. ȼ ɝɥɚɜɟ 4 ɨɛɫɭɠɞɚɸɬɫɹ ɜɨɥɧɨɜɵɟ ɫɜɨɣɫɬɜɚ ɩɥɚɡɦɵ ɢ ɭɫɥɨɜɢɹ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɨɥɧ ɜ ɩɥɚɡɦɟ ɛɟɡ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɜ ɦɚɝɧɢɬɨɚɤɬɢɜɧɨɣ ɩɥɚɡɦɟ, ɚ ɬɚɤɠɟ ɨɫɧɨɜɧɵɟ ɬɢɩɵ ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɢɯ ɢ ɤɢɧɟɬɢɱɟɫɤɢɯ ɧɟɭɫɬɨɣɱɢɜɨɫɬɟɣ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɪɚɡɜɢɜɚɬɶɫɹ ɜ ɩɥɚɡɦɟ. ɗɬɢ ɝɥɚɜɵ ɹɜɥɹɸɬɫɹ, ɩɨ ɫɭɬɢ ɞɟɥɚ, ɪɟɡɭɥɶɬɚɬɨɦ ɨɛɨɛɳɟɧɢɹ, ɧɟɨɛɯɨɞɢɦɨɝɨ ɞɨɩɨɥɧɟɧɢɹ ɢ ɤɪɢɬɢɱɟɫɤɨɝɨ ɩɟɪɟɨɫɦɵɫɥɟɧɢɹ ɦɚɬɟɪɢɚɥɚ, ɨɩɭɛɥɢɤɨɜɚɧɧɨɝɨ ɚɜɬɨɪɚɦɢ ɪɚɧɟɟ ɜ ɩɨɫɨɛɢɹɯ [1,2]. Ɉɛɫɭɠɞɟɧɢɸ ɮɢɡɢɤɢ ɩɭɱɤɨɜ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ, ɜɨɩɪɨɫɚɦ ɢɯ ɮɨɤɭɫɢɪɨɜɤɢ ɢ ɭɫɥɨɜɢɣ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɩɨɫɜɹɳɟɧɵ ɝɥɚɜɵ 5 ɢ 6. ɉɪɨɛɥɟɦɵ ɷɦɢɫɫɢɨɧɧɨɣ ɷɥɟɤɬɪɨɧɢɤɢ ɨɛɫɭɠɞɚɸɬɫɹ ɜ ɝɥɚɜɟ 7 ɢ, ɧɚɤɨɧɟɰ, ɡɚɤɥɸɱɢɬɟɥɶɧɚɹ ɝɥɚɜɚ 8 ɞɚɟɬ ɤɪɚɬɤɢɣ ɷɤɫɤɭɪɫ ɜ ɮɢɡɢɤɭ ɨɫɧɨɜɧɵɯ ɬɢɩɨɜ ɝɚɡɨɜɵɯ ɪɚɡɪɹɞɨɜ. Ɉɬɦɟɬɢɦ ɬɚɤɠɟ, ɱɬɨ ɧɚɦɢ ɩɪɢɧɹɬɚ ɧɭɦɟɪɚɰɢɹ ɪɢɫɭɧɤɨɜ ɢ ɮɨɪɦɭɥ ɩɨ ɝɥɚɜɚɦ.
ȼȼȿȾȿɇɂȿ ȼɫɟɦ ɢɡɜɟɫɬɧɵ ɬɪɢ ɚɝɪɟɝɚɬɧɵɯ ɫɨɫɬɨɹɧɢɹ ɜɟɳɟɫɬɜɚ - ɬɜɟɪɞɨɟ, ɠɢɞɤɨɟ, ɝɚɡɨɨɛɪɚɡɧɨɟ. ɉɥɚɡɦɭ ɱɚɫɬɨ ɧɚɡɵɜɚɸɬ ɱɟɬɜɟɪɬɵɦ ɫɨɫɬɨɹɧɢɟɦ ɜɟɳɟɫɬɜɚ - ɫɚɦɵɦ ɜɵɫɨɤɨɬɟɦɩɟɪɚɬɭɪɧɵɦ, ɢɦɟɹ ɜ ɜɢɞɭ ɰɟɩɨɱɤɭ ɩɪɟɜɪɚɳɟɧɢɣ: ɬɜɟɪɞɨɟ ɬɟɥɨ ɠɢɞɤɨɫɬɶ - ɝɚɡ - ɩɥɚɡɦɚ, ɢɦɟɸɳɭɸ ɦɟɫɬɨ ɩɪɢ ɩɨɜɵɲɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ (Sir William Croocus , 1879). Ƚɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ ɤɨɥɢɱɟɫɬɜɚ ɷɧɟɪɝɢɢ, ɫɨɞɟɪɠɚɳɟɣɫɹ ɜ ɧɟɤɨɬɨɪɨɣ ɦɚɫɫɟ ɜɟɳɟɫɬɜɚ (ɧɚɩɪɢɦɟɪ, ɜ ɨɞɧɨɦ ɝɪɚɦɦɟ), ɨɬ ɟɝɨ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨɞɨɛɟɧ ɝɪɚɮɢɤɭ, ɩɨɤɚɡɚɧɧɨɦɭ ɧɚ ɪɢɫ. ȼ.1. ɉɪɢ ɞɨɫɬɚɬɨɱɧɨ ɧɢɡɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɥɸɛɨɟ ɜɟɳɟɫɬɜɨ ɧɚɯɨɞɢɬɫɹ ɜ ɬɜɟɪɞɨɦ ɫɨɫɬɨɹɧɢɢ; ɩɨ ɦɟɪɟ ɩɨɜɵɲɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɟɝɨ ɷɧɟɪɝɨɫɨɞɟɪɠɚɧɢɟ ɪɚɫɬɟɬ - ɷɬɨ ɭɱɚɫɬɨɤ ɚ-b. ɇɚɤɥɨɧ ɨɬɪɟɡɤɚ ɩɪɹɦɨɣ ɚ-b ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɟɩɥɨɟɦɤɨɫɬɶɸ ɜɟɳɟɫɬɜɚ, ɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɭɱɚɫɬɨɤ ɧɚ ɲɤɚɥɟ ɬɟɦɩɟɪɚɬɭɪ ɞɨ ɬɨɱɤɢ b ɦɨɠɟɬ ɛɵɬɶ ɢ ɨɱɟɧɶ ɦɚɥɵɦ (ɞɥɹ ɜɨɞɨɪɨɞɚ 13,9Ʉ) ɢ ɜɟɫɶɦɚ ɛɨɥɶɲɢɦ (ɞɥɹ ɜɨɥɶɮɪɚɦɚ 3643 Ʉ). ȼ ɬɨɱɤɟ b ɧɚɱɢɧɚɟɬɫɹ ɩɥɚɜɥɟɧɢɟ, ɞɥɹ ɱɢɫɬɵɯ ɜɟɳɟɫɬɜ ɬɟɦɩɟɪɚɬɭɪɚ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ: ɷɧɟɪɝɢɹ ɡɚɬɪɚɱɢɜɚɟɬɫɹ ɧɚ ɪɚɡɪɭɲɟɧɢɟ Ɋɢɫ. ȼ.1. Ɂɚɜɢɫɢɦɨɫɬɶ ɷɧɟɪɝɨɫɨɞɟɪɠɚɧɢɹ ɫɜɹɡɟɣ, ɨɩɪɟɞɟɥɹɸɳɢɯ ɭɩɨɪɹɞɨɱɟɧɧɨɟ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɪɚɫɩɨɥɨɠɟɧɢɟ ɱɚɫɬɢɰ ɜɟɳɟɫɬɜɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɪɭɝ ɞɪɭɝɚ. ȼɟɥɢɱɢɧɚ ɭɱɚɫɬɤɚ b-c ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɚɤ ɧɚɡɵɜɚɟɦɨɣ "ɫɤɪɵɬɨɣ" ɬɟɩɥɨɬɨɣ ɩɥɚɜɥɟɧɢɹ. ɉɪɢ ɞɚɥɶɧɟɣɲɟɦ ɩɨɜɵɲɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚ ɭɱɚɫɬɤɟ c-d ɜɟɳɟɫɬɜɨ ɨɫɬɚɟɬɫɹ ɜ ɠɢɞɤɨɦ ɫɨɫɬɨɹɧɢɢ, ɪɚɫɬɟɬ ɷɧɟɪɝɢɹ ɞɜɢɠɟɧɢɹ ɟɝɨ ɦɨɥɟɤɭɥ. ɇɚɤɥɨɧ ɨɬɪɟɡɤɚ ɩɪɹɦɨɣ c-d ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɟɩɥɨɟɦɤɨɫɬɶɸ ɜɟɳɟɫɬɜɚ ɜ ɠɢɞɤɨɦ ɫɨɫɬɨɹɧɢɢ. ȼ ɬɨɱɤɟ d ɧɚɱɢɧɚɟɬɫɹ ɤɢɩɟɧɢɟ, ɢ ɜɟɳɟɫɬɜɨ ɩɟɪɟɯɨɞɢɬ ɜ ɝɚɡɨɨɛɪɚɡɧɨɟ ɫɨɫɬɨɹɧɢɟ. ɇɚ ɨɬɪɟɡɤɟ d-c ɬɟɦɩɟɪɚɬɭɪɚ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ, ɷɧɟɪɝɢɹ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɪɚɡɪɭɲɟɧɢɟ ɫɜɹɡɟɣ ɦɟɠɞɭ ɦɨɥɟɤɭɥɚɦɢ. ȼɟɥɢɱɢɧɚ ɭɱɚɫɬɤɚ d-ɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɚɤ ɧɚɡɵɜɚɟɦɨɣ ɬɟɩɥɨɬɨɣ ɢɫɩɚɪɟɧɢɹ. ɇɟɨɛɯɨɞɢɦɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɷɬɢ ɪɚɫɫɭɠɞɟɧɢɹ ɜɟɪɧɵ ɩɪɢ ɧɟɤɨɬɨɪɨɦ ɡɚɞɚɧɧɨɦ ɞɚɜɥɟɧɢɢ. ɇɚ ɫɚɦɨɦ ɞɟɥɟ ɢ ɧɚɞ ɬɜɟɪɞɵɦ ɬɟɥɨɦ ɜɫɟɝɞɚ ɢɦɟɟɬɫɹ ɧɟɤɨɬɨɪɨɟ ɞɚɜɥɟɧɢɟ ɧɚɫɵɳɟɧɧɨɝɨ ɩɚɪɚ, ɜɟɫɶɦɚ ɦɚɥɨɟ ɞɥɹ ɛɨɥɶɲɢɧɫɬɜɚ ɜɟɳɟɫɬɜ. Ɉɞɧɚɤɨ ɧɚɞ ɧɟɤɨɬɨɪɵɦɢ ɜɟɳɟɫɬɜɚɦɢ ɨɧɨ ɜɫɟ ɠɟ ɜɟɥɢɤɨ (ɧɚɩɪɢɦɟɪ, ɭ ɣɨɞɚ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ 387 Ʉ ɨɧɨ ɫɨɫɬɚɜɥɹɟɬ 90 ɦɦ ɪɬ. ɫɬ.). ɉɨɷɬɨɦɭ ɩɪɢɜɟɞɟɧɧɵɟ ɜɵɲɟ ɪɚɫɫɭɠɞɟɧɢɹ ɢɦɟɸɬ ɯɚɪɚɤɬɟɪ ɢɥɥɸɫɬɪɚɰɢɢ ɢɡɦɟɧɟɧɢɹ ɩɪɢɜɵɱɧɵɯ ɞɥɹ ɧɚɫ ɚɝɪɟɝɚɬɧɵɯ ɫɨɫɬɨɹɧɢɣ ɜɟɳɟɫɬɜɚ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ. ɉɨ ɦɟɪɟ ɪɨɫɬɚ ɬɟɦɩɟɪɚɬɭɪɵ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɷɧɟɪɝɢɹ ɦɨɥɟɤɭɥ, ɭɦɟɧɶɲɚɸɬɫɹ ɫɜɹɡɢ ɢ ɩɨɫɥɟ ɢɫɩɚɪɟɧɢɹ ɜɫɟ ɦɨɥɟɤɭɥɵ ɫɬɚɧɨɜɹɬɫɹ ɫɜɨɛɨɞɧɵɦɢ. ȿɫɥɢ ɩɪɨɞɨɥɠɚɬɶ ɭɜɟɥɢɱɢɜɚɬɶ ɷɧɟɪɝɢɸ ɷɬɢɯ ɫɜɨɛɨɞɧɵɯ ɦɨɥɟɤɭɥ (ɧɚɩɪɢɦɟɪ, ɧɚɝɪɟɜɚɬɶ ɝɚɡ), ɬɨ ɩɪɢ ɜɡɚɢɦɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɹɯ ɦɨɥɟɤɭɥɵ ɧɚɱɧɭɬ ɪɚɫɩɚɞɚɬɶɫɹ ɧɚ ɚɬɨɦɵ. ɇɨ ɷɬɨ ɭɠɟ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɧɨɜɵɣ ɩɪɨɰɟɫɫ − ɱɚɫɬɶ ɷɧɟɪɝɢɢ ɡɚɬɪɚɱɢɜɚɟɬɫɹ ɧɚ ɩɪɨɰɟɫɫ, ɤɚɱɟɫɬɜɟɧɧɨ ɦɟɧɹɸɳɢɣ ɫɨɫɬɚɜ ɝɚɡɚ. ɏɨɪɨɲɨ ɢɡɜɟɫɬɧɨ, ɱɬɨ ɝɚɡ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɨɜɨɤɭɩɧɨɫɬɶ ɫɜɨɛɨɞɧɵɯ ɱɚɫɬɢɰ − ɦɨɥɟɤɭɥ (ɨɛɵɱɧɨ) ɢɥɢ ɚɬɨɦɨɜ (ɪɟɠɟ). ɗɬɢ ɱɚɫɬɢɰɵ ɫɬɚɥɤɢɜɚɸɬɫɹ ɞɪɭɝ ɫ ɞɪɭɝɨɦ, ɫɨ ɫɬɟɧɤɚɦɢ ɫɨɫɭɞɚ, ɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɫɬɨɥɤɧɨɜɟɧɢɣ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɜɩɨɥɧɟ ɨɩɪɟɞɟɥɟɧɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɱɚɫɬɢɰ ɩɨ ɫɤɨɪɨɫɬɹɦ. ɉɪɢ ɤɚɠɞɨɣ ɞɚɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɨɫɧɨɜɧɚɹ ɱɚɫɬɶ ɱɚɫɬɢɰ ɢɦɟɟɬ ɧɟɤɨɬɨɪɭɸ ɨɩɪɟɞɟɥɟɧɧɭɸ (ɧɚɢɛɨɥɟɟ 1
ɜɟɪɨɹɬɧɭɸ) ɫɤɨɪɨɫɬɶ, ɧɨ ɜɫɟɝɞɚ ɟɫɬɶ ɢ ɛɨɥɟɟ ɦɟɞɥɟɧɧɵɟ ɱɚɫɬɢɰɵ ɢ ɛɨɥɟɟ ɛɵɫɬɪɵɟ. ɑɟɦ ɞɚɥɶɲɟ ɨɬ ɧɚɢɛɨɥɟɟ ɜɟɪɨɹɬɧɨɣ ɫɤɨɪɨɫɬɢ (ɢ ɜ ɫɬɨɪɨɧɭ ɭɦɟɧɶɲɟɧɢɹ ɢ ɜ ɫɬɨɪɨɧɭ ɭɜɟɥɢɱɟɧɢɹ), ɬɟɦ ɦɟɧɶɲɟ ɱɚɫɬɢɰ, ɢɦɟɸɳɢɯ ɬɚɤɭɸ, ɞɚɥɟɤɭɸ ɨɬ ɧɚɢɛɨɥɟɟ ɜɟɪɨɹɬɧɨɣ, ɫɤɨɪɨɫɬɶ. ɇɚ ɪɢɫ. ȼ.2 ɩɪɟɞɫɬɚɜɥɟɧɨ ɜ ɤɚɱɟɫɬɜɟ ɢɥɥɸɫɬɪɚɰɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɱɢɫɥɨ ɱɚɫɬɢɰ dn/ndv, ɩɪɢɯɨɞɹɳɟɟɫɹ ɧɚ ɢɧɬɟɪɜɚɥ ɫɤɨɪɨɫɬɢ dv, ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɟɥɢɱɢɧɵ ɦɨɞɭɥɹ ɫɤɨɪɨɫɬɢ v. ɗɬɨ − ɢɡɜɟɫɬɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ Ɇɚɤɫɜɟɥɥɚ. ɇɚɢɛɨɥɟɟ ɜɚɠɧɨ ɬɨ, ɱɬɨ ɩɪɢ ɥɸɛɵɯ ɬɟɦɩɟɪɚɬɭɪɚɯ ɜɫɟɝɞɚ ɢɦɟɸɬɫɹ ɛɵɫɬɪɵɟ ɱɚɫɬɢɰɵ, ɩɪɢɱɟɦ, ɱɟɦ ɜɵɲɟ ɬɟɦɩɟɪɚɬɭɪɚ, ɬɟɦ ɢɯ ɛɨɥɶɲɟ. ȼ ɨɛɵɱɧɵɯ ɭɫɥɨɜɢɹɯ, ɧɚɩɪɢɦɟɪ ɩɪɢ ɤɨɦɧɚɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ, ɞɨɥɹ ɬɚɤɢɯ ɱɚɫɬɢɰ ɤɪɚɣɧɟ ɦɚɥɚ, ɬɚɤ ɱɬɨ ɷɧɟɪɝɢɹ ɩɨɞɚɜɥɹɸɳɟɝɨ ɱɢɫɥɚ ɱɚɫɬɢɰ ɧɟɞɨɫɬɚɬɨɱɧɚ ɞɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɪɚɡɪɭɲɢɬɶ ɦɨɥɟɤɭɥɭ (ɢɥɢ ɬɟɦ ɛɨɥɟɟ ɚɬɨɦ), ɩɨɷɬɨɦɭ ɩɪɚɤɬɢɱɟɫɤɢ ɩɪɟɨɛɥɚɞɚɸɬ ɬɨɥɶɤɨ ɬɚɤ ɧɚɡɵɜɚɟɦɵɟ ɭɩɪɭɝɢɟ ɫɬɨɥɤɧɨɜɟɧɢɹ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɤɨɬɨɪɵɯ ɩɨɥɧɚɹ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɨɛɟɢɯ ɫɬɚɥɤɢɜɚɸɳɢɯɫɹ ɱɚɫɬɢɰ ɨɫɬɚɟɬɫɹ ɧɟɢɡɦɟɧɧɨɣ. ɗɬɨ ɬɢɩɢɱɧɨ ɞɥɹ ɨɛɵɱɧɨɝɨ ɝɚɡɚ, ɬɚɤɢɟ ɫɬɨɥɤɧɨɜɟɧɢɹ ɢ ɩɪɢɜɨɞɹɬ ɤ ɭɫɬɚɧɨɜɥɟɧɢɸ ɦɚɤɫɜɟɥɥɨɜɫɤɨɝɨ Ɋɢɫ.ȼ.2. Ɏɭɧɤɰɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ. ɪɚɫɩɪɟɞɟɥɟɧɢɹ (ɩɨ ɫɤɨɪɨɫɬɹɦ ɢɥɢ ɷɧɟɪɝɢɹɦ, ɬɚɤ ɤɚɤ ɩɪɢ ɞɚɧɧɨɣ ɦɚɫɫɟ ɱɚɫɬɢɰɵ ɟɟ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɨɞɧɨɡɧɚɱɧɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɤɨɪɨɫɬɶɸ: ȿ=mv2/2; ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɝɚɡ ɜ ɰɟɥɨɦ ɩɨɤɨɢɬɫɹ). ɂɦɟɸɳɢɟɫɹ ɜɫɟɝɞɚ ɛɵɫɬɪɵɟ ɱɚɫɬɢɰɵ ɪɚɡɛɢɜɚɸɬ ɦɨɥɟɤɭɥɵ ɢ ɞɚɠɟ ɚɬɨɦɵ, ɧɨ ɢɯ ɧɢɱɬɨɠɧɨ ɦɚɥɨ, ɟɫɥɢ ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ ɧɟ ɜɟɥɢɤɚ. ɉɪɨɰɟɫɫ ɪɚɫɩɚɞɚ ɦɨɥɟɤɭɥ ɧɚ ɚɬɨɦɵ ɧɚɡɵɜɚɸɬ ɞɢɫɫɨɰɢɚɰɢɟɣ, ɩɪɨɰɟɫɫ ɨɬɪɵɜɚ ɷɥɟɤɬɪɨɧɚ ɨɬ ɚɬɨɦɚ − ɢɨɧɢɡɚɰɢɟɣ, ɚ ɚɬɨɦ, ɩɨɬɟɪɹɜɲɢɣ ɨɞɢɧ ɷɥɟɤɬɪɨɧ (ɢɥɢ ɛɨɥɶɲɟ),- ɢɨɧɨɦ. ɉɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɜ 1 ɫɦ3 ɜɨɡɞɭɯɚ ɫɨɞɟɪɠɢɬɫɹ 103 - 105 ɢɨɧɨɜ, ɱɬɨ ɧɢɱɬɨɠɧɨ ɦɚɥɨ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɱɢɫɥɨɦ ɦɨɥɟɤɭɥ 2.7⋅1019 ɜ ɤɚɠɞɨɦ ɤɭɛɢɱɟɫɤɨɦ ɫɚɧɬɢɦɟɬɪɟ. Ɉɞɧɚɤɨ ɩɪɢ ɩɨɜɵɲɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɜɫɟ ɛɨɥɶɲɟ ɫɬɚɧɨɜɢɬɫɹ ɛɵɫɬɪɵɯ ɱɚɫɬɢɰ, ɜɫɟ ɱɚɳɟ ɩɪɨɢɫɯɨɞɹɬ ɩɪɨɰɟɫɫɵ ɞɢɫɫɨɰɢɚɰɢɢ ɢ ɢɨɧɢɡɚɰɢɢ. ȼ ɷɬɢɯ ɩɪɨɰɟɫɫɚɯ ɱɚɫɬɶ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɱɚɫɬɢɰ ɡɚɬɪɚɱɢɜɚɟɬɫɹ ɧɚ ɜɧɭɬɪɢɦɨɥɟɤɭɥɹɪɧɵɟ (ɢɥɢ ɜɧɭɬɪɢɚɬɨɦɧɵɟ) ɩɪɨɰɟɫɫɵ; ɩɨɷɬɨɦɭ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɫɬɚɥɤɢɜɚɸɳɢɯɫɹ ɱɚɫɬɢɰ ɞɨ ɫɨɭɞɚɪɟɧɢɹ ɭɠɟ ɧɟ ɪɚɜɧɚ ɢɯ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɩɨɫɥɟ ɫɨɭɞɚɪɟɧɢɹ. Ɍɚɤɢɟ ɩɪɨɰɟɫɫɵ ɧɚɡɵɜɚɸɬ ɧɟɭɩɪɭɝɢɦɢ. ȼ ɨɛɵɱɧɨɦ ɝɚɡɟ ɪɨɥɶ ɧɟɭɩɪɭɝɢɯ ɩɪɨɰɟɫɫɨɜ ɩɪɟɧɟɛɪɟɠɢɦɨ ɦɚɥɚ, ɧɨ ɩɪɢ ɞɨɫɬɚɬɨɱɧɨ ɜɵɫɨɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɨɧɢ ɩɪɢɨɛɪɟɬɚɸɬ ɫɭɳɟɫɬɜɟɧɧɨɟ ɡɧɚɱɟɧɢɟ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɨɛɪɚɡɭɸɬɫɹ ɧɨɜɵɟ ɱɚɫɬɢɰɵ: ɩɪɢ ɞɢɫɫɨɰɢɚɰɢɢ − ɚɬɨɦɵ, ɩɪɢ ɢɨɧɢɡɚɰɢɢ − ɢɨɧɵ ɢ ɷɥɟɤɬɪɨɧɵ. ɉɨɫɥɟɞɧɟɟ ɨɫɨɛɟɧɧɨ ɜɚɠɧɨ. Ⱥɬɨɦɵ, ɤɚɤ ɢ ɦɨɥɟɤɭɥɵ, ɷɥɟɤɬɪɢɱɟɫɤɢ ɧɟɣɬɪɚɥɶɧɵ, ɚ ɜɨɬ ɢɨɧɵ ɢ ɷɥɟɤɬɪɨɧɵ ɢɦɟɸɬ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɡɚɪɹɞɵ. ɇɚɥɢɱɢɟ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɡɚɪɹɞɨɜ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɹɟɬ ɯɚɪɚɤɬɟɪ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ. ȼɟɞɶ ɧɟɣɬɪɚɥɶɧɵɟ ɱɚɫɬɢɰɵ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ, ɝɪɭɛɨ ɝɨɜɨɪɹ, ɬɨɥɶɤɨ ɩɪɢ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨɦ ɫɬɨɥɤɧɨɜɟɧɢɢ, ɩɨɞɨɛɧɨ ɭɩɪɭɝɢɦ ɛɢɥɶɹɪɞɧɵɦ ɲɚɪɚɦ, ɬɚɤ ɤɚɤ ɩɨɬɟɧɰɢɚɥ ɩɨɥɹ ɫɢɥ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ (ɫɢɥɵ ȼɚɧ-ɞɟɪȼɚɚɥɶɫɚ) ɛɵɫɬɪɨ ɭɛɵɜɚɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ. Ɍɨɝɞɚ ɤɚɤ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ ɫɨɡɞɚɸɬ ɜɨɤɪɭɝ ɫɟɛɹ ɩɪɨɬɹɠɟɧɧɵɟ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɩɨɥɹ, ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɞɥɟɧɧɟɟ ɭɛɵɜɚɸɳɢɟ ɫ ɪɚɫɫɬɨɹɧɢɟɦ, ɚ ɩɨɬɨɦɭ ɢ ɫɢɥɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɡɚɪɹɠɟɧɧɵɦɢ ɱɚɫɬɢɰɚɦɢ (ɫɢɥɚ Ʉɭɥɨɧɚ) ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɞɥɟɧɧɟɟ ɭɛɵɜɚɟɬ ɫ ɪɨɫɬɨɦ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ. ɂɦɟɧɧɨ ɞɚɥɶɧɨɞɟɣɫɬɜɭɸɳɢɣ ɯɚɪɚɤɬɟɪ ɫɢɥ ɦɟɠɞɭ ɡɚɪɹɠɟɧɧɵɦɢ ɱɚɫɬɢɰɚɦɢ ɢ ɩɪɢɜɨɞɢɬ ɤ
2
ɤɚɱɟɫɬɜɟɧɧɨ ɧɨɜɵɦ - ɩɥɚɡɦɟɧɧɵɦ - ɷɮɮɟɤɬɚɦ ɜ ɝɚɡɟ, ɫɨɞɟɪɠɚɳɟɦ ɫɜɨɛɨɞɧɵɟ ɡɚɪɹɞɵ. ɗɬɨ ɤɚɱɟɫɬɜɟɧɧɨ ɧɨɜɵɣ ɝɚɡ: ɝɚɡ, ɫɨɞɟɪɠɚɳɢɣ ɜ ɡɚɦɟɬɧɨɦ ɱɢɫɥɟ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ. Ɍɚɤɨɣ ɝɚɡ ɢ ɧɚɡɵɜɚɸɬ ɩɥɚɡɦɨɣ. ɋɚɦ ɬɟɪɦɢɧ “ɩɥɚɡɦɚ” ɩɨɹɜɢɥɫɹ ɜ ɨɛɢɯɨɞɟ ɧɚɭɤɢ ɩɨɫɥɟ ɪɚɛɨɬ Ʌɟɧɝɦɸɪɚ ɢ Ɍɨɧɤɫɚ ɜ 1928 ɝ., ɢ ɛɵɥ ɜɜɟɞɟɧ ɞɥɹ ɨɩɢɫɚɧɢɹ ɫɨɜɨɤɭɩɧɨɫɬɢ ɹɜɥɟɧɢɣ, ɫɨɩɪɨɜɨɠɞɚɸɳɢɯ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɪɚɡɪɹɞ ɜ ɝɚɡɟ. Ʌɟɝɤɨ ɩɨɧɹɬɶ, ɱɬɨ ɦɟɠɞɭ ɝɚɡɨɦ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ ɢ ɝɚɡɨɦɩɥɚɡɦɨɣ ɧɟɬ ɱɟɬɤɨɣ ɝɪɚɧɢɰɵ: ɨɛɵɱɧɵɣ ɝɚɡ ɫɬɚɧɨɜɢɬɫɹ ɩɥɚɡɦɨɣ, ɤɚɤ ɬɨɥɶɤɨ ɪɨɥɶ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɫɬɚɧɨɜɢɬɫɹ, ɟɫɥɢ ɧɟ ɨɩɪɟɞɟɥɹɸɳɟɣ, ɬɨ ɫɭɳɟɫɬɜɟɧɧɨɣ ɞɥɹ ɩɨɜɟɞɟɧɢɹ ɞɚɧɧɨɣ ɫɭɛɫɬɚɧɰɢɢ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɷɬɚ ɝɪɚɧɢɰɚ ɞɨɜɨɥɶɧɨ ɪɚɡɦɵɬɚɹ, ɜ ɨɬɥɢɱɢɟ ɨɬ ɪɟɡɤɢɯ ɮɚɡɨɜɵɯ ɩɟɪɟɯɨɞɨɜ, ɢɦɟɸɳɢɯ ɦɟɫɬɨ ɫ ɩɨɜɵɲɟɧɢɟɦ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɫɨɩɪɨɜɨɠɞɚɸɳɢɯ ɩɪɟɜɪɚɳɟɧɢɟ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɜ ɠɢɞɤɨɫɬɶ, ɚ ɡɚɬɟɦ ɠɢɞɤɨɫɬɢ ɜ ɝɚɡ. ɇɟɤɨɬɨɪɨɟ ɪɚɜɧɨɜɟɫɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ (ɨɩɪɟɞɟɥɹɟɦɨɟ ɮɨɪɦɭɥɨɣ ɋɚɯɚ) ɩɪɢɫɭɬɫɬɜɭɟɬ ɜ ɝɚɡɟ ɩɪɢ ɥɸɛɨɣ ɬɟɦɩɟɪɚɬɭɪɟ, ɧɚɩɪɢɦɟɪ, ɫɜɨɛɨɞɧɵɟ ɡɚɪɹɞɵ ɜ ɩɥɚɦɟɧɢ ɨɛɵɱɧɨɣ ɫɜɟɱɢ. ɇɨ ɜɪɹɞ ɥɢ ɫɬɨɥɶ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɵɣ ɝɚɡ ɦɨɠɧɨ ɧɚɡɜɚɬɶ ɩɥɚɡɦɨɣ. ȼɦɟɫɬɟ ɫ ɬɟɦ, ɜ ɞɚɥɶɧɟɣɲɟɦ ɦɵ ɭɜɢɞɢɦ, ɱɬɨ ɬɢɩɢɱɧɨ ɩɥɚɡɦɟɧɧɵɟ ɩɪɨɰɟɫɫɵ ɧɚɛɥɸɞɚɸɬɫɹ ɜ ɝɚɡɟ-ɩɥɚɡɦɟ ɞɚɠɟ ɬɨɝɞɚ, ɤɨɝɞɚ ɢɨɧɢɡɨɜɚɧɵ ɬɨɥɶɤɨ ɞɨɥɢ ɩɪɨɰɟɧɬɚ ɜɫɟɯ ɱɚɫɬɢɰ. Ɇɨɠɧɨ ɪɚɫɫɭɠɞɚɬɶ ɢ ɨɬ ɨɛɪɚɬɧɨɝɨ: “ɢɫɬɢɧɧɚɹ” ɩɥɚɡɦɚ ɫɨɫɬɨɢɬ ɢɡ ɫɜɨɛɨɞɧɵɯ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɨɫɬɚɟɬɫɹ ɩɥɚɡɦɨɣ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɩɪɢɦɟɫɶ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ ɧɟ ɢɡɦɟɧɢɬ ɫɭɳɟɫɬɜɟɧɧɨ ɟɟ ɫɜɨɣɫɬɜ. ɇɨ ɜɨɡɧɢɤɚɟɬ ɜɨɩɪɨɫ ɦɨɠɧɨ ɥɢ, ɧɚɩɪɢɦɟɪ, ɧɚɡɜɚɬɶ ɩɥɚɡɦɨɣ ɧɟɫɤɨɦɩɟɧɫɢɪɨɜɚɧɧɵɟ ɩɨ ɡɚɪɹɞɭ ɩɭɱɤɢ ɭɫɤɨɪɟɧɧɵɯ ɱɚɫɬɢɰ, ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɟɦɵɟ ɜ ɮɢɡɢɱɟɫɤɢɯ ɷɤɫɩɟɪɢɦɟɧɬɚɯ? Ɇɨɠɧɨ ɥɢ ɧɚɡɜɚɬɶ ɩɥɚɡɦɨɣ ɜɟɫɶɦɚ ɪɚɡɪɟɠɟɧɧɵɣ ɦɟɠɡɜɟɡɞɧɵɣ ɢɥɢ ɦɟɠɝɚɥɚɤɬɢɱɟɫɤɢɣ ɝɚɡ, ɢɨɧɢɡɭɟɦɵɣ ɢɡɥɭɱɟɧɢɟɦ ɡɜɟɡɞ? Ɉɱɟɜɢɞɧɚ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɤɨɥɢɱɟɫɬɜɟɧɧɨɝɨ ɤɪɢɬɟɪɢɹ, ɩɨɡɜɨɥɹɸɳɟɝɨ ɨɩɪɟɞɟɥɢɬɶ, ɹɜɥɹɟɬɫɹ ɥɢ ɞɚɧɧɚɹ ɫɨɜɨɤɭɩɧɨɫɬɶ ɡɚɪɹɠɟɧɧɵɯ ɢ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ ɩɥɚɡɦɨɣ. Ɍɚɤɨɣ ɤɪɢɬɟɪɢɣ ɦɨɠɧɨ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ, ɨɩɢɪɚɹɫɶ ɧɚ ɩɨɧɹɬɢɹ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɱɚɫɬɨɬɵ ɢ ɞɟɛɚɟɜɫɤɨɝɨ ɪɚɞɢɭɫɚ (ɢɥɢ ɞɥɢɧɵ) ɷɤɪɚɧɢɪɨɜɚɧɢɹ. ɂɦɟɧɧɨ ɷɬɢ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɟ ɜ ɮɢɡɢɤɟ ɩɥɚɡɦɵ ɩɚɪɚɦɟɬɪɵ ɡɚɞɚɸɬ ɦɢɧɢɦɚɥɶɧɵɟ ɯɚɪɚɤɬɟɪɧɵɟ ɜɪɟɦɟɧɧɨɣ ɢ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɣ ɦɚɫɲɬɚɛɵ ɩɨɞɞɟɪɠɚɧɢɹ (ɢɥɢ ɫɩɨɧɬɚɧɧɨɝɨ ɧɚɪɭɲɟɧɢɹ) ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɢ ɩɥɚɡɦɵ. Ɉɩɢɪɚɹɫɶ ɧɚ ɷɬɢ ɩɨɧɹɬɢɹ, ɦɨɠɧɨ ɭɫɬɚɧɨɜɢɬɶ, ɩɨɱɟɦɭ ɩɥɚɡɦɟɧɧɵɟ ɫɜɨɣɫɬɜɚ ɩɪɨɹɜɥɹɸɬ, ɧɚ ɩɟɪɜɵɣ ɜɡɝɥɹɞ ɪɚɡɥɢɱɧɵɟ ɫɪɟɞɵ ɷɥɟɤɬɪɨɧɧɵɣ ɝɚɡ ɜ ɦɟɬɚɥɥɚɯ, ɷɥɟɤɬɪɨɧɧɨ-ɞɵɪɨɱɧɚɹ “ɠɢɞɤɨɫɬɶ” ɩɨɥɭɩɪɨɜɨɞɧɢɤɨɜ ɢɥɢ, ɧɚɩɪɢɦɟɪ, ɪɚɡɪɟɠɟɧɧɵɣ ɝɚɡ ɤɨɫɦɨɫɚ. ɗɬɢ, ɚ ɬɚɤɠɟ ɞɪɭɝɢɟ ɫɪɟɞɵ, ɧɚɩɪɢɦɟɪ ɷɥɟɤɬɪɨɥɢɬɵ, ɤ ɤɨɬɨɪɵɦ ɨɬɧɨɫɹɬɫɹ ɢ «ɪɚɛɨɱɢɟ ɠɢɞɤɨɫɬɢ» ɠɢɜɵɯ ɫɢɫɬɟɦ, ɢɧɨɝɞɚ ɧɚɡɵɜɚɸɬ ɩɥɚɡɦɨɩɨɞɨɛɧɵɦɢ [3,4]. ɗɬɨ ɩɨɞɱɟɪɤɢɜɚɟɬ ɜɚɠɧɨɫɬɶ ɯɚɪɚɤɬɟɪɧɵɯ ɞɥɹ ɩɥɚɡɦɵ ɡɚɤɨɧɨɜ ɩɪɢ ɨɩɢɫɚɧɢɢ ɫɜɨɣɫɬɜ ɫɬɨɥɶ ɛɨɥɶɲɨɝɨ ɢ ɜɚɠɧɨɝɨ ɜ ɩɪɚɤɬɢɱɟɫɤɨɦ ɩɪɢɦɟɧɟɧɢɢ ɱɢɫɥɚ ɨɛɴɟɤɬɨɜ ɩɪɢɪɨɞɵ. ɗɥɟɤɬɪɨɧɧɚɹ ɩɥɚɡɦɚ ɦɟɬɚɥɥɨɜ ɧɚɡɵɜɚɟɬɫɹ ɜɵɪɨɠɞɟɧɧɨɣ. Ʉɪɢɬɟɪɢɟɦ ɜɵɪɨɠɞɟɧɢɹ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɹɜɥɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɷɧɟɪɝɢɟɣ Ɏɟɪɦɢ, ɜɨɡɪɚɫɬɚɸɳɟɣ ɫ ɪɨɫɬɨɦ ɤɨɧɰɟɧɬɪɚɰɢɢ ɱɚɫɬɢɰ, ɢ ɬɟɩɥɨɜɨɣ ɷɧɟɪɝɢɟɣ. ȿɫɥɢ ɬɟɩɥɨɜɚɹ ɷɧɟɪɝɢɹ ɦɟɧɶɲɟ ɷɧɟɪɝɢɢ Ɏɟɪɦɢ, ɬɨ ɩɥɚɡɦɚ ɜɵɪɨɠɞɟɧɚ ɢ ɫɭɳɟɫɬɜɟɧɧɵ ɤɜɚɧɬɨɜɵɟ ɷɮɮɟɤɬɵ. Ɇɵ ɛɭɞɟɦ ɢɦɟɬɶ ɞɟɥɨ ɫ ɧɟɜɵɪɨɠɞɟɧɧɨɣ ɩɥɚɡɦɨɣ, ɬ.ɟ. ɫ ɬɚɤɨɣ ɩɥɚɡɦɨɣ, ɜ ɤɨɬɨɪɨɣ ɤɨɧɰɟɧɬɪɚɰɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɚ (ɢɥɢ ɬɟɦɩɟɪɚɬɭɪɚ ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɚ). ɋɬɪɨɝɨ ɝɨɜɨɪɹ, ɦɧɨɝɢɟ ɮɢɡɢɤɢ ɜɜɨɞɹɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɭɫɥɨɜɢɹ - ɫɱɢɬɚɸɬ, ɧɚɩɪɢɦɟɪ, ɨɛɹɡɚɬɟɥɶɧɨɣ ɤɨɦɩɨɧɟɧɬɨɣ ɩɥɚɡɦɵ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɟ ɢɡɥɭɱɟɧɢɟ. ɉɨɫɥɟɞɧɟɟ ɛɟɫɫɩɨɪɧɨ ɜɟɪɧɨ ɞɥɹ ɛɨɥɶɲɢɯ ɨɛɴɟɤɬɨɜ ɢɡ ɩɥɨɬɧɨɣ ɩɥɚɡɦɵ, ɧɚɩɪɢɦɟɪ, ɡɜɟɡɞ. ȼ ɧɢɯ ɢɡɥɭɱɟɧɢɟ "ɡɚɩɟɪɬɨ" ɢɡɥɭɱɟɧɢɟ ɦɨɠɟɬ ɜɵɯɨɞɢɬɶ ɥɢɲɶ ɢɡ ɫɪɚɜɧɢɬɟɥɶɧɨ ɬɨɧɤɢɯ ɧɚɪɭɠɧɵɯ ɫɥɨɟɜ. ȼ
3
ɛɨɥɶɲɢɧɫɬɜɟ ɥɚɛɨɪɚɬɨɪɧɵɯ ɭɫɬɪɨɣɫɬɜ ɩɥɚɡɦɚ ɨɩɬɢɱɟɫɤɢ ɬɨɧɤɚɹ, ɢɡɥɭɱɟɧɢɟ ɧɟ ɡɚɩɟɪɬɨ - ɨɧɨ ɫɜɨɛɨɞɧɨ ɩɪɨɯɨɞɢɬ ɱɟɪɟɡ ɜɫɸ ɩɥɚɡɦɭ. ɉɨɞɜɟɞɟɦ ɢɬɨɝɢ. ɉɨ ɫɨɜɪɟɦɟɧɧɵɦ ɩɪɟɞɫɬɚɜɥɟɧɢɹɦ ɩɥɚɡɦɚ - ɱɚɫɬɢɱɧɨ ɢɥɢ ɩɨɥɧɨɫɬɶɸ ɢɨɧɢɡɨɜɚɧɧɵɣ ɝɚɡ, ɜ ɤɨɬɨɪɨɦ ɨɛɴɟɦɧɵɟ ɩɥɨɬɧɨɫɬɢ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɡɚɪɹɞɨɜ ɩɪɚɤɬɢɱɟɫɤɢ ɨɞɢɧɚɤɨɜɵ. Ɍɚɤɨɟ ɫɜɨɣɫɬɜɨ ɩɥɚɡɦɵ ɧɚɡɵɜɚɸɬ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɶɸ. Ɂɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ ɩɥɚɡɦɵ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɫ ɫɢɥɨɣ, ɞɥɹ ɤɨɬɨɪɨɣ ɯɚɪɚɤɬɟɪɧɨ ɞɚɥɶɧɨɞɟɣɫɬɜɢɟ. ɗɬɨ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ ɨɩɪɟɞɟɥɹɟɬ ɢɫɤɥɸɱɢɬɟɥɶɧɭɸ ɪɨɥɶ ɜ ɩɥɚɡɦɟ, ɩɨɦɢɦɨ ɩɚɪɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɨɬɞɟɥɶɧɵɯ ɱɚɫɬɢɰ, ɤɨɥɥɟɤɬɢɜɧɵɯ ɷɮɮɟɤɬɨɜ, ɬ.ɟ. ɩɨɥɟɣ ɨɬ ɦɧɨɝɢɯ ɱɚɫɬɢɰ, ɩɪɨɹɜɥɹɸɳɢɯɫɹ ɜ ɧɚɪɚɫɬɚɧɢɢ ɩɥɚɡɦɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ, ɜɨɥɧ ɢ ɲɭɦɨɜ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɜɨɡɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰ ɩɥɚɡɦɵ. ȿɫɥɢ ɜɨɡɛɭɠɞɚɟɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɦɧɨɝɨ ɤɨɥɥɟɤɬɢɜɧɵɯ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ, ɬɨ ɤɨɥɟɛɚɧɢɹ ɩɥɚɡɦɵ ɫɬɚɧɨɜɹɬɫɹ ɧɟɪɟɝɭɥɹɪɧɵɦɢ, ɨɧɚ ɩɟɪɟɯɨɞɢɬ ɜ ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɬɭɪɛɭɥɟɧɬɧɨɟ ɫɨɫɬɨɹɧɢɟ. ȼ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɫɬɚɧɨɜɹɬɫɹ ɫɭɳɟɫɬɜɟɧɧɵɦɢ ɧɟɥɢɧɟɣɧɵɟ ɷɮɮɟɤɬɵ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɤɨɥɥɟɤɬɢɜɧɵɯ ɜɨɡɛɭɠɞɟɧɢɣ (ɦɨɞ) ɩɥɚɡɦɵ. ɇɟɥɢɧɟɣɧɵɟ ɹɜɥɟɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɫɭɳɟɫɬɜɟɧɧɵ ɢ ɜ ɪɟɝɭɥɹɪɧɵɯ ɩɪɨɰɟɫɫɚɯ, ɧɚɩɪɢɦɟɪ, ɩɪɢ ɜɨɡɞɟɣɫɬɜɢɢ ɧɚ ɩɥɚɡɦɭ ɜɨɥɧ ɤɨɧɟɱɧɨɣ ɚɦɩɥɢɬɭɞɵ. ɉɨɧɹɬɧɨ ɩɨɷɬɨɦɭ, ɱɬɨ ɫɨɜɪɟɦɟɧɧɚɹ ɮɢɡɢɤɚ ɩɥɚɡɦɵ - ɷɬɨ ɮɢɡɢɤɚ ɧɟɥɢɧɟɣɧɵɯ ɹɜɥɟɧɢɣ. ȿɳɟ ɨɞɧɚ ɨɫɨɛɟɧɧɨɫɬɶ ɷɬɨɝɨ ɧɨɜɨɝɨ ɫɨɫɬɨɹɧɢɹ ɜɟɳɟɫɬɜɚ - ɩɥɚɡɦɵ - ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɫɢɥɶɧɨɦ ɜɨɡɞɟɣɫɬɜɢɢ ɧɚ ɧɟɝɨ ɜɧɟɲɧɢɯ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɢ ɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ, ɜɵɡɵɜɚɸɳɢɯ ɩɨɹɜɥɟɧɢɟ ɨɛɴɟɦɧɵɯ ɡɚɪɹɞɨɜ ɢ ɬɨɤɨɜ. ȼɦɟɫɬɟ ɫ ɬɟɦ, ɫɭɳɟɫɬɜɟɧɧɨɟ ɪɚɡɞɟɥɟɧɢɟ ɡɚɪɹɞɨɜ ɜ ɩɥɚɡɦɟ ɡɚɬɪɭɞɧɟɧɨ ɜ ɫɢɥɭ ɟɟ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɢ: ɢɡ-ɡɚ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɣ ɩɥɨɬɧɨɫɬɢ ɡɚɪɹɠɟɧɧɨɣ ɤɨɦɩɨɧɟɧɬɵ ɜ ɩɥɚɡɦɟ ɨɛɴɟɦɧɵɣ ɡɚɪɹɞ ɜɵɡɵɜɚɥ ɛɵ ɩɨɹɜɥɟɧɢɟ ɫɥɢɲɤɨɦ ɛɨɥɶɲɢɯ ɫɨɛɫɬɜɟɧɧɵɯ ɩɨɥɟɣ ɩɥɚɡɦɵ, ɱɟɝɨ ɜ ɞɟɣɫɬɜɢɬɟɥɶɧɨɫɬɢ ɧɟ ɩɪɨɢɫɯɨɞɢɬ. ȼ ɨɩɪɟɞɟɥɟɧɧɨɦ ɫɦɵɫɥɟ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɶ ɩɥɚɡɦɵ ɟɫɬɶ ɩɪɨɹɜɥɟɧɢɟ ɬɨɝɨ ɫɜɨɣɫɬɜɚ, ɱɬɨ ɝɥɚɜɧɭɸ ɪɨɥɶ ɜ ɩɥɚɡɦɟ ɢɝɪɚɟɬ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɱɚɫɬɢɰ ɱɟɪɟɡ ɫɚɦɨɫɨɝɥɚɫɨɜɚɧɧɵɟ ɩɨɥɹ. ȼ ɷɬɨɦ ɨɬɧɨɲɟɧɢɢ ɞɢɧɚɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɜ ɩɥɚɡɦɟ ɹɜɥɹɸɬɫɹ ɜɟɫɶɦɚ ɫɥɨɠɧɵɦɢ ɹɜɥɟɧɢɹɦɢ. Ɉɧɢ ɬɪɟɛɭɸɬ ɢɡɭɱɟɧɢɹ ɧɟ ɬɨɥɶɤɨ ɞɢɧɚɦɢɤɢ ɱɚɫɬɢɰ ɜ ɡɚɞɚɧɧɵɯ ɜɧɟɲɧɢɯ ɩɨɥɹɯ, ɧɨ ɢ ɨɞɧɨɜɪɟɦɟɧɧɨɝɨ ɭɱɟɬɚ ɜɥɢɹɧɢɹ ɫɨɛɫɬɜɟɧɧɵɯ, ɫɨɝɥɚɫɨɜɚɧɧɵɯ ɫ ɞɜɢɠɟɧɢɟɦ ɱɚɫɬɢɰ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ, ɫɚɦɵɦ ɫɭɳɟɫɬɜɟɧɧɵɦ ɨɛɪɚɡɨɦ ɫɤɚɡɵɜɚɸɳɢɯɫɹ ɧɚ ɞɜɢɠɟɧɢɢ ɫɚɦɢɯ ɱɚɫɬɢɰ ɩɥɚɡɦɵ. ȼ ɡɚɤɥɸɱɟɧɢɟ ɧɟɥɢɲɧɟ ɩɨɞɱɟɪɤɧɭɬɶ, ɱɬɨ ɩɥɚɡɦɚ ɜɨ ȼɫɟɥɟɧɧɨɣ ɢ ɜ ɪɚɡɧɨɨɛɪɚɡɧɵɯ ɩɪɢɪɨɞɧɵɯ ɩɪɨɰɟɫɫɚɯ ɢ ɹɜɥɟɧɢɹɯ ɩɪɟɞɫɬɚɜɥɟɧɚ ɜɟɫɶɦɚ ɲɢɪɨɤɨ. Ɇɟɠɝɚɥɚɤɬɢɱɟɫɤɚɹ, ɦɟɠɡɜɟɡɞɧɚɹ ɢ ɦɟɠɩɥɚɧɟɬɧɚɹ ɩɥɚɡɦɚ, ɩɥɚɡɦɚ ɡɜɟɡɞ ɢ ɡɜɟɡɞɧɵɯ ɚɬɦɨɫɮɟɪ, ɨɬ Ȼɟɥɵɯ Ʉɚɪɥɢɤɨɜ ɞɨ Ʉɪɚɫɧɵɯ Ƚɢɝɚɧɬɨɜ, ɧɟɣɬɪɨɧɧɵɯ ɡɜɟɡɞ, ɩɭɥɶɫɚɪɨɜ ɢ ɱɟɪɧɵɯ ɞɵɪ, ɩɥɚɡɦɚ ɜɟɪɯɧɢɯ ɫɥɨɟɜ ɚɬɦɨɫɮɟɪɵ ɩɥɚɧɟɬ ɢ ɩɥɚɡɦɚ ɪɚɞɢɚɰɢɨɧɧɵɯ ɩɨɹɫɨɜ, ɩɥɚɡɦɚ ɝɪɨɡɨɜɵɯ ɪɚɡɪɹɞɨɜ ɢ ɝɚɡɨɪɚɡɪɹɞɧɚɹ ɩɥɚɡɦɚ ɥɚɛɨɪɚɬɨɪɧɵɯ ɭɫɬɪɨɣɫɬɜ, “ɬɟɪɦɨɹɞɟɪɧɚɹ” ɩɥɚɡɦɚ ɫɨɜɪɟɦɟɧɧɵɯ ɬɟɪɦɨɹɞɟɪɧɵɯ ɭɫɬɚɧɨɜɨɤ - ɜɨɬ ɞɚɥɟɤɨ ɧɟ ɩɨɥɧɵɣ ɩɟɪɟɱɟɧɶ ɩɪɢɥɨɠɟɧɢɣ ɧɚɭɤɢ ɨ ɩɥɚɡɦɟ. ɇɚɤɨɧɟɰ, ɜ ɫɚɦɵɟ ɩɟɪɜɵɟ ɦɝɧɨɜɟɧɢɹ ɠɢɡɧɢ ȼɫɟɥɟɧɧɨɣ ɩɨɫɥɟ Ȼɨɥɶɲɨɝɨ ȼɡɪɵɜɚ, ɤɨɝɞɚ ɪɨɞɢɥɫɹ ɧɚɲ ɦɢɪ, ɤɚɤ ɩɨɥɚɝɚɸɬ, ɜɟɳɟɫɬɜɨ ɬɚɤɠɟ ɧɚɯɨɞɢɥɨɫɶ ɜ ɫɨɫɬɨɹɧɢɢ ɝɨɪɹɱɟɣ ɩɥɚɡɦɵ, ɨɬɝɨɥɨɫɤɨɦ ɤɨɬɨɪɨɝɨ ɹɜɥɹɟɬɫɹ ɪɟɥɢɤɬɨɜɨɟ ɢɡɥɭɱɟɧɢɟ, ɫɨɫɬɨɹɳɟɟ ɫɟɣɱɚɫ ɢɡ “ɯɨɥɨɞɧɵɯ” (ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ ɨɤɨɥɨ 2.7Ʉ), ɚ ɬɨɝɞɚ “ɝɨɪɹɱɢɯ” ɤɜɚɧɬɨɜ, ɧɚɯɨɞɢɜɲɢɯɫɹ ɜ ɪɚɜɧɨɜɟɫɢɢ ɫ ɩɥɚɡɦɨɣ ɱɭɞɨɜɢɳɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ - ɜ ɫɨɬɧɢ ɦɢɥɥɢɨɧɨɜ ɢ ɦɢɥɥɢɚɪɞɨɜ ɝɪɚɞɭɫɨɜ.
4
ȽɅȺȼȺ 1
ɈɋɇɈȼɇɕȿ ɉɈɇəɌɂə ɂ ɋȼɈɃɋɌȼȺ ɉɅȺɁɆɕ §1. Ɉɛɪɚɡɨɜɚɧɢɟ ɩɥɚɡɦɵ Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɨɛɵɱɧɵɣ ɝɚɡ ɩɟɪɟɜɟɫɬɢ ɜ ɩɥɚɡɦɟɧɧɨɟ ɫɨɫɬɨɹɧɢɟ, ɧɟɨɛɯɨɞɢɦɨ ɢɨɧɢɡɢɪɨɜɚɬɶ ɡɚɦɟɬɧɭɸ ɱɚɫɬɶ ɦɨɥɟɤɭɥ ɢɥɢ ɚɬɨɦɨɜ. ɉɪɨɰɟɫɫ ɢɨɧɢɡɚɰɢɢ ɹɜɥɹɟɬɫɹ ɩɨɪɨɝɨɜɵɦ. ɑɬɨɛɵ ɚɬɨɦ ɫɬɚɥ ɢɨɧɢɡɢɪɨɜɚɧɧɵɦ, ɷɥɟɤɬɪɨɧ ɜ ɚɬɨɦɟ ɞɨɥɠɟɧ ɩɪɢɨɛɪɟɫɬɢ ɷɧɟɪɝɢɸ ɛɨɥɶɲɭɸ, ɱɟɦ ɟɝɨ ɷɧɟɪɝɢɹ ɫɜɹɡɢ. ɉɟɪɟɞɚɱɚ ɷɧɟɪɝɢɢ, ɞɨɫɬɚɬɨɱɧɨɣ ɞɥɹ ɪɚɡɪɵɜɚ ɷɬɨɣ ɫɜɹɡɢ, ɜɨɡɦɨɠɧɚ ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ ɚɬɨɦɚ ɢɥɢ ɦɨɥɟɤɭɥɵ ɫ ɞɪɭɝɨɣ ɛɵɫɬɪɨɣ ɱɚɫɬɢɰɟɣ - ɷɥɟɤɬɪɨɧɨɦ, ɢɨɧɨɦ, ɚɬɨɦɨɦ ɢɥɢ ɦɨɥɟɤɭɥɨɣ, ɩɪɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɫ ɮɨɬɨɧɨɦ, ɩɪɢ ɜɨɡɞɟɣɫɬɜɢɢ ɞɨɫɬɚɬɨɱɧɨ ɫɢɥɶɧɨɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. ɋɜɨɟɨɛɪɚɡɧɵɣ ɩɪɨɰɟɫɫ ɢɨɧɢɡɚɰɢɢ - ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ ɥɨɪɟɧɰ-ɢɨɧɢɡɚɰɢɹ, ɜɨɡɦɨɠɟɧ ɩɪɢ ɞɜɢɠɟɧɢɢ ɛɵɫɬɪɨɝɨ ɚɬɨɦɚ ɜ ɫɢɥɶɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ. Ⱦɟɥɨ ɡɞɟɫɶ ɜ ɬɨɦ, ɱɬɨ ɜ ɫɨɛɫɬɜɟɧɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ, ɬ.ɟ. ɜ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɨɬɨɪɨɣ ɚɬɨɦ ɧɟɩɨɞɜɢɠɟɧ, ɧɚ ɧɟɝɨ, ɫɨɝɥɚɫɧɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɦ Ʌɨɪɟɧɰɚ, ɞɟɣɫɬɜɭɟɬ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ E=(v/c)B. ȿɫɥɢ ɜɟɥɢɱɢɧɚ ɷɬɨɝɨ ɩɨɥɹ ɞɨɫɬɚɬɨɱɧɚ, ɚɬɨɦ ɦɨɠɟɬ ɛɵɬɶ ɢɨɧɢɡɢɪɨɜɚɧ. Ɋɚɫɫɦɨɬɪɢɦ ɩɪɨɰɟɫɫɵ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɩɪɨɢɡɨɣɬɢ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɞɜɭɯ ɛɵɫɬɪɵɯ (ɷɧɟɪɝɢɱɧɵɯ) ɦɨɥɟɤɭɥ Ⱥȼ ɢ CD: 1) Ⱥȼ + CD → Ⱥȼ + ɋD 2) Ⱥȼ + CD → Ⱥȼ* + ɋD
3) Ⱥȼ + ɋD → Ⱥ + ȼ + ɋD Ⱥȼ + CD → Ⱥȼ +ɋ+D Ⱥȼ + ɋD → Ⱥ + ȼ + ɋ + D 4) Ⱥȼ + ɋD → Ⱥȼ+ + ɋD + ɟ Ⱥȼ + ɋD → Ⱥȼ + CD+ + ɟ Ⱥȼ + ɋD → Aȼ+ + ȼɋ+ + 2ɟ
- ɭɩɪɭɝɨɟ ɪɚɫɫɟɹɧɢɟ; - ɧɟɭɩɪɭɝɨɟ ɪɚɫɫɟɹɧɢɟ. Ɇɨɥɟɤɭɥɚ Ⱥȼ* ɨɤɚɡɚɥɚɫɶ ɜ ɜɨɡɛɭɠɞɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ (ɡɧɚɱɨɤ * ). Ɇɨɠɟɬ ɨɤɚɡɚɬɶɫɹ ɜɨɡɛɭɠɞɟɧɧɨɣ CD* ɢɥɢ Ⱥȼ* ɢ ɋD* ɨɞɧɨɜɪɟɦɟɧɧɨ. ɉɨɥɧɚɹ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɭɦɟɧɶɲɢɥɚɫɶ ɧɚ ɷɧɟɪɝɢɸ ɜɨɡɛɭɠɞɟɧɢɹ. ȼɨɡɦɨɠɧɵ ɪɚɡɥɢɱɧɵɟ ɜɢɞɵ ɜɨɡɛɭɠɞɟɧɢɣ; -ɞɢɫɫɨɰɢɚɰɢɹ. Ɉɞɧɚ ɢɡ ɦɨɥɟɤɭɥ ɢɥɢ ɨɛɟ ɦɨɥɟɤɭɥɵ ɪɚɫɩɚɥɢɫɶ ɧɚ ɚɬɨɦɵ; -ɢɨɧɢɡɚɰɢɹ. Ɉɞɧɚ ɢɡ ɦɨɥɟɤɭɥ “ɩɨɬɟɪɹɥɚ” ɷɥɟɤɬɪɨɧ ɢ ɫɬɚɥɚ ɢɨɧɨɦ.
(ɢɥɢ
ɨɛɟ)
ȼ ɪɟɡɭɥɶɬɚɬɟ ɷɬɢɯ ɩɪɨɰɟɫɫɨɜ, ɤɚɤ ɦɵ ɜɢɞɢɦ, ɩɨɹɜɢɥɢɫɶ ɧɨɜɵɟ ɱɚɫɬɢɰɵ: ɜɨɡɛɭɠɞɟɧɧɵɟ ɦɨɥɟɤɭɥɵ, ɨɬɞɟɥɶɧɵɟ ɚɬɨɦɵ, ɢɨɧɵ ɢ ɷɥɟɤɬɪɨɧɵ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɥɸɛɚɹ ɢɡ ɦɨɥɟɤɭɥ ɦɨɠɟɬ ɫɬɨɥɤɧɭɬɶɫɹ ɫ ɥɸɛɨɣ ɢɡ ɷɬɢɯ ɧɨɜɵɯ ɱɚɫɬɢɰ, ɢ ɜɫɟ ɨɧɢ ɦɨɝɭɬ ɫɬɚɥɤɢɜɚɬɶɫɹ ɞɪɭɝ ɫ ɞɪɭɝɨɦ. ɉɪɢ ɷɬɨɦ ɜɨɡɦɨɠɧɵ ɧɟ ɬɨɥɶɤɨ “ɩɪɹɦɵɟ” ɩɪɨɰɟɫɫɵ, ɩɟɪɟɱɢɫɥɟɧɧɵɟ ɜɵɲɟ, ɧɨ ɢ ɨɛɪɚɬɧɵɟ. ɇɚɩɪɢɦɟɪ, ɩɪɨɰɟɫɫɨɦ ɨɛɪɚɬɧɵɦ ɞɢɫɫɨɰɢɚɰɢɢ ɹɜɥɹɟɬɫɹ ɚɫɫɨɰɢɚɰɢɹ - ɩɪɨɰɟɫɫ ɨɛɴɟɞɢɧɟɧɢɹ ɚɬɨɦɨɜ ɜ ɦɨɥɟɤɭɥɭ. ɉɪɨɰɟɫɫɨɦ, ɨɛɪɚɬɧɵɦ ɢɨɧɢɡɚɰɢɢ, ɹɜɥɹɟɬɫɹ ɪɟɤɨɦɛɢɧɚɰɢɹ. ɋɚɦɚ ɩɨ ɫɟɛɟ ɪɟɤɨɦɛɢɧɚɰɢɹ ɦɨɠɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɩɨ ɪɚɡɧɨɦɭ, ɧɚɩɪɢɦɟɪ ɜɨɡɦɨɠɧɵ: ɬɪɨɣɧɚɹ ɪɟɤɨɦɛɢɧɚɰɢɹ, ɢɡɥɭɱɚɬɟɥɶɧɚɹ ɪɟɤɨɦɛɢɧɚɰɢɹ ɢ ɞɢɫɫɨɰɢɚɬɢɜɧɚɹ ɪɟɤɨɦɛɢɧɚɰɢɹ. ȼ ɨɬɥɢɱɢɟ ɨɬ ɢɨɧɢɡɚɰɢɢ ɪɟɤɨɦɛɢɧɚɰɢɹ ɜɨɡɦɨɠɧɚ ɬɨɥɶɤɨ ɩɪɢ ɧɚɥɢɱɢɢ “ɬɪɟɬɶɟɝɨ ɬɟɥɚ”, ɭɧɨɫɹɳɟɝɨ ɢɡɛɵɬɨɤ ɷɧɟɪɝɢɢ, ɪɚɜɧɵɣ ɷɧɟɪɝɢɢ ɫɜɹɡɢ ɪɟɤɨɦɛɢɧɢɪɭɸɳɢɯ ɱɚɫɬɢɰ. 1
Ɍɚɤɢɦ ɬɪɟɬɶɢɦ ɬɟɥɨɦ ɦɨɠɟɬ ɛɵɬɶ ɟɳɟ ɨɞɢɧ ɷɥɟɤɬɪɨɧ, ɬɨɝɞɚ ɷɬɨ ɬɪɨɣɧɚɹ ɪɟɤɨɦɛɢɧɚɰɢɹ, ɮɨɬɨɧ - ɢɡɥɭɱɚɬɟɥɶɧɚɹ ɪɟɤɨɦɛɢɧɚɰɢɹ, ɢɥɢ ɷɧɟɪɝɢɹ ɫɜɹɡɢ ɚɬɨɦɨɜ ɜ ɦɨɥɟɤɭɥɹɪɧɨɦ ɢɨɧɟ - ɩɪɢ ɪɟɤɨɦɛɢɧɚɰɢɢ ɦɨɥɟɤɭɥɚ ɪɚɡɪɭɲɚɟɬɫɹ, ɩɨɷɬɨɦɭ ɷɬɨɬ ɩɪɨɰɟɫɫ ɧɚɡɵɜɚɟɬɫɹ ɞɢɫɫɨɰɢɚɬɢɜɧɨɣ ɪɟɤɨɦɛɢɧɚɰɢɟɣ. Ⱥɬɨɦɵ ɢ ɦɨɥɟɤɭɥɵ ɧɟ ɦɨɝɭɬ ɞɨɥɝɨ ɨɫɬɚɜɚɬɶɫɹ ɜ ɜɨɡɛɭɠɞɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ, ɩɨɫɤɨɥɶɤɭ ɜɨɡɛɭɠɞɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɢɦɟɸɬ ɜɩɨɥɧɟ ɨɩɪɟɞɟɥɟɧɧɨɟ ɤɨɧɟɱɧɨɟ ɜɪɟɦɹ ɠɢɡɧɢ, ɫɩɭɫɬɹ ɤɨɬɨɪɨɟ ɩɪɨɢɫɯɨɞɢɬ ɩɟɪɟɯɨɞ ɜ ɨɫɧɨɜɧɨɟ ɫɨɫɬɨɹɧɢɟ, ɫɨɩɪɨɜɨɠɞɚɸɳɢɣɫɹ ɢɡɥɭɱɟɧɢɟɦ ɤɜɚɧɬɚ. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜ ɚɬɨɦɚɯ ɜɨɡɦɨɠɧɵ ɜɨɡɛɭɠɞɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɬɨɥɶɤɨ ɷɥɟɤɬɪɨɧɧɵɯ ɭɪɨɜɧɟɣ, ɚ ɜ ɦɨɥɟɤɭɥɚɯ - ɬɚɤɠɟ ɟɳɟ ɜɨɡɛɭɠɞɟɧɢɹ ɤɨɥɟɛɚɬɟɥɶɧɵɯ ɢ ɜɪɚɳɚɬɟɥɶɧɵɯ ɭɪɨɜɧɟɣ. Ʉɨɥɟɛɚɬɟɥɶɧɵɟ ɜɨɡɛɭɠɞɟɧɢɹ ɨɬɦɟɱɚɸɬ ɢɧɞɟɤɫɨɦ ν, ɧɚɩɪɢɦɟɪ Ⱥȼν, ɜɪɚɳɚɬɟɥɶɧɵɟ, ɤɚɤ ɩɪɚɜɢɥɨ, ɢɧɞɟɤɫɨɦ j ɢɥɢ r (ɨɬ ɚɧɝɥɢɣɫɤɨɝɨ rotation), ɧɚɩɪɢɦɟɪ Dɋj (ɢɥɢ Dɋr). ȼɨɡɛɭɠɞɟɧɧɵɟ ɱɚɫɬɢɰɵ ɦɨɝɭɬ ɫɬɨɥɤɧɭɬɶɫɹ ɫ ɞɪɭɝɨɣ ɦɨɥɟɤɭɥɨɣ, ɚɬɨɦɨɦ, ɢɥɢ ɢɨɧɨɦ, ɩɟɪɟɞɚɬɶ ɢɦ ɜɫɸ ɷɧɟɪɝɢɸ ɜɨɡɛɭɠɞɟɧɢɹ (ɢɥɢ ɱɚɫɬɶ ɟɟ), ɢɥɢ ɜɵɞɟɥɢɬɶ ɷɧɟɪɝɢɸ ɜɨɡɛɭɠɞɟɧɢɹ ɜ ɜɢɞɟ ɤɜɚɧɬɚ (ɢɥɢ ɧɟɫɤɨɥɶɤɢɯ ɤɜɚɧɬɨɜ) ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɢɡɥɭɱɟɧɢɹ. Ɂɧɚɱɢɬ, ɩɨɹɜɥɟɧɢɟ ɜɨɡɛɭɠɞɟɧɧɵɯ ɱɚɫɬɢɰ ɨɛɹɡɚɬɟɥɶɧɨ ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɩɨɹɜɥɟɧɢɟɦ ɤɜɚɧɬɨɜ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɢɡɥɭɱɟɧɢɹ - ɮɨɬɨɧɨɜ. Ɍɚɤ ɤɚɤ ɱɚɫɬɢɰ ɭɠɟ ɦɧɨɝɨ: ɦɨɥɟɤɭɥɵ, ɚɬɨɦɵ, ɦɨɥɟɤɭɥɹɪɧɵɟ ɢ ɚɬɨɦɚɪɧɵɟ ɢɨɧɵ (ɜ ɨɫɧɨɜɧɨɦ ɢ ɜ ɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɹɯ), ɷɥɟɤɬɪɨɧɵ, ɮɨɬɨɧɵ, ɬɨ ɱɢɫɥɨ ɜɨɡɦɨɠɧɵɯ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣ ɫɬɚɧɨɜɢɬɫɹ ɨɱɟɧɶ ɛɨɥɶɲɢɦ ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɭɞɨɛɧɟɟ ɭɠɟ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɜɢɞɵ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣ, ɢɯ ɜɨɡɦɨɠɧɨɫɬɶ (ɢɥɢ ɧɟɜɨɡɦɨɠɧɨɫɬɶ), ɚ ɩɪɢ ɜɨɡɦɨɠɧɨɫɬɢ - ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ ɢɥɢ ɢɧɨɝɨ ɩɪɨɰɟɫɫɚ. Ɍɚɤɭɸ ɫɨɜɨɤɭɩɧɨɫɬɶ ɫɜɨɛɨɞɧɵɯ ɡɚɪɹɠɟɧɧɵɯ ɢ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ ɢ ɤɜɚɧɬɨɜ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɢɡɥɭɱɟɧɢɹ ɚɦɟɪɢɤɚɧɫɤɢɣ ɮɢɡɢɤ Ʌɟɧɝɦɸɪ ɜ 1928 ɝ. ɧɚɡɜɚɥ ɩɥɚɡɦɨɣ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɥɚɡɦɚ - ɷɬɨ ɝɚɡ, ɧɨ ɝɚɡ ɫɩɟɰɢɮɢɱɟɫɤɢɣ: ɜ ɧɟɦ ɦɨɝɭɬ ɩɪɢɫɭɬɫɬɜɨɜɚɬɶ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ, ɨɱɟɧɶ ɫɢɥɶɧɨ ɪɚɡɥɢɱɚɸɳɢɟɫɹ ɩɨ ɦɚɫɫɟ (ɜ ɬɵɫɹɱɢ ɢ ɞɟɫɹɬɤɢ ɬɵɫɹɱ ɪɚɡ). ɇɚɩɪɢɦɟɪ, ɩɨɥɧɨɫɬɶɸ ɢɨɧɢɡɢɪɨɜɚɧɧɚɹ ɜɨɞɨɪɨɞɧɚɹ ɩɥɚɡɦɚ ɜ ɤɚɱɟɫɬɜɟ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɤɨɦɩɨɧɟɧɬɵ ɫɨɞɟɪɠɢɬ ɢɨɧɵ ɜɨɞɨɪɨɞɚ, ɬ.ɟ. “ɝɨɥɵɟ” ɩɪɨɬɨɧɵ, ɚ ɨɬɪɢɰɚɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɨɣ ɤɨɦɩɨɧɟɧɬɨɣ, ɧɟɣɬɪɚɥɢɡɭɸɳɟɣ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɡɚɪɹɞ ɩɪɨɬɨɧɨɜ, ɹɜɥɹɸɬɫɹ ɷɥɟɤɬɪɨɧɵ. Ʉɚɤ ɢɡɜɟɫɬɧɨ, ɦɚɫɫɵ ɷɬɢɯ ɱɚɫɬɢɰ mp = 1.67⋅10-24 ɝ , me = 0.91⋅10-27 ɝ, ɢ ɞɥɹ ɨɬɧɨɲɟɧɢɹ ɷɬɢɯ ɦɚɫɫ ɩɨɥɭɱɚɟɦ ɩɪɢɛɥɢɠɟɧɧɨ mp/me≅1836. Ɇɚɫɫɵ ɷɥɟɦɟɧɬɚɪɧɵɯ ɱɚɫɬɢɰ ɱɚɫɬɨ ɢɡɦɟɪɹɸɬ ɜ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɟɞɢɧɢɰɚɯ. Ⱦɥɹ ɷɥɟɤɬɪɨɧɚ ɢ ɩɪɨɬɨɧɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɜɟɥɢɱɢɧɵ ɪɚɜɧɵ meɫ2≅511ɤɷȼ, mɪɫ2≅938ɦɷȼ. ɋɬɨɥɤɧɨɜɟɧɢɹ ɱɚɫɬɢɰ ɞɪɭɝ ɫ ɞɪɭɝɨɦ ɩɪɢɧɹɬɨ ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɫɟɱɟɧɢɹɦɢ ɫɬɨɥɤɧɨɜɟɧɢɣ σ . Ⱦɥɹ ɭɩɪɭɝɢɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɚɬɨɦɚɪɧɵɯ ɢɥɢ ɦɨɥɟɤɭɥɹɪɧɵɯ ɱɚɫɬɢɰ ɩɪɢ ɧɟɛɨɥɶɲɢɯ ɷɧɟɪɝɢɹɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɫɟɱɟɧɢɹ ɢɦɟɸɬ ɩɨɪɹɞɨɤ ɤɜɚɞɪɚɬɚ ɩɨɩɟɪɟɱɧɨɝɨ ɪɚɡɦɟɪɚ ɱɚɫɬɢɰ, ɚ ɞɥɹ ɫɬɨɥɤɧɨɜɟɧɢɣ ɦɟɞɥɟɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɫ ɚɬɨɦɨɦ − ɨɧɢ ɩɨɪɹɞɤɚ ɤɜɚɞɪɚɬɚ ɪɚɡɦɟɪɚ ɚɬɨɦɚ. ɇɚɩɪɢɦɟɪ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɪɚɡɦɟɪ ɚɬɨɦɚ ɜɨɞɨɪɨɞɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɞɢɭɫɨɦ Ȼɨɪɚ ɚB = 0.529⋅10-8ɫɦ, ɬɚɤ ɱɬɨ ɫɟɱɟɧɢɹ ɭɩɪɭɝɢɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɫɨɫɬɚɜɥɹɸɬ σ ɭɩɪ~10-16ɫɦ2. ɋɟɱɟɧɢɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ ɜ ɦɚɤɫɢɦɭɦɟ ɫɟɱɟɧɢɣ ɢɦɟɸɬ ɬɚɤɨɣ ɠɟ ɩɨɪɹɞɨɤ ɜɟɥɢɱɢɧɵ. ɉɪɢ ɷɬɨɦ ɧɚ ɩɨɪɨɝɟ ɢɨɧɢɡɚɰɢɢ, ɬɨ ɟɫɬɶ ɤɨɝɞɚ ɷɧɟɪɝɢɹ ɧɚɥɟɬɚɸɳɟɝɨ ɧɚ ɚɬɨɦ ɷɥɟɤɬɪɨɧɚ ɪɚɜɧɚ ɷɧɟɪɝɢɢ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚ, ɫɟɱɟɧɢɟ ɢɨɧɢɡɚɰɢɢ ɨɛɪɚɳɚɟɬɫɹ ɜ ɧɨɥɶ, ɡɚɬɟɦ ɩɨɫɥɟ ɩɪɨɯɨɠɞɟɧɢɹ ɦɚɤɫɢɦɭɦɚ ɭɛɵɜɚɟɬ ɫ ɪɨɫɬɨɦ ɷɧɟɪɝɢɢ ɫɬɨɥɤɧɨɜɟɧɢɹ. 2
ȼ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɩɪɢɜɟɞɟɦ ɮɨɪɦɭɥɭ, ɪɟɤɨɦɟɧɞɨɜɚɧɧɭɸ ɜ [5] ɞɥɹ ɨɰɟɧɤɢ ɜɟɥɢɱɢɧɵ ɫɟɱɟɧɢɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚɪɧɨɝɨ ɜɨɞɨɪɨɞɚ ɢɥɢ ɜɨɞɨɪɨɞɨɩɨɞɨɛɧɨɝɨ ɚɬɨɦɚ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ: 2
nl § R· σi = π a ¨ ¸ Φ ( u ), © I ¹ 2l + 1 2 B
(1.1)
ɝɞɟ ɷɧɟɪɝɢɹ R=(Ɋɢɞɛɟɪɝ)≅13.6 ɷȼ – ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɚ ɧɚ ɩɟɪɜɨɦ ɛɨɪɨɜɫɤɨɦ ɪɚɞɢɭɫɟ ɚɬɨɦɚ ɜɨɞɨɪɨɞɚ, I- ɷɧɟɪɝɢɹ ɢɨɧɢɡɚɰɢɢ, nl ɱɢɫɥɨ ɷɤɜɢɜɚɥɟɧɬɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɜ ɨɛɨɥɨɱɤɟ ɚɬɨɦɚ, l ɨɪɛɢɬɚɥɶɧɨɟ ɤɜɚɧɬɨɜɨɟ ɱɢɫɥɨ, E -ɷɧɟɪɝɢɹ ɢɨɧɢɡɢɪɭɸɳɟɝɨ ɷɥɟɤɬɪɨɧɚ, ɚ u=(E-I)/I. Ɏɭɧɤɰɢɹ Ɏ(u) ɜ ɛɨɪɧɨɜɫɤɨɦ ɩɪɢɛɥɢɠɟɧɢɢ, ɫɩɪɚɜɟɞɥɢɜɨɦ, ɤɨɝɞɚ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɚ ɜɟɥɢɤɚ (u>1), ɪɚɜɧɚ
Φ ( u > 1) =
0.57 u + 1 . ln u + 1 0.012
(1.2)
ɋɟɱɟɧɢɹ ɢɨɧɢɡɚɰɢɢ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ ɞɥɹ ɭɩɨɬɪɟɛɢɬɟɥɶɧɵɯ ɧɚ ɩɪɚɤɬɢɤɟ ɝɚɡɨɜ ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 1.1. Ɋɢɫ. 1.1. ɋɟɱɟɧɢɹ ɢɨɧɢɡɚɰɢɢ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ ɢɡ ɨɫɧɨɜɧɨɝɨ ɫɨɫɬɨɹɧɢɹ
ɋɟɱɟɧɢɹ ɮɨɬɨɢɨɧɢɡɚɰɢɢ ɨɛɵɱɧɨ ɧɚ ɞɜɚ - ɬɪɢ ɩɨɪɹɞɤɚ ɧɢɠɟ ɫɟɱɟɧɢɣ ɢɨɧɢɡɚɰɢɢ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ.
ȼ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɩɪɢɜɟɞɟɦ ɮɨɪɦɭɥɭ ɞɥɹ ɪɚɫɱɟɬɚ ɫɟɱɟɧɢɹ ɮɨɬɨɢɨɧɢɡɚɰɢɢ ɜɨɞɨɪɨɞɚ ɢɥɢ ɜɨɞɨɪɨɞɨɩɨɞɨɛɧɨɝɨ ɢɨɧɚ[5]: 4
σ ph ɝɞɟ
π 2 α a B2 § ωth · exp( −4κ arctgκ ) =2 , ¨ ¸ 3 Z 2 © ω ¹ 1 − exp( −2πκ )
α = 1137
9
- ɩɨɫɬɨɹɧɧɚɹ ɬɨɧɤɨɣ ɫɬɪɭɤɬɭɪɵ,
ω
κ=
ω ω − ωth
,
(1.3)
- ɤɪɭɝɨɜɚɹ ɱɚɫɬɨɬɚ ɮɨɬɨɧɚ, ɢɨɧɢɡɢɪɭɸɳɟɝɨ ɚɬɨɦ,
ωth - ɝɪɚɧɢɱɧɚɹ ɱɚɫɬɨɬɚ, ɧɢɠɟ ɤɨɬɨɪɨɣ ɢɨɧɢɡɚɰɢɹ ɧɟɜɨɡɦɨɠɧɚ. Ⱦɥɹ ɜɨɞɨɪɨɞɚ ɝɪɚɧɢɱɧɚɹ ɱɚɫɬɨɬɚ, ɢɡɦɟɪɟɧɧɚɹ ɜ ɨɛɪɚɬɧɵɯ ɫɚɧɬɢɦɟɬɪɚɯ, ɤɚɤ ɷɬɨ ɨɛɵɱɧɨ ɞɟɥɚɸɬ ɜ ɫɩɟɤɬɪɨɫɤɨɩɢɢ, ɪɚɜɧɚ 109678,758 ɫɦ-1. Ʌɸɛɨɩɵɬɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ, ɜ ɨɬɥɢɱɢɟ ɨɬ ɫɟɱɟɧɢɹ ɢɨɧɢɡɚɰɢɢ ɷɥɟɤɬɪɨɧɚɦɢ, ɫɟɱɟɧɢɟ ɮɨɬɨɧɧɨɣ ɢɨɧɢɡɚɰɢɢ ɧɟ ɨɛɪɚɳɚɟɬɫɹ ɜ ɧɨɥɶ ɧɚ ɩɨɪɨɝɟ, ɚ ɫɬɪɟɦɢɬɫɹ, ɤɚɤ ɥɟɝɤɨ ɩɪɨɜɟɪɢɬɶ, ɤ ɤɨɧɟɱɧɨɦɭ ɩɪɟɞɟɥɭ. Cɟɱɟɧɢɟ ɮɨɬɨɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚ ɜɨɞɨɪɨɞɚ ɮɨɬɨɧɚɦɢ, ɷɧɟɪɝɢɹ ɤɨɬɨɪɵɯ ɦɧɨɝɨ ɛɨɥɶɲɟ ɷɧɟɪɝɢɢ ɫɜɹɡɢ ɷɥɟɤɬɪɨɧɚ ɜ ɚɬɨɦɟ, ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɫ ɩɨɦɨɳɶɸ ɝɨɪɚɡɞɨ ɦɟɧɟɟ ɝɪɨɦɨɡɞɤɨɣ ɮɨɪɦɭɥɵ [6]: /2 σ ph [ ɫɦ 2 ] = 23.8 λ7[ ɫɦ ].
ɋɟɱɟɧɢɟ ɮɨɬɨɢɨɧɢɡɚɰɢɢ ɞɥɹ ɫɢɥɶɧɨɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɫ ɝɥɚɜɧɵɦ ɤɜɚɧɬɨɜɵɦ ɱɢɫɥɨɦ n ɭɦɟɧɶɲɚɟɬɫɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ n−5.
ɇɚɤɨɧɟɰ. ɨɬɦɟɬɢɦ, ɱɬɨ ɞɥɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ (ɩɨɥɟɜɚɹ ɢɨɧɢɡɚɰɢɹ) ɩɨɪɨɝɨɜɨɟ ɡɧɚɱɟɧɢɟ ɩɨɥɹ ɫɨɫɬɚɜɥɹɟɬ E ~ 108 ȼ/ɫɦ, ɚ ɢɨɧɢɡɚɰɢɹ ɢɡ ɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɜɨɡɦɨɠɧɚ ɩɪɢ ɦɟɧɶɲɢɯ ɩɨɥɹɯ E ~ 106 ȼ/ɫɦ.
3
§2. Ʉɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɶ, ɩɥɚɡɦɟɧɧɚɹ ɱɚɫɬɨɬɚ ɉɥɚɡɦɚ ɜ ɰɟɥɨɦ ɞɨɥɠɧɚ ɛɵɬɶ ɷɥɟɤɬɪɢɱɟɫɤɢ ɧɟɣɬɪɚɥɶɧɚ, ɤɨɥɢɱɟɫɬɜɚ ɪɚɡɧɨɢɦɟɧɧɵɯ ɡɚɪɹɞɨɜ ɜ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɣ ɟɞɢɧɢɰɟ ɟɟ ɨɛɴɟɦɚ ɪɚɜɧɵ. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɜɨɡɧɢɤɧɭɬ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɩɨɥɹ, ɬɟɦ ɛɨɥɶɲɢɟ, ɱɟɦ ɛɨɥɶɲɟ ɞɢɫɛɚɥɚɧɫ ɡɚɪɹɞɨɜ, ɚ ɫɨɡɞɚɧɢɟ ɬɚɤɢɯ ɩɨɥɟɣ ɬɪɟɛɭɟɬ ɫɨɜɟɪɲɟɧɢɹ ɪɚɛɨɬɵ ɩɨ ɪɚɡɞɟɥɟɧɢɸ ɡɚɪɹɞɨɜ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɧɟɲɧɢɯ ɜɨɡɞɟɣɫɬɜɢɣ ɷɬɚ ɪɚɛɨɬɚ ɦɨɠɟɬ ɩɪɨɢɡɜɨɞɢɬɶɫɹ ɬɨɥɶɤɨ ɡɚ ɫɱɟɬ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɫɚɦɢɯ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ. ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɜ ɧɟɤɨɬɨɪɨɦ ɨɛɴɟɦɟ ɮɥɭɤɬɭɚɬɢɜɧɨ ɪɚɡɨɲɥɢɫɶ ɡɚɪɹɞɵ (ɪɢɫ.1.2, ɫɱɢɬɚɟɦ, ɱɬɨ ɢɨɧɵ ɩɨɤɨɹɬɫɹ, ɚ ɷɥɟɤɬɪɨɧɵ ɭɯɨɞɹɬ), ɢ ɨɰɟɧɢɦ ɦɚɤɫɢɦɚɥɶɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɬɚɤɨɝɨ Ɋɢɫ. 1.2. ɋɯɟɦɚ ɪɚɡɞɟɥɟɧɢɹ ɡɚɪɹɞɨɜ ɪɚɫɯɨɠɞɟɧɢɹ. Ɋɚɫɯɨɞɹɳɢɟɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɟ x ɡɚɪɹɞɵ ɫɨɡɞɚɸɬ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ȿ=4πnex. Ɂɞɟɫɶ n - ɤɨɧɰɟɧɬɪɚɰɢɹ ɩɥɚɡɦɵ, ɚ ɟ - ɷɥɟɦɟɧɬɚɪɧɵɣ ɡɚɪɹɞ (ɪɚɜɧɵɣ ɩɨ ɜɟɥɢɱɢɧɟ ɡɚɪɹɞɭ ɷɥɟɤɬɪɨɧɚ). ɋɢɥɚ ɫɨ ɫɬɨɪɨɧɵ ɩɨɥɹ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɷɥɟɦɟɧɬɚɪɧɵɣ ɡɚɪɹɞ, ɪɚɜɧɚ ɟȿ; ɪɚɛɨɬɚ ɩɨ ɪɚɡɞɟɥɟɧɢɸ ɡɚɪɹɞɨɜ ɧɚ ɪɚɫɫɬɨɹɧɢɟ d ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ: d
A = ³ eEdx = 0
4π ⋅ e 2 n 2 d , 2
(1.4)
ɢ ɨɧɚ ɧɟ ɦɨɠɟɬ ɩɪɟɜɵɲɚɬɶ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɬɟɩɥɨɜɨɝɨ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰɵ, ɞɥɹ ɨɞɧɨɦɟɪɧɨɝɨ ɞɜɢɠɟɧɢɹ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɪɚɜɧɭɸ (1/2)Ɍ (ɡɞɟɫɶ, ɤɚɤ ɷɬɨ ɱɚɫɬɨ ɞɟɥɚɟɬɫɹ ɞɥɹ ɤɪɚɬɤɨɫɬɢ, ɦɵ ɢɫɩɨɥɶɡɭɟɦ ɨɛɨɡɧɚɱɟɧɢɟ Ɍ ɜɦɟɫɬɨ ɩɪɨɢɡɜɟɞɟɧɢɹ kȻT, ɢɡɦɟɪɹɹ, ɬɟɦ ɫɚɦɵɦ, ɬɟɦɩɟɪɚɬɭɪɭ ɜ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɟɞɢɧɢɰɚɯ). Ɉɬɫɸɞɚ
d=
T . 4πne 2
(1.5)
ɇɚ ɦɚɫɲɬɚɛɚɯ, ɦɟɧɶɲɢɯ d, ɜɫɟɝɞɚ ɛɭɞɭɬ ɜɨɡɧɢɤɚɬɶ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɩɨɥɹ; ɮɥɭɤɬɭɚɰɢɢ ɧɟɢɡɛɟɠɧɵ. Ⱥ ɜɨɬ ɪɚɡɨɣɬɢɫɶ ɧɚ ɪɚɫɫɬɨɹɧɢɹ, ɫɭɳɟɫɬɜɟɧɧɨ ɛɨɥɶɲɢɟ ɱɟɦ d, ɱɚɫɬɢɰɵ ɧɟ ɦɨɝɭɬ. ɉɨɷɬɨɦɭ ɩɥɚɡɦɚ ɢ ɹɜɥɹɟɬɫɹ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɣ - ɧɟɣɬɪɚɥɶɧɚɹ ɜ ɛɨɥɶɲɢɯ ɨɛɴɟɦɚɯ, ɧɨ ɜɫɟɝɞɚ ɫ ɷɥɟɤɬɪɢɱɟɫɤɢɦɢ ɩɨɥɹɦɢ ɧɚ ɪɚɫɫɬɨɹɧɢɹɯ ɦɚɫɲɬɚɛɚ d, ɡɚɜɢɫɹɳɟɝɨ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ. ȼɟɥɢɱɢɧɭ d ɨɛɵɱɧɨ ɧɚɡɵɜɚɸɬ ɞɟɛɚɟɜɫɤɢɦ ɪɚɞɢɭɫɨɦ (ɫɦ. ɫɥɟɞɭɸɳɢɣ ɩɚɪɚɝɪɚɮ). Ⱦɥɹ ɬɟɪɦɨɹɞɟɪɧɨɣ ɩɥɚɡɦɵ ɫ ɩɚɪɚɦɟɬɪɚɦɢ n≅1014ɫɦ-3, Ɍ≅104ɷȼ, ɩɨɥɭɱɚɟɦ d≅5⋅10-3ɫɦ. ɗɥɟɤɬɪɢɱɟɫɤɢɟ ɩɨɥɹ ɪɚɡɞɟɥɟɧɢɹ ɡɚɪɹɞɨɜ ɛɭɞɭɬ ɞɟɣɫɬɜɨɜɚɬɶ ɧɚ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ. ɉɨɥɚɝɚɹ, ɱɬɨ ɢɨɧɵ ɩɨɤɨɹɬɫɹ, ɪɚɫɫɦɨɬɪɢɦ ɞɜɢɠɟɧɢɟ ɧɟɤɨɬɨɪɨɝɨ ɜɵɞɟɥɟɧɧɨɝɨ ɷɥɟɤɬɪɨɧɚ ɜ ɬɚɤɨɦ ɨɞɧɨɦɟɪɧɨɦ ɩɨɥɟ ȿ (ɫɦ. ɪɢɫ. 1.2). ɍɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɧɚ ɨɤɚɡɵɜɚɟɬɫɹ ɫɥɟɞɭɸɳɢɦ
me x = − eE = −4πne 2 x ,
(1.6)
ɢ ɫɨɜɩɚɞɚɟɬ ɩɨ ɜɢɞɭ ɫ ɭɪɚɜɧɟɧɢɟɦ ɞɜɢɠɟɧɢɹ ɞɥɹ ɨɞɧɨɦɟɪɧɨɝɨ ɨɫɰɢɥɥɹɬɨɪɚ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɷɥɟɤɬɪɨɧ ɛɭɞɟɬ ɫɨɜɟɪɲɚɬɶ ɤɨɥɟɛɚɧɢɹ ɫ ɱɚɫɬɨɬɨɣ
ωp =
4πne 2 . me
(1.7)
ɗɬɭ ɱɚɫɬɨɬɭ, ɹɜɥɹɸɳɭɸɫɹ ɯɚɪɚɤɬɟɪɧɨɣ ɨɫɨɛɟɧɧɨɫɬɶɸ ɩɥɚɡɦɵ, ɧɚɡɵɜɚɸɬ ɩɥɚɡɦɟɧɧɨɣ (ɢ ɨɛɨɡɧɚɱɚɸɬ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɤɚɤ ωɪ ɢɥɢ ω0) ɢɥɢ ɷɥɟɤɬɪɨɧɧɨɣ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɱɚɫɬɨɬɨɣ (ɢ ɨɛɨɡɧɚɱɚɸɬ ɤɚɤ ωLe). ɋɥɟɞɭɟɬ ɩɨɞɱɟɪɤɧɭɬɶ, ɱɬɨ ɨɧɚ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ.
Ⱦɥɹ ɬɟɪɦɨɹɞɟɪɧɨɣ ɩɥɚɡɦɵ ɫ ɩɥɨɬɧɨɫɬɶɸ n≅1014ɫɦ-3 ɱɚɫɬɨɬɚ ɥɟɧɝɦɸɪɨɜɫɤɢɯ ɤɨɥɟɛɚɧɢɣ ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ ωp≅6⋅1011c-1.
§ 3. Ⱦɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ, ɞɟɛɚɟɜɫɤɢɣ ɫɥɨɣ Ʉɚɠɞɚɹ ɡɚɪɹɠɟɧɧɚɹ ɱɚɫɬɢɰɚ ɜ ɩɥɚɡɦɟ ɜɡɚɢɦɨɞɟɣɫɬɜɭɟɬ ɫ ɞɪɭɝɢɦɢ ɡɚɪɹɠɟɧɧɵɦɢ ɱɚɫɬɢɰɚɦɢ. ɉɨɷɬɨɦɭ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ϕ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜɵɞɟɥɟɧɧɨɣ ɱɚɫɬɢɰɵ ɢ ɨɤɪɭɠɚɸɳɢɯ ɟɺ ɱɚɫɬɢɰ ɡɚɜɢɫɢɬ ɨɬ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɝɨ ɪɚɫɩɨɥɨɠɟɧɢɹ ɷɬɢɯ ɱɚɫɬɢɰ. ȼ ɩɨɥɟ ɞɚɧɧɨɣ ɱɚɫɬɢɰɵ ɩɥɨɬɧɨɫɬɶ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɪɚɜɧɨɜɟɫɢɢ ɞɨɥɠɧɚ ɛɵɬɶ ɪɚɫɩɪɟɞɟɥɟɧɚ ɩɨ ɡɚɤɨɧɭ Ȼɨɥɶɰɦɚɧɚ § eϕ · (1.8) n = n0 exp¨ − ¸ , © T ¹ ɝɞɟ n0 – ɤɨɧɰɟɧɬɪɚɰɢɹ ɱɚɫɬɢɰ ɧɟɜɨɡɦɭɳɟɧɧɨɣ ɩɥɚɡɦɵ ɜɞɚɥɢ ɨɬ ɜɵɞɟɥɟɧɧɨɣ ɱɚɫɬɢɰɵ, ϕ ɩɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ. ɇɚɩɢɲɟɦ ɬɟɩɟɪɶ ɭɪɚɜɧɟɧɢɟ ɉɭɚɫɫɨɧɚ (ɜ ɫɮɟɪɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ) ɞɥɹ ɩɨɥɹ ɱɚɫɬɢɰ ɩɥɚɡɦɵ, ɨɤɪɭɠɚɸɳɢɯ ɜɵɞɟɥɟɧɧɭɸ ɱɚɫɬɢɰɭ: 1 ∂2 ( rϕ ) = −4πe( Zni − ne ) , r ∂r 2 ɝɞɟ ni,e – ɤɨɧɰɟɧɬɪɚɰɢɹ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɩɥɚɡɦɵ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, Z – ɤɪɚɬɧɨɫɬɶ ɢɨɧɢɡɚɰɢɢ ɢɨɧɚ ɩɥɚɡɦɵ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɫɱɢɬɚɟɦ, ɱɬɨ ɩɥɚɡɦɚ ɫɨɫɬɨɢɬ ɢɡ ɷɥɟɤɬɪɨɧɨɜ ɢ ɨɞɢɧɚɤɨɜɵɯ ɩɨɥɨɠɢɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɵɯ ɢɨɧɨɜ ɫ ɨɞɢɧɚɤɨɜɨɣ ɤɪɚɬɧɨɫɬɶɸ ɢɨɧɢɡɚɰɢɢ. Ⱦɥɹ ɦɧɨɝɨɤɨɦɩɨɧɟɧɬɧɨɣ ɩɥɚɡɦɵ ɫ ɢɨɧɚɦɢ ɪɚɡɧɵɯ ɫɨɪɬɨɜ ɢ ɫ ɪɚɡɧɨɣ ɤɪɚɬɧɨɫɬɶɸ ɢɨɧɢɡɚɰɢɢ ɧɟɨɛɯɨɞɢɦɨ ɛɵɥɨ ɛɵ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ ɩɪɨɢɡɜɨɞɢɬɶ ɫɭɦɦɢɪɨɜɚɧɢɟ ɩɨ ɜɫɟɦ ɫɨɪɬɚɦ ɢ ɜɫɟɦ ɤɪɚɬɧɨɫɬɹɦ ɢɨɧɢɡɚɰɢɢ ɱɚɫɬɢɰ. ɋɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɨɛɨɛɳɟɧɢɟ ɨɱɟɜɢɞɧɨ ɢ ɦɨɠɟɬ ɛɵɬɶ ɛɟɡ ɬɪɭɞɚ ɩɨɥɭɱɟɧɨ, ɩɨɷɬɨɦɭ, ɱɬɨɛɵ ɧɟ ɭɫɥɨɠɧɹɬɶ ɮɨɪɦɵ ɡɚɩɢɫɢ ɨɤɨɧɱɚɬɟɥɶɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ, ɡɞɟɫɶ ɨɝɪɚɧɢɱɢɦɫɹ ɭɤɚɡɚɧɧɨɣ ɩɪɨɫɬɨɣ ɦɨɞɟɥɶɸ ɞɜɭɯɤɨɦɩɨɧɟɧɬɧɨɣ ɢɨɧ-ɷɥɟɤɬɪɨɧɧɨɣ ɩɥɚɡɦɵ.
ɍɱɬɟɦ, ɱɬɨ ɩɥɨɬɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɜ ɩɨɥɟ ɜɵɞɟɥɟɧɧɨɣ ɱɚɫɬɢɰɵ ɩɨɞɱɢɧɹɸɬɫɹ ɡɚɤɨɧɭ Ȼɨɥɶɰɦɚɧɚ (1.8), ɢ ɩɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɬɟɦɩɟɪɚɬɭɪɵ Ɍe ɢ Ɍi ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɩɥɚɡɦɵ ɦɨɝɭɬ ɛɵɬɶ ɪɚɡɧɵɦɢ. Ɉɝɪɚɧɢɱɢɜɚɹɫɶ ɥɢɧɟɣɧɵɦ ɩɪɢɛɥɢɠɟɧɢɟɦ, ɬ.ɟ. ɫɱɢɬɚɹ |eϕ|d (ɪɢɫ.1.3). ɉɪɢɦɟɦ ɞɥɹ ɩɪɨɫɬɨɬɵ, ɱɬɨ ɩɥɚɡɦɚ ɹɜɥɹɟɬɫɹ ɢɡɨɬɟɪɦɢɱɟɫɤɨɣ Ɍe=Ɍi, ɢ ɫɨɫɬɨɢɬ ɢɡ ɷɥɟɤɬɪɨɧɨɜ ɢ ɨɞɧɨɡɚɪɹɞɧɵɯ ɢɨɧɨɜ ɫ ɤɪɚɬɧɨɫɬɶɸ ɢɨɧɢɡɚɰɢɢ Z=1, ɬɚɤ ɱɬɨ ɭɫɥɨɜɢɟ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɢ ɡɚɩɢɫɵɜɚɟɬɫɹ ɬɟɩɟɪɶ ɜ ɜɢɞɟ noi=noe=no. Ɍɨɝɞɚ ɭɪɚɜɧɟɧɢɟ ɉɭɚɫɫɨɧɚ ɞɥɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɚ ɜɛɥɢɡɢ ɷɥɟɤɬɪɨɞɚ ɫ ɭɱɟɬɨɦ (1.8) ɛɭɞɟɬ ɫɥɟɞɭɸɳɢɦ: dE d 2ϕ § eϕ · = − 2 = 4πe( ni − ne ) = −8πen0 sh¨ ¸ . (1.12) © T ¹ dx dx ɉɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɨɫɶ ɯ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚ ɤ ɷɥɟɤɬɪɨɞɭ. Ɋɟɲɟɧɢɟ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ, ɱɬɨ eϕ/TɌe, ɬɨ ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ, ɫɨɜɩɚɞɚɸɳɟɟ ɫ ɮɨɪɦɭɥɨɣ (1.5) (ɬɟɩɟɪɶ c ɬɟɦɩɟɪɚɬɭɪɨɣ Ɍe ɜ ɤɚɱɟɫɬɜɟ Ɍ), ɢ ɨɬɥɢɱɚɸɳɟɟɫɹ ɨɬ ɜɵɪɚɠɟɧɢɹ, ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɮɨɪɦɭɥɨɣ (1.13), ɜɫɟɝɨ ɜ 2 ɪɚɡ. ɉɨɷɬɨɦɭ ɜ ɥɸɛɨɣ ɩɥɚɡɦɟ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɟ ɦɚɫɲɬɚɛɵ ɷɤɪɚɧɢɪɨɜɚɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ ɢ ɮɥɭɤɬɭɚɬɢɜɧɨɝɨ ɪɚɡɞɟɥɟɧɢɹ ɡɚɪɹɞɨɜ ɩɪɢɦɟɪɧɨ ɨɞɢɧɚɤɨɜɵ. ɉɪɢ ɷɬɨɦ ɪɚɞɢɭɫ ɷɤɪɚɧɢɪɨɜɚɧɢɹ ɩɨɥɹ ɩɪɨɛɧɨɝɨ ɡɚɪɹɞɚ ɢɥɢ ɞɥɢɧɚ ɫɥɨɹ ɷɤɪɚɧɢɪɨɜɚɧɢɹ ɜɧɟɲɧɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɫɨɜɩɚɞɚɸɬ. Ɍɚɤ ɠɟ, ɤɚɤ ɢ ɧɚɥɢɱɢɟ ɥɟɧɝɦɸɪɨɜɫɤɢɯ ɤɨɥɟɛɚɧɢɣ ɫ ɩɥɚɡɦɟɧɧɨɣ ɱɚɫɬɨɬɨɣ, ɷɤɪɚɧɢɪɨɜɚɧɢɟ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ - ɜɚɠɧɚɹ ɯɚɪɚɤɬɟɪɧɚɹ ɨɫɨɛɟɧɧɨɫɬɶ ɩɥɚɡɦɵ.
je =
ɉɨɞɱɟɪɤɧɟɦ ɜ ɡɚɤɥɸɱɟɧɢɟ ɟɳɟ ɨɞɧɨ ɜɚɠɧɨɟ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ. ȼ ɩɪɟɞɵɞɭɳɟɦ ɩɚɪɚɝɪɚɮɟ ɩɪɢ ɜɵɜɨɞɟ ɮɨɪɦɭɥɵ ɞɥɹ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɱɚɫɬɨɬɵ ɩɪɟɧɟɛɪɟɝɚɥɨɫɶ ɜɨɡɦɨɠɧɨɫɬɶɸ ɜɨɜɥɟɱɟɧɢɹ ɜ ɞɜɢɠɟɧɢɟ ɢɨɧɨɜ, ɩɪɨɫɬɨ ɤɚɤ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɟɟ ɦɚɫɫɢɜɧɨɣ ɤɨɦɩɨɧɟɧɬɵ ɩɥɚɡɦɵ. ɇɟɬɪɭɞɧɨ ɨɬɤɚɡɚɬɶɫɹ ɨɬ ɷɬɨɝɨ ɩɪɟɞɩɨɥɨɠɟɧɢɹ ɢ ɮɚɤɬɢɱɟɫɤɢ ɩɨɜɬɨɪɹɹ ɷɬɨɬ ɜɵɜɨɞ, ɧɨ, ɭɱɢɬɵɜɚɹ ɬɟɩɟɪɶ ɤɨɧɟɱɧɨɫɬɶ ɨɬɧɨɲɟɧɢɹ ɦɚɫɫ ɱɚɫɬɢɰ, ɦɨɠɧɨ ɩɨɤɚɡɚɬɶ, ɱɬɨ ɩɨɥɧɚɹ ɮɨɪɦɭɥɚ, ɜɦɟɫɬɨ (1.7), ɞɥɹ ɱɚɫɬɨɬɵ ɩɥɚɡɦɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɨɤɚɡɵɜɚɟɬɫɹ ɫɥɟɞɭɸɳɟɣ:
ω p = ω Le2 + ω Li2 , ω Le =
4πe 2 ne , ω Li = me
4πZ 2 e 2 ni , mi
ɝɞɟ ωLe,Li ɦɨɠɧɨ ɧɚɡɜɚɬɶ «ɷɥɟɤɬɪɨɧɧɨɣ» ɢ «ɢɨɧɧɨɣ» ɥɟɧɝɦɸɪɨɜɫɤɢɦɢ ɱɚɫɬɨɬɚɦɢ. ɑɬɨɛɵ ɩɨɞɱɟɪɤɧɭɬɶ, ɤɚɤɢɦ ɨɛɪɚɡɨɦ ɜɯɨɞɹɬ ɩɚɪɚɦɟɬɪɵ ɤɨɦɩɨɧɟɧɬ ɩɥɚɡɦɵ ɜ ɮɨɪɦɭɥɭ (1.10) ɞɥɹ ɞɟɛɚɟɜɫɤɨɝɨ ɪɚɞɢɭɫɚ, ɩɟɪɟɩɢɲɟɦ ɟɟ ɜ ɜɢɞɟ:
1 = d
1 1 2 + 2 , rDe = rDe rDi
Te ,r = 4πe 2 ne Di
Ti , 4πZ 2 e 2 ni
ɝɞɟ rDe,i – «ɷɥɟɤɬɪɨɧɧɵɣ» ɢ «ɢɨɧɧɵɣ» ɞɟɛɚɟɜɫɤɢɟ ɪɚɞɢɭɫɵ. Ʉɚɤ ɦɵ ɜɢɞɢɦ, ɨɛɟ ɤɨɦɩɨɧɟɧɬɵ ɩɥɚɡɦɵ ɞɚɸɬ ɜɤɥɚɞ ɢ ɜ ɩɥɚɡɦɟɧɧɭɸ ɱɚɫɬɨɬɭ ɢ ɜ ɪɚɞɢɭɫ ɷɤɪɚɧɢɪɨɜɚɧɢɹ. ɇɨ ɷɬɨɬ ɜɤɥɚɞ ɨɤɚɡɵɜɚɟɬɫɹ ɧɟɨɞɢɧɚɤɨɜɵɦ: ɜ ɜɟɥɢɱɢɧɭ ɪɚɞɢɭɫɚ ɷɤɪɚɧɢɪɨɜɚɧɢɹ ɩɪɢ ɫɨɩɨɫɬɚɜɢɦɵɯ ɤɨɧɰɟɧɬɪɚɰɢɹɯ ɢ ɬɟɦɩɟɪɚɬɭɪɚɯ ɢɨɧɵ ɢ ɷɥɟɤɬɪɨɧɵ ɩɥɚɡɦɵ ɞɚɸɬ ɪɚɜɧɨɩɪɚɜɧɵɣ ɜɤɥɚɞ, ɬɨɝɞɚ ɤɚɤ ɜ ɜɟɥɢɱɢɧɭ ɩɥɚɡɦɟɧɧɨɣ ɱɚɫɬɨɬɵ ɜɜɢɞɭ ɝɨɪɚɡɞɨ ɦɟɧɶɲɟɣ ɦɚɫɫɵ ɨɩɪɟɞɟɥɹɸɳɢɣ ɜɤɥɚɞ ɞɚɟɬ ɷɥɟɤɬɪɨɧɧɚɹ ɤɨɦɩɨɧɟɧɬɚ. ɗɬɚ «ɧɟɪɚɜɧɨɩɪɚɜɧɨɫɬɶ» ɷɥɟɤɬɪɨɧɧɨɣ ɢ ɢɨɧɧɨɣ ɤɨɦɩɨɧɟɧɬ ɩɥɚɡɦɵ ɢɦɟɟɬ ɩɪɨɫɬɨɟ ɨɛɴɹɫɧɟɧɢɟ. Ⱦɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ ɹɜɥɹɟɬɫɹ ɩɨ ɫɭɳɟɫɬɜɭ ɫɬɚɬɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ, ɨɩɪɟɞɟɥɹɸɳɟɣ ɭɫɬɚɧɨɜɢɜɲɭɸɫɹ ɞɥɢɧɭ ɷɤɪɚɧɢɪɨɜɚɧɢɹ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɨɧ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɦɚɫɫɵ ɱɚɫɬɢɰ, ɬɚɤ ɤɚɤ ɡɚ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɟ ɜɪɟɦɹ ɭɫɩɟɜɚɸɬ ɩɟɪɟɫɬɪɨɢɬɫɹ ɨɛɟ ɤɨɦɩɨɧɟɧɬɵ ɩɥɚɡɦɵ, ɧɟɫɦɨɬɪɹ ɧɚ ɫɭɳɟɫɬɜɟɧɧɨɟ ɪɚɡɥɢɱɢɟ ɢɯ ɦɚɫɫ. ȼ ɬɨ ɜɪɟɦɹ ɤɚɤ ɥɟɧɝɦɸɪɨɜɫɤɚɹ ɱɚɫɬɨɬɚ – ɷɬɨ ɞɢɧɚɦɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ, ɨɩɪɟɞɟɥɹɸɳɚɹ ɨɬɤɥɢɤ ɩɥɚɡɦɵ ɧɚ ɞɢɧɚɦɢɱɟɫɤɨɟ ɢɡɦɟɧɟɧɢɟ ɩɨɥɹ. ɉɪɢ «ɛɵɫɬɪɨɦ ɜɤɥɸɱɟɧɢɢ» ɩɨɥɹ, ɨɱɟɜɢɞɧɨ, ɱɬɨ ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɛɭɞɭɬ ɨɬɤɥɢɤɚɬɶɫɹ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɟɟ ɦɚɫɫɢɜɧɵɟ ɷɥɟɤɬɪɨɧɵ. ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɩɥɚɡɦɟɧɧɚɹ ɱɚɫɬɨɬɚ ɞɥɹ ɢɨɧ-ɷɥɟɤɬɪɨɧɧɨɣ ɩɥɚɡɦɵ ɦɚɥɨ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɷɥɟɤɬɪɨɧɧɨɣ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɱɚɫɬɨɬɵ. Ɉɬɦɟɬɢɦ, ɱɬɨ ɩɨ ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧɵ 1/ωp ɟɫɬɶ ɜɪɟɦɹ ɩɪɨɥɟɬɚ ɞɟɛɚɟɜɫɤɨɝɨ ɫɥɨɹ ɬɟɩɥɨɜɵɦ ɷɥɟɤɬɪɨɧɨɦ.
§ 4. ɂɞɟɚɥɶɧɨɫɬɶ ɩɥɚɡɦɵ ɉɨ ɚɧɚɥɨɝɢɢ ɫ ɝɚɡɨɦ ɩɥɚɡɦɭ ɫɱɢɬɚɸɬ ɢɞɟɚɥɶɧɨɣ, ɟɫɥɢ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɞɜɢɠɟɧɢɹ ɟɟ ɱɚɫɬɢɰ ɫɭɳɟɫɬɜɟɧɧɨ ɛɨɥɶɲɟ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɢɯ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ. ȼ ɝɚɡɟ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɱɚɫɬɢɰ ɨɛɭɫɥɨɜɥɟɧɚ ɫɢɥɚɦɢ ȼɚɧ-ɞɟɪ-ȼɚɚɥɶɫɚ, ɜ ɩɥɚɡɦɟ - ɤɭɥɨɧɨɜɫɤɢɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟɦ. ɗɧɟɪɝɢɹ ɤɭɥɨɧɨɜɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɞɜɭɯ ɱɚɫɬɢɰ ɫ ɡɚɪɹɞɨɦ ɟ, ɧɚɯɨɞɹɳɢɯɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ R ɞɪɭɝ ɨɬ ɞɪɭɝɚ, ɪɚɜɧɚ e2/R. ɋɪɟɞɧɟɟ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ ɩɪɢ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ n ɫɨɫɬɚɜɥɹɟɬ R∼n−1/3, ɚ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɱɚɫɬɢɰɵ ɩɨ ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧɵ ɪɚɜɧɚ ɬɟɦɩɟɪɚɬɭɪɟ T, ɢɡɦɟɪɹɟɦɨɣ ɜ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɟɞɢɧɢɰɚɯ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɭɫɥɨɜɢɟ ɢɞɟɚɥɶɧɨɫɬɢ ɩɥɚɡɦɵ ɦɨɠɧɨ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: e 2 n 1 / 3 >tɷ. ɉɨ ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧɵ tɚɬ=a/v, ɝɞɟ a - ɪɚɡɦɟɪ ɚɬɨɦɚ, a v - ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɫɤɨɪɨɫɬɶ. ɉɨ ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧɵ tɷ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɢɡ ɩɪɢɧɰɢɩɚ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɢ:
t ɷ = ! δE ,
ɝɞɟ δE - ɪɚɡɧɨɫɬɶ ɷɧɟɪɝɢɣ ɭɪɨɜɧɟɣ. ɉɨɷɬɨɦɭ ɩɨɥɭɱɚɟɦ ɭɫɥɨɜɢɟ
a / v >> ! δE
ɢɥɢ
aδE / v! >>1, ɱɬɨ ɢ ɹɜɥɹɟɬɫɹ ɤɪɢɬɟɪɢɟɦ ɦɚɥɨɜɟɪɨɹɬɧɨɫɬɢ ɩɟɪɟɯɨɞɚ ɢ ɧɚɡɵɜɚɟɬɫɹ ɚɞɢɚɛɚɬɢɱɟɫɤɢɦ ɤɪɢɬɟɪɢɟɦ Ɇɟɫɫɢ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɟɫɥɢ ɪɚɡɧɨɫɬɶ ɭɪɨɜɧɟɣ δȿ ɦɚɥɚ, ɬɨ ɩɪɨɰɟɫɫ ɛɨɥɟɟ ɜɟɪɨɹɬɟɧ. Ɍɚɤɢɟ ɩɪɨɰɟɫɫɵ ɧɚɡɵɜɚɸɬ ɪɟɡɨɧɚɧɫɧɵɦɢ (ɧɚɩɪɢɦɟɪ, ɪɟɡɨɧɚɧɫɧɚɹ ɩɟɪɟɡɚɪɹɞɤɚ, ɜɡɚɢɦɧɚɹ ɧɟɣɬɪɚɥɢɡɚɰɢɹ ɢɨɧɨɜ, ɩɟɪɟɞɚɱɚ ɜɨɡɛɭɠɞɟɧɢɹ). ɋɧɹɬɢɟ ɷɥɟɤɬɪɨɧɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɜɨɡɦɨɠɧɨ ɦɧɨɝɢɦɢ ɩɭɬɹɦɢ, ɧɚɩɪɢɦɟɪ:
ɚ) Ⱥ* → Ⱥ + γ
ɛ) Ⱥ* + ȼɋ → Ⱥ + ȼɋ Ⱥ+ȼ+ɋ ɜ) Ⱥ* + ȼ → Ⱥȼ+ + ɟ ɝ) Ⱥ* + ȼ → Ⱥ + ȼ+ + ɟ ɞ) Ⱥ* + ȼ → ȼ* + Ⱥ
- ɜɵɫɜɟɱɢɜɚɧɢɟ ɩɪɢ ɜɨɡɜɪɚɳɟɧɢɢ ɷɥɟɤɬɪɨɧɚ ɧɚ ɨɫɧɨɜɧɨɣ ɭɪɨɜɟɧɶ (ɜɨɡɦɨɠɧɨ ɫɬɭɩɟɧɱɚɬɨɟ ɩɭɬɟɦ ɢɫɩɭɫɤɚɧɢɹ ɪɹɞɚ ɮɨɬɨɧɨɜ); - ɬɭɲɟɧɢɟ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɫ ɦɨɥɟɤɭɥɨɣ, ɷɧɟɪɝɢɹ ɜɨɡɛɭɠɞɟɧɢɹ ɩɟɪɟɯɨɞɢɬ ɢɥɢ ɜ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɱɚɫɬɢɰ, ɢɥɢ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɞɢɫɫɨɰɢɚɰɢɸ ɦɨɥɟɤɭɥɵ. Ɍɭɲɟɧɢɟ ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ ɫ ɚɬɨɦɨɦ ɦɚɥɨɜɟɪɨɹɬɧɨ; - ɚɫɫɨɰɢɚɬɢɜɧɚɹ ɢɨɧɢɡɚɰɢɹ. ɗɧɟɪɝɢɹ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɢɨɧɢɡɚɰɢɸ. ȼɟɫɶɦɚ ɜɟɪɨɹɬɧɵɣ ɩɪɨɰɟɫɫ ɞɥɹ ɧɟɤɨɬɨɪɵɯ ɫɨɫɬɨɹɧɢɣ; - ɷɮɮɟɤɬ ɉɟɧɧɢɝɚ; ɩɪɨɰɟɫɫ ɩɪɨɢɫɯɨɞɢɬ, ɟɫɥɢ ɷɧɟɪɝɢɹ ɜɨɡɛɭɠɞɟɧɢɹ ɚɬɨɦɚ Ⱥ* ɜ ɦɟɬɚɫɬɚɛɢɥɶɧɨɟ ɫɨɫɬɨɹɧɢɟ ɛɨɥɶɲɟ ɩɨɬɟɧɰɢɚɥɚ ɢɨɧɢɡɚɰɢɢ ɱɚɫɬɢɰɵ ȼ. - ɩɟɪɟɞɚɱɚ ɜɨɡɛɭɠɞɟɧɢɹ ɪɟɚɥɢɡɭɟɬɫɹ ɫ ɛɨɥɶɲɨɣ ɜɟɪɨɹɬɧɨɫɬɶɸ, ɟɫɥɢ ɦɚɥɨ ɢɡɦɟɧɟɧɢɟ ɷɧɟɪɝɢɢ ɩɟɪɟɯɨɞɚ (ɪɟɡɨɧɚɧɫɧɵɣ ɩɪɨɰɟɫɫ).
ȼɢɞɧɨ, ɱɬɨ ɧɟɤɨɬɨɪɵɟ ɩɭɬɢ ɬɭɲɟɧɢɹ ɩɪɢɜɨɞɹɬ ɤ ɨɛɪɚɡɨɜɚɧɢɸ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ, ɬ.ɟ. ɤ ɜɨɡɪɚɫɬɚɧɢɸ ɫɬɟɩɟɧɢ ɢɨɧɢɡɚɰɢɢ ɩɥɚɡɦɵ. ɂɨɧɢɡɚɰɢɹ ɢ ɪɟɤɨɦɛɢɧɚɰɢɹ ɉɪɨɰɟɫɫɵ ɨɛɪɚɡɨɜɚɧɢɹ ɢ ɪɚɡɪɭɲɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɨɩɪɟɞɟɥɹɸɬ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɩɥɚɡɦɵ. Ⱦɥɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚɪɧɨɣ ɢɥɢ ɦɨɥɟɤɭɥɹɪɧɨɣ ɱɚɫɬɢɰɵ ɧɟɨɛɯɨɞɢɦɨ ɫɨɨɛɳɢɬɶ ɯɨɬɹ ɛɵ ɨɞɧɨɦɭ ɟɟ ɷɥɟɤɬɪɨɧɭ ɷɧɟɪɝɢɸ ɛɨɥɶɲɭɸ, ɱɟɦ ɷɧɟɪɝɢɹ ɟɝɨ ɫɜɹɡɢ ɫ ɷɬɨɣ ɱɚɫɬɢɰɟɣ. ɗɧɟɪɝɢɹ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɢɨɧɢɡɚɰɢɢ, ɜɵɪɚɠɟɧɧɚɹ ɜ ɷɥɟɤɬɪɨɧɜɨɥɶɬɚɯ, ɱɢɫɥɟɧɨ ɪɚɜɧɚ ɪɚɡɧɨɫɬɢ ɩɨɬɟɧɰɢɚɥɨɜ ɜ ɜɨɥɶɬɚɯ, ɤɨɬɨɪɭɸ ɞɨɥɠɟɧ ɩɪɨɣɬɢ ɷɥɟɤɬɪɨɧ ɞɥɹ ɟɟ ɩɪɢɨɛɪɟɬɟɧɢɹ. ɉɨɷɬɨɦɭ ɱɚɫɬɨ ɝɨɜɨɪɹɬ ɧɟ ɨɛ ɷɧɟɪɝɢɢ ɢɨɧɢɡɚɰɢɢ, ɚ ɨ ɩɨɬɟɧɰɢɚɥɟ ɢɨɧɢɡɚɰɢɢ. Ʌɟɝɱɟ ɜɫɟɝɨ ɨɬɨɪɜɚɬɶ ɩɟɪɜɵɣ, ɤɚɤ ɩɪɚɜɢɥɨ, ɜɧɟɲɧɢɣ, ɷɥɟɤɬɪɨɧ, ɜɬɨɪɨɣ ɢ ɩɨɫɥɟɞɭɸɳɢɟ - ɜɫɟ ɬɪɭɞɧɟɟ. ɇɚɢɛɨɥɶɲɢɣ ɩɟɪɜɵɣ ɩɨɬɟɧɰɢɚɥ ɢɨɧɢɡɚɰɢɢ ɭ ɇɟ (24,5 ȼ), ɧɚɢɦɟɧɶɲɢɣ ɭ Cs (3,9 ȼ). ȼɬɨɪɨɣ ɩɨɬɟɧɰɢɚɥ ɨɛɵɱɧɨ ɩɪɟɜɵɲɚɟɬ ɩɟɪɜɵɣ ɜ 2-3 ɪɚɡɚ, ɢɫɤɥɸɱɟɧɢɟɦ ɹɜɥɹɸɬɫɹ ɳɟɥɨɱɧɵɟ ɦɟɬɚɥɥɵ: ɧɚɢɛɨɥɶɲɚɹ ɪɚɡɧɢɰɚ ɭ Li (5,4 ɢ 75,6 ȼ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ). ɗɧɟɪɝɢɸ ɢɨɧɢɡɚɰɢɢ ɦɨɠɧɨ ɫɨɨɛɳɢɬɶ ɩɪɢ ɨɞɢɧɨɱɧɨɦ ɫɨɭɞɚɪɟɧɢɢ ɫ ɞɨɫɬɚɬɨɱɧɨ ɷɧɟɪɝɢɱɧɨɣ ɱɚɫɬɢɰɟɣ (ɫ ɷɥɟɤɬɪɨɧɨɦ, ɚɬɨɦɨɦ, ɢɨɧɨɦ, ɮɨɬɨɧɨɦ), ɧɨ ɟɟ ɦɨɠɧɨ ɩɟɪɟɞɚɬɶ ɢ ɜ ɩɪɨɰɟɫɫɟ ɧɟɫɤɨɥɶɤɢɯ ɫɨɭɞɚɪɟɧɢɣ, ɩɪɢɱɟɦ ɜ ɤɚɠɞɨɦ ɩɟɪɟɞɚɟɬɫɹ ɷɧɟɪɝɢɹ ɦɟɧɶɲɟ, ɱɟɦ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɨɬɪɵɜɚ ɷɥɟɤɬɪɨɧɚ. ɉɪɢ ɤɚɠɞɨɦ ɫɨɭɞɚɪɟɧɢɢ ɱɚɫɬɢɰɚ ɩɨɥɭɱɚɟɬ ɷɧɟɪɝɢɸ, ɩɟɪɟɯɨɞɢɬ ɜ ɛɨɥɟɟ ɜɨɡɛɭɠɞɟɧɧɨɟ ɫɨɫɬɨɹɧɢɟ, ɚ ɡɚɬɟɦ ɢɨɧɢɡɭɟɬɫɹ ɭɠɟ ɢɡ ɜɨɡɛɭɠɞɟɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ. Ɍɚɤɚɹ ɫɬɭɩɟɧɱɚɬɚɹ ɢɨɧɢɡɚɰɢɹ ɨɫɨɛɟɧɧɨ ɜɚɠɧɚ ɜ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɨɣ ɩɥɚɡɦɟ, ɤɨɝɞɚ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɨɜ ɦɟɧɶɲɟ ɩɨɬɟɧɰɢɚɥɚ ɢɨɧɢɡɚɰɢɢ. ɉɪɨɰɟɫɫɨɦ, ɨɛɪɚɬɧɵɦ ɢɨɧɢɡɚɰɢɢ, ɹɜɥɹɟɬɫɹ ɨɛɴɟɞɢɧɟɧɢɟ ɢɨɧɚ ɢ ɷɥɟɤɬɪɨɧɚ ɨɛɪɚɡɨɜɚɧɢɟ ɧɟɣɬɪɚɥɶɧɨɣ ɱɚɫɬɢɰɵ ɢɥɢ ɩɨɧɢɠɟɧɢɟ ɡɚɪɹɞɧɨɫɬɢ ɢɨɧɚ, ɟɝɨ ɧɚɡɵɜɚɸɬ ɪɟɤɨɦɛɢɧɚɰɢɟɣ. ɉɪɢ ɪɟɤɨɦɛɢɧɚɰɢɢ ɜɵɞɟɥɹɟɬɫɹ ɷɧɟɪɝɢɹ, ɪɚɜɧɚɹ ɷɧɟɪɝɢɢ ɫɜɹɡɢ ɪɟɤɨɦɛɢɧɢɪɭɸɳɢɯ ɱɚɫɬɢɰ. ɗɬɚ ɷɧɟɪɝɢɹ ɦɨɠɟɬ ɜɵɞɟɥɢɬɶɫɹ ɜ ɜɢɞɟ ɢɡɥɭɱɟɧɢɹ, ɢɥɢ ɦɨɠɟɬ ɛɵɬɶ ɩɟɪɟɞɚɧɚ ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɟ (ɨɛɵɱɧɨ ɨɞɧɨɦɭ ɢɡ ɷɥɟɤɬɪɨɧɨɜ ɩɥɚɡɦɵ). ȼ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɝɨɜɨɪɹɬ ɨ ɪɟɤɨɦɛɢɧɚɰɢɢ ɫ ɢɡɥɭɱɟɧɢɟɦ (ɢɥɢ ɢɡɥɭɱɚɬɟɥɶɧɨɣ ɪɟɤɨɦɛɢɧɚɰɢɢ), ɜɨ ɜɬɨɪɨɦ - ɨ ɪɟɤɨɦɛɢɧɚɰɢɢ ɩɪɢ ɬɪɨɣɧɵɯ ɫɨɭɞɚɪɟɧɢɹɯ (ɢɥɢ ɬɪɨɣɧɨɣ ɪɟɤɨɦɛɢɧɚɰɢɢ). Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɜɬɨɪɨɣ ɫɥɭɱɚɣ ɪɟɚɥɢɡɭɟɬɫɹ ɩɪɢ ɜɵɫɨɤɢɯ ɩɥɨɬɧɨɫɬɹɯ ɩɥɚɡɦɵ. Ⱦɥɹ ɧɟɤɨɬɨɪɵɯ ɚɬɨɦɨɜ (ɧɚɩɪɢɦɟɪ, ɇɟ) ɢ ɜɨɡɛɭɠɞɟɧɧɵɯ ɢɨɧɨɜ ɫɭɳɟɫɬɜɟɧɧɨ ɨɛɪɚɡɨɜɚɧɢɟ ɚɜɬɨɢɨɧɢɡɚɰɢɨɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɪɟɤɨɦɛɢɧɚɰɢɹ. Ⱥɜɬɨɢɨɧɢɡɚɰɢɨɧɧɵɦ ɫɨɫɬɨɹɧɢɟɦ ɧɚɡɵɜɚɸɬ ɫɜɹɡɚɧɧɨɟ ɫɨɫɬɨɹɧɢɟ ɜɨɡɛɭɠɞɟɧɧɨɝɨ ɢɨɧɚ ɢ ɷɥɟɤɬɪɨɧɚ, ɟɫɥɢ ɫɭɦɦɚɪɧɚɹ ɷɧɟɪɝɢɹ ɜɨɡɛɭɠɞɟɧɢɹ ɛɨɥɶɲɟ ɩɨɬɟɧɰɢɚɥɚ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚ. ȿɫɥɢ ɜɨɡɛɭɠɞɟɧɨ ɧɟɫɤɨɥɶɤɨ ɷɥɟɤɬɪɨɧɨɜ, ɢ ɟɫɥɢ ɷɧɟɪɝɢɹ ɜɨɡɛɭɠɞɟɧɢɹ ɛɭɞɟɬ ɩɟɪɟɞɚɧɚ ɨɞɧɨɦɭ ɷɥɟɤɬɪɨɧɭ, ɬɨ ɩɪɨɢɡɨɣɞɟɬ ɢɨɧɢɡɚɰɢɹ - ɷɥɟɤɬɪɨɧ ɩɟɪɟɣɞɟɬ ɜ ɫɜɨɛɨɞɧɨɟ ɫɨɫɬɨɹɧɢɟ, ɚ ɢɨɧ ɨɫɬɚɧɟɬɫɹ ɜ ɨɫɧɨɜɧɨɦ (ɧɟɜɨɡɛɭɠɞɟɧɧɨɦ) ɫɨɫɬɨɹɧɢɢ. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜɪɟɦɹ ɠɢɡɧɢ ɱɚɫɬɢɰɵ ɜ ɚɜɬɨɢɨɧɢɡɚɰɢɨɧɧɨɦ ɫɨɫɬɨɹɧɢɢ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ ɯɚɪɚɤɬɟɪɧɨɝɨ ɚɬɨɦɧɨɝɨ. ȼɨɡɦɨɠɟɧ ɢ ɩɪɨɰɟɫɫ, ɨɛɪɚɬɧɵɣ ɚɫɫɨɰɢɚɬɢɜɧɨɣ ɢɨɧɢɡɚɰɢɢ - ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ ɞɢɫɫɨɰɢɚɬɢɜɧɚɹ ɪɟɤɨɦɛɢɧɚɰɢɹ: Ⱥȼ+ + ɟ → Ⱥ + ȼ+; ɨɧ ɩɪɨɯɨɞɢɬ ɱɟɪɟɡ ɚɜɬɨɢɨɧɢɡɚɰɢɨɧɧɨɟ ɫɨɫɬɨɹɧɢɟ ɦɨɥɟɤɭɥɵ Ⱥȼ*. ɂɧɨɝɞɚ ɪɟɤɨɦɛɢɧɚɰɢɟɣ ɧɚɡɵɜɚɸɬ ɢ ɚɫɫɨɰɢɚɰɢɸ ɦɨɥɟɤɭɥ ɢɡ ɚɬɨɦɨɜ, ɬ.ɟ. ɩɪɨɰɟɫɫɵ ɬɢɩɚ Ⱥ + 2ȼ → Ⱥȼ + ȼ, Ⱥ + ȼ + ɋ → Ⱥȼ + ɋ, ɢɥɢ Ⱥ + 2Ⱥ → Ⱥ2 + Ⱥ. Ⱦɢɫɫɨɰɢɚɰɢɹ ɢ ɚɫɫɨɰɢɚɰɢɹ Ⱦɢɫɫɨɰɢɚɰɢɟɣ ɧɚɡɵɜɚɸɬ ɩɪɨɰɟɫɫ ɪɚɡɞɟɥɟɧɢɹ ɫɥɨɠɧɵɯ ɦɨɥɟɤɭɥ (ɢɥɢ ɦɨɥɟɤɭɥɹɪɧɵɯ ɢɨɧɨɜ) ɧɚ ɛɨɥɟɟ ɩɪɨɫɬɵɟ ɦɨɥɟɤɭɥɵ, ɢɥɢ ɧɚ ɚɬɨɦɵ (ɢɥɢ ɢɨɧ ɢ ɚɬɨɦ, ɢɨɧ ɢ ɦɨɥɟɤɭɥɚ). ɗɧɟɪɝɢɹ ɪɚɡɪɵɜɚ ɦɨɥɟɤɭɥɹɪɧɵɯ ɫɜɹɡɟɣ ɩɨɱɬɢ ɜɫɟɝɞɚ ɦɟɧɶɲɟ ɷɧɟɪɝɢɢ ɢɨɧɢɡɚɰɢɢ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɩɨɠɚɥɭɣ, ɦɨɥɟɤɭɥ ɋɈ2 ɢ ɋ2ɇ2). ɑɚɫɬɨ ɞɢɫɫɨɰɢɚɰɢɸ ɨɛɥɟɝɱɚɟɬ ɧɚɤɨɩɥɟɧɢɟ ɷɧɟɪɝɢɢ ɧɚ ɤɨɥɟɛɚɬɟɥɶɧɨ-ɜɪɚɳɚɬɟɥɶɧɵɯ ɭɪɨɜɧɹɯ ɦɨɥɟɤɭɥɵ. Ⱥɫɫɨɰɢɚɰɢɟɣ ɧɚɡɵɜɚɸɬ ɨɛɪɚɬɧɵɣ ɩɪɨɰɟɫɫ: ɨɛɴɟɞɢɧɟɧɢɟ ɚɬɨɦɨɜ (ɢɥɢ ɢɨɧɚ ɢ ɚɬɨɦɚ) ɜ ɦɨɥɟɤɭɥɭ (ɢɥɢ ɩɪɨɫɬɵɯ ɦɨɥɟɤɭɥ ɜ ɛɨɥɟɟ ɫɥɨɠɧɵɟ).
ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɢ ɞɢɫɫɨɰɢɚɰɢɹ ɢ ɚɫɫɨɰɢɚɰɢɹ ɧɟɪɟɞɤɨ ɛɵɜɚɸɬ ɫɥɨɠɧɵɦɢ, ɪɟɚɥɶɧɨ ɦɧɨɝɨɫɬɚɞɢɣɧɵɦɢ, ɩɪɨɰɟɫɫɚɦɢ: ɜ ɧɢɯ ɭɱɚɫɬɜɭɟɬ ɧɟ ɦɟɧɟɟ ɬɪɟɯ ɱɚɫɬɢɰ, ɢ ɩɪɨɫɬɨɦɭ ɩɪɹɦɨɦɭ ɩɪɨɰɟɫɫɭ ɞɢɫɫɨɰɢɚɰɢɢ Ⱥȼ + ɋ →Ⱥ + ȼ + ɋ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɥɨɠɧɵɣ ɬɪɨɣɧɨɣ ɩɪɨɰɟɫɫ ɚɫɫɨɰɢɚɰɢɢ Ⱥ + ȼ + ɋ → Ⱥȼ + ɋ, ɤɨɝɞɚ ɱɚɫɬɢɰɚ Ⱥȼ ɨɛɪɚɡɭɟɬɫɹ ɜ ɜɨɡɛɭɠɞɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ ɢ ɩɟɪɟɯɨɞɢɬ ɜ ɨɫɧɨɜɧɨɟ ɫɨɫɬɨɹɧɢɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɹɞɚ ɩɨɫɥɟɞɭɸɳɢɯ ɩɚɪɧɵɯ ɫɬɨɥɤɧɨɜɟɧɢɣ.
§ 6. ɍɩɪɭɝɨɟ ɪɚɫɫɟɹɧɢɟ ȿɫɥɢ ɜ ɩɪɨɰɟɫɫɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɩɨɥɧɚɹ ɩɨɫɬɭɩɚɬɟɥɶɧɚɹ ɷɧɟɪɝɢɹ ɱɚɫɬɢɰ ɨɫɬɚɟɬɫɹ ɧɟɢɡɦɟɧɧɨɣ, ɬɨ ɩɪɨɰɟɫɫ ɹɜɥɹɟɬɫɹ ɭɩɪɭɝɢɦ ɪɚɫɫɟɹɧɢɟɦ. ȼ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɟ ɜɚɠɧɵ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫ ɧɟɣɬɪɚɥɶɧɵɦɢ ɱɚɫɬɢɰɚɦɢ. ȼ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɫ ɧɟɣɬɪɚɥɶɧɵɦɢ ɱɚɫɬɢɰɚɦɢ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɧɟɣɬɪɚɥɶɧɵɟ ɱɚɫɬɢɰɵ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɦɟɠɞɭ ɫɨɛɨɣ. Ɉɞɧɚɤɨ ɩɪɢ ɛɨɥɟɟ ɫɬɪɨɝɨɦ ɩɨɞɯɨɞɟ ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ, ɱɬɨ ɡɚɪɹɠɟɧɧɚɹ ɱɚɫɬɢɰɚ ɫɜɨɢɦ ɩɨɥɟɦ ɩɨɥɹɪɢɡɭɟɬ ɧɟɣɬɪɚɥɶɧɭɸ ɱɚɫɬɢɰɭ, ɢ ɷɬɨ ɭɫɥɨɠɧɹɟɬ ɯɚɪɚɤɬɟɪ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ. ɋɟɱɟɧɢɟ ɪɚɫɫɟɹɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɧɟ ɬɨɥɶɤɨ ɝɟɨɦɟɬɪɢɱɟɫɤɢɦɢ ɪɚɡɦɟɪɚɦɢ ɧɟɣɬɪɚɥɶɧɨɣ ɱɚɫɬɢɰɵ, ɧɨ ɢ ɟɟ ɩɨɥɹɪɢɡɭɟɦɨɫɬɶɸ. Ɉɫɨɛɟɧɧɨ ɛɨɥɶɲɨɣ ɩɨɥɹɪɢɡɭɟɦɨɫɬɶɸ ɨɛɥɚɞɚɸɬ ɚɬɨɦɵ ɳɟɥɨɱɧɵɯ ɦɟɬɚɥɥɨɜ ɢ ɧɟɤɨɬɨɪɵɟ ɚɬɨɦɵ ɜ ɜɨɡɛɭɠɞɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ. ɉɨɥɹɪɢɡɭɟɦɨɫɬɶ ɦɨɥɟɤɭɥ ɫɭɳɟɫɬɜɟɧɧɨ ɧɢɠɟ, ɨɧɚ ɛɥɢɡɤɚ ɤ ɩɨɥɹɪɢɡɭɟɦɨɫɬɢ ɧɟ ɳɟɥɨɱɧɵɯ ɚɬɨɦɨɜ. ȼɟɪɨɹɬɧɨɫɬɶ ɭɩɪɭɝɨɝɨ ɪɚɫɫɟɹɧɢɹ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ ɫɥɚɛɨ ɡɚɜɢɫɢɬ ɨɬ ɢɯ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɫɤɨɪɨɫɬɟɣ. ɉɪɨɰɟɫɫɵ ɩɟɪɟɧɨɫɚ ɜ ɫɥɚɛɨ ɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɟ ɨɱɟɧɶ ɛɥɢɡɤɢ ɤ ɬɚɤɨɜɵɦ ɜ ɝɚɡɟ, ɤɪɨɦɟ, ɟɫɬɟɫɬɜɟɧɧɨ, ɩɨɞɜɢɠɧɨɫɬɢ ɧɚɩɪɚɜɥɟɧɧɨɣ ɫɤɨɪɨɫɬɢ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ, ɩɪɢɨɛɪɟɬɚɟɦɨɣ ɢɦɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. ɍɩɪɭɝɢɟ ɫɬɨɥɤɧɨɜɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɢɦɟɸɬ ɢɧɨɣ ɯɚɪɚɤɬɟɪ, ɢ ɜ ɫɢɥɶɧɨ ɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɟ ɢɦɟɧɧɨ ɨɧɢ ɨɩɪɟɞɟɥɹɸɬ ɮɨɪɦɭ ɮɭɧɤɰɢɣ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɢ ɩɪɨɰɟɫɫɵ ɩɟɪɟɧɨɫɚ. Ɋɚɫɫɦɨɬɪɢɦ ɩɨɜɟɞɟɧɢɟ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ (ɧɚɡɨɜɟɦ ɟɟ ɩɪɨɛɧɨɣ), ɩɪɨɥɟɬɚɸɳɟɣ ɱɟɪɟɡ ɨɛɥɚɤɨ ɩɨɤɨɹɳɢɯɫɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ (ɧɚɡɨɜɟɦ ɢɯ ɩɨɥɟɜɵɦɢ). ȼ ɢɞɟɚɥɶɧɨɣ ɩɥɚɡɦɟ ɤɚɠɞɨɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɞɜɭɯ ɱɚɫɬɢɰ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɧɚɥɢɱɢɹ ɨɫɬɚɥɶɧɵɯ, ɧɨ ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ ɩɨɥɧɨɝɨ ɫɟɱɟɧɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɧɚɞɨ ɭɱɟɫɬɶ ɷɤɪɚɧɢɪɨɜɚɧɢɟ ɩɥɚɡɦɨɣ ɩɨɥɹ ɞɚɧɧɨɣ ɱɚɫɬɢɰɵ. ȿɫɥɢ ɩɪɨɛɧɚɹ ɱɚɫɬɢɰɚ ɞɜɢɠɟɬɫɹ ɬɚɤ, ɱɬɨ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɨɧɚ ɩɪɨɥɟɬɟɥɚ ɛɵ ɦɢɦɨ ɩɨɥɟɜɨɣ ɧɚ ɪɚɫɫɬɨɹɧɢɢ ρ (ɟɝɨ ɧɚɡɵɜɚɸɬ ɩɪɢɰɟɥɶɧɵɦ ɩɚɪɚɦɟɬɪɨɦ, ɪɢɫ. 1.6), ɬɨ ɨɧɚ ɨɬɤɥɨɧɢɬɫɹ ɧɚ ɭɝɨɥ θ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɩɪɢɜɟɞɟɧɧɨɣ ɦɚɫɫɵ ɱɚɫɬɢɰ µ, ɢɯ ɡɚɪɹɞɨɜ Z ɢ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɫɤɨɪɨɫɬɢ v: Ɋɢɫ.1.6. ɋɯɟɦɚ ɭɩɪɭɝɨɝɨ ɫɨɭɞɚɪɟɧɢɹ Z1 Z 2 e 2 tg(θ/2) = ρ⊥/ρ, ρ⊥ = (1.17) µv 2 ɝɞɟ ρ⊥ - ɩɪɢɰɟɥɶɧɵɣ ɩɚɪɚɦɟɬɪ, ɩɪɢ ɤɨɬɨɪɨɦ ɩɪɨɛɧɚɹ ɱɚɫɬɢɰɚ ɨɬɤɥɨɧɹɟɬɫɹ ɧɚ ɭɝɨɥ π/2. ɉɨ ɫɭɳɟɫɬɜɭ ɬɚɤɨɟ ɪɚɫɫɦɨɬɪɟɧɢɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɩɢɫɚɧɢɸ ɞɜɢɠɟɧɢɹ ɨɞɧɨɣ ɱɚɫɬɢɰɵ ɫ ɩɪɢɜɟɞɟɧɧɨɣ ɦɚɫɫɨɣ µ ɜ ɩɨɥɟ ɰɟɧɬɪɚɥɶɧɵɯ ɫɢɥ. ɋ ɩɨɦɨɳɶɸ ɤɢɧɟɦɚɬɢɱɟɫɤɨɝɨ ɫɨɨɬɧɨɲɟɧɢɹ (1.17) ɜɵɜɨɞɢɬɫɹ ɮɨɪɦɭɥɚ Ɋɟɡɟɪɮɨɪɞɚ 2
· ρ⊥ dσ ρ dρ § ¸ . = = ¨¨ (1.18) dΩ sin θ dθ © 2 sin 2 (θ 2) ¸¹ ɋɤɨɪɨɫɬɶ ɩɪɨɛɧɨɣ ɱɚɫɬɢɰɵ ɩɪɢ ɭɩɪɭɝɨɦ ɪɚɫɫɟɹɧɢɢ ɦɟɧɹɟɬɫɹ ɬɨɥɶɤɨ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ, ɭɦɟɧɶɲɚɹɫɶ ɜ ɩɪɨɟɤɰɢɢ ɧɚ ɩɟɪɜɨɧɚɱɚɥɶɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɧɚ δv = v(1-cosθ) ɢ ɭɜɟɥɢɱɢɜɚɹɫɶ ɜ ɩɪɨɟɤɰɢɢ ɧɚ ɧɚɩɪɚɜɥɟɧɢɟ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɟ ɤ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɧɚ ɜɟɥɢɱɢɧɭ ∆v = v⋅sinθ. Ʉɚɠɞɚɹ ɢɡ ɧɢɯ ɨɩɪɟɞɟɥɹɟɬ ɡɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɟɪɟɧɨɫɚ: ∆v ɞɢɮɮɭɡɢɸ, δv - ɜɹɡɤɨɟ ɬɪɟɧɢɟ ɢ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ. Ɉɞɧɚɤɨ ɬɨɱɧɵɟ ɪɚɫɱɟɬɵ ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɢɧɬɟɝɪɚɥɶɧɵɟ ɫɟɱɟɧɢɹ ɷɬɢɯ ɩɪɨɰɟɫɫɨɜ ɨɬɥɢɱɚɸɬɫɹ ɧɟɡɧɚɱɢɬɟɥɶɧɨ ɢ ɩɨɷɬɨɦɭ ɨɛɵɱɧɨ ɪɚɫɫɦɚɬɪɢɜɚɸɬ ɜɟɥɢɱɢɧɭ δv, ɨɬɜɟɬɫɬɜɟɧɧɭɸ ɡɚ ɪɚɫɫɟɹɧɢɟ. ɉɪɨɜɟɞɹ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ δv ɩɨ ɜɫɟɦ ɭɝɥɚɦ ɪɚɫɫɟɹɧɢɹ θ (ɢɥɢ ɩɨ ɜɫɟɦ ɡɧɚɱɟɧɢɹɦ ɩɪɢɰɟɥɶɧɨɝɨ ɩɚɪɚɦɟɬɪɚ ρ), ɭɦɧɨɠɢɜ ɧɚ ɱɢɫɥɨ ɩɨɥɟɜɵɯ ɱɚɫɬɢɰ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ n ɢ ɧɚ ɩɭɬɶ ɩɪɨɛɧɨɣ ɱɚɫɬɢɰɵ dx, ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɜɟɥɢɱɢɧɭ ɢɡɦɟɧɟɧɢɹ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ ɜ ɩɟɪɜɨɧɚɱɚɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ:
dv = −2πnvdx ³ ( 1 − cos θ ) ρdρ , ɩɨɞɫɬɚɜɥɹɹ (1.18) ɢ ɭɱɢɬɵɜɚɹ, ɱɬɨ sin (θ 2) = 2
ρ ⊥2
ρ 2 + ρ ⊥2
,
ɨɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɢɦ: ∞
dv = −4πnvdxρ⊥2 ³ 0
ρ dρ . ρ + ρ2 2 ⊥
(1.19)
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɷɬɨɬ ɢɧɬɟɝɪɚɥ ɥɨɝɚɪɢɮɦɢɱɟɫɤɢ ɪɚɫɯɨɞɢɬɫɹ ɧɚ ɜɟɪɯɧɟɦ ɩɪɟɞɟɥɟ. Ɉɞɧɚɤɨ ɫɥɟɞɭɟɬ ɭɱɟɫɬɶ, ɱɬɨ ɪɟɚɥɶɧɨ ɜɵɞɟɥɟɧɧɚɹ ɧɚɦɢ ɩɨɥɟɜɚɹ ɱɚɫɬɢɰɚ ɷɤɪɚɧɢɪɭɟɬɫɹ ɨɤɪɭɠɚɸɳɟɣ ɩɥɚɡɦɨɣ ɢ ɟɟ ɩɨɥɟ ɛɵɫɬɪɨ ɭɦɟɧɶɲɚɟɬɫɹ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɪɚɫɫɬɨɹɧɢɹ. ɏɚɪɚɤɬɟɪɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɷɤɪɚɧɢɪɨɜɚɧɢɹ - ɞɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ d, ɢ ɢɧɬɟɝɪɢɪɨɜɚɬɶ ɫɥɟɞɭɟɬ ɜ ɩɪɟɞɟɥɚɯ 0 < ρ < d. Ɍɨɝɞɚ ɩɨɥɭɱɢɦ dv = −4πnvρ⊥2dxLc, (1.20) ɝɞɟ Lc = ln(d/ρ⊥) (1.21) - ɤɭɥɨɧɨɜɫɤɢɣ ɥɨɝɚɪɢɮɦ. ȼɟɥɢɱɢɧɚ Lc ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɫɫɟɹɧɢɟɦ ɧɚ ɦɚɥɵɟ ɭɝɥɵ, ɢ ɨɛɵɱɧɨ Lc ≈ 10÷20 ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɩɚɪɚɦɟɬɪɨɜ ɩɥɚɡɦɵ ɜ ɲɢɪɨɤɢɯ ɩɪɟɞɟɥɚɯ. Ɇɨɠɧɨ ɜɜɟɫɬɢ ɞɥɢɧɭ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ λ ɢ ɫɟɱɟɧɢɟ ɪɚɫɫɟɹɧɢɹ σc: dv dx =− , λ v 1 λ= , (1.22) nσ c σc = 4πρ⊥2Lc. Ɉɱɟɧɶ ɜɚɠɧɨ, ɱɬɨ ɫɟɱɟɧɢɟ ɪɚɫɫɟɹɧɢɹ σc ɫɢɥɶɧɨ ɡɚɜɢɫɢɬ ɨɬ ɷɧɟɪɝɢɢ ɱɚɫɬɢɰɵ, ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɤɜɚɞɪɚɬɭ ɟɟ ɷɧɟɪɝɢɢ (ɢɥɢ ɤɜɚɞɪɚɬɭ ɬɟɦɩɟɪɚɬɭɪɵ): 1 1 σc ~ 2 ∼ 2 . (1.23) T E ȼɜɨɞɹɬ ɢ ɩɨɧɹɬɢɟ ɜɪɟɦɟɧɢ ɪɚɫɫɟɹɧɢɹ ɢɥɢ ɤɭɥɨɧɨɜɫɤɨɝɨ ɜɪɟɦɟɧɢ, ɨɩɪɟɞɟɥɹɹ ɟɝɨ ɤɚɤ: λ 1 τc = = . (1.24) v nσ c v Ʌɟɝɤɨ ɜɢɞɟɬɶ, ɱɬɨ ɜɪɟɦɹ ɪɚɫɫɟɹɧɢɹ ɛɵɫɬɪɨ ɪɚɫɬɟɬ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ τc ∼ T3/2. (1.25) Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɩɨ ɦɟɪɟ ɪɨɫɬɚ ɬɟɦɩɟɪɚɬɭɪɵ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ ɪɚɫɫɟɢɜɚɸɬɫɹ ɦɟɞɥɟɧɧɟɟ. Ɍɪɚɟɤɬɨɪɢɹ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɜ ɩɥɚɡɦɟ ɫɭɳɟɫɬɜɟɧɧɨ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɬɪɚɟɤɬɨɪɢɢ ɧɟɣɬɪɚɥɶɧɨɣ ɱɚɫɬɢɰɵ ɜ ɝɚɡɟ (ɪɢɫ. 1.7): ɜ ɩɥɚɡɦɟ - ɷɬɨ ɦɟɞɥɟɧɧɨ ɦɟɧɹɸɳɚɹɫɹ ɩɥɚɜɧɚɹ ɤɪɢɜɚɹ. ɉɟɪɟɡɚɪɹɞɤɚ ȼɟɫɶɦɚ ɜɚɠɧɵɦ ɹɜɥɹɟɬɫɹ ɩɪɨɰɟɫɫ ɩɟɪɟɞɚɱɢ ɡɚɪɹɞɚ ɨɬ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɤ ɧɟɣɬɪɚɥɶɧɨɣ: Ⱥ+ + ȼ ↔ Ⱥ + ȼ+. ȼ ɫɥɭɱɚɟ ɬɨɠɞɟɫɬɜɟɧɧɵɯ ɱɚɫɬɢɰ Ⱥ ɢ ȼ (ɤɪɨɦɟ ɡɚɪɹɞɨɜɨɝɨ ɫɨɫɬɨɹɧɢɹ): A ≡ B - ɷɬɨ ɩɪɨɰɟɫɫ ɭɩɪɭɝɢɣ: ɩɨɥɧɚɹ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɨɛɟɢɯ ɱɚɫɬɢɰ ɫɨɯɪɚɧɹɟɬɫɹ ɧɟɢɡɦɟɧɧɨɣ. Ɋɢɫ.1.7. Ɍɪɚɟɤɬɨɪɢɢ ɱɚɫɬɢɰ
ȿɫɥɢ ɠɟ Ⱥ ≠ ȼ, ɬɨ ɩɪɨɰɟɫɫ ɩɟɪɟɡɚɪɹɞɤɢ ɧɟɭɩɪɭɝɢɣ, ɬɚɤ ɤɚɤ ɷɧɟɪɝɢɢ ɢɨɧɢɡɚɰɢɢ ɱɚɫɬɢɰ Ⱥ ɢ ȼ ɪɚɡɥɢɱɧɵ. ȿɫɥɢ ɩɨɬɟɧɰɢɚɥ ɢɨɧɢɡɚɰɢɢ ɧɟɣɬɪɚɥɶɧɨɣ ɱɚɫɬɢɰɵ ɛɨɥɶɲɟ ɩɨɬɟɧɰɢɚɥɚ ɢɨɧɢɡɚɰɢɢ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ, ɬɨ ɧɚ ɜɟɥɢɱɢɧɭ ɷɧɟɪɝɢɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɷɬɨɣ ɪɚɡɧɢɰɟ, ɭɦɟɧɶɲɢɬɫɹ ɩɨɥɧɚɹ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɱɚɫɬɢɰ. ȼ ɫɥɭɱɚɟ, ɟɫɥɢ ɷɧɟɪɝɢɹ ɢɨɧɢɡɚɰɢɢ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɛɨɥɶɲɟ ɷɧɟɪɝɢɢ ɢɨɧɢɡɚɰɢɢ ɧɟɣɬɪɚɥɶɧɨɣ ɱɚɫɬɢɰɵ, ɬɨ ɢɡɛɵɬɨɤ ɷɧɟɪɝɢɢ ɜɵɞɟɥɢɬɫɹ ɢɥɢ ɜ ɜɢɞɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɱɚɫɬɢɰ, ɢɥɢ ɩɨɣɞɟɬ ɧɚ ɜɨɡɛɭɠɞɟɧɢɟ (ɭ ɚɬɨɦɨɜ ɩɨɫɥɟɞɧɟɟ ɛɵɜɚɟɬ ɪɟɞɤɨ ).
§ 7. Ɋɚɜɧɨɜɟɫɢɹ ɜ ɩɥɚɡɦɟ ɉɪɢ ɩɨɥɧɨɦ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɦ ɪɚɜɧɨɜɟɫɢɢ ɞɨɥɠɧɨ ɭɫɬɚɧɨɜɢɬɶɫɹ ɪɚɜɟɧɫɬɜɨ ɫɤɨɪɨɫɬɟɣ ɜɫɟɯ ɩɪɹɦɵɯ ɢ ɨɛɪɚɬɧɵɯ ɩɪɨɰɟɫɫɨɜ, ɚ ɬɚɤɠɟ ɪɚɜɟɧɫɬɜɨ ɜɫɟɯ ɬɟɦɩɟɪɚɬɭɪ (ɜɪɚɳɚɬɟɥɶɧɵɯ, ɤɨɥɟɛɚɬɟɥɶɧɵɯ, ɷɥɟɤɬɪɨɧɧɨɣ, ɢɨɧɧɨɣ, ɚɬɨɦɧɨɣ). Ɍɚɤɭɸ ɫɥɨɠɧɭɸ ɫɯɟɦɭ ɪɚɫɫɦɨɬɪɟɬɶ ɤɪɚɣɧɟ ɬɪɭɞɧɨ, ɚ ɦɨɠɟɬ ɛɵɬɶ ɢ ɧɟɜɨɡɦɨɠɧɨ. ɑɚɫɬɨ ɝɨɜɨɪɹɬ ɨ ɱɚɫɬɢɱɧɵɯ ɪɚɜɧɨɜɟɫɢɹɯ — ɩɪɢ ɦɚɥɵɯ ɬɟɦɩɟɪɚɬɭɪɚɯ ɩɨ ɜɫɟɦ ɫɬɟɩɟɧɹɦ ɫɜɨɛɨɞɵ (ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ, ɤɨɥɟɛɚɬɟɥɶɧɵɦ, ɜɪɚɳɚɬɟɥɶɧɵɦ ɫɨɫɬɨɹɧɢɹɦ), ɩɪɢ ɛɨɥɶɲɢɯ, ɤɨɝɞɚ ɦɨɥɟɤɭɥ ɢ ɚɬɨɦɨɜ ɭɠɟ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɬ, - ɨɬɞɟɥɶɧɨ ɨ ɬɟɦɩɟɪɚɬɭɪɚɯ ɯɚɨɬɢɱɟɫɤɨɝɨ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ. Ɋɚɫɫɦɨɬɪɢɦ ɩɪɢɦɟɪɵ ɢɨɧɢɡɚɰɢɨɧɧɨɝɨ ɪɚɜɧɨɜɟɫɢɹ ɜ ɚɬɨɦɚɪɧɨɦ ɝɚɡɟ (ɪɚɫɫɦɨɬɪɟɧɢɟ ɦɨɥɟɤɭɥ ɪɟɡɤɨ ɭɫɥɨɠɧɹɟɬ ɡɚɞɚɱɭ: ɧɚɞɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɨɥɟɛɚɬɟɥɶɧɨ ɜɨɡɛɭɠɞɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ, ɚɫɫɨɰɢɚɬɢɜɧɭɸ ɢɨɧɢɡɚɰɢɸ ɢ ɬ.ɞ.; ɧɟ ɪɚɫɫɦɚɬɪɢɜɚɟɦ ɬɚɤɠɟ ɢ ɚɜɬɨɢɨɧɢɡɚɰɢɨɧɧɵɟ ɫɨɫɬɨɹɧɢɹ). ɉɪɨɫɬɟɣɲɢɦɢ, ɢ ɨɞɧɨɜɪɟɦɟɧɧɨ ɧɚɢɛɨɥɟɟ ɱɚɫɬɨ ɜɫɬɪɟɱɚɸɳɢɦɢɫɹ, ɹɜɥɹɸɬɫɹ ɫɥɟɞɭɸɳɢɟ ɬɪɢ ɫɥɭɱɚɹ. Ȼɚɥɚɧɫ ɦɟɠɞɭ ɢɨɧɢɡɚɰɢɟɣ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ ɢ ɬɪɨɣɧɨɣ ɪɟɤɨɦɛɢɧɚɰɢɟɣ ɉɪɨɰɟɫɫ (ɩɪɹɦɨɣ/ɨɛɪɚɬɧɵɣ) a+e→i+2e (ɢɨɧɢɡɚɰɢɹ) i+2e→a+e (ɪɟɤɨɦɛɢɧɚɰɢɹ)
ɋɤɨɪɨɫɬɶ ɩɪɨɰɟɫɫɚ wi = kinane wr = krnine2
Ɂɞɟɫɶ na, ni, ne - ɩɥɨɬɧɨɫɬɢ ɚɬɨɦɨɜ, ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ; ki, kr ɤɨɷɮɮɢɰɢɟɧɬɵ ɫɤɨɪɨɫɬɢ ɢɨɧɢɡɚɰɢɢ ɢ ɪɟɤɨɦɛɢɧɚɰɢɢ. ɋɤɨɪɨɫɬɶ ɩɪɨɢɡɜɨɞɫɬɜɚ, ɧɚɩɪɢɦɟɪ, ɢɨɧɧɨɣ ɤɨɦɩɨɧɟɧɬɵ ɜ ɬɚɤɢɯ ɩɪɨɰɟɫɫɚɯ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ: dni = wi − wr . (1.26) dt ȼ ɪɚɜɧɨɜɟɫɢɢ ɫɤɨɪɨɫɬɢ ɩɪɹɦɨɝɨ ɢ ɨɛɪɚɬɧɨɝɨ ɩɪɨɰɟɫɫɨɜ ɫɨɜɩɚɞɚɸɬ, ɬɚɤ ɱɬɨ ɞɨɥɠɧɨ ɛɵɬɶ wi = wr. ɉɨɷɬɨɦɭ ɤɨɧɫɬɚɧɬɚ ɪɚɜɧɨɜɟɫɢɹ K, ɤɨɬɨɪɭɸ ɨɩɪɟɞɟɥɢɦ ɤɚɤ ɨɬɧɨɲɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɫɤɨɪɨɫɬɢ ɩɪɹɦɨɝɨ ɢ ɨɛɪɚɬɧɨɝɨ ɩɪɨɰɟɫɫɨɜ – ɡɞɟɫɶ ɢɨɧɢɡɚɰɢɢ ɢ ɪɟɤɨɦɛɢɧɚɰɢɢ, ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ: k nn K= i = e i. (1.27) kr na Ɂɚɦɟɬɢɦ, ɱɬɨ ɜɜɟɞɟɧɧɚɹ ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɤɨɧɫɬɚɧɬɚ ɪɚɜɧɨɜɟɫɢɹ ɢɦɟɟɬ ɪɚɡɦɟɪɧɨɫɬɶ ɤɭɛɚ ɨɛɪɚɬɧɨɣ ɞɥɢɧɵ. Ȼɚɥɚɧɫ ɦɟɠɞɭ ɮɨɬɨɢɨɧɢɡɚɰɢɟɣ ɢ ɢɡɥɭɱɚɬɟɥɶɧɨɣ ɪɟɤɨɦɛɢɧɚɰɢɟɣ ɉɪɨɰɟɫɫ (ɩɪɹɦɨɣ/ɨɛɪɚɬɧɵɣ) a+γ→i+e (ɢɨɧɢɡɚɰɢɹ) i+e→a+γ
(ɪɟɤɨɦɛɢɧɚɰɢɹ)
ɋɤɨɪɨɫɬɶ ɩɪɨɰɟɫɫɚ
wi′ = k i′na j w ′p = k p′ ni ne
Ɂɞɟɫɶ na, ni, ne - ɩɥɨɬɧɨɫɬɢ ɚɬɨɦɨɜ, ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, k i′ j , k p′ ɤɨɷɮɮɢɰɢɟɧɬɵ ɫɤɨɪɨɫɬɢ ɮɨɬɨɢɨɧɢɡɚɰɢɢ ɢ ɢɡɥɭɱɚɬɟɥɶɧɨɣ ɪɟɤɨɦɛɢɧɚɰɢɢ. ȼ ɪɚɜɧɨɜɟɫɢɢ wi′ = w ′p ,
(1.28)
ɢ ɤɨɧɫɬɚɧɬɚ ɪɚɜɧɨɜɟɫɢɹ, ɨɩɪɟɞɟɥɟɧɧɚɹ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɫɥɭɱɚɟ, ɨɤɚɡɵɜɚɟɬɫɹ k′j n n (1.29) K= i = i e, k p′ na (ɩɨ ɩɪɢɧɰɢɩɭ ɞɟɬɚɥɶɧɨɝɨ ɪɚɜɧɨɜɟɫɢɹ), ɬɚɤ ɱɬɨ ɜ ɨɛɨɢɯ ɫɥɭɱɚɹɯ
K=
ni ne . na
(1.30)
Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɨɨɬɧɨɲɟɧɢɹ ɱɢɫɥɚ ɡɚɪɹɠɟɧɧɵɯ ɢ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ ɜ ɩɥɚɡɦɟ ɜɜɨɞɹɬ ɩɨɧɹɬɢɟ ɫɬɟɩɟɧɢ ɢɨɧɢɡɚɰɢɢ α (ɢɧɨɝɞɚ ɷɬɨɬ ɩɚɪɚɦɟɬɪ ɧɚɡɵɜɚɸɬ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɢɨɧɢɡɚɰɢɢ) - ɨɬɧɨɲɟɧɢɟ ɱɢɫɥɚ ɢɨɧɨɜ ɤ ɫɭɦɦɟ ɱɢɫɥɚ ɢɨɧɨɜ ɢ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ: ni n α= = i , n0 = ni + na , (1.31) ni + na no ɝɞɟ n0 - ɩɨɥɧɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ ɢɨɧɨɜ ɢ ɚɬɨɦɨɜ (ɧɚɱɚɥɶɧɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ).
Ʌɟɝɤɨ ɭɫɬɚɧɨɜɢɬɶ ɫɜɹɡɶ ɦɟɠɞɭ ɫɬɟɩɟɧɶɸ ɢɨɧɢɡɚɰɢɢ ɢ ɤɨɧɫɬɚɧɬɨɣ ɢɨɧɢɡɚɰɢɨɧɧɨɝɨ ɪɚɜɧɨɜɟɫɢɹ K [9]. ȼ ɩɪɟɞɩɨɥɨɠɟɧɢɢ, ɱɬɨ ni = nɟ., ɢɫɩɨɥɶɡɭɹ ɮɨɪɦɭɥɵ (1.27), (1.30) ɢ (1.31), ɩɨɥɭɱɚɟɦ ɫɨɨɬɧɨɲɟɧɢɟ
ni2 = Kna = K ( n0 − ni ) ,
ɩɪɟɞɫɬɚɜɥɹɸɳɟɟ ɫɨɛɨɣ ɤɜɚɞɪɚɬɧɨɟ ɭɪɚɜɧɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ni. Ɋɟɲɢɜ ɟɝɨ ɢ ɩɨɞɫɬɚɜɢɜ ɪɟɡɭɥɶɬɚɬ ɜ (1.31), ɜɵɪɚɡɢɦ ɫɬɟɩɟɧɶ ɢɨɧɢɡɚɰɢɢ ɱɟɪɟɡ ɤɨɧɫɬɚɧɬɭ ɪɚɜɧɨɜɟɫɢɹ ɢ ɧɚɱɚɥɶɧɭɸ ɤɨɧɰɟɧɬɪɚɰɢɸ ɝɚɡɚ: 2
§ K · K K . α=− + ¨ ¸ + n0 2 no © 2 no ¹
(1.32)
ɉɪɢ ɦɚɥɨɣ ɫɬɟɩɟɧɢ ɢɨɧɢɡɚɰɢɢ, ɤɨɝɞɚ ɤɨɧɰɟɧɬɪɚɰɢɹ ɢɨɧɨɜ ɦɚɥɚ, ni > nɚ, ɩɨɥɭɱɚɟɦ α→1.
Ȼɚɥɚɧɫ ɦɟɠɞɭ ɢɨɧɢɡɚɰɢɟɣ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ ɢ ɢɡɥɭɱɚɬɟɥɶɧɨɣ ɪɟɤɨɦɛɢɧɚɰɢɟɣ ȼ ɩɪɟɞɵɞɭɳɟɦ ɩɪɢɦɟɪɟ ɩɪɟɞɩɨɥɚɝɚɥɨɫɶ, ɱɬɨ ɢɡɥɭɱɟɧɢɟ ɡɚɩɟɪɬɨ ɢ ɧɟ ɜɵɯɨɞɢɬ ɢɡ ɪɟɚɤɰɢɨɧɧɨɝɨ ɨɛɴɟɦɚ. ȿɫɥɢ ɠɟ ɩɥɚɡɦɚ ɩɪɨɡɪɚɱɧɚ ɞɥɹ ɢɡɥɭɱɟɧɢɹ, ɬ.ɟ. ɟɺ ɩɥɨɬɧɨɫɬɶ ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɚ, ɬɨ ɦɚɥɚ ɫɤɨɪɨɫɬɶ ɮɨɬɨɢɨɧɢɡɚɰɢɢ, ɢ ɢɨɧɢɡɚɰɢɹ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɨɛɭɫɥɨɜɥɟɧɚ ɫɨɭɞɚɪɟɧɢɹɦɢ. ȼ ɩɥɚɡɦɟ ɦɚɥɨɣ ɩɥɨɬɧɨɫɬɢ ɦɚɥɨɜɟɪɨɹɬɧɵ ɢ ɬɪɨɣɧɵɟ ɫɨɭɞɚɪɟɧɢɹ, ɩɨɷɬɨɦɭ ɝɥɚɜɧɵɦ ɤɨɧɤɭɪɢɪɭɸɳɢɦ ɫ ɢɨɧɢɡɚɰɢɟɣ ɩɪɨɰɟɫɫɨɦ ɹɜɥɹɟɬɫɹ ɢɡɥɭɱɚɬɟɥɶɧɚɹ ɪɟɤɨɦɛɢɧɚɰɢɹ: ɉɪɨɰɟɫɫ (ɩɪɹɦɨɣ/ɨɛɪɚɬɧɵɣ) a+e→i+2e (ɢɨɧɢɡɚɰɢɹ) i+e→a+γ
(ɪɟɤɨɦɛɢɧɚɰɢɹ)
ɋɤɨɪɨɫɬɶ ɩɪɨɰɟɫɫɚ
wi = k i na ne w ′p = k p′ ni ne
ɉɪɢɪɚɜɧɢɜɚɹ ɫɤɨɪɨɫɬɢ ɩɪɹɦɨɝɨ ɢ ɨɛɪɚɬɧɨɝɨ ɩɪɨɰɟɫɫɨɜ, ɩɨɥɭɱɢɦ ɮɨɪɦɭɥɭ ɗɥɶɜɟɪɬɚ: n k (1.34) K′ = i = i , na k p′ ɢɡ ɤɨɬɨɪɨɣ ɜɢɞɧɨ, ɱɬɨ ɫɬɟɩɟɧɶ ɢɨɧɢɡɚɰɢɢ K′ α= (1.35) 1+ K′ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɬɨɥɶɤɨ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɩɥɨɬɧɨɫɬɢ. Ⱦɥɹ ɩɥɚɡɦɵ, ɧɚɯɨɞɹɳɟɣɫɹ ɜ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɦ ɪɚɜɧɨɜɟɫɢɢ, ɤɨɧɫɬɚɧɬɚ ɪɚɜɧɨɜɟɫɢɹ Ʉ ɦɨɠɟɬ ɛɵɬɶ ɩɨɥɭɱɟɧɚ ɤɚɤ ɩɨ ɚɧɚɥɨɝɢɢ ɫ ɤɨɧɫɬɚɧɬɨɣ ɯɢɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ, ɬɚɤ ɢ ɢɡ ɤɢɧɟɬɢɱɟɫɤɢɯ ɫɨɨɛɪɚɠɟɧɢɣ [9], ɢ ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ: 3/ 2 ne ni g i g e § me′T · K= = ¨ ¸ e−I /T , na g a © 2π! 2 ¹
ɝɞɟ gi, ge, ga — ɫɬɚɬɢɫɬɢɱɟɫɤɢɟ ɜɟɫɚ ɢɨɧɨɜ, ɷɥɟɤɬɪɨɧɨɜ ɢ ɚɬɨɦɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ; I - ɷɧɟɪɝɢɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚ, me′ = me mi / ( me + mi ) - ɩɪɢɜɟɞɟɧɧɚɹ ɦɚɫɫɚ. Ɉɬɜɟɱɚɸɳɚɹ ɷɬɨɦɭ ɪɚɜɧɨɜɟɫɢɸ ɫɬɟɩɟɧɶ ɢɨɧɢɡɚɰɢɢ α, ɤɚɤ ɥɟɝɤɨ ɜɵɜɟɫɬɢ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ 3/ 2 g i g e § me′T · T − I / T α2 , (1.36) = e ¨ ¸ g a © 2π! 2 ¹ p 1−α2 ɝɞɟ ɪ = (ne+ni+na)T - ɞɚɜɥɟɧɢɟ, ɨɩɪɟɞɟɥɹɟɦɨɟ ɱɢɫɥɨɦ ɱɚɫɬɢɰ ɜɫɟɯ ɫɨɪɬɨɜ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ, ɤɚɤ ɢ ɞɨɥɠɧɨ ɛɵɬɶ ɜ ɭɫɥɨɜɢɹɯ ɩɨɥɧɨɝɨ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ, ɪɚɜɧɨɜɟɫɧɚɹ ɫɬɟɩɟɧɶ ɢɨɧɢɡɚɰɢɢ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɞɚɜɥɟɧɢɹ ɩɥɚɡɦɵ. Ɏɨɪɦɭɥɚ (1.36) - ɮɨɪɦɭɥɚ ɋɚɯɚ - ɫɜɹɡɵɜɚɟɬ ɨɫɧɨɜɧɵɟ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɱɚɫɬɢɰ: ɩɪɢɜɟɞɟɧɧɭɸ ɦɚɫɫɭ (ɞɥɹ ɩɪɨɰɟɫɫɚ ɢɨɧɢɡɚɰɢɢ ɨɧɚ ɩɪɢɦɟɪɧɨ ɪɚɜɧɚ ɦɚɫɫɟ ɷɥɟɤɬɪɨɧɚ me ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɦɚɥɨɝɨ ɨɬɧɨɲɟɧɢɹ me/mi, ɝɞɟ mi - ɦɚɫɫɚ ɢɨɧɚ), ɫɬɚɬɢɫɬɢɱɟɫɤɢɟ ɜɟɫɚ ɱɚɫɬɢɰ (ɢɨɧɚ, ɷɥɟɤɬɪɨɧɚ, ɚɬɨɦɚ), ɷɧɟɪɝɢɸ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚ ɢ ɬɟɦɩɟɪɚɬɭɪɭ ɩɥɚɡɦɵ ɫ ɤɨɧɫɬɚɧɬɨɣ ɪɚɜɧɨɜɟɫɢɹ Ʉ. Ɏɭɧɞɚɦɟɧɬɚɥɶɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɯɨɪɨɲɨ ɢɡɜɟɫɬɧɵ: ɫɬɚɬɢɫɬɢɱɟɫɤɢɣ ɜɟɫ ɷɥɟɤɬɪɨɧɚ ɪɚɜɟɧ ɞɜɭɦ, ɚ ɫɬɚɬɢɫɬɢɱɟɫɤɢɟ ɜɟɫɚ ɚɬɨɦɚ ɢ ɢɨɧɚ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɧɟɡɚɜɢɫɢɦɨ. Ɉɧɢ ɪɚɜɧɵ ɱɢɫɥɭ ɫɨɫɬɨɹɧɢɣ ɫ ɞɚɧɧɵɦ ɝɥɚɜɧɵɦ ɤɜɚɧɬɨɜɵɦ ɱɢɫɥɨɦ, ɧɚɩɪɢɦɟɪ, ɞɥɹ ɚɬɨɦɚ ɜɨɞɨɪɨɞɚ, ɜ ɫɨɫɬɨɹɧɢɢ ɫ ɝɥɚɜɧɵɦ ɤɜɚɧɬɨɜɵɦ ɱɢɫɥɨɦ, ɪɚɜɧɵɦ n, ɫɬɚɬɢɫɬɢɱɟɫɤɢɣ ɜɟɫ ɪɚɜɟɧ 2n2.
ɏɨɬɹ ɮɨɪɦɭɥɚ ɋɚɯɚ (ɢ ɟɟ ɚɧɚɥɨɝɢ) ɩɪɢɦɟɧɢɦɚ ɤ ɩɥɚɡɦɟ, ɧɚɯɨɞɹɳɟɣɫɹ ɜ ɩɨɥɧɨɦ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɦ ɪɚɜɧɨɜɟɫɢɢ, ɟɟ ɢɫɩɨɥɶɡɭɸɬ ɩɪɢ ɨɰɟɧɤɟ ɢ ɞɥɹ ɩɥɚɡɦɵ ɜ ɫɥɭɱɚɟ ɧɟɩɨɥɧɨɝɨ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ. ɋɥɟɞɭɟɬ ɢɦɟɬɶ ɜ ɜɢɞɭ, ɤɪɨɦɟ ɬɨɝɨ, ɱɬɨ ɨɧɚ ɜɟɪɧɚ ɥɢɲɶ ɩɪɢ ɧɟɤɨɬɨɪɵɯ ɭɩɪɨɳɚɸɳɢɯ ɩɪɟɞɩɨɥɨɠɟɧɢɹɯ ɨɬɧɨɫɢɬɟɥɶɧɨ ɷɬɨɝɨ ɪɚɜɧɨɜɟɫɢɹ: ɝɚɡ ɫɱɢɬɚɟɬɫɹ ɤɥɚɫɫɢɱɟɫɤɢɦ, ɩɨɞɱɢɧɹɸɳɢɦɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɸ ɆɚɤɫɜɟɥɥɚȻɨɥɶɰɦɚɧɚ. Ɍɟɦ ɫɚɦɵɦ, ɧɚɢɦɟɧɶɲɚɹ ɞɥɢɧɚ ɜɨɥɧɵ ɞɟ Ȼɪɨɣɥɹ, ɷɥɟɤɬɪɨɧɧɚɹ, ɞɨɥɠɧɚ ɛɵɬɶ ɦɟɧɶɲɟ ɫɪɟɞɧɟɝɨ ɦɟɠɱɚɫɬɢɱɧɨɝɨ ɪɚɫɫɬɨɹɧɢɹ. ɉɥɚɡɦɚ ɞɨɥɠɧɚ ɛɵɬɶ ɪɚɡɪɟɠɟɧɧɨɣ ɧɚ ɫɬɨɥɶɤɨ, ɱɬɨ ɫɪɟɞɧɟɟ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ ɜɟɥɢɤɨ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɚɦɩɥɢɬɭɞɨɣ ɪɚɫɫɟɹɧɢɹ. Ɍɨɝɞɚ ɷɥɟɤɬɪɨɧɵ, ɢɨɧɵ ɢ ɚɬɨɦɵ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɫɦɟɫɶ ɢɞɟɚɥɶɧɵɯ ɝɚɡɨɜ. ɇɚɤɨɧɟɰ, ɬɟɦɩɟɪɚɬɭɪɚ ɷɬɨɣ ɫɦɟɫɢ ɞɨɥɠɧɚ ɛɵɬɶ ɦɚɥɚ ɜ ɫɪɚɜɧɟɧɢɢ ɫ ɷɧɟɪɝɢɟɣ ɢɨɧɢɡɚɰɢɢ – ɬɨɥɶɤɨ ɩɪɢ ɷɬɨɦ ɭɫɥɨɜɢɢ ɤɨɥɢɱɟɫɬɜɨ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ ɦɚɥɨ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɱɢɫɥɨɦ ɚɬɨɦɨɜ ɜ ɨɫɧɨɜɧɨɦ ɫɨɫɬɨɹɧɢɢ. ȼ ɧɟɤɨɬɨɪɵɯ ɭɫɥɨɜɢɹɯ ɨɤɚɡɵɜɚɟɬɫɹ ɫɭɳɟɫɬɜɟɧɧɨɣ ɫɬɭɩɟɧɱɚɬɚɹ ɢɨɧɢɡɚɰɢɹ - ɨɛɪɚɡɨɜɚɧɢɟ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɢɡ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ, ɩɨɫɬɟɩɟɧɧɨ "ɞɨɜɨɡɛɭɠɞɚɟɦɵɯ" ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɹɯ ɱɟɪɟɡ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɞɨ ɢɨɧɢɡɚɰɢɢ. Ɋɟɚɥɢɡɚɰɢɹ ɷɬɨɣ ɜɨɡɦɨɠɧɨɫɬɢ ɡɚɜɢɫɢɬ ɨɬ ɜɪɟɦɟɧɢ ɠɢɡɧɢ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ, ɩɥɨɬɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ, ɩɨɬɟɧɰɢɚɥɨɜ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɜ ɨɫɧɨɜɧɨɦ ɢ ɜ ɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɹɯ. Ɋɟɚɥɶɧɨ ɫ ɩɨɥɧɨɫɬɶɸ ɬɟɪɦɨɥɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɨɣ ɫɬɚɥɤɢɜɚɸɬɫɹ, ɩɨɠɚɥɭɣ, ɬɨɥɶɤɨ ɚɫɬɪɨɮɢɡɢɤɢ, ɞɚ ɢ, ɜɨɡɦɨɠɧɨ, ɩɪɢ ɚɬɨɦɧɵɯ ɢ ɬɟɪɦɨɹɞɟɪɧɵɯ ɜɡɪɵɜɚɯ. ȼ ɬɟɪɦɨɹɞɟɪɧɵɯ ɭɫɬɚɧɨɜɤɚɯ ɫɬɪɟɦɹɬɫɹ ɩɨɥɭɱɢɬɶ ɬɚɤɭɸ ɬɟɪɦɨɥɢɡɨɜɚɧɧɭɸ ɩɥɚɡɦɭ; ɧɚɢɛɨɥɟɟ ɛɥɢɡɤɢ ɤ ɧɟɣ ɩɥɚɡɦɵ ɜ ɢɦɩɭɥɶɫɧɵɯ "ɜɡɪɵɜɧɵɯ" ɫɢɫɬɟɦɚɯ. ȼ ɫɢɫɬɟɦɚɯ ɫ ɦɚɝɧɢɬɧɨɣ ɬɟɪɦɨɢɡɨɥɹɰɢɟɣ (ɚɞɢɚɛɚɬɢɱɟɫɤɢɯ ɥɨɜɭɲɤɚɯ, ɬɨɤɚɦɚɤɚɯ ɢ ɬ.ɞ.) ɩɥɚɡɦɵ ɜɫɟɝɞɚ ɧɟɪɚɜɧɨɜɟɫɧɵɟ, ɯɨɬɹ ɢɧɨɝɞɚ ɢ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɱɚɫɬɢɱɧɨɟ ɪɚɜɧɨɜɟɫɢɟ - ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɛɥɢɡɤɢɟ ɤ ɦɚɤɫɜɟɥɥɨɜɫɤɢɦ, ɫɜɨɢ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɫɜɨɢ ɞɥɹ ɢɨɧɨɜ.
§ 8. ɇɟɪɚɜɧɨɜɟɫɧɨɫɬɶ ɩɥɚɡɦɟɧɧɵɯ ɫɢɫɬɟɦ Ɉɛɵɱɧɨ ɜ ɩɥɚɡɦɟ ɜɫɟɝɞɚ ɟɫɬɶ ɱɚɫɬɢɰɵ, ɨɱɟɧɶ ɫɢɥɶɧɨ ɪɚɡɥɢɱɚɸɳɢɟɫɹ ɩɨ ɦɚɫɫɟ: ɬɹɠɟɥɵɟ ɦɨɥɟɤɭɥɵ, ɚɬɨɦɵ ɢ ɢɯ ɢɨɧɵ, ɢ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɟɟ ɥɟɝɤɢɟ ɷɥɟɤɬɪɨɧɵ (ɨɬɧɨɲɟɧɢɟ ɦɚɫɫ ɩɪɨɬɨɧɚ ɢ ɷɥɟɤɬɪɨɧɚ ɪɚɜɧɨ mp/me≅1836). ȼɡɚɢɦɨɞɟɣɫɬɜɢɟ ɬɹɠɟɥɵɯ ɢ ɥɟɝɤɢɯ ɱɚɫɬɢɰ ɧɟ ɫɢɦɦɟɬɪɢɱɧɨ: ɥɟɝɤɢɟ ɱɚɫɬɢɰɵ ɫɢɥɶɧɨ ɪɚɫɫɟɢɜɚɸɬɫɹ ɧɚ ɬɹɠɟɥɵɯ ɢ ɨɱɟɧɶ ɦɟɞɥɟɧɧɨ ɩɟɪɟɞɚɸɬ ɢɦ ɫɜɨɸ ɷɧɟɪɝɢɸ, ɬɨɝɞɚ ɤɚɤ ɬɹɠɟɥɵɟ ɱɚɫɬɢɰɵ ɧɚ ɥɟɝɤɢɯ ɱɚɫɬɢɰɚɯ ɩɨɱɬɢ ɧɟ ɪɚɫɫɟɢɜɚɸɬɫɹ, ɧɨ ɞɨɜɨɥɶɧɨ ɢɧɬɟɧɫɢɜɧɨ ɬɨɪɦɨɡɹɬɫɹ. ȼ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɩɥɚɡɦɭ ɫɨɡɞɚɸɬ, ɩɪɢɦɟɧɹɹ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ: ɢɥɢ ɩɪɹɦɨ ɩɨɦɟɳɚɹ ɜ ɝɚɡ ɷɥɟɤɬɪɨɞɵ ɫ ɧɟɤɨɬɨɪɨɣ ɪɚɡɧɨɫɬɶɸ ɩɨɬɟɧɰɢɚɥɨɜ (ɧɚɩɪɢɦɟɪ, ɞɭɝɨɜɵɟ ɩɥɚɡɦɨɬɪɨɧɵ, ɩɪɢɛɨɪɵ ɫ ɬɥɟɸɳɢɦ ɪɚɡɪɹɞɨɦ, Z-ɩɢɧɱɢ ɢ ɬ.ɞ.), ɢɥɢ ɢɧɞɭɤɬɢɜɧɨ ɧɚɜɨɞɹ ɩɟɪɟɦɟɧɧɭɸ ɗȾɋ ɜ ɨɛɴɟɦɟ (ɧɚɩɪɢɦɟɪ, ɋȼɑɩɥɚɡɦɨɬɪɨɧɵ, θ-ɩɢɧɱɢ, ɬɨɤɚɦɚɤɢ ɢ ɬ.ɞ.). ɉɨɞɜɢɠɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ɫɢɥɶɧɨ ɪɚɡɥɢɱɚɸɬɫɹ, ɫɟɱɟɧɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɢɯ ɫ ɚɬɨɦɚɪɧɵɦɢ ɱɚɫɬɢɰɚɦɢ ɪɚɡɧɵɟ, ɢ ɨɛɵɱɧɨ ɷɥɟɤɬɪɨɧɵ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ɩɪɢɨɛɪɟɬɚɸɬ ɛɨɥɶɲɭɸ ɷɧɟɪɝɢɸ, ɱɟɦ ɢɨɧɵ. ȼ ɪɚɡɥɢɱɧɵɯ ɩɨ ɤɨɧɫɬɪɭɤɰɢɢ ɫɢɫɬɟɦɚɯ ɪɚɡɪɹɞɵ ɪɚɡɜɢɜɚɸɬɫɹ ɩɨɪɚɡɧɨɦɭ, ɧɨ, ɤɚɤ ɩɪɚɜɢɥɨ, ɧɟ ɬɨɥɶɤɨ ɧɚɩɪɚɜɥɟɧɧɵɟ ɫɤɨɪɨɫɬɢ, ɧɨ ɢ ɷɧɟɪɝɢɹ, ɩɪɢɨɛɪɟɬɚɟɦɚɹ ɷɥɟɤɬɪɨɧɨɦ ɜ ɪɚɡɪɹɞɟ, ɛɨɥɶɲɟ ɷɧɟɪɝɢɢ, ɩɪɢɨɛɪɟɬɚɟɦɨɣ ɢɨɧɨɦ. Ɉɫɨɛɟɧɧɨ ɱɟɬɤɨ ɷɬɨ ɩɪɨɹɜɥɹɟɬɫɹ ɜ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɟ ɝɚɡɨɜɨɝɨ ɪɚɡɪɹɞɚ. Ɋɚɫɫɦɨɬɪɢɦ ɜ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɵ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ (§ 51), ɫɬɟɩɟɧɶ ɢɨɧɢɡɚɰɢɢ ɤɨɬɨɪɨɝɨ ɫɨɫɬɚɜɥɹɟɬ ~0.01. ɗɬɨ ɭɱɚɫɬɨɤ ɪɚɡɪɹɞɚ, ɝɞɟ ɩɨɬɟɧɰɢɚɥ ɦɟɧɹɟɬɫɹ ɧɚɢɛɨɥɟɟ ɩɥɚɜɧɨ ɢ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɩɪɢɦɟɪɧɨ ɩɨɫɬɨɹɧɧɚɹ. ȼ ɬɢɩɢɱɧɵɯ ɭɫɥɨɜɢɹɯ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɩɨɥɹ ɧɟ ɩɪɟɜɵɲɚɟɬ 1-10 ȼ/ɫɦ, ɚ ɞɚɜɥɟɧɢɟ ɝɚɡɚ ɫɨɫɬɚɜɥɹɟɬ 1-10 Ɍɨɪɪ. ɉɨɫɤɨɥɶɤɭ ɩɥɚɡɦɚ ɹɜɥɹɟɬɫɹ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ, ɦɨɠɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ ɫɬɚɥɤɢɜɚɸɬɫɹ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɫ ɧɟɣɬɪɚɥɶɧɵɦɢ ɚɬɨɦɚɦɢ, ɚ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɦɟɠɞɭ ɫɨɛɨɣ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ. ɋɟɱɟɧɢɹ ɭɩɪɭɝɢɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɦɟɞɥɟɧɧɵɯ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɫ ɚɬɨɦɚɦɢ ɢ ɦɨɥɟɤɭɥɚɦɢ ɝɚɡɚ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɧɟɡɚɜɢɫɹɳɢɦɢ ɨɬ ɷɧɟɪɝɢɢ ɱɚɫɬɢɰ. Ʉɨɧɟɱɧɨ, ɜɟɥɢɱɢɧɵ ɫɟɱɟɧɢɣ ɡɚɜɢɫɹɬ ɨɬ ɪɨɞɚ ɝɚɡɚ, ɜ ɤɨɬɨɪɨɦ ɩɪɨɢɡɜɨɞɢɬɫɹ ɪɚɡɪɹɞ, ɧɨ ɜ ɬɢɩɢɱɧɵɯ ɭɫɥɨɜɢɹɯ ɫɟɱɟɧɢɟ ɭɩɪɭɝɨɝɨ ɪɚɫɫɟɹɧɢɹ ɞɥɹ ɢɨɧɨɜ ɦɨɠɟɬ ɞɨɫɬɢɝɚɬɶ ɜɟɥɢɱɢɧɵ σi~10-14ɫɦ2, ɬɨɝɞɚ ɤɚɤ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɨɧɨ ɩɪɢɦɟɪɧɨ ɧɚ ɩɨɪɹɞɨɤ ɦɟɧɶɲɟ σi~1015 ɫɦ2. ȼ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɫɪɟɞɧɹɹ ɞɥɢɧɚ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ λe ,i ~ 1 naσ e ,i , ɝɞɟ na ɩɥɨɬɧɨɫɬɶ ɝɚɡɚ, ɨɤɚɡɵɜɚɟɬɫɹ ɦɚɫɲɬɚɛɚ λi~10-4-10-3ɫɦ ɢ λɟ~10-3-10-2ɫɦ ɞɥɹ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. Ɍɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ ɨɛɵɱɧɨ ɩɪɢɦɟɪɧɨ ɪɚɜɧɚ ɢɨɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɢ ɞɥɹ ɪɚɡɪɹɞɚ ɦɚɥɨɣ ɦɨɳɧɨɫɬɢ ɩɨɪɹɞɤɚ ɤɨɦɧɚɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ, ɬ.ɟ. ɪɚɜɧɚ ɩɪɢɦɟɪɧɨ 0.03 ɷȼ, ɬɨɝɞɚ ɤɚɤ ɷɥɟɤɬɪɨɧɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ ɢ ɫɨɫɬɚɜɥɹɟɬ ~1ɷȼ. Ɉɛɫɭɞɢɦ ɩɪɢɱɢɧɭ ɬɚɤɨɝɨ ɧɟɪɚɜɧɨɜɟɫɢɹ. ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɫ ɧɚɩɪɹɠɟɧɧɨɫɬɶɸ ȿ, ɢɨɧ ɩɪɢɨɛɪɟɬɚɟɬ ɧɚ ɞɥɢɧɟ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɦɟɠɞɭ ɫɨɭɞɚɪɟɧɢɹɦɢ ɷɧɟɪɝɢɸ ∆İi = eEλi, (1.37) ɚ ɷɥɟɤɬɪɨɧ ɷɧɟɪɝɢɸ ∆İe = eEλe. (1.38) ɋɱɢɬɚɟɦ, ɱɬɨ ɢɨɧɵ − ɨɞɧɨɡɚɪɹɞɧɵɟ, ɬɚɤ ɱɬɨ ɩɨ ɦɨɞɭɥɸ ɡɚɪɹɞ ɢɨɧɚ ɪɚɜɟɧ ɡɚɪɹɞɭ ɷɥɟɤɬɪɨɧɚ. Ⱦɥɹ ɩɪɢɜɟɞɟɧɧɵɯ ɜɵɲɟ ɩɚɪɚɦɟɬɪɨɜ ɨɰɟɧɤɚ ɞɚɟɬ ɞɥɹ ɷɬɢɯ ɜɟɥɢɱɢɧ ∆İi ≅10-4-10-3ɷȼ, ∆İɟ ≅10-3-10-2ɷȼ. ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɢ ɢɨɧɵ, ɢ ɷɥɟɤɬɪɨɧɵ ɩɪɢɨɛɪɟɬɚɸɬ ɧɚɩɪɚɜɥɟɧɧɭɸ ɫɤɨɪɨɫɬɶ, ɤɨɬɨɪɭɸ ɦɨɠɧɨ ɨɰɟɧɢɬɶ ɤɚɤ eE eE < ∆ui >≅ τi , < ∆ue >≅ − τ . (1.39) mi me e ȼ ɮɨɪɦɭɥɚɯ (1.39) ɜɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɫ ɧɟɣɬɪɚɥɶɧɵɦɢ ɱɚɫɬɢɰɚɦɢ
τ e ,i =
λe ,i < v e ,i >
, < v e ,i >=
2 < εe ,i > , me ,i
(1.40)
ɝɞɟ εe ,i - ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ȼɜɢɞɭ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟɣ ɩɨɞɜɢɠɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ (ɢɡ-ɡɚ ɦɚɥɨɣ ɦɚɫɫɵ), ɩɨ ɜɟɥɢɱɢɧɟ ɢɯ ɧɚɩɪɚɜɥɟɧɧɚɹ ɫɤɨɪɨɫɬɶ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ ɧɚɩɪɚɜɥɟɧɧɨɣ ɫɤɨɪɨɫɬɢ ɢɨɧɨɜ. ɋɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɢɨɧɚ ɛɭɞɟɬ ɩɪɚɤɬɢɱɟɫɤɢ ɪɚɜɧɚ ɫɪɟɞɧɟɣ ɷɧɟɪɝɢɢ ɧɟɣɬɪɚɥɶɧɵɯ ɱɚɫɬɢɰ, ɬɚɤ ɤɚɤ, ɩɪɢɨɛɪɟɬɚɹ ɦɟɠɞɭ ɫɨɭɞɚɪɟɧɢɹɦɢ ɦɚɥɭɸ ɞɨɩɨɥɧɢɬɟɥɶɧɭɸ ɷɧɟɪɝɢɸ ɩɨɪɹɞɤɚ ∆İi, ɢɨɧ ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ ɫ ɚɬɨɦɚɦɢ ɟɟ ɨɬɞɚɟɬ, ɚ ɩɨɫɥɟɞɧɢɟ, ɩɨɥɭɱɢɜɲɢɟ ɷɧɟɪɝɢɸ ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ, ɩɟɪɟɧɨɫɹɬ ɟɟ ɧɚ ɫɬɟɧɤɢ. ɗɥɟɤɬɪɨɧ ɠɟ, ɩɪɢɨɛɪɟɬɚɹ ɦɟɠɞɭ ɫɨɭɞɚɪɟɧɢɹɦɢ ɷɧɟɪɝɢɸ ɛɨɥɶɲɭɸ, ɱɟɦ ɢɨɧ, ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ ɫ ɚɬɨɦɚɦɢ ɬɟɪɹɟɬ ɥɢɲɶ ɦɚɥɭɸ ɱɚɫɬɶ, ɩɨɪɹɞɤɚ ( me ma ) ε e , ɫɜɨɟɣ ɫɪɟɞɧɟɣ ɷɧɟɪɝɢɢ εe . ɇɨ ɜ ɫɬɚɰɢɨɧɚɪɧɵɯ ɭɫɥɨɜɢɹɯ ɢɦɟɧɧɨ ɷɬɚ ɦɚɥɚɹ ɩɨɬɟɪɹ ɷɧɟɪɝɢɢ ɢ ɨɝɪɚɧɢɱɢɜɚɟɬ ɧɚɛɨɪ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚɦɢ ɜ ɩɨɥɟ. ɉɨɷɬɨɦɭ ɫɪɟɞɧɸɸ ɷɧɟɪɝɢɸ ɷɥɟɤɬɪɨɧɨɜ ɦɨɠɧɨ ɨɰɟɧɢɬɶ, ɩɨɬɪɟɛɨɜɚɜ ɛɚɥɚɧɫɚ ɷɧɟɪɝɢɢ, ɩɪɢɨɛɪɟɬɚɟɦɨɣ ɜ ɩɨɥɟ ɢ ɬɟɪɹɟɦɨɣ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɹɯ ɫ ɚɬɨɦɚɦɢ: 2
2
me ∆ue me m § eE · (1.41) εe ≅ = e ¨ τe ¸ . ma 2 2 © me ¹ ɉɨɫɤɨɥɶɤɭ ɜɯɨɞɹɳɟɟ ɜ ɷɬɭ ɮɨɪɦɭɥɭ ɯɚɪɚɤɬɟɪɧɨɟ ɜɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ɷɥɟɤɬɪɨɧɚ ɫ ɧɟɣɬɪɚɥɶɧɵɦɢ ɱɚɫɬɢɰɚɦɢ τɟ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɫɨɝɥɚɫɧɨ (1.40), ɡɚɜɢɫɢɬ ɨɬ ɫɪɟɞɧɟɣ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɨɜ, ɬɨ, ɜɵɪɚɡɢɜ ɢɡ (1.41) εe ɜ ɹɜɧɨɦ ɜɢɞɟ, ɩɨɥɭɱɢɦ
ma 1 eEλe . (1.42) me 2 ɉɨɥɭɱɟɧɧɵɣ ɪɟɡɭɥɶɬɚɬ ɥɢɲɶ ɱɢɫɥɟɧɧɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ (1/2 ɜɦɟɫɬɨ 0.43) ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɪɟɡɭɥɶɬɚɬɚ ɪɟɲɟɧɢɹ ɤɢɧɟɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ, ɩɪɢɜɟɞɟɧɧɨɝɨ ɜ [20]. ɋɪɚɜɧɢɜ (1.42) ɢ (1.38), ɦɵ ɜɢɞɢɦ, ɱɬɨ ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɨɜ ɩɨɫɥɟ ɦɧɨɝɢɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɨɤɚɡɵɜɚɟɬɫɹ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ (ɩɪɢɦɟɪɧɨ ɜ ɤɨɪɟɧɶ ɢɡ ɨɬɧɨɲɟɧɢɹ ɦɚɫɫ ɧɟɣɬɪɚɥɶɧɨɣ ɱɚɫɬɢɰɵ ɢ ɷɥɟɤɬɪɨɧɚ) ɜɟɥɢɱɢɧɵ ɞɨɩɨɥɧɢɬɟɥɶɧɨɣ ɷɧɟɪɝɢɢ, ɩɪɢɨɛɪɟɬɚɟɦɨɣ ɷɥɟɤɬɪɨɧɨɦ ɧɚ ɞɥɢɧɟ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ. ɉɨɷɬɨɦɭ ɝɥɚɜɧɨɣ ɩɪɢɱɢɧɨɣ “ɩɟɪɟɝɪɟɜɚ” ɷɥɟɤɬɪɨɧɨɜ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɢɨɧɚɦɢ ɹɜɥɹɟɬɫɹ, ɩɨ ɫɭɳɟɫɬɜɭ, ɧɟ ɬɨɥɶɤɨ ɧɚɛɨɪ ɢɦɢ ɧɟɫɤɨɥɶɤɨ ɛɨɥɶɲɟɣ ɷɧɟɪɝɢɢ ɧɚ ɞɥɢɧɟ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ, ɚ ɝɨɪɚɡɞɨ ɛɨɥɟɟ ɫɥɚɛɵɣ ɬɟɦɩ ɩɨɬɟɪɶ ɩɨɥɭɱɟɧɧɨɣ ɜ ɩɨɥɟ ɷɧɟɪɝɢɢ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɹɯ ɫ ɚɬɨɦɚɦɢ. ɉɪɢ ɛɨɥɶɲɢɯ ɧɚɩɪɹɠɟɧɧɨɫɬɹɯ ɩɨɥɹ ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ (1.42) ɫɭɳɟɫɬɜɟɧɧɨ ɜɵɲɟ ɬɟɦɩɟɪɚɬɭɪɵ ɝɚɡɚ. Ʉɚɤ ɭɩɨɦɢɧɚɥɨɫɶ ɪɚɧɟɟ, ɷɬɨ ɨɛɟɫɩɟɱɢɜɚɟɬ ɢɧɜɟɪɫɧɭɸ ɡɚɫɟɥɟɧɧɨɫɬɶ ɜ ɦɨɥɟɤɭɥɹɪɧɵɯ ɝɚɡɚɯ, ɩɪɚɜɞɚ, ɬɨɥɶɤɨ ɩɪɢ ɧɢɡɤɢɯ ɬɟɦɩɟɪɚɬɭɪɚɯ ɝɚɡɚ: ɜɟɪɨɹɬɧɨɫɬɶ ɤɨɥɟɛɚɬɟɥɶɧɨɣ ɪɟɥɚɤɫɚɰɢɢ ɨɱɟɧɶ ɛɵɫɬɪɨ ɜɨɡɪɚɫɬɟɬ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ. ɉɨɷɬɨɦɭ ɢ ɩɪɢɯɨɞɢɬɫɹ ɨɯɥɚɠɞɚɬɶ ɥɚɡɟɪɵ, ɞɟɥɚɬɶ ɫɢɫɬɟɦɵ ɫ ɩɪɨɬɨɤɨɦ ɝɚɡɚ, ɬ.ɟ. ɨɛɟɫɩɟɱɢɜɚɬɶ ɭɫɥɨɜɢɹ, ɩɪɢ ɤɨɬɨɪɵɯ ɬɟɦɩɟɪɚɬɭɪɚ ɯɚɨɬɢɱɟɫɤɨɝɨ ɞɜɢɠɟɧɢɹ ɦɨɥɟɤɭɥ ɫɭɳɟɫɬɜɟɧɧɨ ɧɢɠɟ, ɱɟɦ «ɤɨɥɟɛɚɬɟɥɶɧɚɹ» ɬɟɦɩɟɪɚɬɭɪɚ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ. ɇɚɩɪɢɦɟɪ, ɜ ɥɚɡɟɪɚɯ ɧɚ ɨɤɢɫɢ ɭɝɥɟɪɨɞɚ ɩɪɢ ɤɨɦɧɚɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɝɚɡɚ ɞɨɫɬɢɠɢɦɵ ɤɨɥɟɛɚɬɟɥɶɧɵɟ ɬɟɦɩɟɪɚɬɭɪɵ, ɪɚɜɧɵɟ 7000 – 8000 Ʉ. ɇɟɪɚɜɧɨɜɟɫɧɨɫɬɶ, ɩɪɢ ɤɨɬɨɪɨɣ ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɨɜ ɫɨɫɬɚɜɥɹɟɬ ɟɞɢɧɢɰɵ ɷɥɟɤɬɪɨɧ-ɜɨɥɶɬ, ɢ ɬɟɦɩɟɪɚɬɭɪɚ ɨɫɧɨɜɧɨɣ ɫɪɟɞɵ, ɤɨɬɨɪɚɹ ɧɟɦɧɨɝɨ ɛɨɥɶɲɟ ɤɨɦɧɚɬɧɨɣ, ɨɛɟɫɩɟɱɢɜɚɸɬ ɢ ɜɨɡɦɨɠɧɨɫɬɶ ɢɧɬɟɧɫɢɜɧɨɝɨ ɩɪɨɜɟɞɟɧɢɹ ɧɟɤɨɬɨɪɵɯ ɯɢɦɢɱɟɫɤɢɯ ɪɟɚɤɰɢɣ. ɗɥɟɤɬɪɨɧɵ ɩɟɪɟɞɚɸɬ ɷɧɟɪɝɢɸ ɧɚ ɜɨɡɛɭɠɞɟɧɢɟ ɤɨɥɟɛɚɬɟɥɶɧɵɯ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɦɨɥɟɤɭɥ, ɚ ɜɵɫɨɤɚɹ ɤɨɥɟɛɚɬɟɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɨɛɟɫɩɟɱɢɜɚɟɬ ɢ ɜɵɫɨɤɢɟ ɫɤɨɪɨɫɬɢ ɯɢɦɢɱɟɫɤɢɯ ɪɟɚɤɰɢɣ. ɇɟɨɛɯɨɞɢɦɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɩɪɢ ɷɬɨɦ ɫɭɳɟɫɬɜɟɧɧɨ ɜɨɡɪɚɫɬɚɟɬ ɢ ɄɉȾ ɩɨ ɜɵɯɨɞɭ ɤɨɧɟɱɧɨɝɨ ɩɪɨɞɭɤɬɚ ɭɫɬɚɧɨɜɨɤ, ɨɫɧɨɜɚɧɧɵɯ ɧɚ ɝɚɡɨɜɨɦ ɪɚɡɪɹɞɟ: ɷɥɟɤɬɪɨɧɧɨɟ ɜɨɡɛɭɠɞɟɧɢɟ ɨɛɟɫɩɟɱɢɜɚɟɬ ɩɟɪɟɞɚɱɭ ɷɧɟɪɝɢɢ ɢɦɟɧɧɨ ɧɚ “ɧɭɠɧɵɟ”
εe ≅
ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ, ɚ ɧɟ ɪɚɜɧɨɦɟɪɧɨ ɧɚ ɜɫɟ. Ɍɚɤ ɄɉȾ ɋɈ2-ɥɚɡɟɪɚ ɞɨɜɟɥɢ ɞɨ ∼25%, ɡɚɬɪɚɬɵ ɷɧɟɪɝɢɢ ɩɪɢ ɩɨɥɭɱɟɧɢɢ NO ɢɡ N2 ɢ O2 ɫɧɢɡɢɥɢ ɜ 6-7 ɪɚɡ. Ɇɵ ɪɚɫɫɦɨɬɪɟɥɢ ɧɟɪɚɜɧɨɜɟɫɧɨɫɬɶ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɵ. ɇɨ ɢ ɩɪɚɤɬɢɱɟɫɤɢ ɩɨɥɧɨɫɬɶɸ ɢɨɧɢɡɨɜɚɧɧɚɹ ɝɨɪɹɱɚɹ ɩɥɚɡɦɚ ɬɨɠɟ, ɤɚɤ ɩɪɚɜɢɥɨ, ɧɟ ɪɚɜɧɨɜɟɫɧɚɹ. ɇɚɩɪɢɦɟɪ, ɜ ɢɡɜɟɫɬɧɵɯ ɬɨɤɚɦɚɤɚɯ ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɪɚɡɧɵɟ ɬɟɦɩɟɪɚɬɭɪɵ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ, ɧɟ ɝɨɜɨɪɹ ɭɠɟ ɨɛ ɨɬɫɭɬɫɬɜɢɢ ɪɚɜɧɨɜɟɫɢɹ ɫ ɢɡɥɭɱɟɧɢɟɦ.
§ 9. ɉɪɨɰɟɫɫɵ ɪɟɥɚɤɫɚɰɢɢ ɜ ɩɥɚɡɦɟ ɉɪɨɰɟɫɫɵ ɪɟɥɚɤɫɚɰɢɢ ɩɪɢɜɨɞɹɬ ɤ ɭɫɬɚɧɨɜɥɟɧɢɸ ɦɚɤɫɜɟɥɥɨɜɫɤɨɣ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɱɚɫɬɢɰ ɩɨ ɷɧɟɪɝɢɹɦ, ɬ.ɟ. ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ, ɤɨɝɞɚ ɦɨɠɧɨ ɝɨɜɨɪɢɬɶ ɨ ɬɟɦɩɟɪɚɬɭɪɟ. ȼ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɟ ɬɟɦɩɟɪɚɬɭɪɚ ɢɨɧɨɜ ɪɚɜɧɚ ɬɟɦɩɟɪɚɬɭɪɟ ɝɚɡɚ, ɦɚɫɫɵ ɢɨɧɨɜ ɢ ɚɬɨɦɨɜ ɩɪɚɤɬɢɱɟɫɤɢ ɨɞɢɧɚɤɨɜɵ. Ɍɟɦɩɟɪɚɬɭɪɚ ɷɥɟɤɬɪɨɧɨɜ ɦɨɠɟɬ ɛɵɬɶ ɞɪɭɝɨɣ, ɱɟɦ ɭ ɚɬɨɦɨɜ ɝɚɡɚ, ɞɚɠɟ ɬɨɝɞɚ, ɤɨɝɞɚ ɷɥɟɤɬɪɨɧɨɜ ɨɱɟɧɶ ɦɚɥɨ [8]. ȼ ɩɨɥɧɨɫɬɶɸ ɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɟ ɩɪɚɤɬɢɱɟɫɤɢ ɟɫɬɶ ɬɨɥɶɤɨ ɷɥɟɤɬɪɨɧɵ ɢ ɢɨɧɵ. Ɋɚɜɧɨɜɟɫɢɟ ɛɭɞɟɬ ɭɫɬɚɧɚɜɥɢɜɚɬɶɫɹ ɜɫɥɟɞɫɬɜɢɟ ɤɭɥɨɧɨɜɫɤɢɯ ɫɨɭɞɚɪɟɧɢɣ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ. Ɍɚɤ ɤɚɤ ɦɚɫɫɵ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɫɢɥɶɧɨ ɪɚɡɥɢɱɧɵ, ɬɨ ɪɚɫɫɦɨɬɪɢɦ ɨɬɞɟɥɶɧɨ ɷɥɟɤɬɪɨɧ-ɷɥɟɤɬɪɨɧɧɵɟ ɢ ɢɨɧ-ɢɨɧɧɵɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ. ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ Ʉ ɫɨɭɞɚɪɟɧɢɣ ɩɪɢɜɨɞɹɬ ɤ ɦɚɤɫɜɟɥɥɢɡɚɰɢɢ ɞɚɧɧɨɝɨ, ɧɚɩɪɢɦɟɪ, ɷɥɟɤɬɪɨɧɧɨɝɨ ɚɧɫɚɦɛɥɹ. Ɍɨɝɞɚ ɜɪɟɦɹ ɭɫɬɚɧɨɜɥɟɧɢɹ ɦɚɤɫɜɟɥɥɨɜɫɤɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɪɟɞɢ ɷɥɟɤɬɪɨɧɨɜ 1 τ ee = K . (1.43) nvTeσ c ɝɞɟ σc ɤɭɥɨɧɨɜɫɤɨɟ ɫɟɱɟɧɢɟ, ɚ vTe – ɬɟɩɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ. ɉɨɞɫɬɚɜɥɹɹ ɡɧɚɱɟɧɢɟ ɤɭɥɨɧɨɜɫɤɨɝɨ ɫɟɱɟɧɢɹ σc ɢɡ (1.23) ɢ vTe = 3Te me , ɩɨɥɭɱɢɦ:
τ ee = K
3 3 4π e 4 Lc
me 3 / 2 T . n e
(1.44)
ɋɬɪɨɝɢɣ ɪɚɫɱɟɬ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ Ʉ>Di ɢ, ɤɚɤ ɫɥɟɞɫɬɜɢɟ, ɷɥɟɤɬɪɨɧɵ ɡɧɚɱɢɬɟɥɶɧɨ ɩɨɞɜɢɠɧɟɟ ɢɨɧɨɜ, ɩɨɥɭɱɚɟɦ § T· Da = Di ¨ 1 + e ¸ . (1.60) Ti ¹ © Ɉɱɟɜɢɞɧɨ, ɢɦɟɸɬ ɦɟɫɬɨ ɧɟɪɚɜɟɧɫɬɜɚ Di mevTe. (1.72) ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɷɬɨɝɨ ɭɫɥɨɜɢɹ ɱɚɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɩɥɚɡɦɵ ɩɨɩɚɞɚɟɬ, ɤɚɤ ɝɨɜɨɪɹɬ, ɜ ɪɟɠɢɦ «ɩɚɞɚɸɳɟɝɨ ɬɪɟɧɢɹ», ɤɨɝɞɚ ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɧɢɯ ɷɮɮɟɤɬɢɜɧɚɹ ɫɢɥɚ ɬɪɟɧɢɹ ɭɦɟɧɶɲɚɟɬɫɹ ɫ ɪɨɫɬɨɦ ɢɯ ɷɧɟɪɝɢɢ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɬɟɪɹ ɢɦɩɭɥɶɫɚ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɹɯ ɫ ɢɨɧɚɦɢ ɧɟ ɦɨɠɟɬ ɨɝɪɚɧɢɱɢɬɶ ɧɚɛɨɪ ɢɦɩɭɥɶɫɚ ɷɥɟɤɬɪɨɧɚɦɢ ɜɨ ɜɧɟɲɧɟɦ ɩɨɥɟ, ɬɚɤ ɱɬɨ ɱɚɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɦɨɠɟɬ ɩɟɪɟɣɬɢ ɜ ɪɟɠɢɦ ɧɟɩɪɟɪɵɜɧɨɝɨ ɭɫɤɨɪɟɧɢɹ. Ɍɚɤɢɟ ɷɥɟɤɬɪɨɧɵ ɩɨɥɭɱɢɥɢ ɧɚɡɜɚɧɢɟ "ɩɪɨɫɜɢɫɬɧɵɯ" ɢɥɢ "ɭɛɟɝɚɸɳɢɯ" ɷɥɟɤɬɪɨɧɨɜ. ȿɫɥɢ ɩɪɟɞɩɨɥɨɠɢɬɶ, ɱɬɨ τ≈τei, ɬɨ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɧɟɤɨɬɨɪɨɟ ɩɪɟɞɟɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɩɨɥɹ ȿɤɪ, ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɩɨɥɟ Ⱦɪɚɣɫɟɪɚ, ɜɵɲɟ ɤɨɬɨɪɨɝɨ ɷɥɟɤɬɪɨɧɵ ɧɚɱɧɭɬ "ɭɯɨɞɢɬɶ ɜ ɩɪɨɫɜɢɫɬ", ɬ.ɟ. ɛɭɞɭɬ ɧɟɩɪɟɪɵɜɧɨ ɭɫɤɨɪɹɬɶɫɹ [11]: E > Eɤɪ ≈ 0.214Lce/rDe2. (1.73)
ɉɪɚɤɬɢɱɟɫɤɢ, ɡɚɦɟɬɧɚɹ ɱɚɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɩɥɚɡɦɵ ɧɚɱɢɧɚɟɬ «ɭɯɨɞɢɬɶ ɜ ɩɪɨɫɜɢɫɬ» ɭɠɟ ɩɪɢ ȿ > 0.1Eɤɪ.
§ 11. Ⱦɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɥɚɡɦɵ ɉɨɦɟɫɬɢɦ ɩɥɚɡɦɭ ɜɨ ɜɧɟɲɧɟɟ ɩɟɪɟɦɟɧɧɨɟ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɢ ɩɨɩɵɬɚɟɦɫɹ ɩɪɨɫɥɟɞɢɬɶ ɢɡɦɟɧɟɧɢɟ ɟɟ ɫɜɨɣɫɬɜ, ɩɨɫɬɟɩɟɧɧɨ ɭɜɟɥɢɱɢɜɚɹ ɟɝɨ ɱɚɫɬɨɬɭ. ɋɬɚɬɢɱɟɫɤɨɟ ɜɧɟɲɧɟɟ ɩɨɥɟ, ɤɚɤ ɦɵ ɭɠɟ ɡɧɚɟɦ, ɩɪɨɧɢɤɚɟɬ ɜ ɩɥɚɡɦɭ ɧɚ ɬɨɥɳɢɧɭ ɦɚɫɲɬɚɛɚ ɞɟɛɚɟɜɫɤɨɝɨ ɫɥɨɹ. ɗɬɨ ɜɵɬɟɤɚɟɬ ɢɡ ɭɪɚɜɧɟɧɢɹ ɷɤɪɚɧɢɪɨɜɤɢ (ɫɦ. §3), ɤɨɬɨɪɨɟ, ɧɚɩɪɢɦɟɪ, ɞɥɹ ɨɞɧɨɦɟɪɧɨɝɨ ɫɥɭɱɚɹ ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɜɢɞɟ: d 2ϕ ϕ = 2 . (1.74) dx 2 rDe Ɂɞɟɫɶ rDe – ɷɥɟɤɬɪɨɧɧɵɣ ɞɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ. ɍɞɨɛɧɨ ɩɟɪɟɩɢɫɚɬɶ ɷɬɨ ɭɪɚɜɧɟɧɢɟ, ɢɫɩɨɥɶɡɭɹ ɩɪɟɞɫɬɚɜɥɟɧɢɟ Ɏɭɪɶɟ ϕ ~ ϕ k exp( ikx − iωt ) . Ɋɟɡɭɥɶɬɚɬ ɞɥɹ ɚɦɩɥɢɬɭɞɵ Ɏɭɪɶɟ-ɝɚɪɦɨɧɢɤɢ ɩɨɬɟɧɰɢɚɥɚ ϕɤ, ɤɚɤ ɥɟɝɤɨ ɩɪɨɜɟɪɢɬɶ, ɛɭɞɟɬ ɫɥɟɞɭɸɳɢɦ: 1 k 2 ( 1 + 2 2 )ϕ k = 0. (1.75) k rDe ɋɪɚɜɧɢɦ ɷɬɨ ɭɪɚɜɧɟɧɢɟ ɫ ɭɪɚɜɧɟɧɢɟɦ ɞɥɹ ɢɧɞɭɤɰɢɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ dD =0 . (1.76) dx Ⱦɥɹ Ɏɭɪɶɟ-ɝɚɪɦɨɧɢɤɢ ɟɝɨ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ: k 2 εk ϕ k = 0 , (1.77) ɝɞɟ εk - ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɥɚɡɦɵ, ɨɩɢɫɵɜɚɸɳɚɹ ɨɬɤɥɢɤ ɩɥɚɡɦɵ ɧɚ ɫɬɚɬɢɱɟɫɤɨɟ ɜɨɡɞɟɣɫɬɜɢɟ. Ʉɚɤ ɜɢɞɢɦ ɢɡ ɫɪɚɜɧɟɧɢɹ (1.75) ɢ (1.77), ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ 1 εk = 1 + 2 2 . (1.78) k rDe Ɉɬɤɥɢɤ ɩɥɚɡɦɵ ɧɚ ɫɬɚɬɢɱɟɫɤɨɟ ɜɨɡɞɟɣɫɬɜɢɟ ɨɤɚɡɵɜɚɟɬɫɹ ɜɩɨɥɧɟ ɷɤɜɢɜɚɥɟɧɬɟɧ ɷɮɮɟɤɬɭ ɩɨɥɹɪɢɡɚɰɢɢ ɨɛɵɱɧɨɝɨ ɞɢɷɥɟɤɬɪɢɤɚ, ɩɨɦɟɳɟɧɧɨɝɨ ɜɨ ɜɧɟɲɧɟɟ ɩɨɥɟ, ɯɨɬɹ, ɤɨɧɟɱɧɨ, ɦɟɯɚɧɢɡɦ ɩɨɥɹɪɢɡɚɰɢɢ ɢɧɨɣ: ɟɫɥɢ ɞɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ ɦɚɥ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɯɚɪɚɤɬɟɪɧɨɣ ɞɥɢɧɨɣ ɜɨɥɧɵ, ɬɨ ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɨɤɚɡɵɜɚɟɬɫɹ ɨɱɟɧɶ ɛɨɥɶɲɨɣ ɢ ɩɨɥɟ ɜ ɩɥɚɡɦɭ, ɮɚɤɬɢɱɟɫɤɢ, ɧɟ ɩɪɨɧɢɤɚɟɬ. ɉɪɢ ɧɢɡɤɢɯ, ɧɨ ɧɟɧɭɥɟɜɵɯ, ɱɚɫɬɨɬɚɯ ω ɤɚɱɟɫɬɜɟɧɧɨ ɤɚɪɬɢɧɚ ɧɟ ɢɡɦɟɧɢɬɫɹ − ɡɚɪɹɞɵ ɛɭɞɭɬ ɷɤɪɚɧɢɪɨɜɚɬɶ ɜɧɟɲɧɟɟ ɩɨɥɟ ɜ ɫɥɨɹɯ ɦɚɫɲɬɚɛɚ ɞɟɛɚɟɜɫɤɢɯ. ɉɥɚɡɦɚ ɛɭɞɟɬ ɜɟɫɬɢ ɫɟɛɹ ɤɚɤ ɩɪɨɜɨɞɧɢɤ − ɜɧɟɲɧɟɟ ɩɨɥɟ ɜ ɧɟɟ ɧɟ ɛɭɞɟɬ ɩɪɨɧɢɤɚɬɶ. ɇɨ ɟɫɥɢ ɱɚɫɬɨɬɚ ɩɨɥɹ ɛɭɞɟɬ ɜɟɥɢɤɚ, ɢ ɛɭɞɟɬ ɩɪɟɜɵɲɚɬɶ ɩɥɚɡɦɟɧɧɭɸ ɱɚɫɬɨɬɭ, ɬɨ ɤɚɪɬɢɧɚ ɤɚɱɟɫɬɜɟɧɧɨ ɢɡɦɟɧɢɬɫɹ: ɷɥɟɤɬɪɨɧɵ ɢɡ-ɡɚ ɢɧɟɪɰɢɢ ɧɟ ɛɭɞɭɬ ɭɫɩɟɜɚɬɶ ɩɨɞɫɬɪɚɢɜɚɬɶɫɹ ɩɨɞ ɤɨɥɟɛɚɧɢɹ ɩɨɥɹ, ɨɧɢ ɛɭɞɭɬ ɨɫɰɢɥɥɢɪɨɜɚɬɶ ɨɤɨɥɨ ɧɟɤɨɬɨɪɨɝɨ ɫɪɟɞɧɟɝɨ ɩɨɥɨɠɟɧɢɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɟ ɫɦɨɠɟɬ ɩɪɨɧɢɤɧɭɬɶ ɜ ɩɥɚɡɦɭ. ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ, ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɫɬɶ ɫɥɭɱɚɸ ɧɢɡɤɢɯ ɱɚɫɬɨɬ, ɩɪɨɧɢɤɚɸɳɟɟ ɜ ɩɥɚɡɦɭ ɩɨɥɟ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɨɞɧɨɪɨɞɧɵɦ. ɑɬɨɛɵ ɧɚɣɬɢ ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɥɚɡɦɵ ɜ ɷɬɨɦ ɩɪɟɞɟɥɟ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬ, ɛɭɞɟɦ ɫɱɢɬɚɬɶ ɩɟɪɟɦɟɧɧɨɟ ɩɨɥɟ ɝɚɪɦɨɧɢɱɟɫɤɢɦ: ~ = E e iω t . E (1.79) 0 ɋɦɟɳɟɧɢɟ ∆ɯ ɷɥɟɤɬɪɨɧɚ ɢɡ ɩɨɥɨɠɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɬɚɤɨɝɨ ɩɨɥɹ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɫ ɩɨɦɨɳɶɸ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ~ = eE e iωt , me x = eE 0 (1.80) e ~ ∆x = − E . mω 2 ɉɨɞɫɱɢɬɚɟɦ ɬɟɩɟɪɶ ɢɧɞɭɤɰɢɸ ɩɨɥɹ ɜ ɩɥɚɡɦɟ ~=ε E ~=E ~ + 4π P , D (1.81) ω
ɝɞɟ Ɋ = ɩɟ∆x - ɞɢɩɨɥɶɧɵɣ ɦɨɦɟɧɬ ɟɞɢɧɢɰɵ ɨɛɴɟɦɚ ɩɥɚɡɦɵ, ɨɛɭɫɥɨɜɥɟɧɧɵɣ ɫɦɟɳɟɧɢɟɦ ɷɥɟɤɬɪɨɧɨɜ. ɉɪɨɢɡɜɟɞɹ ɩɨɞɫɬɚɧɨɜɤɭ, ɩɨɥɭɱɢɦ ɜɟɥɢɱɢɧɭ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ: 2
§ ωp · 4πne 2 2 εω = 1 − ¨ ¸ , ω p = , me ©ω¹
(1.82)
ɨɩɢɫɵɜɚɸɳɟɣ ɨɬɤɥɢɤ ɩɥɚɡɦɵ ɧɚ ɜɵɫɨɤɨɱɚɫɬɨɬɧɨɟ ɢ ɨɞɧɨɪɨɞɧɨɟ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ. ɉɨɥɭɱɟɧɧɭɸ ɮɨɪɦɭɥɭ ɞɥɹ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɢ ɩɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɜɨɡɞɟɣɫɬɜɢɹ ɧɚ ɩɥɚɡɦɭ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɜɨɥɧɵ, ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɤɨɬɨɪɨɣ ɨɩɪɟɞɟɥɹɟɬ ɭɪɚɜɧɟɧɢɟ (ɩɨɞɪɨɛɧɟɟ ɫɦ. Ƚɥɚɜɭ 3):
N2 = ε ,
(1.83)
ɝɞɟ N=ɤɫ/ω – ɩɨɤɚɡɚɬɟɥɶ ɩɪɟɥɨɦɥɟɧɢɹ. ɂɡ ɮɨɪɦɭɥɵ (1.82) ɨɱɟɜɢɞɧɨ, ɱɬɨ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɟ ɜɨɥɧɵ ɫ ɱɚɫɬɨɬɨɣ ω > ωp ɦɨɝɭɬ ɩɪɨɧɢɤɚɬɶ ɜ ɩɥɚɡɦɭ ɢ ɪɚɫɩɪɨɫɬɪɚɧɹɬɶɫɹ ɜ ɧɟɣ, ɬɚɤ ɤɚɤ ɞɥɹ ɧɢɯ ɛɭɞɟɬ N2>0. ɇɚɩɪɨɬɢɜ, ɜ ɨɛɥɚɫɬɢ ɱɚɫɬɨɬ ω> Tɥɚ ɪ ɦ , ∆lɩɨɥɹ >> ρɥɚ ɪ ɦ . Ʉɨɥɢɱɟɫɬɜɟɧɧɨ ɷɬɢ ɤɪɢɬɟɪɢɢ ɦɨɠɧɨ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
∂B∂t = ρBe = ɝɞɟ
vE = c
me v E c mv c ; < ∆i >= ρ Bi = i E , eB eB
E , ɚ ɡɚɪɹɞɵ ɱɚɫɬɢɰ ɩɨ ɜɟɥɢɱɢɧɟ ɫɱɢɬɚɸɬɫɹ ɨɞɢɧɚɤɨɜɵɦɢ. B
Ɂɚɪɹɞɵ ɜ ɫɪɟɞɧɟɦ “ɪɚɡɨɣɞɭɬɫɹ” ɧɚ ɜɟɥɢɱɢɧɭ
(2.100)
( me + mi )c 2 E⊥ ∆ =< ∆e > + < ∆i >= . eB 2
(2.101)
ɍɦɧɨɠɢɜ ɷɬɭ ɜɟɥɢɱɢɧɭ ɧɚ ɡɚɪɹɞ ɢ ɧɚ ɩɥɨɬɧɨɫɬɶ, ɩɨɥɭɱɢɦ ɞɢɩɨɥɶɧɵɣ ɦɨɦɟɧɬ Ɋ ɟɞɢɧɢɰɵ ɨɛɴɟɦɚ
n( me + mi )c 2 E E P = ne∆ = = ρm c 2 2 , 2 B B
(2.102)
ɢ ɩɨɩɟɪɟɱɧɭɸ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɤɨɦɩɨɧɟɧɬɭ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɩɥɚɡɦɵ
P c2 ε ⊥ = 1 + 4π = 1 + 4πρm 2 . E B ȼ ɨɛɟɢɯ ɮɨɪɦɭɥɚɯ ρm = n( me + mi ) - ɦɚɫɫɨɜɚɹ ɩɥɨɬɧɨɫɬɶ ɩɥɚɡɦɵ.
(2.103)
Ɋɚɫɱɟɬɵ ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɜɟɥɢɱɢɧɚ ε⊥ ɦɨɠɟɬ ɛɵɬɶ ɛɨɥɶɲɨɣ, ɩɨɷɬɨɦɭ ɩɨɥɟ ɜ ɩɥɚɡɦɟ ɫɢɥɶɧɨ ɨɫɥɚɛɥɹɟɬɫɹ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɞɟɣɬɟɪɢɟɜɨɣ ɩɥɚɡɦɵ ɫ ɩɚɪɚɦɟɬɪɚɦɢ n=1010ɫɦ-3, ȼ=103Ƚɫ ɩɨɥɭɱɚɟɦ ε⊥≈102. ȿɫɥɢ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɦɟɞɥɟɧɧɨ ɦɟɧɹɟɬɫɹ ɜɨ ɜɪɟɦɟɧɢ, ɬɚɤ ɱɬɨ ɜɪɟɦɟɧɧɨɣ ɦɚɫɲɬɚɛ ɟɝɨ ɢɡɦɟɧɟɧɢɹ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɟɬ ɥɚɪɦɨɪɨɜɫɤɢɣ ɩɟɪɢɨɞ, ɬɨ ɩɪɢɜɟɞɟɧɧɚɹ ɮɨɪɦɭɥɚ ɞɥɹ ε⊥ ɫɩɪɚɜɟɞɥɢɜɚ ɢ ɜ ɷɬɨɦ ɫɥɭɱɚɟ. ɇɚɩɨɦɧɢɦ, ɱɬɨ ɮɨɪɦɭɥɚ (2.103) ɪɚɧɟɟ ɛɵɥɚ ɩɨɥɭɱɟɧɚ ɩɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɩɨɥɹɪɢɡɚɰɢɨɧɧɨɝɨ ɞɪɟɣɮɚ.
Ⱦɢɷɥɟɤɬɪɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɩɥɚɡɦɵ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɪɟɬɟɪɩɟɜɚɸɬ ɫɭɳɟɫɬɜɟɧɧɨɟ ɢɡɦɟɧɟɧɢɟ, ɜɟɥɢɱɢɧɵ ε|| ɢ ε⊥ ɪɚɡɥɢɱɧɵ, ɢ ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɵ ɫɬɚɧɨɜɢɬɫɹ ɬɟɧɡɨɪɧɨɣ ɜɟɥɢɱɢɧɨɣ. ɉɪɢ ɷɬɨɦ ɤɨɦɩɨɧɟɧɬɚ ε|| ɨɫɬɚɟɬɫɹ ɬɚɤɨɣ ɠɟ, ɤɚɤ ɢ ɜ ɫɥɭɱɚɟ ɩɥɚɡɦɵ ɛɟɡ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. Ɉɧɚ ɡɚɜɢɫɢɬ ɨɬ ɱɚɫɬɨɬɵ ɩɚɞɚɸɳɟɣ ɜɨɥɧɵ ɢ ɩɥɨɬɧɨɫɬɢ ɱɢɫɥɚ ɱɚɫɬɢɰ ɩɥɚɡɦɵ, ɬɨɝɞɚ ɤɚɤ ɤɨɦɩɨɧɟɧɬɚ ε⊥ − ɨɬ ɦɚɫɫɨɜɨɣ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ ɢ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. • ɉɨɩɟɪɟɱɧɚɹ ɩɪɨɜɨɞɢɦɨɫɬɶ. Ʉɚɪɬɢɧɚ ɫɨ ɫɜɨɛɨɞɧɵɦ ɞɪɟɣɮɨɦ ɩɥɚɡɦɵ ɜ ɫɤɪɟɳɟɧɧɵɯ ɩɨɥɹɯ ɫɩɪɚɜɟɞɥɢɜɚ ɥɢɲɶ ɩɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɧɟɬ ɩɪɢɱɢɧ, ɦɟɲɚɸɳɢɯ ɷɬɨɦɭ ɫɜɨɛɨɞɧɨɦɭ ɞɜɢɠɟɧɢɸ ɩɥɚɡɦɵ. Ɋɟɚɥɢɡɨɜɚɬɶ ɬɚɤɨɣ ɫɥɭɱɚɣ ɦɨɠɧɨ, ɧɚɩɪɢɦɟɪ, ɜ ɫɥɭɱɚɟ ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɨɝɨ ɫɨɥɟɧɨɢɞɚ ɫ ɞɨɩɨɥɧɢɬɟɥɶɧɵɦ ɪɚɞɢɚɥɶɧɵɦ ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɩɨɥɟɦ. ȿɫɥɢ ɨɫɶ Z ɧɚɩɪɚɜɢɬɶ ɜɞɨɥɶ ɨɫɢ ɫɨɥɟɧɨɢɞɚ, ɚ ɨɫɶ Y − ɩɨ ɪɚɞɢɭɫɭ, ɬɨɝɞɚ ɨɫɶ X ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɜɪɚɳɟɧɢɸ ɩɨ ɭɝɥɭ ϕ ɜɨɤɪɭɝ ɨɫɢ ɫɨɥɟɧɨɢɞɚ. Ɍɚɤɢɟ ɫɢɫɬɟɦɵ ɫɭɳɟɫɬɜɭɸɬ, ɢ ɜ ɞɜɢɠɭɳɟɣɫɹ ɩɥɚɡɦɟ ɭɞɚɟɬɫɹ ɧɚɤɚɩɥɢɜɚɬɶ ɜɟɫɶɦɚ ɡɚɦɟɬɧɭɸ ɷɧɟɪɝɢɸ - ɩɨ ɫɭɳɟɫɬɜɭ ɫɨɡɞɚɸɬɫɹ ɩɥɚɡɦɟɧɧɵɟ ɤɨɧɞɟɧɫɚɬɨɪɵ ɫ ɛɨɥɶɲɢɦ ɡɧɚɱɟɧɢɟɦ ε⊥ . Ⱦɪɭɝɨɟ ɩɪɢɦɟɧɟɧɢɟ − ɩɥɚɡɦɟɧɧɵɟ ɰɟɧɬɪɢɮɭɝɢ − ɛɵɥɨ ɪɚɫɫɦɨɬɪɟɧɨ ɪɚɧɟɟ. ȿɫɥɢ ɠɟ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɞɪɟɣɮɚ ɜɨɡɧɢɤɚɟɬ ɤɚɤɨɟ-ɥɢɛɨ ɩɪɟɩɹɬɫɬɜɢɟ, ɬɨ ɩɪɨɢɫɯɨɞɢɬ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɥɨɬɧɨɫɬɢ ɱɚɫɬɢɰ, ɬɚɤ ɤɚɤ ɜɛɥɢɡɢ ɩɪɟɩɹɬɫɬɜɢɹ ɱɚɫɬɢɰɵ ɧɚɤɚɩɥɢɜɚɸɬɫɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɜɨɡɧɢɤɚɟɬ ɝɪɚɞɢɟɧɬ ɞɚɜɥɟɧɢɹ ɢ ɫɢɥɚ (ɜ ɪɚɫɱɟɬɟ ɧɚ ɨɞɧɭ ɱɚɫɬɢɰɭ) F= −∇p/n. ɗɬɚ ɫɢɥɚ ɩɪɢɜɨɞɢɬ ɤ ɩɨɹɜɥɟɧɢɸ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɞɪɟɣɮɚ, ɩɪɢɱɟɦ ɷɥɟɤɬɪɨɧɵ ɢ ɢɨɧɵ ɞɪɟɣɮɭɸɬ ɜ ɪɚɡɧɵɟ ɫɬɨɪɨɧɵ − ɜɨɡɧɢɤɚɟɬ ɬɨɤ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɨɫɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɩɪɨɜɨɞɢɦɨɫɬɶ ɩɨɩɟɪɺɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ȼ. ɇɚ ɪɢɫ. 2.18 ɩɨɥɟ ȼ ɧɚɩɪɚɜɥɟɧɨ ɜɞɨɥɶ Ɋɢɫ.2.18. ɋɯɟɦɚ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɩɪɨɜɨɞɢɦɨɫɬɢ ɨɫɢ Z, ɚ ɩɨɥɟ ȿ - ɜɞɨɥɶ ɨɫɢ Y ɢ ɜɨɡɧɢɤɚɟɬ ɞɪɟɣɮ ɜɞɨɥɶ ɨɫɢ X. ȿɫɥɢ ɢɦɟɟɬɫɹ ɤɚɤɨɟ-ɥɢɛɨ ɩɪɟɩɹɬɫɬɜɢɟ, ɬɨ ɜɛɥɢɡɢ ɧɟɝɨ ɩɥɨɬɧɨɫɬɶ ɩɨɜɵɲɚɟɬɫɹ; ɜɨɡɧɢɤɚɟɬ ∇p ɢ ɨɬɜɟɱɚɸɳɚɹ ɟɦɭ ɫɢɥɚ F. Ⱦɪɟɣɮ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɢɥɵ F ɧɚɩɪɚɜɥɟɧ ɞɥɹ ɢɨɧɨɜ ɜɞɨɥɶ ɨɫɢ Y, ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɚɧɬɢɩɚɪɚɥɥɟɥɶɧɨ Y. ɉɨɹɜɥɹɟɬɫɹ ɬɨɤ j, ɧɚɩɪɚɜɥɟɧɧɵɣ ɜɞɨɥɶ ɨɫɢ Y, ɬɨ ɟɫɬɶ ɜɞɨɥɶ ɜɟɤɬɨɪɚ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ - ɩɪɨɜɨɞɢɦɨɫɬɶ «ɜɨɫɫɬɚɧɚɜɥɢɜɚɟɬɫɹ». ȼɵɱɢɫɥɹɹ ɷɬɨɬ
ɬɨɤ, ɧɚɞɨ ɭɱɢɬɵɜɚɬɶ ɬɪɟɧɢɟ, ɜɨɡɧɢɤɚɸɳɟɟ ɩɪɢ ɨɬɧɨɫɢɬɟɥɶɧɨɦ ɞɜɢɠɟɧɢɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ.
Ɍɨɱɧɵɣ ɜɵɜɨɞ, ɫɬɪɨɝɨ ɭɱɢɬɵɜɚɸɳɢɣ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ [13], ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɩɨɩɟɪɟɱɧɚɹ ɩɪɨɜɨɞɢɦɨɫɬɶ ɧɟ ɪɚɜɧɚ ɩɪɨɞɨɥɶɧɨɣ, σ⊥≠σ||, ɬ.ɟ. ɩɪɨɜɨɞɢɦɨɫɬɶ ɩɥɚɡɦɵ ɚɧɢɡɨɬɪɨɩɧɚ. ɉɪɢ ɷɬɨɦ ɨɬɧɨɲɟɧɢɟ σ⊥/σ|| ɡɚɜɢɫɢɬ ɨɬ ɡɚɪɹɞɨɜɨɝɨ ɱɢɫɥɚ ɢɨɧɚ. Ⱦɥɹ ɢɨɧɨɜ ɫ Z=1, ɧɚɩɪɢɦɟɪ, ɞɥɹ ɜɨɞɨɪɨɞɧɨɣ ɩɥɚɡɦɵ σ ⊥ ≈ 0 ,5σ|| (2.104) ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɬɨɤ ɬɟɱɟɬ ɩɨɞ ɭɝɥɨɦ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɢ ɡɚɤɨɧ Ɉɦɚ ɞɥɹ ɩɥɚɡɦɵ ɜɵɝɥɹɞɢɬ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ [13]:
& & j|| & j 1 && + ⊥ + E′ = [ jB ] , σ || σ ⊥ enc
(2.105)
Ɂɞɟɫɶ ɫɩɪɚɜɚ ɜɵɞɟɥɟɧɵ ɜɫɟ ɫɥɚɝɚɟɦɵɟ, ɜ ɤɨɬɨɪɵɟ ɜɯɨɞɢɬ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ, ɜ ɬɨɦ ɱɢɫɥɟ ɩɨɫɥɟɞɧɟɟ ɢɡ ɧɢɯ ɨɬɜɟɱɚɟɬ ɷɮɮɟɤɬɭ ɏɨɥɥɚ, ɚ ɫɥɟɜɚ ɜ ɮɨɪɦɭɥɟ ɮɢɝɭɪɢɪɭɟɬ ɷɮɮɟɤɬɢɜɧɨɟ ɩɨɥɟ, ɪɚɜɧɨɟ
& & 1 && & 1 E ′ = E + [ VB ] + ( ∇pe − RT ) . c en
(2.106)
Ɂɞɟɫɶ ɩɟɪɜɨɟ ɫɥɚɝɚɟɦɨɟ − ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɜɬɨɪɨɟ ɭɱɢɬɵɜɚɟɬ ɷɮɮɟɤɬ ɢɧɞɭɤɰɢɢ, ɜɨɡɧɢɤɚɸɳɢɣ ɩɪɢ ɩɟɪɟɫɟɱɟɧɢɢ ɩɨɬɨɤɨɦ ɩɥɚɡɦɵ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɬɪɟɬɶɟ ɫɜɹɡɚɧɨ ɫ ɝɪɚɞɢɟɧɬɨɦ ɷɥɟɤɬɪɨɧɧɨɝɨ ɞɚɜɥɟɧɢɹ, ɚ ɩɨɫɥɟɞɧɟɟ ɭɱɢɬɵɜɚɟɬ ɜɥɢɹɧɢɟ ɬɟɪɦɨ-ɗȾɋ, ɜɨɡɧɢɤɚɸɳɟɣ ɢɡ-ɡɚ ɬɟɪɦɨɫɢɥɵ, ɜ ɫɢɥɶɧɨ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɟ ɩɪɢɦɟɪɧɨ ɪɚɜɧɨɣ:
& & & & B & 3 ne RT = −0.71ne ( b ∇ )Te − [ b ∇Te ], b = . B 2 ω eτ ei
(2.107)
Ɏɨɪɦɭɥɚ (2.105) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ, ɩɨ ɫɭɳɟɫɬɜɭ, ɨɞɧɭ ɢɡ ɜɨɡɦɨɠɧɵɯ ɮɨɪɦ ɡɚɩɢɫɢ ɡɚɤɨɧɚ Ɉɦɚ ɞɥɹ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɵ. ɂɡ ɧɟɺ ɫɥɟɞɭɟɬ, ɱɬɨ ɜ ɫɢɥɶɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɜɞɨɥɶ ɩɨɥɹ ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɤɨɦɩɨɧɟɧɬɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɢ ɩɥɨɬɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ ɬɚɤɨɟ ɠɟ, ɤɚɤ ɢ ɜ ɨɬɫɭɬɫɬɜɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
E||′ =
j||
σ
.
(2.108ɚ)
||
ɉɨɩɟɪɟɱɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ, ɨɞɧɚɤɨ, ɩɪɟɬɟɪɩɟɜɚɟɬ ɫɭɳɟɫɬɜɟɧɧɨɟ ɢɡɦɟɧɟɧɢɟ: ɷɮɮɟɤɬɢɜɧɨɟ ɩɨɥɟ ɨɤɚɡɵɜɚɟɬɫɹ ɩɪɚɤɬɢɱɟɫɤɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵɦ ɤ ɬɨɤɭ. ɉɪɨɟɤɰɢɹ ɩɨɩɟɪɟɱɧɨɝɨ ɩɨɥɹ ɧɚ ɬɨɤ ɫɜɹɡɚɧɚ ɫ ɩɨɩɟɪɟɱɧɨɣ ɤɨɦɩɨɧɟɧɬɨɣ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ ɫɨɨɬɧɨɲɟɧɢɟɦ, ɤɨɬɨɪɨɟ ɮɚɤɬɢɱɟɫɤɢ ɧɟ ɫɢɥɶɧɨ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɩɪɟɞɵɞɭɳɟɝɨ:
E⊥′ j =
j⊥
σ⊥
.
(2.108ɛ)
ɇɨ ɞɥɹ ɩɪɨɬɟɤɚɧɢɹ ɬɨɤɚ ɩɨɩɟɪɟɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɭɠɧɚ ɫɨɫɬɚɜɥɹɸɳɚɹ ɷɮɮɟɤɬɢɜɧɨɝɨ ɩɨɥɹ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚɹ ɢ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ, ɢ ɤ ɬɨɤɭ - ɷɬɨ ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɯɨɥɥɨɜɫɤɨɟ ɩɨɥɟ:
ω Beτ ei & & & 1 && [ jB ] = [ jB ] . E ′ɏɨɥɥ = σ⊥ enc
(2.109)
Ɂɚɱɚɫɬɭɸ ɯɨɥɥɨɜɫɤɨɟ ɩɨɥɟ ɜɨɡɧɢɤɚɟɬ ɜ ɩɥɚɡɦɟ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɡɚ ɫɱɟɬ ɧɟɛɨɥɶɲɨɝɨ ɧɚɪɭɲɟɧɢɹ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɢ, ɚ ɜɧɟɲɧɢɟ ɩɨɥɹ, ɤɨɬɨɪɵɟ ɧɚɞɨ ɩɪɢɤɥɚɞɵɜɚɬɶ ɤ ɩɥɚɡɦɟ, ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɨɨɬɧɨɲɟɧɢɹɦɢ (2.108,ɚ) ɢ (2.108,ɛ). ɂɧɨɝɞɚ ɝɨɜɨɪɹɬ, ɱɬɨ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɟ ɜɥɢɹɟɬ ɧɚ ɩɪɨɜɨɞɢɦɨɫɬɶ ɩɥɚɡɦɵ. ɗɬɨ ɧɚɞɨ ɩɨɧɢɦɚɬɶ ɢɦɟɧɧɨ ɜ ɭɤɚɡɚɧɧɨɦ ɫɦɵɫɥɟ.
• Ⱦɪɟɣɮɨɜɵɟ ɬɨɤɢ. ȼɫɟɝɞɚ, ɤɨɝɞɚ ɜɨɡɧɢɤɚɟɬ ɝɪɚɞɢɟɧɬ ɞɚɜɥɟɧɢɹ, ɩɨɹɜɥɹɟɬɫɹ ɢ ɨɬɜɟɱɚɸɳɚɹ ɟɦɭ ɫɢɥɚ, ɜ & ɪɚɫɱɟɬɟ ɧɚ ɨɞɧɭ ɱɚɫɬɢɰɭ (ɷɥɟɤɬɪɨɧ ɢɥɢ ɢɨɧ), ɪɚɜɧɚɹ Fe ,i = −∇pe ,i / n . Ɉɧɚ ɜɵɡɵɜɚɟɬ ɞɪɟɣɮ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɫɨ ɫɤɨɪɨɫɬɶɸ & & & c B × ∇p c F×B & vd = = , (2.110) en B 2 e B2 ɩɪɢɱɟɦ ɱɚɫɬɢɰɵ ɫ ɡɚɪɹɞɚɦɢ ɪɚɡɧɵɯ ɡɧɚɤɨɜ ɞɪɟɣɮɭɸɬ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɟ ɫɬɨɪɨɧɵ. ɗɬɨ ɩɪɢɜɨɞɢɬ ɤ ɩɟɪɟɧɨɫɭ ɡɚɪɹɞɚ, ɬ.ɟ. ɤ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɩɨɹɜɥɟɧɢɸ ɬɚɤ ɧɚɡɵɜɚɟɦɵɯ ɬɨɤɨɜ ɧɚɦɚɝɧɢɱɟɧɢɹ ɢɥɢ ɞɪɟɣɮɨɜɵɯ ɬɨɤɨɜ & B × ∇p & & . (2.111) j = ¦ nev d = c B2 e ,i
ɉɨɹɜɥɟɧɢɟ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɬɨɤɨɜ ɜɫɥɟɞɫɬɜɢɟ ɧɟɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɪɢɱɢɧ − ɫɩɟɰɢɮɢɱɟɫɤɚɹ ɨɫɨɛɟɧɧɨɫɬɶ ɩɥɚɡɦɵ, ɩɪɢɫɭɳɚɹ ɟɣ ɜɫɟɝɞɚ, ɤɨɝɞɚ ɟɫɬɶ ɤɚɤɢɟ-ɥɢɛɨ ɧɟɨɞɧɨɪɨɞɧɨɫɬɢ ɩɥɚɡɦɵ. & ɂɡ ɬɟɨɪɢɢ ɦɚɝɧɟɬɢɡɦɚ [15] ɢɡɜɟɫɬɧɨ, ɱɬɨ ɧɚɦɚɝɧɢɱɟɧɢɟ ɫɪɟɞɵ I ɢ ɩɥɨɬɧɨɫɬɶ ɦɨɥɟɤɭɥɹɪɧɵɯ ɬɨɤɨɜ & j µ ɫɜɹɡɚɧɵ ɫɨɨɬɧɨɲɟɧɢɟɦ & & jµ = c rot I . (2.112) & & ȼ ɩɥɚɡɦɟ ɧɚɦɚɝɧɢɱɟɧɢɟ ɪɚɜɧɨ ɫɭɦɦɟ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɱɚɫɬɢɰ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ: I = n < µ > ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (2.9),
& mv ⊥2 & I = −¦ n < > B. 2 B2 e ,i
(2.113)
Ɍɚɤ ɤɚɤ ɞɜɢɠɟɧɢɟ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɟ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ, ɢɦɟɟɬ ɞɜɟ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ, ɬɨ, ɩɪɨɢɡɜɨɞɹ ɭɫɪɟɞɧɟɧɢɟ, ɢ ɨɛɨɡɧɚɱɢɜ p⊥=nT⊥, ɩɨɥɭɱɚɟɦ
& p⊥ B & j = − c rot 2 . B
(2.114)
ȼ ɷɬɨɣ ɮɨɪɦɟ ɡɚɩɢɫɢ ɭɱɢɬɵɜɚɸɬɫɹ ɞɪɟɣɮɨɜɵɟ ɬɨɤɢ, ɜɨɡɧɢɤɚɸɳɢɟ ɜɫɥɟɞɫɬɜɢɟ ɝɪɚɞɢɟɧɬɚ ɩɥɨɬɧɨɫɬɢ ɢ ɝɪɚɞɢɟɧɬɚ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȿɫɥɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɨɞɧɨɪɨɞɧɨ, ɬɨ ɮɨɪɦɭɥɚ (2.114) ɮɚɤɬɢɱɟɫɤɢ ɫɨɜɩɚɞɚɟɬ ɫ (2.111).
ȽɅȺȼȺ 3 ɆȺȽɇɂɌɈȽɂȾɊɈȾɂɇȺɆɂɑȿɋɄɂɃ ɆȿɌɈȾ ɈɉɂɋȺɇɂə ɉɅȺɁɆɕ § 21. ɂɞɟɚɥɶɧɚɹ ɨɞɧɨɠɢɞɤɨɫɬɧɚɹ ɝɢɞɪɨɞɢɧɚɦɢɤɚ ɩɥɚɡɦɵ. ɍɫɥɨɜɢɹ ɩɪɢɦɟɧɢɦɨɫɬɢ Ⱦɨ ɫɢɯ ɩɨɪ ɦɵ ɪɚɫɫɦɚɬɪɢɜɚɥɢ ɩɥɚɡɦɭ ɤɚɤ ɫɨɜɨɤɭɩɧɨɫɬɶ ɨɬɞɟɥɶɧɵɯ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɢ ɢɫɫɥɟɞɨɜɚɥɢ ɢɯ ɞɜɢɠɟɧɢɟ ɜ ɡɚɞɚɧɧɵɯ ɩɨɥɹɯ. Ɉɞɧɚɤɨ ɬɚɤɨɣ ɩɨɞɯɨɞ ɤ ɨɩɢɫɚɧɢɸ ɩɥɚɡɦɟɧɧɵɯ ɹɜɥɟɧɢɣ ɧɟ ɦɨɠɟɬ ɩɪɟɬɟɧɞɨɜɚɬɶ ɧɚ ɩɨɥɧɨɬɭ. ɉɪɢ ɞɜɢɠɟɧɢɢ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɜɨɡɧɢɤɚɸɬ ɬɨɤɢ ɢ ɨɬɜɟɱɚɸɳɟɟ ɢɦ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɜɥɢɹɸɳɟɟ ɧɚ ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰ, ɤɨɬɨɪɨɟ, ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɨɤɚɡɵɜɚɟɬɫɹ ɫɚɦɨɫɨɝɥɚɫɨɜɚɧɧɵɦ ɫ ɩɨɥɟɦ. ɉɥɚɡɦɭ ɫ ɷɬɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɫɩɥɨɲɧɭɸ ɫɪɟɞɭ, ɤɚɤ ɧɟɤɭɸ ɩɪɨɜɨɞɹɳɭɸ ɫɭɛɫɬɚɧɰɢɸ − ɩɪɨɜɨɞɹɳɢɣ ɝɚɡ. ȿɫɥɢ ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ ɩɥɚɡɦɵ ɧɟ ɫɥɢɲɤɨɦ ɜɟɥɢɤɢ (ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ ɫɤɨɪɨɫɬɢ ɡɜɭɤɚ), ɬɨ ɪɨɥɶ ɫɠɢɦɚɟɦɨɫɬɢ ɷɬɨɣ ɫɭɛɫɬɚɧɰɢɢ ɧɟɡɧɚɱɢɬɟɥɶɧɚ, ɚ ɭɪɚɜɧɟɧɢɹ ɝɚɡɨɞɢɧɚɦɢɤɢ ɢ ɝɢɞɪɨɞɢɧɚɦɢɤɢ ɫɨɜɩɚɞɚɸɬ; ɬɨɝɞɚ ɩɥɚɡɦɭ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɩɪɨɜɨɞɹɳɭɸ ɠɢɞɤɨɫɬɶ. Ɍɚɤɨɣ ɩɨɞɯɨɞ ɤ ɨɩɢɫɚɧɢɸ ɞɢɧɚɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɜ ɩɥɚɡɦɟ ɩɨɥɭɱɢɥ ɧɚɡɜɚɧɢɟ ɦɚɝɧɢɬɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɢ ɢɥɢ ɫɨɤɪɚɳɟɧɧɨ ɆȽȾ. ȼɩɟɪɜɵɟ ɨɧ ɛɵɥ ɩɪɟɞɥɨɠɟɧ ɜ ɫɨɪɨɤɨɜɵɯ ɝɨɞɚɯ ɞɜɚɞɰɚɬɨɝɨ ɫɬɨɥɟɬɢɹ Ⱥɥɶɜɟɧɨɦ ɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɞɢɧɚɦɢɤɟ ɤɨɫɦɢɱɟɫɤɨɣ ɩɥɚɡɦɵ. ɉɨɜɟɞɟɧɢɟ ɩɪɨɜɨɞɹɳɟɣ ɠɢɞɤɨɫɬɢ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɜ ɛɨɥɶɲɨɣ ɫɬɟɩɟɧɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɟɟ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɜɨɞɢɦɨɫɬɶɸ, ɢɦɟɧɧɨ ɨɧɚ ɨɛɭɫɥɚɜɥɢɜɚɟɬ ɫɤɨɪɨɫɬɶ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɩɪɨɜɨɞɧɢɤ. ȼ ɢɞɟɚɥɶɧɵɣ ɩɪɨɜɨɞɧɢɤ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɜɨɨɛɳɟ ɧɟ ɦɨɠɟɬ ɩɪɨɧɢɤɧɭɬɶ. Ɉɞɧɚɤɨ ɟɫɥɢ ɜ ɩɪɨɜɨɞɧɢɤɟ ɭɠɟ ɟɫɬɶ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɬɨ ɷɬɨ ɩɨɥɟ ɛɭɞɟɬ “ɜɦɨɪɨɠɟɧɨ” ɜ ɧɟɝɨ − ɩɪɢ ɫɜɨɟɦ ɞɜɢɠɟɧɢɢ ɩɪɨɜɨɞɧɢɤ ɭɜɥɟɱɟɬ ɡɚ ɫɨɛɨɣ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ. Ɋɟɚɥɶɧɨ ɩɥɚɡɦɚ ɜɫɟɝɞɚ ɢɦɟɟɬ ɤɨɧɟɱɧɭɸ ɩɪɨɜɨɞɢɦɨɫɬɶ, ɧɨ ɟɫɥɢ ɢɧɬɟɪɟɫɭɸɳɢɟ ɧɚɫ ɩɪɨɰɟɫɫɵ ɩɪɨɬɟɤɚɸɬ ɛɵɫɬɪɨ, ɡɚ ɜɪɟɦɟɧɚ, ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɢɟ ɜɪɟɦɟɧɢ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɩɥɚɡɦɭ, ɬɨ ɩɥɚɡɦɭ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɢɞɟɚɥɶɧɵɣ ɩɪɨɜɨɞɧɢɤ. Ʉɚɤ ɢɡɜɟɫɬɧɨ [15], ɜɪɟɦɹ τs (ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɫɤɢɧɨɜɨɟ ɜɪɟɦɹ) ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɩɨɥɹ ɧɚ ɡɚɞɚɧɧɭɸ ɝɥɭɛɢɧɭ δ ɜ ɩɪɨɜɨɞɧɢɤɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ δ2 4πσ τs = 2 δ 2 = , (3.1) c Dɦɚɝ ɝɞɟ σ - ɩɪɨɜɨɞɢɦɨɫɬɶ; c2 Dɦɚɝ = (3.2) 4πσ ɤɨɷɮɮɢɰɢɟɧɬ ɦɚɝɧɢɬɧɨɣ ɞɢɮɮɭɡɢɢ ɩɨɥɹ ɜ ɩɪɨɜɨɞɧɢɤ. Ⱦɥɹ ɜɪɟɦɟɧ tme ɬɨ ɜɤɥɚɞɨɦ ɦɚɫɫɵ ɷɥɟɤɬɪɨɧɨɜ ɜ ɩɥɨɬɧɨɫɬɶ ρ ɨɛɵɱɧɨ ɩɪɟɧɟɛɪɟɝɚɸɬ; • ɦɚɫɫɨɜɚɹ ɫɤɨɪɨɫɬɶ & 1 & & v = ¦ nα mα vα ≈ v i ,
ρ (α )
ɩɨ ɬɨɣ ɠɟ ɩɪɢɱɢɧɟ ɩɪɢɦɟɪɧɨ ɪɚɜɧɚ ɫɤɨɪɨɫɬɢ ɢɨɧɧɨɣ ɤɨɦɩɨɧɟɧɬɵ; • ɩɥɨɬɧɨɫɬɶ ɡɚɪɹɞɚ ρq = ¦ nα qα = | e|( zni − ne ) , (α )
ɝɞɟ |e| - ɚɛɫɨɥɸɬɧɚɹ ɜɟɥɢɱɢɧɚ ɡɚɪɹɞɚ ɷɥɟɤɬɪɨɧɚ; • ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ & & j = ¦ nα qα vα . (α )
ȿɫɥɢ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɫɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ve ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɨɫɯɨɞɢɬ ɫɤɨɪɨɫɬɶ ɢɨɧɨɜ vi, ɬɨ & & j = −| e| ne v e . ɂɫɩɨɥɶɡɭɹ ɩɪɢɧɹɬɵɟ ɨɛɨɡɧɚɱɟɧɢɹ, ɡɚɩɢɲɟɦ: • Ɂɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɦɚɫɫɵ (ɧɟɪɚɡɪɵɜɧɨɫɬɢ ɫɬɪɭɢ): ∂ρ & + div( ρv ) = 0 . (3.4) ∂t • ɍɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɟɞɢɧɢɰɵ ɨɛɴɟɦɚ ɩɥɚɡɦɵ (ɫɨɯɪɚɧɟɧɢɹ ɢɦɩɭɥɶɫɚ): & & dv 1 & & = j × B − ∇p + F , ρ (3.5) dt c ɝɞɟ p=pe+pi - ɩɨɥɧɨɟ ɞɚɜɥɟɧɢɟ ɩɥɚɡɦɵ, ɪɚɜɧɨɟ ɫɭɦɦɟ ɞɚɜɥɟɧɢɣ ɷɥɟɤɬɪɨɧɨɜ ɢ & & & dv ∂ v & & ɢɨɧɨɜ, F - ɜɧɟɲɧɹɹ ɫɢɥɚ (ɧɚɩɪɢɦɟɪ, ɫɢɥɚ ɬɹɠɟɫɬɢ), = + ( v ∇ )v − ɩɨɥɧɚɹ dt ∂ t ɩɪɨɢɡɜɨɞɧɚɹ (ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ ɫɭɛɫɬɚɰɢɨɧɚɥɶɧɚɹ ɩɪɨɢɡɜɨɞɧɚɹ) ɩɨ ɜɪɟɦɟɧɢ ɨɬ ɫɤɨɪɨɫɬɢ ɩɥɚɡɦɵ. ɍɪɚɜɧɟɧɢɟ (3.5) ɦɨɠɟɬ ɛɵɬɶ ɩɨɥɭɱɟɧɨ ɫɭɦɦɢɪɨɜɚɧɢɟɦ ɭɪɚɜɧɟɧɢɣ ɞɜɢɠɟɧɢɹ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ (ɫɦ. ɮɨɪɦɭɥɭ (2.1)) ɫ ɩɨɫɥɟɞɭɸɳɢɦ ɩɪɟɧɟɛɪɟɠɟɧɢɟɦ ɤɨɧɟɱɧɨɫɬɶɸ ɢɧɟɪɰɢɢ ɷɥɟɤɬɪɨɧɨɜ. ȼɨ ɦɧɨɝɢɯ ɤɨɧɤɪɟɬɧɵɯ ɫɥɭɱɚɹɯ ɜ ɭɪɚɜɧɟɧɢɢ (3.5) ɫɢɥɨɣ F ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ.
• ɍɪɚɜɧɟɧɢɹ & Ɇɚɤɫɜɟɥɥɚ: div E = 4πρq = 4π| e|( zni − ne ) ; & div B = 0 ; (3.6) & & 1 ∂B rot E = − ; c ∂t & 4π & rot B = j. c ɉɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɜɫɟ ɩɪɨɰɟɫɫɵ ɦɟɞɥɟɧɧɵɟ ɢ ɬɨɤɚɦɢ ɫɦɟɳɟɧɢɹ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ, ɱɬɨ ɢ ɢɫɩɨɥɶɡɨɜɚɧɨ ɜ ɩɨɫɥɟɞɧɟɦ ɢɡ ɭɪɚɜɧɟɧɢɣ (3.6). • Ɂɚɤɨɧ Ɉɦɚ (ɫɨɝɥɚɫɧɨ ɪɚɛɨɬɟ [13]): & & j || & j⊥ 1 & & (3.7) j ×B, + + E′ = σ ⊥ σ|| cne| e| ɝɞɟ ȿ′ - ɷɮɮɟɤɬɢɜɧɨɟ ɩɨɥɟ, ɨɛɭɫɥɨɜɥɟɧɧɨɟ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɧɟ ɬɨɥɶɤɨ ɩɪɢɥɨɠɟɧɧɨɣ ɜɧɟɲɧɟɣ ɗȾɋ, ɧɨ ɢ ɫɚɦɢɦ ɞɜɢɠɟɧɢɟɦ ɩɥɚɡɦɵ, ɚ ɬɚɤɠɟ ɧɚɥɢɱɢɟɦ ɷɥɟɤɬɪɨɧɧɨɝɨ ɞɚɜɥɟɧɢɹ ɢ ɩɟɪɟɩɚɞɚ ɷɥɟɤɬɪɨɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ; σ||,⊥ - ɩɪɨɞɨɥɶɧɚɹ ɢ ɩɨɩɟɪɟɱɧɚɹ (ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ) ɩɪɨɜɨɞɢɦɨɫɬɶ 1 & & j × B - ɯɨɥɥɨɜɫɤɨɟ ɩɨɥɟ. ɩɥɚɡɦɵ; cne| e| ɍɩɨɬɪɟɛɢɬɟɥɶɧɨ ɧɟɫɤɨɥɶɤɨ ɪɚɡɥɢɱɧɵɯ ɮɨɪɦ ɡɚɩɢɫɢ ɡɚɤɨɧɚ Ɉɦɚ ɞɥɹ ɩɥɚɡɦɵ. ɗɬɨ ɫɜɹɡɚɧɨ ɫ ɬɟɦ, ɱɬɨ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɤɨɧɤɪɟɬɧɵɯ ɭɫɥɨɜɢɣ ɦɨɠɟɬ ɨɤɚɡɚɬɶɫɹ ɧɚɢɛɨɥɟɟ ɫɭɳɟɫɬɜɟɧɧɨɣ ɬɚ ɢɥɢ ɢɧɚɹ ɩɪɢɱɢɧɚ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɗȾɋ (ɩɨɞɪɨɛɧɟɟ ɫɦ.[13]). ɑɚɫɬɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɫɥɟɞɭɸɳɚɹ ɭɩɪɨɳɟɧɧɚɹ ɮɨɪɦɚ ɡɚɩɢɫɢ ɡɚɤɨɧɚ Ɉɦɚ: & 1 & & ½ 1 & & 1 & j = σ ®E + v × B − j ×B+ ∇pe ¾ . (3.8) c n| e| c n| e| ¯ ¿ • ɍɪɚɜɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ - ɷɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɜɢɞɚ: p = p( ρ ,T ) . (3.9) ɍɪɚɜɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ ɩɪɢɨɛɪɟɬɚɟɬ ɩɪɨɫɬɨɣ ɜɢɞ, ɟɫɥɢ ɩɥɚɡɦɭ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɢɞɟɚɥɶɧɨɣ. Ⱦɥɹ ɤɥɚɫɫɢɱɟɫɤɨɝɨ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɭɪɚɜɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ ɪ = nT. ɝɞɟ n – ɤɨɧɰɟɧɬɪɚɰɢɹ (ɩɥɨɬɧɨɫɬɶ ɱɢɫɥɚ ɱɚɫɬɢɰ) ɝɚɡɚ. Ⱦɥɹ ɫɦɟɫɢ ɞɜɭɯ ɢɞɟɚɥɶɧɵɯ «ɝɚɡɚ» ɷɥɟɤɬɪɨɧɨɜ ɫ ɤɨɧɰɟɧɬɪɚɰɢɟɣ ne ɢ «ɝɚɡɚ» ɢɨɧɨɜ ɫ «ɝɚɡɨɜ» − ɤɨɧɰɟɧɬɪɚɰɢɟɣ ni p = neTe+niTi. ȼ ɱɚɫɬɧɨɦ ɫɥɭɱɚɟ ɢɞɟɚɥɶɧɨɣ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɣ ɢɡɨɬɟɪɦɢɱɟɫɤɨɣ ɩɥɚɡɦɵ, ɤɨɝɞɚ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɤɨɧɰɟɧɬɪɚɰɢɢ ɟɟ ɤɨɦɩɨɧɟɧɬ ɫɨɜɩɚɞɚɸɬ Te=Ti=Ɍ, ne=ni=n, ɷɬɨ ɭɪɚɜɧɟɧɢɟ ɩɪɢɨɛɪɟɬɚɟɬ ɨɫɨɛɟɧɧɨ ɩɪɨɫɬɨɣ ɜɢɞ p = 2nT. (3.10) ɇɨ ɬɟɩɟɪɶ ɜ ɭɪɚɜɧɟɧɢɹɯ ɞɢɧɚɦɢɤɢ ɩɥɚɡɦɵ ɩɨɹɜɥɹɟɬɫɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɣ ɩɚɪɚɦɟɬɪ − ɬɟɦɩɟɪɚɬɭɪɚ, ɢ ɧɟɨɛɯɨɞɢɦɨ ɭɤɚɡɚɬɶ ɩɪɚɜɢɥɨ ɟɝɨ ɜɵɱɢɫɥɟɧɢɹ, ɜɵɪɚɠɚɸɳɟɟ ɛɚɥɚɧɫ ɬɟɩɥɚ. ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɷɬɨ ɞɨɫɬɚɬɨɱɧɨ ɫɥɨɠɧɨɟ ɭɪɚɜɧɟɧɢɟ, ɭɱɢɬɵɜɚɸɳɟɟ ɤɨɧɟɱɧɭɸ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ ɩɥɚɡɦɵ, ɜɹɡɤɨɟ ɬɟɩɥɨɜɵɞɟɥɟɧɢɟ, ɞɠɨɭɥɟɜɨ ɬɟɩɥɨ, ɨɛɭɫɥɨɜɥɟɧɧɨɟ ɩɪɨɬɟɤɚɧɢɟɦ ɩɨ ɩɥɚɡɦɟ ɬɨɤɚ ɢ ɞɪɭɝɢɟ ɢɫɬɨɱɧɢɤɢ ɧɚɝɪɟɜɚ ɢɥɢ ɨɯɥɚɠɞɟɧɢɹ ɩɥɚɡɦɵ. Ɇɵ ɧɟ ɛɭɞɟɦ ɟɝɨ ɜɵɩɢɫɵɜɚɬɶ, ɞɟɬɚɥɶɧɵɣ ɚɧɚɥɢɡ ɛɚɥɚɧɫɚ ɬɟɩɥɚ ɜ ɩɥɚɡɦɟ ɦɨɠɧɨ ɧɚɣɬɢ, ɧɚɩɪɢɦɟɪ, ɜ [13].
ɉɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɨɞɧɨɠɢɞɤɨɫɬɧɨɣ ɦɚɝɧɢɬɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɟ ɜ ɤɨɧɤɪɟɬɧɵɯ ɩɪɢɥɨɠɟɧɢɹɯ ɱɚɫɬɨ ɢɫɩɨɥɶɡɭɸɬɫɹ ɪɚɡɥɢɱɧɵɟ ɭɩɪɨɳɟɧɧɵɟ ɩɨɞɯɨɞɵ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɦɟɞɥɟɧɧɵɯ, ɫɭɳɟɫɬɜɟɧɧɨ ɞɨɡɜɭɤɨɜɵɯ, ɬɟɱɟɧɢɣ, ɩɥɚɡɦɭ ɩɪɢɛɥɢɠɟɧɧɨ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɧɟɫɠɢɦɚɟɦɨɣ, ρ=const , ɢ ɬɨɝɞɚ, ɫɨɝɥɚɫɧɨ ɭɪɚɜɧɟɧɢɸ ɧɟɪɚɡɪɵɜɧɨɫɬɢ (3.4), ɬɟɱɟɧɢɟ ɩɥɚɡɦɵ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɫɥɨɜɢɸ & divv = 0 , ɚ ɞɚɜɥɟɧɢɟ ɩɥɚɡɦɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɫɥɨɜɢɟɦ ɫɨɜɦɟɫɬɢɦɨɫɬɢ ɞɢɧɚɦɢɱɟɫɤɢɯ ɭɪɚɜɧɟɧɢɣ. ȼ ɭɫɥɨɜɢɹɯ, ɤɨɝɞɚ ɬɟɩɥɨɨɛɦɟɧ ɫ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɨɣ ɧɟɫɭɳɟɫɬɜɟɧ, ɢɫɩɨɥɶɡɭɟɬɫɹ ɚɞɢɚɛɚɬɢɱɟɫɤɢɣ ɡɚɤɨɧɚ ɜɢɞɚ p ~ ρ γ . ɉɪɢ ɷɬɨɦ ɢɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɫɥɟɞɭɟɬ ɫɨɨɬɧɨɲɟɧɢɸ T ~ ρ γ −1 . Ɂɞɟɫɶ γ − ɩɨɤɚɡɚɬɟɥɶ ɚɞɢɚɛɚɬɵ, ɧɚɩɪɢɦɟɪ, ɞɥɹ ɦɨɞɟɥɢ ɨɞɧɨɚɬɨɦɧɨɝɨ ɝɚɡɚ ɪɚɜɧɵɣ γ=5/3. ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ, ɧɚɩɨɦɧɢɦ, γ = 1 + 2 N , ɝɞɟ N=1,2,3… - ɱɢɫɥɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ. ɂɫɩɨɥɶɡɭɹ ɩɪɢɜɟɞɟɧɧɵɟ ɭɪɚɜɧɟɧɢɹ ɦɚɝɧɢɬɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɢ, ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɩɨɜɟɞɟɧɢɟ ɩɥɚɡɦɵ ɜɨ ɦɧɨɝɢɯ ɜɟɫɶɦɚ ɫɥɨɠɧɵɯ ɫɥɭɱɚɹɯ. ɇɟɫɨɦɧɟɧɧɵɦ ɩɪɟɢɦɭɳɟɫɬɜɨɦ ɬɚɤɨɝɨ ɩɨɞɯɨɞɚ ɤ ɨɩɢɫɚɧɢɸ ɩɥɚɡɦɵ ɹɜɥɹɟɬɫɹ ɟɝɨ ɫɪɚɜɧɢɬɟɥɶɧɚɹ ɩɪɨɫɬɨɬɚ ɢ ɧɚɝɥɹɞɧɨɫɬɶ. ɂɧɨɝɞɚ ɷɬɨ ɨɱɟɧɶ ɜɚɠɧɨ, ɧɚɩɪɢɦɟɪ, ɩɪɢ ɨɩɢɫɚɧɢɢ ɞɢɧɚɦɢɤɢ ɬɨɤɨɜɵɯ ɫɢɫɬɟɦ. ɉɪɢ ɷɬɨɦ, ɤɨɧɟɱɧɨ, ɜ ɤɚɠɞɨɦ ɤɨɧɤɪɟɬɧɨɦ ɫɥɭɱɚɟ, ɢɫɩɨɥɶɡɭɹ ɭɪɚɜɧɟɧɢɹ ɦɚɝɧɢɬɧɨɣ ɝɢɞɪɨɞɢɧɚɦɢɤɢ ɩɥɚɡɦɵ, ɧɟɨɛɯɨɞɢɦɨ ɢɦɟɬɶ ɜ ɜɢɞɭ ɭɫɥɨɜɢɹ (3.3) ɩɪɢɦɟɧɢɦɨɫɬɢ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɩɪɟɞɫɬɚɜɥɟɧɢɣ.
§ 23. Ɇɚɝɧɢɬɧɨɟ ɞɚɜɥɟɧɢɟ ȼɟɫɶɦɚ ɜɚɠɧɵɟ ɜɵɜɨɞɵ ɨɛɳɟɝɨ ɯɚɪɚɤɬɟɪɚ ɦɨɝɭɬ ɛɵɬɶ ɩɨɥɭɱɟɧɵ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɢɡ ɚɧɚɥɢɡɚ ɭɪɚɜɧɟɧɢɣ (3.4) ɢ&(3.5). ȼ ɩɪɟɧɟɛɪɟɠɟɧɢɢ ɜɧɟɲɧɢɦɢ ɫɢɥɚɦɢ F , ɞɜɢɠɟɧɢɟ ɩɥɚɡɦɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɢɥɨɣ Ⱥɦɩɟɪɚ (ɢɧɚɱɟ ɧɚɡɵɜɚɟɦɨɣ ɩɨɧɞɟɪɨɦɨɬɨɪɧɨɣ ɫɢɥɨɣ) ɢ ɝɪɚɞɢɟɧɬɨɦ ɝɚɡɨɤɢɧɟɬɢɱɟɫɤɨɝɨ ɞɚɜɥɟɧɢɹ & dv 1 & & = j × B − ∇p . ρ (3.11) dt c ɂɫɩɨɥɶɡɭɹ ɢɡɜɟɫɬɧɨɟ ɬɨɠɞɟɫɬɜɨ ɢɡ ɜɟɤɬɨɪɧɨɝɨ ɚɧɚɥɢɡɚ, ɫɩɪɚɜɟɞɥɢɜɨɟ ɞɥɹ ɞɜɭɯ & & ɥɸɛɵɯ ɜɟɤɬɨɪɨɜ a ɢ b , & & && & & & & & & ∇( ab ) = ( a∇ )b + ( b ∇ )a + a × rotb + b × rota , ɢ ɭɪɚɜɧɟɧɢɟ (3.6), ɩɨɧɞɟɪɨɦɨɬɨɪɧɭɸ ɫɢɥɭ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ: & & 1& & 1 1 & & B2 + ( B∇ )B ≡ − ∇ ⋅ p ɦɚɝ . (3.12) j×B= rotB × B = − ∇ 4π 8π 4π c ɝɞɟ ^ B2 p ɦɚɝ = (3.13) ( δ − 2 ττ ), 8π & & B − ɟɞɢɧɢɱɧɵɣ ɬɟɧɡɨɪ ɦɚɝɧɢɬɧɨɝɨ ɞɚɜɥɟɧɢɹ; δ - ɟɞɢɧɢɱɧɚɹ ɦɚɬɪɢɰɚ, ɚ τ = B ɜɟɤɬɨɪ, ɧɚɩɪɚɜɥɟɧɧɵɣ ɩɨ ɤɚɫɚɬɟɥɶɧɨɣ ɤ ɫɢɥɨɜɨɣ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȼ & ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɫ ɨɫɶɸ z, ɧɚɩɪɚɜɥɟɧɧɨɣ ɜɞɨɥɶ ɜɟɤɬɨɪɚ B , ɷɬɨɬ ɬɟɧɡɨɪ ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɜɢɞɟ ɫɥɟɞɭɸɳɟɣ ɞɢɚɝɨɧɚɥɶɧɨɣ ɬɚɛɥɢɰɵ: § B2 · 0 0 ¸ ¨ ¸ ¨ 8π 2 B ¨ 0 ¸¸ . (3.14) p ɦɚɝ = ¨ 0 8π ¨ B2 ¸ ¸ ¨ 0 0 − 8π ¹ © Ɂɧɚɤ ɤɨɦɩɨɧɟɧɬ ɬɟɧɡɨɪɚ ɦɚɝɧɢɬɧɨɝɨ ɞɚɜɥɟɧɢɹ ɧɟ ɫɥɭɱɚɟɧ: ɩɨɩɟɪɟɱɧɵɟ ɤɨɦɩɨɧɟɧɬɵ ɩɨɥɨɠɢɬɟɥɶɧɵ, ɱɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɪɚɫɬɚɥɤɢɜɚɧɢɸ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɩɨɩɟɪɟɱɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ, ɬɨɝɞɚ ɤɚɤ ɩɪɨɞɨɥɶɧɚɹ ɤɨɦɩɨɧɟɧɬɚ ɷɬɨɝɨ ɬɟɧɡɨɪɚ ɨɬɪɢɰɚɬɟɥɶɧɚ − ɜ ɩɪɨɞɨɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɧɚɬɹɧɭɬɵ. ȼɟɥɢɱɢɧɭ B2 pm = (3.15) 8π ɨɛɵɱɧɨ ɧɚɡɵɜɚɸɬ ɦɚɝɧɢɬɧɵɦ ɞɚɜɥɟɧɢɟɦ. ɉɨɥɟɡɧɨ ɬɚɤ ɩɟɪɟɩɢɫɚɬɶ ɫɨɨɬɧɨɲɟɧɢɟ (3.12), ɱɬɨɛɵ ɪɚɫɬɚɥɤɢɜɚɧɢɟ ɢ ɧɚɬɹɠɟɧɢɟ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɩɪɨɹɜɥɹɥɢɫɶ ɜ ɧɟɦ ɟɳɟ ɛɨɥɟɟ ɹɜɧɨ. Ⱦɥɹ ɷɬɨɝɨ, ɩɨɥɶɡɭɹɫɶ ɨɩɪɟɞɟɥɟɧɢɟɦ ɤɚɫɚɬɟɥɶɧɨɝɨ ɜɟɤɬɨɪɚ, ɡɚɩɢɲɟɦ
& & & & & & & & ( B∇ )B = ( Bτ ∇ )( Bτ ) = B 2 ( τ ∇ )τ + Bτ ( τ ∇B ) .
ɍɱɢɬɵɜɚɹ, ɞɚɥɟɟ, ɱɬɨ ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ
&
& & & n ( τ ∇ )τ = , R
ɝɞɟ n - ɧɨɪɦɚɥɶ ɤ ɫɢɥɨɜɨɣ ɥɢɧɢɢ, ɚ
R - ɪɚɞɢɭɫ ɟɟ ɤɪɢɜɢɡɧɵ, ɩɨɥɭɱɢɦ
1& & B2 B2 & + n, j × B = −∇ ⊥ c 8π 4πR
(3.16)
ɝɞɟ ɨɛɨɡɧɚɱɟɧɨ ɞɥɹ ɤɪɚɬɤɨɫɬɢ & & ∇⊥ = ∇ − τ ( τ ∇ ) . ɉɟɪɜɨɟ ɫɥɚɝɚɟɦɨɟ ɜ (3.16) ɨɬɜɟɱɚɟɬ ɮɚɪɚɞɟɟɜɫɤɨɦɭ “ɪɚɫɬɚɥɤɢɜɚɧɢɸ”, ɚ ɜɬɨɪɨɟ, ɫɜɹɡɚɧɧɨɟ ɫ ɢɫɤɪɢɜɥɟɧɢɟɦ ɦɚɝɧɢɬɧɨɣ ɫɢɥɨɜɨɣ ɥɢɧɢɢ, ɨɩɢɫɵɜɚɟɬ ɜɥɢɹɧɢɟ ɧɚɬɹɠɟɧɢɹ ɦɚɝɧɢɬɧɵɯ ɫɢɥɨɜɵɯ ɥɢɧɢɣ, ɢɥɢ ɮɚɪɚɞɟɟɜɫɤɨɟ “ɫɨɤɪɚɳɟɧɢɟ ɞɥɢɧɵ”. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɜ ɜɚɤɭɭɦɟ, ɬɨ ɟɫɬɶ ɜ ɨɛɥɚɫɬɢ & ɜɧɟ ɬɨɤɨɜ, ɤɨɝɞɚ j ≡ 0 , ɢɡ (3.16) ɫɥɟɞɭɟɬ ɫɨɨɬɧɨɲɟɧɢɟ
& ∇⊥ B n = , B R
ɤɨɬɨɪɨɟ ɭɠɟ ɢɫɩɨɥɶɡɨɜɚɥɨɫɶ ɧɚɦɢ ɪɚɧɟɟ ɩɪɢ ɨɛɫɭɠɞɟɧɢɢ ɞɪɟɣɮɨɜɨɝɨ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɜ ɧɟɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ. Ɉɛɟ ɮɨɪɦɵ ɡɚɩɢɫɢ (3.12) ɢ (3.16) ɜɩɨɥɧɟ ɪɚɜɧɨɡɧɚɱɧɵ, ɢ ɦɨɠɧɨ ɩɨɥɶɡɨɜɚɬɶɫɹ ɥɸɛɨɣ ɢɡ ɧɢɯ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɨɧɞɟɪɨɦɨɬɨɪɧɚɹ ɫɢɥɚ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɚ ɜ ɜɢɞɟ ɫɭɦɦɵ ɝɪɚɞɢɟɧɬɚ ɦɚɝɧɢɬɧɨɝɨ ɞɚɜɥɟɧɢɹ ɢ ɤɨɦɩɨɧɟɧɬɵ, ɨɛɹɡɚɧɧɨɣ ɫɜɨɟɦɭ ɩɨɹɜɥɟɧɢɸ ɧɚɬɹɠɟɧɢɸ ɦɚɝɧɢɬɧɵɯ ɫɢɥɨɜɵɯ ɥɢɧɢɣ. ȼ ɨɞɧɨɪɨɞɧɨɦ ɩɨɥɟ ɢɦɟɟɦ R→∞, ɢ ɜɤɥɚɞ ɨɬ ɷɬɨɣ ɤɨɦɩɨɧɟɧɬɵ ɨɛɪɚɳɚɟɬɫɹ ɜ ɧɭɥɶ.
ȼ ɩɪɨɛɥɟɦɟ ɦɚɝɧɢɬɧɨɝɨ ɭɞɟɪɠɚɧɢɹ ɩɥɚɡɦɵ ɜɚɠɧɭɸ ɪɨɥɶ ɢɝɪɚɟɬ ɩɚɪɚɦɟɬɪ p 8πp β= = 2 , (3.17) pm B ɨɩɪɟɞɟɥɹɸɳɢɣ ɨɬɧɨɲɟɧɢɟ ɝɚɡɨɤɢɧɟɬɢɱɟɫɤɨɝɨ ɞɚɜɥɟɧɢɹ ɩɥɚɡɦɵ ɤ ɦɚɝɧɢɬɧɨɦɭ ɞɚɜɥɟɧɢɸ. ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɟɥɢɱɢɧɵ ɷɬɨɝɨ ɩɚɪɚɦɟɬɪɚ ɩɪɢɧɹɬɨ ɝɨɜɨɪɢɬɶ ɨ ɩɥɚɡɦɟ ɜɵɫɨɤɨɝɨ ɞɚɜɥɟɧɢɹ, ɟɫɥɢ β>1, ɢɥɢ ɨ ɩɥɚɡɦɟ ɧɢɡɤɨɝɨ ɞɚɜɥɟɧɢɹ, ɟɫɥɢ β 2
τ ei
.
(3.25)
ȼɟɥɢɱɢɧɚ ɪɚɡɦɵɬɢɹ ɝɪɚɧɢɰɵ ɩɥɚɡɦɵ lp ɡɚ ɜɪɟɦɹ t ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɟɩɟɪɶ ɜɵɪɚɠɟɧɢɟɦ: l p ~ D⊥ t . Ʌɸɛɨɩɵɬɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɮɨɪɦɚɥɶɧɨ ɢɦɟɟɬ ɦɟɫɬɨ ɫɨɨɬɧɨɲɟɧɢɟ [17] 1 D⊥ = βDɦɚɝ , (3.26) 2 ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɡɚ ɬɨɠɟ ɫɚɦɨɟ ɜɪɟɦɹ ɬɨɥɳɢɧɚ ɫɥɨɹ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɩɥɚɡɦɵ ɧɢɡɤɨɝɨ ɞɚɜɥɟɧɢɹ ɫ β vTe , vTi . (4.20) k ɉɨɫɤɨɥɶɤɭ ɷɬɨ ɭɫɥɨɜɢɟ ɨɝɪɚɧɢɱɢɜɚɟɬ ɱɚɫɬɨɬɭ ɜɨɥɧ ɫɧɢɡɭ, ɬɨ ɨɧɨ ɨɬɜɟɱɚɟɬ ɜɵɫɨɤɨɱɚɫɬɨɬɧɨɦɭ ɩɪɟɞɟɥɭ, ɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɮɨɪɦɭɥɚ (4.19) ɨɩɪɟɞɟɥɹɟɬ ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɥɚɡɦɵ ɜ ɜɵɫɨɤɨɱɚɫɬɨɬɧɨɦ ɩɪɟɞɟɥɟ. ȼɨ-ɜɬɨɪɵɯ, ɧɚɩɨɦɧɢɦ, ɱɬɨ ɩɪɢ ɨɛɫɭɠɞɟɧɢɢ ɞɟɛɚɟɜɫɤɨɣ ɞɥɢɧɵ ɷɤɪɚɧɢɪɨɜɚɧɢɹ (ɫɦ. §3 ɢ §11) ɛɵɥɨ ɩɨɥɭɱɟɧɨ ɭɪɚɜɧɟɧɢɟ ɷɤɪɚɧɢɪɨɜɤɢ
∆ϕ =
ϕ
, (4.21) rD2 ɝɞɟ rD - ɪɚɞɢɭɫ Ⱦɟɛɚɹ ɞɥɹ ɩɥɚɡɦɵ. ɗɤɪɚɧɢɪɨɜɤɚ ɡɞɟɫɶ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ ɫɬɚɬɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ, ɩɨɷɬɨɦɭ ɭɪɚɜɧɟɧɢɟ (4.21) ɨɬɪɚɠɚɟɬ ɞɢɷɥɟɤɬɪɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɩɥɚɡɦɵ ɜ ɫɬɚɬɢɱɟɫɤɨɦ ɩɪɟɞɟɥɟ. ɉɨɥɚɝɚɹ ɜ (4.21) && ϕ ~ e ikr , ɩɪɢɯɨɞɢɦ ɤ ɫɥɟɞɭɸɳɟɦɭ ɪɟɡɭɥɶɬɚɬɭ: 1 1 1 1 ε =1+ 2 2 , (4.22) 2 ≡ 2 + 2 , k rD rD rDe rDi ɨɩɪɟɞɟɥɹɸɳɟɦɭ ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɥɚɡɦɵ ɜ ɫɬɚɬɢɱɟɫɤɨɦ ɩɪɟɞɟɥɟ, ɫɩɪɚɜɟɞɥɢɜɨɦ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɭɫɥɨɜɢɹ, ɨɛɪɚɬɧɨɝɨ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ (4.19):
vɮ ≡
ω
c, k 2c2 ɛɨɥɶɲɟ ɫɤɨɪɨɫɬɢ ɫɜɟɬɚ. ɉɨɷɬɨɦɭ ɞɥɹ ɬɚɤɢɯ ɜɨɥɧ ɧɟɫɭɳɟɫɬɜɟɧɧɵ ɪɟɡɨɧɚɧɫɧɵɟ ɷɮɮɟɤɬɵ. ɉɪɨɫɬɨ ɩɨɬɨɦɭ, ɱɬɨ ɢɯ ɮɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ ɡɚɜɟɞɨɦɨ ɩɪɟɜɵɲɚɟɬ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰ ɩɥɚɡɦɵ, ɜɫɟɝɞɚ ɦɟɧɶɲɢɯ ɫɤɨɪɨɫɬɢ ɫɜɟɬɚ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɝɪɭɩɩɨɜɚɹ ɫɤɨɪɨɫɬɶ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ, ɨɬɜɟɱɚɸɳɚɹ ɡɚ ɩɟɪɟɧɨɫ ɜɨɥɧɨɜɨɣ ɷɧɟɪɝɢɢ, c ∂ω vɝ ɪ = = < c, ∂k ω02 1+ 2 2 k c ɨɤɚɡɵɜɚɟɬɫɹ, ɤɚɤ ɷɬɨ ɢ ɞɨɥɠɧɨ ɛɵɬɶ, ɦɟɧɶɲɟ ɫɤɨɪɨɫɬɢ ɫɜɟɬɚ ɜ ɜɚɤɭɭɦɟ.
§ 30. əɜɥɟɧɢɟ ɨɬɫɟɱɤɢ ɧɢɡɤɨɱɚɫɬɨɬɧɨɣ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ Ʉɚɤ ɦɵ ɜɢɞɢɦ ɢɡ ɮɨɪɦɭɥɵ (4.36), ɱɚɫɬɨɬɚ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ ɜ ɩɥɚɡɦɟ ɜɫɟɝɞɚ ɛɨɥɶɲɟ ɩɥɚɡɦɟɧɧɨɣ ɱɚɫɬɨɬɵ, ɩɨɷɬɨɦɭ ɩɨɩɟɪɟɱɧɵɟ ɜɨɥɧɵ, ɱɚɫɬɨɬɚ ɤɨɬɨɪɵɯ ɦɟɧɶɲɟ ɩɥɚɡɦɟɧɧɨɣ ɱɚɫɬɨɬɵ, ɧɟ ɦɨɝɭɬ ɜ ɧɟɣ ɪɚɫɩɪɨɫɬɪɚɧɹɬɶɫɹ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɩɚɞɚɸɳɚɹ ɢɡ ɜɚɤɭɭɦɚ ɧɚ ɝɪɚɧɢɰɭ ɩɥɚɡɦɵ ɩɨɩɟɪɟɱɧɚɹ ɜɨɥɧɚ ɫ ɦɚɥɨɣ ɱɚɫɬɨɬɨɣ ɞɨɥɠɧɚ ɨɬɪɚɠɚɬɶɫɹ. ɂɦɟɟɬ ɦɟɫɬɨ, ɤɚɤ ɝɨɜɨɪɹɬ ɹɜɥɟɧɢɟ ɨɬɫɟɱɤɢ ɜɨɥɧɵ (ɜ ɚɧɝɥɢɣɫɤɨɣ ɥɢɬɟɪɚɬɭɪɟ - cut off). Ʉɪɢɬɢɱɟɫɤɚɹ ɱɚɫɬɨɬɚ − ɱɚɫɬɨɬɚ ɨɬɫɟɱɤɢ,
ωɤ ɪ = ω p ≡
4πn0 e 2 § Zme · ¨1 + ¸, me © mi ¹
(4.37)
ɡɚɜɢɫɢɬ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɥɚɡɦɵ. Ɍɚɤ ɱɬɨ, ɢɡɦɟɪɹɹ ɤɪɢɬɢɱɟɫɤɭɸ ɱɚɫɬɨɬɭ, ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɤɨɧɰɟɧɬɪɚɰɢɸ ɩɥɚɡɦɵ. ɗɬɨ ɨɞɢɧ ɢɡ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɯ ɦɟɬɨɞɨɜ ɞɢɚɝɧɨɫɬɢɤɢ ɩɥɚɡɦɵ. ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɢɡɤɨɱɚɫɬɨɬɧɨɣ ɜɨɥɧɵ ɱɚɫɬɢɱɧɨ ɜɫɟ ɠɟ ɩɪɨɧɢɤɚɟɬ ɜ ɩɥɚɡɦɭ, ɧɨ ɟɝɨ ɚɦɩɥɢɬɭɞɚ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ ɭɦɟɧɶɲɚɟɬɫɹ ɜɝɥɭɛɶ ɩɥɚɡɦɵ. Ƚɥɭɛɢɧɚ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɜ ɩɥɚɡɦɭ ɩɨɥɹ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ ɫ ɧɢɡɤɨɣ ɱɚɫɬɨɬɨɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɨɥɳɢɧɨɣ ɜɚɤɭɭɦɧɨɝɨ ɫɤɢɧ-ɫɥɨɹ, ɤɨɬɨɪɚɹ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɩɥɚɡɦɟɧɧɨɣ ɱɚɫɬɨɬɟ: c . (4.38) δɜɚɤ =
ωp
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɝɥɭɛɢɧɚ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɜɨɥɧɵ ɜ ɩɥɚɡɦɭ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɧɟɪɰɢɟɣ ɟɟ ɱɚɫɬɢɰ, ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ - ɷɥɟɤɬɪɨɧɨɜ. ȼ ɩɪɟɧɟɛɪɟɠɟɧɢɢ ɢɧɟɪɰɢɟɣ ɝɥɭɛɢɧɚ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɩɨɥɹ ɛɵɥɚ ɛɵ ɧɭɥɟɜɨɣ. ɉɪɨɢɥɥɸɫɬɪɢɪɭɟɦ ɫɤɚɡɚɧɧɨɟ ɩɪɨɫɬɵɦ ɩɪɢɦɟɪɨɦ. ɉɭɫɬɶ ɢɡ ɜɚɤɭɭɦɚ ɧɚ ɩɥɨɫɤɭɸ ɝɪɚɧɢɰɭ ɩɥɚɡɦɵ ɩɚɞɚɟɬ ɧɢɡɤɨɱɚɫɬɨɬɧɚɹ ɜɨɥɧɚ, ɫɥɟɜɚ ɧɚɩɪɚɜɨ, ɤɚɤ ɷɬɨ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 4.2. ɋɥɟɜɚ ɢ ɫɩɪɚɜɚ ɨɬ ɝɪɚɧɢɰɵ ɪɚɡɞɟɥɚ ɡɚɤɨɧɵ ɞɢɫɩɟɪɫɢɢ ɜɨɥɧɵ ɪɚɡɧɵɟ:
ω 2 , x > 0 , ω 2 − k 2c2 = ® p ¯ 0 , x < 0.
ɗɬɢ ɫɨɨɬɧɨɲɟɧɢɹ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɦ ɜɢɞɟ. ɉɭɫɬɶ ɱɚɫɬɨɬɚ ɜɨɥɧɵ ɮɢɤɫɢɪɨɜɚɧɚ, ɡɚɦɟɧɢɜ k → − i∂x , ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɹ
ω p2 − ω 2 f , x > 0, °° 2 2 c ∂x f = ® 2 ° − ω f , x < 0, °¯ c2 Ɋɢɫ. 4.2. Ɉɬɫɟɱɤɚ ɧɢɡɤɨɱɚɫɬɨɬɧɨɣ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ ɧɚ ɝɪɚɧɢɰɟ ɩɥɚɡɦɵ
(4.39)
ɝɞɟ ɮɭɧɤɰɢɹ f ɡɚɞɚɟɬ ɩɨɥɟ ɜɨɥɧɵ: ɧɚɩɪɢɦɟɪ, ɷɬɨ ɦɨɠɟɬ ɛɵɬɶ ɤɨɦɩɨɧɟɧɬɚ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. ɇɚ ɝɪɚɧɢɰɟ ɪɚɡɞɟɥɚ ɩɨɬɪɟɛɭɟɦ ɜɵɩɨɥɧɟɧɢɹ ɭɫɥɨɜɢɣ ɧɟɩɪɟɪɵɜɧɨɫɬɢ:
∂x f |x =+0 = ∂x f |x =−0 ,
(4.40)
f |x =+0 = f |x =−0 .
ɇɟɬɪɭɞɧɨ ɧɚɣɬɢ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ (4.39), (4.40), ɭɞɨɜɥɟɬɜɨɪɹɸɳɟɟ ɷɬɢɦ ɭɫɥɨɜɢɹɦ. ɉɪɟɞɥɚɝɚɟɦ ɱɢɬɚɬɟɥɸ ɩɪɨɜɟɪɢɬɶ, ɱɬɨ ɬɚɤɨɜɵɦ ɹɜɥɹɟɬɫɹ ɪɟɲɟɧɢɟ, ɜ ɤɨɬɨɪɨɦ ɜ ɨɛɥɚɫɬɢ ɜɚɤɭɭɦɚ ɩɨɥɟ ɫɤɥɚɞɵɜɚɟɬɫɹ ɢɡ ɩɨɥɹ ɩɚɞɚɸɳɟɣ ɢ ɨɬɪɚɠɟɧɧɨɣ ɜɨɥɧɵ, ɚ ɜ ɨɛɥɚɫɬɢ ɩɥɚɡɦɵ ɜɨɥɧɨɜɨɟ ɩɨɥɟ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ ɡɚɬɭɯɚɟɬ:
§ ω °exp¨ i f = f0 ® © c °¯
· § ω · x ¸ + α exp¨ − i x ¸ , x < 0 , ¹ © c ¹ β exp( − κx ) , x > 0,
ɝɞɟ ɨɛɨɡɧɚɱɟɧɨ
κ=
ω p2 − ω 2 c2
>0
(4.41)
- ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɝɨ ɡɚɬɭɯɚɧɢɹ ɩɨɥɹ ɜɨɥɧɵ ɜ ɩɥɚɡɦɟ, f0 − ɚɦɩɥɢɬɭɞɚ ɩɚɞɚɸɳɟɣ ɧɚ ɝɪɚɧɢɰɭ ɪɚɡɞɟɥɚ ɜɨɥɧɵ. Ⱥɦɩɥɢɬɭɞɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ α ɞɥɹ ɨɬɪɚɠɟɧɧɨɣ ɜɨɥɧɵ ɢ β ɞɥɹ ɩɨɥɹ ɜ ɩɥɚɡɦɟ, ɤɚɤ ɷɬɨ ɜɵɬɟɤɚɟɬ ɢɡ ɭɫɥɨɜɢɣ ɧɟɩɪɟɪɵɜɧɨɣ ɫɲɢɜɤɢ (4.40), ɨɤɚɡɵɜɚɸɬɫɹ ɪɚɜɧɵɦɢ:
α=
ω − i κc 2ω . , β= ω + i κc ω + iκc
Ɉɛɪɚɬɢɦ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɱɢɫɥɢɬɟɥɶ ɢ ɡɧɚɦɟɧɚɬɟɥɶ ɩɟɪɜɨɣ ɮɨɪɦɭɥɵ ɹɜɥɹɸɬɫɹ ɤɨɦɩɥɟɤɫɧɨ-ɫɨɩɪɹɠɟɧɧɵɦɢ. ɉɨɷɬɨɦɭ ɩɨɥɭɱɚɟɦ |α | = 1 , ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɚɦɩɥɢɬɭɞɵ ɩɚɞɚɸɳɟɣ ɜɨɥɧɵ ɢ ɨɬɪɚɠɟɧɧɨɣ ɫɨɜɩɚɞɚɸɬ. ɗɬɨ ɢ ɨɡɧɚɱɚɟɬ ɧɚɥɢɱɢɟ ɩɨɥɧɨɝɨ ɨɬɪɚɠɟɧɢɹ ɩɚɞɚɸɳɟɣ ɧɚ ɩɥɚɡɦɭ ɜɨɥɧɵ. ȼ ɩɪɟɞɟɥɟ ɫɨɜɫɟɦ ɧɢɡɤɢɯ ɱɚɫɬɨɬ, ɤɨɝɞɚ ω → 0 , ɩɨɥɭɱɚɟɦ ɩɪɢɛɥɢɠɟɧɧɨ
α ≈ −1 − 2 i
ω ω −1 → − 1, β = − 2 i → 0 , κ ≈ δɜɚɤ , ωp ωp
ɢ ɞɥɢɧɚ ɡɚɬɭɯɚɧɢɹ ɩɨɥɹ ɜ ɩɥɚɡɦɟ ɫɨɜɩɚɞɚɟɬ ɫ ɞɥɢɧɨɣ ɜɚɤɭɭɦɧɨɝɨ ɫɤɢɧ-ɫɥɨɹ.
§ 31. Ʌɟɧɝɦɸɪɨɜɫɤɢɟ ɤɨɥɟɛɚɧɢɹ ɢ ɜɨɥɧɵ ɜ ɩɥɚɡɦɟ. ɉɥɚɡɦɨɧɵ Ɋɚɫɫɦɨɬɪɢɦ ɬɟɩɟɪɶ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɯ ɩɪɨɞɨɥɶɧɵɯ ɩɥɚɡɦɟɧɧɵɯ ɜɨɥɧ ɫ ɱɚɫɬɨɬɨɣ ɜ ɨɛɥɚɫɬɢ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɱɚɫɬɨɬɵ. Ɉɧɢ ɢɡɜɟɫɬɧɵ ɤɚɤ ɥɟɧɝɦɸɪɨɜɫɤɢɟ ɜɨɥɧɵ ɢ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɜɚɠɧɟɣɲɢɣ ɬɢɩ ɜɨɡɦɭɳɟɧɢɣ, ɫɩɨɫɨɛɧɵɯ ɫɭɳɟɫɬɜɨɜɚɬɶ ɢ ɪɚɫɩɪɨɫɬɪɚɧɹɬɶɫɹ ɜ ɩɥɚɡɦɟ. Ɂɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɩɪɨɞɨɥɶɧɵɯ ɜɨɥɧ ɨɩɪɟɞɟɥɹɟɬ, ɤɚɤ ɛɵɥɨ ɩɨɤɚɡɚɧɨ ɜɵɲɟ, ɭɪɚɜɧɟɧɢɟ εl = 0 , ɜ ɤɨɬɨɪɨɟ ɫɥɟɞɭɟɬ ɩɨɞɫɬɚɜɢɬɶ ɩɪɨɞɨɥɶɧɭɸ ɤɨɦɩɨɧɟɧɬɭ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ. ȿɫɥɢ ɩɥɚɡɦɭ ɫɱɢɬɚɬɶ ɯɨɥɨɞɧɨɣ, ɬɨ ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɫɥɟɞɭɟɬ ɨɩɪɟɞɟɥɹɬɶ ɩɨ ɮɨɪɦɭɥɟ (4.19), ɢ ɦɵ ɩɪɢɯɨɞɢɦ ɤ ɭɪɚɜɧɟɧɢɸ
ω p2 1− 2 = 0. ω Ɉɧɨ ɢɦɟɟɬ ɞɜɚ ɪɟɲɟɧɢɹ, ɨɬɥɢɱɚɸɳɢɟɫɹ ɡɧɚɤɨɦ. ɉɨɥɨɠɢɬɟɥɶɧɵɣ ɤɨɪɟɧɶ ɪɚɜɟɧ ω = ωp
(4.42)
Ʉɚɤ ɦɵ ɜɢɞɢɦ, ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɫɥɭɱɚɟ ɱɚɫɬɨɬɚ ɜɨɥɧɵ ɫɨɜɩɚɞɚɟɬ ɫ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɱɚɫɬɨɬɨɣ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɜɟɥɢɱɢɧɵ ɜɨɥɧɨɜɨɝɨ ɱɢɫɥɚ. Ɏɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ ɬɚɤɢɯ ɜɨɥɧ vɮ ≡
ω
=
ωp
(4.43) k k ɭɦɟɧɶɲɚɟɬɫɹ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɜɨɥɧɨɜɨɝɨ ɱɢɫɥɚ, ɚ ɝɪɭɩɩɨɜɚɹ ɫɤɨɪɨɫɬɶ ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɣ ɧɭɥɸ: ∂ω ∂ω p & vɝ ɪ ≡ & = & ≡ 0 . (4.44) ∂k ∂k Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɯɨɥɨɞɧɨɣ ɩɥɚɡɦɟ ɥɟɧɝɦɸɪɨɜɫɤɢɟ ɜɨɥɧɵ ɧɟ ɦɨɝɭɬ ɩɟɪɟɧɨɫɢɬɶ ɷɧɟɪɝɢɸ: ɮɚɤɬɢɱɟɫɤɢ ɷɬɨ ɨɛɵɱɧɵɟ ɤɨɥɟɛɚɧɢɹ ɩɥɨɬɧɨɫɬɢ ɡɚɪɹɞɚ, ɜɨɡɧɢɤɚɸɳɢɟ ɜɫɥɟɞɫɬɜɢɟ ɧɚɪɭɲɟɧɢɹ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɢ ɩɥɚɡɦɵ. ȿɫɥɢ ɠɟ ɦɵ ɭɱɬɟɦ ɬɟɩɟɪɶ ɬɟɩɥɨɜɨɟ ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰ ɩɥɚɡɦɵ, ɬɨ ɫɢɬɭɚɰɢɹ ɢɡɦɟɧɢɬɫɹ ɤɚɪɞɢɧɚɥɶɧɨ. Ⱦɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɨɩɪɟɞɟɥɹɟɬ ɬɟɩɟɪɶ ɮɨɪɦɭɥɚ (4.32) ɢ ɞɢɫɩɟɪɫɢɨɧɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɩɪɨɞɨɥɶɧɵɯ ɜɨɥɧ ɫɬɚɧɨɜɢɬɫɹ ɬɚɤɢɦ:
εl = 1 −
¦ω
α = e ,i
ω p2α 2
− k 2 cs2α
= 0,
ɢɥɢ
ω pe2
ω pi2
Te ,i . (4.45) ω −k c ω −k c me ,i ɗɬɨ ɭɪɚɜɧɟɧɢɟ ɧɟɫɥɨɠɧɨ ɪɟɲɢɬɶ ɜ ɨɛɳɟɦ ɜɢɞɟ. ɇɨ ɜ ɢɧɬɟɪɟɫɭɸɳɟɣ ɧɚɫ ɫɟɣɱɚɫ ɜɵɫɨɤɨɱɚɫɬɨɬɧɨɣ ɨɛɥɚɫɬɢ ɫɥɟɞɭɟɬ ɭɱɟɫɬɶ, ɱɬɨ ɢɨɧɵ ɩɥɚɡɦɵ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɧɟɩɨɞɜɢɠɧɵɦɢ, ɚ ɩɨɬɨɦɭ ɢɯ ɜɤɥɚɞ ɜ ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɛɭɞɟɬ ɩɪɟɧɟɛɪɟɠɢɦɨ ɦɚɥɵɦ. Ɏɨɪɦɚɥɶɧɨ ɷɬɨ ɨɬɜɟɱɚɟɬ ɩɪɟɞɟɥɭ mi→∞, ɢ ɭɪɚɜɧɟɧɢɟ (4.45) ɭɩɪɨɳɚɟɬɫɹ: ω pe2 T 1− 2 cs2e = γ e e . 2 2 = 0, ω − k cse me Ɍɟɩɟɪɶ ɟɝɨ ɭɠɟ ɧɟ ɫɥɨɠɧɨ ɪɟɲɢɬɶ, ɢ ɦɵ, ɜɧɨɜɶ ɜɵɛɢɪɚɹ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɤɨɪɟɧɶ, ɩɨɥɭɱɚɟɦ: ω = ω pe2 + k 2 cse2 . (4.46) 1−
2
2 2 se
−
2
2 2 si
= 0 , cs2e ,i = γ e ,i
ɗɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɢ ɨɩɪɟɞɟɥɹɟɬ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ ɥɟɧɝɦɸɪɨɜɫɤɨɣ ɜɨɥɧɵ ɜ ɩɥɚɡɦɟ ɫ ɤɨɧɟɱɧɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ.
Ʌɸɛɨɩɵɬɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɷɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɩɨ ɜɢɞɭ ɨɤɚɡɵɜɚɟɬɫɹ ɜɩɨɥɧɟ ɚɧɚɥɨɝɢɱɧɵɦ ɢɡɜɟɫɬɧɨɣ ɮɨɪɦɭɥɟ, ɨɩɪɟɞɟɥɹɸɳɟɣ ɫɜɹɡɶ ɷɧɟɪɝɢɢ ɢ ɢɦɩɭɥɶɫɚ ɪɟɥɹɬɢɜɢɫɬɫɤɨɣ ɱɚɫɬɢɰɵ:
ε=
( mc )
2 2
+ p2c2 .
ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɨ ɡɚɤɨɧɟ ɞɢɫɩɟɪɫɢɢ (4.46) ɝɨɜɨɪɹɬ ɤɚɤ ɨ «ɱɚɫɬɢɰɟ-ɩɨɞɨɛɧɨɦ», ɚ ɥɟɧɝɦɸɪɨɜɫɤɢɟ ɜɨɥɧɵ ɜ ɷɬɨɦ ɩɥɚɧɟ ɹɜɥɹɸɬɫɹ «ɤɜɚɡɢɱɚɫɬɢɰɚɦɢ», ɤɨɬɨɪɵɟ ɩɪɢɧɹɬɨ ɧɚɡɵɜɚɬɶ ɩɥɚɡɦɨɧɚɦɢ. ɉɨɥɟɡɧɨ ɨɬɦɟɬɢɬɶ ɬɚɤɠɟ, ɱɬɨ ɡɚɤɨɧ ɞɢɫɩɟɪɫɢɢ (4.46) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ: ω = ω pe 1 + γ e k 2 rDe2 . (4.47) ȼɬɨɪɨɟ ɫɥɚɝɚɟɦɨɟ ɩɨɞ ɤɨɪɧɟɦ ɛɭɞɟɬ ɛɨɥɶɲɟ ɢɥɢ ɩɨɪɹɞɤɚ ɟɞɢɧɢɰɵ, ɤɨɝɞɚ ɞɥɢɧɚ ɜɨɥɧɵ ɛɭɞɟɬ ɦɟɧɶɲɟ ɞɟɛɚɟɜɫɤɨɝɨ ɪɚɞɢɭɫɚ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɥɟɧɝɦɸɪɨɜɫɤɚɹ ɜɨɥɧɚ ɫɢɥɶɧɨ ɩɨɝɥɨɳɚɟɬɫɹ ɡɚ ɫɱɟɬ ɦɟɯɚɧɢɡɦɚ ɛɟɫɫɬɨɥɤɧɨɜɢɬɟɥɶɧɨɝɨ ɩɨɝɥɨɳɟɧɢɹ Ʌɚɧɞɚɭ, ɬɚɤ ɤɚɤ ɨɤɚɡɵɜɚɟɬɫɹ ɪɟɡɨɧɚɧɫɧɨɣ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɷɥɟɤɬɪɨɧɚɦ ɩɥɚɡɦɵ, v ɮ ~ vTe . ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɥɟɧɝɦɸɪɨɜɫɤɢɟ ɜɨɥɧɵ ɦɨɝɭɬ ɫɭɳɟɫɬɜɨɜɚɬɶ ɜ ɩɥɚɡɦɟ ɛɟɡ ɫɭɳɟɫɬɜɟɧɧɨɝɨ ɩɨɝɥɨɳɟɧɢɹ ɥɢɲɶ ɜ ɨɛɪɚɬɧɨɦ ɩɪɟɞɟɥɟ, ɤɨɝɞɚ ɢɯ ɞɥɢɧɚ ɜɨɥɧɵ ɦɟɧɶɲɟ ɞɟɛɚɟɜɫɤɨɝɨ ɪɚɞɢɭɫɚ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜ (4.47) ɜɬɨɪɨɟ ɫɥɚɝɚɟɦɨɟ ɩɨɞ ɤɨɪɧɟɦ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɦɚɥɵɦ ɢ ɪɚɡɥɨɠɢɬɶ ɩɨ ɷɬɨɣ ɦɚɥɨɫɬɢ: γ · § ω ≈ ω pe ¨ 1 + e k 2 rDe2 ¸ , k 2 rDe2 0, ɬ. ɟ. ɥɢɧɡɚ ɜɫɟɝɞɚ ɫɨɛɢɪɚɸɳɚɹ. Ⱦɥɹ ɨɞɢɧɨɱɧɨɣ ɞɢɚɮɪɚɝɦɵ ɫ ɤɪɭɝɥɵɦ ɨɬɜɟɪɫɬɢɟɦ: D=
E − E2 1 = 1 , fd 4U d
(5.10)
ɝɞɟ E1 ɢ E2 – ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ ɫɥɟɜɚ ɢ ɫɩɪɚɜɚ ɨɬ ɞɢɚɮɪɚɝɦɵ, Ud – ɩɨɬɟɧɰɢɚɥ ɞɢɚɮɪɚɝɦɵ. Ⱦɥɹ ɫɢɫɬɟɦɵ ɢɡ ɞɜɭɯ ɥɢɧɡ – ɞɢɚɮɪɚɝɦ ɫ ɮɨɤɭɫɚɦɢ f1 ɢ f2 ɢ ɪɚɫɫɬɨɹɧɢɟɦ ɦɟɠɞɭ ɥɢɧɡɚɦɢ l ɨɩɬɢɱɟɫɤɚɹ ɫɢɥɚ ɡɚɞɚɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ:
l 1 1 1 = + + . f f1 f 2 f1 f 2
(5.11)
ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɨɝɨ ɩɨɥɹ ɬɪɚɟɤɬɨɪɢɹ ɷɥɟɤɬɪɨɧɚ ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɹɦɢ:
er '' ⋅⋅ °m r = −eEr ≈ − 2 U ( z ) , ® ° ⋅⋅ ' ¯m z = −eEz ≈ eU ( z )
(5.12)
ɬ.ɟ. ɮɨɤɭɫɢɪɭɸɳɚɹ ɫɢɥɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɧɚɤɨɦ ɜɬɨɪɨɣ ɩɪɨɢɡɜɨɞɧɨɣ ɨɬ ɩɨɬɟɧɰɢɚɥɚ ɧɚ ɨɫɢ ɫɢɫɬɟɦɵ. ȿɫɥɢ U′′(z) > 0, ɬɨ ɫɢɫɬɟɦɚ ɮɨɤɭɫɢɪɭɸɳɚɹ, ɟɫɥɢ U′′(z) < 0, ɬɨ ɪɚɫɮɨɤɭɫɢɪɭɸɳɚɹ. §40. Ɇɚɝɧɢɬɧɵɟ ɥɢɧɡɵ
Ɏɨɤɭɫɢɪɨɜɤɭ ɩɭɱɤɨɜ ɜ ɚɤɫɢɚɥɶɧɨɫɢɦɦɟɬɪɢɱɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɪɨɳɟ ɜɫɟɝɨ ɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɬɶ ɧɚ ɩɪɢɦɟɪɟ ɩɚɪɚɤɫɢɚɥɶɧɨɝɨ ɩɭɱɤɚ ɷɥɟɤɬɪɨɧɨɜ, ɫɤɨɪɨɫɬɶ ɤɨɬɨɪɵɯ ɜɞɨɥɶ ɨɫɢ ɫɢɫɬɟɦɵ ɦɧɨɝɨ ɛɨɥɶɲɟ ɫɤɨɪɨɫɬɢ ɜ ɪɚɞɢɚɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ vz >> vr. ɇɚ ɷɥɟɤɬɪɨɧ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ Ʌɨɪɟɧɰɚ & e& & F = − v × B . Ɋɚɞɢɚɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ c ɷɬɨɣ ɫɢɥɵ ɹɜɥɹɟɬɫɹ ɮɨɤɭɫɢɪɭɸɳɟɣ: Fr = (e/c)vϕBz (ɪɢɫ.5.6). Ⱥɡɢɦɭɬɚɥɶɧɚɹ
Ɋɢɫ. 5.6. Ɏɨɤɭɫɢɪɨɜɤɚ ɜ ɚɤɫɢɚɥɶɧɨɫɢɦɦɟɬɪɢɱɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ
ɫɨɫɬɚɜɥɹɸɳɚɹ ɫɤɨɪɨɫɬɢ ɷɥɟɤɬɪɨɧɚ ɩɨɹɜɥɹɟɬɫɹ ɡɚ ɫɱɟɬ ɚɡɢɦɭɬɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɫɢɥɵ Ʌɨɪɟɧɰɚ: Fϕ = -(e/c)(vzBr + vrBz) ≈ -(e/c)vzBr , ɬɚɤ ɤɚɤ vz >> vr. ɋɨɫɬɚɜɥɹɸɳɚɹ ɫɤɨɪɨɫɬɢ vz ɧɟ ɦɟɧɹɟɬ ɡɧɚɤɚ, ɪɚɞɢɚɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ Br ɦɨɠɟɬ ɦɟɧɹɬɶ ɡɧɚɤ, ɩɪɢ ɷɬɨɦ ɚɡɢɦɭɬɚɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɫɤɨɪɨɫɬɢ ɷɥɟɤɬɪɨɧɚ vϕ ɛɭɞɟɬ ɭɦɟɧɶɲɚɬɶɫɹ (ɜɪɚɳɟɧɢɟ ɡɚɦɟɞɥɹɬɶɫɹ), ɧɨ ɧɚɩɪɚɜɥɟɧɢɟ ɜɪɚɳɟɧɢɟ ɧɢɤɨɝɞɚ ɧɟ ɦɟɧɹɟɬɫɹ, ɩɨɷɬɨɦɭ ɮɨɤɭɫɢɪɭɸɳɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɫɢɥɵ Ʌɨɪɟɧɰɚ Fr ɜɫɟɝɞɚ ɫɨɯɪɚɧɹɟɬ ɡɧɚɤ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɚɝɧɢɬɧɚɹ ɥɢɧɡɚ ɜɫɟɝɞɚ ɫɨɛɢɪɚɸɳɚɹ. ɋ ɭɱɟɬɨɦ ɬɟɨɪɟɦɵ Ƚɚɭɫɫɚ, ɞɚɸɳɟɣ ɫɨɨɬɧɨɲɟɧɢɹ ɦɟɠɞɭ ɩɪɨɞɨɥɶɧɨɣ Bz ɢ ɪɚɞɢɚɥɶɧɨɣ ɤɨɦɩɨɧɟɧɬɚɦɢ Br ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ & B (Bz,Br) Br = -(r/2)(dBz/dz), ɞɜɢɠɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɜɞɨɥɶ ɨɫɢ ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ: dB d 2z e2 (5.13) r 2 B z 2z . = − 2 2 2 dt 4m c dz
Ⱥɡɢɦɭɬɚɥɶɧɨɟ ɞɜɢɠɟɧɢɟ (ɩɨɜɨɪɨɬ) ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ: dϕ eB z = dt 2mc
(5.14)
(ɥɚɪɦɨɪɨɜɫɤɨɟ ɜɪɚɳɟɧɢɟ), ɬ. ɟ. ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɫɟɯ ɷɥɟɤɬɪɨɧɨɜ ɨɞɢɧɚɤɨɜɚ ɢ ɢɡɨɛɪɚɠɟɧɢɟ ɜɪɚɳɚɟɬɫɹ ɤɚɤ ɰɟɥɨɟ, ɩɪɢɱɟɦ, ɧɚɩɪɚɜɥɟɧɢɟ ɜɪɚɳɟɧɢɹ ɡɚɜɢɫɢɬ ɨɬ ɧɚɩɪɚɜɥɟɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȿɫɥɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɫɥɨɜɢɸ: b
³B
z
( z )dz = 0, ɬɨ ɜɪɚɳɟɧɢɟ ɢɡɨɛɪɚɠɟɧɢɹ ɛɭɞɟɬ ɨɬɫɭɬɫɬɜɨɜɚɬɶ. ɍɱɢɬɵɜɚɹ, ɱɬɨ ɞɥɹ
a
ɩɚɪɚɤɫɢɚɥɶɧɵɯ ɩɭɱɤɨɜ vz>>vr (ɜ ɩɪɢɛɥɢɠɟɧɢɢ
mv 2 ≈ U 0 ), ɞɜɢɠɟɧɢɟ ɩɨ ɪɚɞɢɭɫɭ 2
ɡɚɞɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ: eB z2 d 2r =− r, 8mc 2U 0 dz 2
(5.15)
ɝɞɟ U0 – ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɨɜ. Ⱦɚɧɧɨɟ ɭɪɚɜɧɟɧɢɟ ɨɩɢɫɵɜɚɟɬ ɬɪɚɟɤɬɨɪɢɸ ɜ ɩɥɨɫɤɨɫɬɢ, ɤɨɬɨɪɚɹ ɜɪɚɳɚɟɬɫɹ ɫ ɥɚɪɦɨɪɨɜɫɤɨɣ ɱɚɫɬɨɬɨɣ. Ʉɚɤ ɜɢɞɧɨ ɢɡ ɭɪɚɜɧɟɧɢɣ ɞɜɢɠɟɧɢɹ, ɬɪɚɟɤɬɨɪɢɹ ɷɥɟɤɬɪɨɧɚ ɩɨɥɧɨɫɬɶɸ ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɧɚɱɟɧɢɟɦ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɚ ɨɫɢ Bz. ȼ ɭɪɚɜɧɟɧɢɹ ɜɯɨɞɹɬ ɡɚɪɹɞ ɢ ɦɚɫɫɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɪɚɡɧɵɟ ɱɚɫɬɢɰɵ ɞɜɢɠɭɬɫɹ ɩɨ ɪɚɡɧɵɦ ɬɪɚɟɤɬɨɪɢɹɦ. ɍɪɚɜɧɟɧɢɹ ɥɢɧɟɣɧɵ ɢ ɨɞɧɨɪɨɞɧɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɪɚɫɫɬɨɹɧɢɹ ɨɬ ɨɫɢ r, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɥɸɛɨɟ ɚɤɫɢɚɥɶɧɨɫɢɦɦɟɬɪɢɱɧɨɟ ɩɨɥɟ ɫɩɨɫɨɛɧɨ ɫɨɡɞɚɬɶ ɢɡɨɛɪɚɠɟɧɢɟ ɢ ɹɜɥɹɟɬɫɹ ɥɢɧɡɨɣ. Ⱦɥɹ ɬɨɧɤɨɣ ɦɚɝɧɢɬɧɨɣ ɥɢɧɡɵ (ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɚ ɨɫɢ ɛɵɫɬɪɨ ɩɚɞɚɟɬ ɩɨ ɦɟɪɟ ɭɞɚɥɟɧɢɹ ɨɬ ɥɢɧɡɵ) ɨɩɬɢɱɟɫɤɚɹ ɫɢɥɚ: b
b
1 e 1 1 0.022 = B z2 dz ɢɥɢ [ ] = B z2 [ Ƚɫ]dz . ³ ³ 2 f ɫɦ U 0 [ ɷȼ ] a f 8mc U 0 a ɍɝɨɥ ɩɨɜɨɪɨɬɚ ɜ ɦɚɝɧɢɬɧɨɣ ɥɢɧɡɟ
(5.16)
ϕ ( z) =
1 e c 8mU 0
b
b
³ B z dz ɢɥɢ ϕ[ ɪɚɞ] = a
0.15 B z [ Ƚɫ]dz . U 0 [ ɷȼ] ³a
(5.17)
Bm , z 2 3/ 2 (1 + 2 ) R ɝɞɟ Bm – ɩɨɥɟ ɜ ɰɟɧɬɪɟ ɜɢɬɤɚ (ɮɨɪɦɭɥɚ Ȼɢɨ-ɋɚɜɚɪɚ). ɂɧɬɟɝɪɢɪɭɹ (5.16), ɦɨɠɧɨ ɧɚɣɬɢ ɮɨɤɭɫɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɞɥɹ ɨɞɧɨɝɨ ɬɨɤɨɜɨɝɨ ɜɢɬɤɚ:
Ⱦɥɹ ɦɚɝɧɢɬɧɨɝɨ ɜɢɬɤɚ ɫ ɬɨɤɨɦ I ɪɚɞɢɭɫɚ R ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ Bz=
U 0 [ ɷȼ ]R[ɫɦ] . I 2 [ A] Ⱦɥɹ ɤɚɬɭɲɤɢ ɢɡ N ɜɢɬɤɨɜ: f [ɫɦ] ≈ 96.8
f [ɫɦ] ≈ 96.8
(5.18ɚ)
U 0 [ ɷȼ ]R[ɫɦ] . ( NI [ A]) 2
(5.18ɛ)
NI [ A] . U 0 [ ɷȼ]
(5.19)
ɍɝɨɥ ɩɨɜɨɪɨɬɚ:
ϕ [ ɪɚɞ] ≈ 10.7
Ⱦɥɹ ɷɤɪɚɧɢɪɨɜɚɧɧɨɣ ɥɢɧɡɵ fɷ = kf, ɝɞɟ k – ɩɨɩɪɚɜɨɱɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ, k = 0.5÷0.7. §41. Ɉɬɤɥɨɧɹɸɳɢɟ ɢ ɮɨɤɭɫɢɪɭɸɳɢɟ ɷɥɟɤɬɪɨɧɧɨ-ɨɩɬɢɱɟɫɤɢɟ ɫɢɫɬɟɦɵ
Ɉɬɤɥɨɧɟɧɢɟ ɢ ɮɨɤɭɫɢɪɨɜɤɚ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɢ ɦɚɝɧɢɬɧɨɦ ɩɨɥɹɯ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɫɨɡɞɚɧɢɹ ɢ ɞɢɚɝɧɨɫɬɢɤɢ ɩɥɚɡɦɵ, ɚ ɬɚɤɠɟ ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɩɪɨɰɟɫɫɨɜ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɩɥɚɡɦɵ ɫ ɬɜɟɪɞɵɦ ɬɟɥɨɦ. Ɋɚɫɫɦɨɬɪɢɦ ɧɟɤɨɬɨɪɵɟ ɢɡ ɬɚɤɢɯ ɫɢɫɬɟɦ. ɗɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɢɟ ɷɧɟɪɝɨɚɧɚɥɢɡɚɬɨɪɵ
ɇɚɢɛɨɥɟɟ ɩɪɨɫɬɨɣ ɹɜɥɹɟɬɫɹ ɫɢɫɬɟɦɚ ɜ ɜɢɞɟ ɩɥɨɫɤɨɝɨ ɤɨɧɞɟɧɫɚɬɨɪɚ. ȿɫɥɢ ɩɭɱɨɤ ɱɚɫɬɢɰ ɡɚɩɭɫɤɚɟɬɫɹ ɩɚɪɚɥɥɟɥɶɧɨ ɩɥɚɫɬɢɧɚɦ (ɪɢɫ. 5.7 ), ɬɨ ɭɝɨɥ ɨɬɤɥɨɧɟɧɢɹ ɩɭɱɤɚ α ɡɚɜɢɫɢɬ ɨɬ ɷɧɟɪɝɢɢ ɱɚɫɬɢɰ U0: α(U0) = ∆UlE/(2U0d),
(5.20)
ɝɞɟ ∆U - ɪɚɡɧɨɫɬɶ ɩɨɬɟɧɰɢɚɥɨɜ, ɩɪɢɥɨɠɟɧɧɚɹ ɤ ɩɥɚɫɬɢɧɚɦ, lE - ɞɥɢɧɚ ɩɥɚɫɬɢɧ ɜɞɨɥɶ ɞɜɢɠɟɧɢɹ ɩɭɱɤɚ, d ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɩɥɚɫɬɢɧɚɦɢ. Ȼɥɚɝɨɞɚɪɹ ɪɚɡɥɢɱɧɵɦ ɡɧɚɱɟɧɢɹɦ ɩɨɬɟɧɰɢɚɥɚ ɧɚ Ɋɢɫ. 5.7. Ɏɨɤɭɫɢɪɨɜɤɚ ɜ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɦ ɩɨɥɟ ɩɥɨɫɤɨɝɨ ɤɨɧɞɟɧɫɚɬɨɪɚ ɜɟɪɯɧɟɣ ɢ ɧɢɠɧɟɣ ɝɪɚɧɢɰɟ ɩɭɱɤɚ, ɚ ɡɧɚɱɢɬ ɢ ɪɚɡɥɢɱɧɵɦ ɫɤɨɪɨɫɬɹɦ ɱɚɫɬɢɰ, ɩɪɨɢɫɯɨɞɢɬ ɮɨɤɭɫɢɪɨɜɤɚ ɩɭɱɤɚ. ɏɨɪɨɲɭɸ ɮɨɤɭɫɢɪɨɜɤɭ ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɢɬɶ ɰɢɥɢɧɞɪɢɱɟɫɤɢɣ ɤɨɧɞɟɧɫɚɬɨɪ (ɪɢɫ. 5.8). ɗɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɤɨɧɞɟɧɫɚɬɨɪɚ ɨɛɪɚɬɧɨ
ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɪɚɞɢɭɫɭ E(r) = a/r, ɢɧɬɟɝɪɢɪɭɹ ɭɪɚɜɧɟɧɢɟ dU(r)/dr = a/r, ɦɨɠɧɨ ɧɚɣɬɢ ɤɨɷɮɮɢɰɢɟɧɬ a = (U2 – U1)/ln(R2/R1), ɚ ɡɧɚɱɢɬ E(r) == (U2 – U1)/(rln(R2/R1)), ɝɞɟ U1, U2, R1, R2 – ɩɨɬɟɧɰɢɚɥɵ ɢ ɪɚɞɢɭɫɵ ɜɧɭɬɪɟɧɧɟɝɨ ɢ ɜɧɟɲɧɟɝɨ ɰɢɥɢɧɞɪɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ɑɟɪɟɡ ɭɡɤɭɸ ɜɵɯɨɞɧɭɸ ɳɟɥɶ ɛɭɞɭɬ «ɭɫɩɟɲɧɨ» ɩɪɨɯɨɞɢɬɶ ɬɨɥɶɤɨ ɱɚɫɬɢɰɵ, ɢɦɟɸɳɢɟ ɤɪɭɝɨɜɵɟ ɬɪɚɟɤɬɨɪɢɢ ɢ ɫɤɨɪɨɫɬɢ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɭɫɥɨɜɢɸ: mv2/r = qE (ɨɫɬɚɥɶɧɵɟ ɩɨɩɚɞɭɬ ɧɚ ɫɬɟɧɤɢ ɰɢɥɢɧɞɪɚ), ɬ. ɟ. ɱɚɫɬɢɰɵ, ɢɦɟɸɳɢɟ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ: U0[ɷȼ]= q(U2 – U1)/(2ln(R2/R1)).
(5.21)
Ⱦɥɹ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɞɥɹ ɧɟɤɪɭɝɨɜɵɯ ɬɪɚɟɤɬɨɪɢɣ ɜ ɩɨɥɹɪɧɵɯ qa , ɫ ɭɱɟɬɨɦ ɤɨɨɪɞɢɧɚɬɚɯ: r − rϕ 2 = − mr ɩɨɫɬɨɹɧɫɬɜɚ ɫɟɤɬɨɪɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ 2 r ϕ = const , ɭɞɨɛɧɨ ɪɚɫɫɦɨɬɪɟɬɶ ɨɬɤɥɨɧɟɧɢɟ u ɬɪɚɟɤɬɨɪɢɢ ɨɬ ɤɪɭɝɨɜɨɣ: r = r0+u (u xm, “-“ ɩɪɢ x < xm). Ɉɤɨɥɨ ɤɚɬɨɞɚ ɜɨɡɧɢɤɚɟɬ «ɜɢɪɬɭɚɥɶɧɵɣ ɤɚɬɨɞ» (ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ) ɝɥɭɛɢɧɨɣ eUm=mv02/2 ɧɚ ɪɚɫɫɬɨɹɧɢɢ mv03 ɨɬ ɤɚɬɨɞɚ (ɪɢɫ.6.1). 18πej Ⱦɥɹ ɰɢɥɢɧɞɪɢɱɟɫɤɢɯ ɞɢɨɞɨɜ ɩɪɟɞɟɥɶɧɚɹ ɩɥɨɬɧɨɫɬɶ ɷɥɟɤɬɪɨɧɧɨɝɨ ɬɨɤɚ ɬɚɤ ɠɟ ɡɚɜɢɫɢɬ ɨɬ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɚɧɨɞɟ, ɤɚɤ ɫɬɟɩɟɧɶ «3/2», ɧɨ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ ɧɨɫɢɬ ɛɨɥɟɟ ɫɥɨɠɧɵɣ ɯɚɪɚɤɬɟɪ (ɤɚɤ ɪɟɡɭɥɶɬɚɬ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɹ ɉɭɚɫɫɨɧɚ ɜ ɰɢɥɢɧɞɪɢɱɟɫɤɢɯ ɤɨɨɪɞɢɧɚɬɚɯ) ɢ r ɨɩɢɫɵɜɚɟɬɫɹ ɫɩɟɰɢɚɥɶɧɨɣ ɮɭɧɤɰɢɟɣ Ȼɨɝɭɫɥɚɜɫɤɨɝɨ β ( a ) , ɝɞɟ ra ɢ rk – ɪɚɞɢɭɫɵ rk ɚɧɨɞɚ ɢ ɤɚɬɨɞɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ: xm =
U a3 / 2 . (6.7) 2 ra ra β ( ) rk Ⱦɥɹ ɩɨɥɧɨɝɨ ɬɨɤɚ, ɩɪɢɯɨɞɹɳɟɝɨ ɧɚ ɚɧɨɞ, I3/2=J3/2Sa (Sa=2πrala – ɩɥɨɳɚɞɶ ɚɧɨɞɚ.): J3/ 2 =
2 9π
J 3 / 2 [ Ⱥ] =
2e me
1 9π
U 3 / 2 [ ȼ]S a [ɫɦ 2 ] 2e U a3 / 2 S a = 2.33 ⋅ 10 −6 a r me 2 2 ra ra β ( ) ra2 [ɫɦ]β 2 ( a ) rk rk
(6.8)
- ɮɨɪɦɭɥɚ Ʌɟɧɝɦɸɪɚ-Ȼɨɝɭɫɥɚɜɫɤɨɝɨ. Ɂɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ Ȼɨɝɭɫɥɚɜɫɤɨɝɨ ɞɥɹ ɲɢɪɨɤɨɝɨ ɞɢɚɩɚɡɨɧɚ ra/rk ɦɨɠɧɨ ɧɚɣɬɢ ɜ ɬɚɛɥɢɰɚɯ [29]. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɦɟɠɭɬɤɟ ɨɩɢɫɵɜɚɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ:
β 2 (r / rk ) 2 / 3 r U (r ) = U a ( ) 3 / 2 ( 2 ) . ra β (ra / rk )
(6.9)
Ⱦɥɹ ɫɮɟɪɢɱɟɫɤɨɝɨ ɞɢɨɞɚ ɩɨɥɧɵɣ ɬɨɤ ɧɚ ɚɧɨɞ Ia: 3/ 2 4 2e U a3 / 2 −6 U a [ ȼ] I a [ Ⱥ] = = 29.3 ⋅ 10 , (6.10) 9 m e 2 rk 2 rk α ( ) α ( ) ra ra ɝɞɟ α(ra/rk) – ɬɚɛɭɥɢɪɨɜɚɧɧɚɹ ɮɭɧɤɰɢɹ Ʌɟɧɝɦɸɪɚ [30]. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ:
U (r ) = U (a )(
α (rk / r ) 2 ) . α (rk / ra )
(6.11)
§43. ɉɪɟɞɟɥɶɧɚɹ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ ɩɭɱɤɚ ɱɚɫɬɢɰ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɜ ɜɚɤɭɭɦɟ
ɉɥɨɬɧɨɫɬɶ ɬɨɤɚ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɦɟɠɞɭ ɷɥɟɤɬɪɨɞɚɦɢ ɫ ɨɞɢɧɚɤɨɜɵɦ ɩɨɬɟɧɰɢɚɥɨɦ ɬɚɤɠɟ ɨɝɪɚɧɢɱɟɧɚ ɢɡ-ɡɚ ɫɨɛɫɬɜɟɧɧɨɝɨ ɨɛɴɟɦɧɨɝɨ ɡɚɪɹɞɚ ɢ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɩɨɬɟɧɰɢɚɥɚ ɩɭɱɤɚ. Ɋɚɫɫɦɨɬɪɢɦ ɷɬɭ ɡɚɞɚɱɭ (ɡɚɞɚɱɭ Ȼɭɪɫɢɚɧɚ) ɧɚ ɩɪɢɦɟɪɟ ɩɨɬɨɤɚ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɞɥɢɧɵ d ɢɨɧɨɜ ɦɚɫɫɵ M, ɭɫɤɨɪɟɧɧɵɯ ɞɨ ɷɬɨɝɨ ɜ ɩɥɨɫɤɨɦ ɞɢɨɞɟ ɩɨɬɟɧɰɢɚɥɨɦ U0 (ɪɢɫ. 6.2). Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɦɟɠɭɬɤɟ ɡɚɞɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ ɉɭɚɫɫɨɧɚ: 4πj M / 2e d 2U =− . 2 dx U0 −U
(6.12)
ɍɫɬɨɣɱɢɜɨɟ ɪɟɲɟɧɢɟ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɩɪɢ ɝɪɚɧɢɱɧɵɯ ɭɫɥɨɜɢɹɯ U(0) = U(d) = 0 ɫɭɳɟɫɬɜɭɟɬ ɬɨɥɶɤɨ ɩɪɢ ɞɨɩɨɥɧɢɬɟɥɶɧɨɦ ɝɪɚɧɢɱɧɨɦ ɭɫɥɨɜɢɢ ɧɚ ɩɨɥɟ [31]:
Ε0 = dψ/dξ0 < 2 , ψ
ɝɞɟ
=
U/U0,
(6.13)
ξ
=
x/rd,
2
rd = Mv 0 /(4πne 2 ) - ɞɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ
ɩɭɱɤɚ. ɗɬɨ ɭɫɥɨɜɢɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɭɫɥɨɜɢɸ ɧɚ ɦɚɤɫɢɦɚɥɶɧɭɸ ɞɥɢɧɭ ɩɪɨɥɟɬɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ: d < (4 2 /3)rd = dm
Ɋɢɫ. 6.2. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ
(6.14).
ɗɤɫɬɪɟɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ dm ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɤɪɢɬɢɱɟɫɤɨɦɭ ɡɧɚɱɟɧɢɸ ɦɚɤɫɢɦɭɦɚ ɩɨɬɟɧɰɢɚɥɚ: (6.15) Um = (3/4)U0.
ɉɪɢ ɜɨɡɪɚɫɬɚɧɢɢ ɩɥɨɬɧɨɫɬɢ ɢɨɧɧɨɝɨ ɬɨɤɚ ɩɨɬɟɧɰɢɚɥ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɛɭɞɟɬ ɜɨɡɪɚɫɬɚɬɶ ɞɨ Um, ɡɚɬɟɦ ɫɤɚɱɤɨɦ ɜɨɡɧɢɤɚɟɬ «ɜɢɪɬɭɚɥɶɧɵɣ ɚɧɨɞ» ɫ Um = U0, ɨɬ ɤɨɬɨɪɨɝɨ ɩɪɨɢɡɨɣɞɟɬ ɨɬɪɚɠɟɧɢɟ ɱɚɫɬɢ ɢɨɧɨɜ ɨɛɪɚɬɧɨ ɜ ɫɬɨɪɨɧɭ ɢɫɬɨɱɧɢɤɚ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɱɟɝɨ ɬɨɤ ɧɚ ɤɨɥɥɟɤɬɨɪ ɭɦɟɧɶɲɢɬɫɹ ɜ 4.5 ɪɚɡɚ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɬɨɤ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɨɝɪɚɧɢɱɟɧ ɬɨɤɨɦ Ȼɭɪɫɢɚɧɚ: 8 jȻ = 9π
2e U 03 / 2 = 8 j3 / 2 . M d2
(6.16)
Ɇɟɯɚɧɢɡɦ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ Ȼɭɪɫɢɚɧɚ ɫɜɹɡɚɧ ɫ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɨɛɪɚɬɧɨɣ ɫɜɹɡɶɸ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ ɩɭɱɤɚ ɢ ɜɧɟɲɧɟɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɰɟɩɶɸ, ɤɨɝɞɚ ɩɨɜɵɲɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɩɭɱɤɚ ɧɚ ɦɚɥɭɸ ɜɟɥɢɱɢɧɭ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɜɵɡɵɜɚɟɬ ɞɚɥɶɧɟɣɲɟɟ ɟɝɨ ɩɨɜɵɲɟɧɢɟ. ɗɬɚ ɫɜɹɡɶ ɜɨɡɧɢɤɚɟɬ, ɤɨɝɞɚ ɞɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ ɩɭɱɤɚ ɫɬɚɧɨɜɢɬɫɹ ɦɟɧɶɲɟ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɷɥɟɤɬɪɨɞɚɦɢ. Ɍɨɱɧɨ ɬɚɤɨɟ ɠɟ ɨɝɪɚɧɢɱɟɧɢɟ ɫɭɳɟɫɬɜɭɟɬ ɢ ɞɥɹ ɩɨɬɨɤɚ ɷɥɟɤɬɪɨɧɨɜ ɜ ɜɚɤɭɭɦɟ. Ⱦɚɠɟ ɜ ɫɥɭɱɚɟ ɫɤɨɦɩɟɧɫɢɪɨɜɚɧɧɨɝɨ ɩɭɱɤɚ ɷɥɟɤɬɪɨɧɨɜ, ɤɨɝɞɚ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɣ ɡɚɪɹɞ ɷɥɟɤɬɪɨɧɨɜ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɫɤɨɦɩɟɧɫɢɪɨɜɚɧ ɢɨɧɚɦɢ (ɡɚɞɚɱɚ ɉɢɪɫɚ), ɜɨɡɧɢɤɚɟɬ ɨɝɪɚɧɢɱɟɧɢɟ ɧɚ ɦɚɤɫɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɭɸ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ ɢɡ-ɡɚ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ, ɬɚɤɠɟ ɩɪɢɜɨɞɹɳɟɣ ɤ ɨɛɪɚɡɨɜɚɧɢɸ ɜɢɪɬɭɚɥɶɧɨɝɨ ɤɚɬɨɞɚ ɢ ɡɚɩɢɪɚɧɢɸ ɩɭɱɤɚ. Ɏɢɡɢɱɟɫɤɚɹ ɩɪɢɱɢɧɚ ɩɢɪɫɨɜɫɤɨɣ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɬɚ ɠɟ, ɱɬɨ ɢ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ Ȼɭɪɫɢɚɧɚ, – ɩɨɥɨɠɢɬɟɥɶɧɚɹ ɨɛɪɚɬɧɚɹ ɫɜɹɡɶ ɷɥɟɤɬɪɨɧɨɜ ɩɭɱɤɚ ɫ ɷɥɟɤɬɪɨɧɚɦɢ ɜɧɟɲɧɟɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɰɟɩɢ, ɤɨɬɨɪɚɹ ɜɨɡɧɢɤɚɟɬ, ɟɫɥɢ ɞɟɛɚɟɜɫɤɢɣ ɪɚɞɢɭɫ ɩɭɱɤɚ ɫɬɚɧɨɜɢɬɫɹ ɦɟɧɶɲɟ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɷɥɟɤɬɪɨɞɚɦɢ. Ʉɚɱɟɫɬɜɟɧɧɨ ɷɬɢ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɫɪɨɞɧɢ ɩɭɱɤɨɜɨɣ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ, ɩɪɢ ɤɨɬɨɪɨɣ ɷɧɟɪɝɢɹ ɧɚɩɪɚɜɥɟɧɧɨɝɨ ɞɜɢɠɟɧɢɹ ɩɟɪɟɞɚɟɬɫɹ ɜ ɷɧɟɪɝɢɸ ɩɥɚɡɦɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ (ɫɦ. §37). ɍɫɥɨɜɢɟɦ ɭɫɬɨɣɱɢɜɨɫɬɢ ɧɚ ɞɥɢɧɭ ɩɪɨɥɟɬɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ ɜ ɫɥɭɱɚɟ ɫɤɨɦɩɟɧɫɢɪɨɜɚɧɧɨɝɨ ɩɨɬɨɤɚ ɹɜɥɹɟɬɫɹ d < πrd, ɚ ɩɪɟɞɟɥɶɧɚɹ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ (ɬɨɤ ɉɢɪɫɚ) ɪɚɜɧɚ:
jɉ =
2e U 03 / 2 9π 2 ≈ j3 / 2 . 4 4(1 + (m / M ) 1 / 3 ) m d 2
π
(6.17)
Ɋɚɫɯɨɠɞɟɧɢɟ ɩɭɱɤɨɜ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɨɛɫɬɜɟɧɧɨɝɨ ɨɛɴɟɦɧɨɝɨ ɡɚɪɹɞɚ
Ɉɫɧɨɜɧɨɣ ɩɪɨɛɥɟɦɨɣ ɬɪɚɧɫɩɨɪɬɢɪɨɜɤɢ ɢɧɬɟɧɫɢɜɧɵɯ ɩɭɱɤɨɜ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɹɜɥɹɟɬɫɹ ɢɯ ɪɚɫɯɨɠɞɟɧɢɟ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɨɛɫɬɜɟɧɧɨɝɨ ɨɛɴɟɦɧɨɝɨ ɡɚɪɹɞɚ. Ⱦɥɹ ɨɬɵɫɤɚɧɢɹ ɮɨɪɦɵ ɩɭɱɤɚ ɧɟɨɛɯɨɞɢɦɨ ɪɟɲɚɬɶ ɭɪɚɜɧɟɧɢɟ ɉɭɚɫɫɨɧɚ (ɞɥɹ ɥɟɧɬɨɱɧɨɝɨ ɩɭɱɤɚ ɞɜɭɦɟɪɧɨɟ): d 2U d 2U + = −4πρ ( x, y ) , (6.18) dx 2 dy 2 ɚ ɬɚɤɠɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɞɥɹ ɝɪɚɧɢɱɧɨɣ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ. ȼ ɫɥɭɱɚɟ ɛɟɫɤɨɧɟɱɧɨɝɨ ɥɟɧɬɨɱɧɨɝɨ ɩɭɱɤɚ (ɪɢɫ.6.3), ɭ ɤɨɬɨɪɨɝɨ ɲɢɪɢɧɚ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ ɬɨɥɳɢɧɵ 2X, ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɧɚ ɝɪɚɧɢɰɟ ɜɦɟɫɬɨ ɭɪɚɜɧɟɧɢɹ ɉɭɚɫɫɨɧɚ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɟɨɪɟɦɭ Ƚɚɭɫɫɚ ɨ ɪɚɜɟɧɫɬɜɟ ɩɨɬɨɤɚ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɱɟɪɟɡ ɩɨɜɟɪɯɧɨɫɬɶ ɢ ɡɚɪɹɞɚ, ɡɚɤɥɸɱɟɧɧɨɝɨ ɜ ɨɛɴɟɦɟ,
ɨɝɪɚɧɢɱɟɧɧɨɦ ɷɬɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ. Ɍɨɝɞɚ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɧɚ ɝɪɚɧɢɰɟ: Ex = J/(2ε0v)=J(/2ε0 2eU 0 / m ),
(6.19)
ɝɞɟ J – ɥɢɧɟɣɧɚɹ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ (ɬɨɤ ɧɚ ɟɞɢɧɢɰɭ ɲɢɪɢɧɵ ɛɟɫɤɨɧɟɱɧɨɝɨ ɥɟɧɬɨɱɧɨɝɨ ɩɭɱɤɚ), U0 – ɩɨɬɟɧɰɢɚɥ, ɤɨɬɨɪɵɦ ɛɵɥ ɭɫɤɨɪɟɧ ɩɭɱɨɤ ɞɨ ɜɯɨɞɚ ɜ ɩɪɨɥɟɬɧɵɣ ɩɪɨɦɟɠɭɬɨɤ. Ɋɟɲɚɹ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ mx = eE x , ɩɨɥɭɱɢɦ ɩɪɨɮɢɥɶ ɝɪɚɧɢɰɵ ɩɭɱɤɚ, ɤɨɬɨɪɚɹ ɨɩɢɫɵɜɚɟɬɫɹ ɡɚɜɢɫɢɦɨɫɬɶɸ x(z): x = x0 + tgγ⋅z + pz2/2 ,
(6.20)
Ɋɢɫ. 6.3. ɉɥɨɫɤɢɣ ɷɥɟɤɬɪɨɧɧɵɣ ɥɟɧɬɨɱɧɵɣ ɩɭɱɨɤ
J
, ɝɞɟ γ - ɭɝɨɥ 2e 3 / 2 4ε 0 U0 m ɫɯɨɞɢɦɨɫɬɢ ɩɭɱɤɚ ɧɚ ɜɯɨɞɟ, ɬ. ɟ. ɭɝɨɥ ɦɟɠɞɭ ɧɚɩɪɚɜɥɟɧɢɟɦ ɫɤɨɪɨɫɬɢ ɝɪɚɧɢɱɧɨɝɨ ɷɥɟɤɬɪɨɧɚ ɢ ɧɚɩɪɚɜɥɟɧɢɟɦ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɩɭɱɤɚ ɩɨ ɨɫɢ z. Ɇɟɫɬɨɩɨɥɨɠɟɧɢɟ ɫɚɦɨɝɨ ɭɡɤɨɝɨ ɜ ɩɨɩɟɪɟɱɧɨɦ ɪɚɡɦɟɪɟ ɭɱɚɫɬɤɚ ɩɭɱɤɚ, ɬɚɤ ɧɚɡɵɜɚɟɦɨɝɨ «ɤɪɨɫɫɨɜɟɪɚ» xɤɪ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɭɫɥɨɜɢɹ: ɝɞɟ
p=
dx/dz = 0, ɬ.ɟ. zɤɪ= tgγ/p.
(6.21)
Ⱦɥɹ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɩɭɱɤɚ, ɜɥɟɬɚɸɳɟɝɨ ɜ ɩɪɨɥɟɬɧɵɣ ɭɱɚɫɬɨɤ ɩɚɪɚɥɥɟɥɶɧɨ ɨɫɢ z ɫ ɧɚɱɚɥɶɧɵɦ ɪɚɞɢɭɫɨɦ r0, ɡɚɜɢɫɢɦɨɫɬɶ ɪɚɞɢɭɫɚ ɩɭɱɤɚ r(z) ɡɚɞɚɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ: z 4 e U 03 / 4 = 2m I 1 / 2 r0
R
³ 1
Ɋɢɫ. 6.4. Ɋɚɫɯɨɞɢɦɨɫɬɶ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɷɥɟɤɬɪɨɧɧɨɝɨ ɩɭɱɤɚ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɨɛɫɬɜɟɧɧɨɝɨ ɨɛɴɟɦɧɨɝɨ ɡɚɪɹɞɚ
U 03 / 4 [ɤȼ] R dς = 32.3 1 / 2 , I [ ɦȺ] ³1 ln ς ln ς
dς
(6.22)
ɝɞɟ I – ɩɨɥɧɵɣ ɬɨɤ ɩɭɱɤɚ, ɭɫɤɨɪɟɧɧɨɝɨ ɩɨɬɟɧɰɢɚɥɨɦ U0, R=r/r0 (ɱɢɫɥɨɜɨɣ ɤɨɷɮɮɢɰɢɟɧɬ ɞɚɧ ɞɥɹ ɷɥɟɤɬɪɨɧɧɨɝɨ ɩɭɱɤɚ). Ⱦɥɹ ɫɯɨɞɹɳɟɝɨɫɹ ɩɭɱɤɚ, ɜɯɨɞɹɳɟɝɨ ɜ ɩɪɨɥɟɬɧɵɣ ɩɪɨɦɟɠɭɬɨɤ ɩɨɞ ɭɝɥɨɦ γ ɤ ɨɫɢ z (ɪɢɫ. 6.4): R
z 2e U0 ³ = r0 m 1
dς 8e 2e I ln ς + U 0 ⋅ tg 2 γ mU 0 m
.
(6.23)
Ɋɚɞɢɭɫ ɩɭɱɤɚ ɜ ɧɚɢɛɨɥɟɟ ɭɡɤɨɦ ɦɟɫɬɟ (ɜ ɤɪɨɫɫɨɜɟɪɟ) ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ r U 3/ 2 e 2 U 3 / 2 [ɤȼ] 2 ɫɨɨɬɧɨɲɟɧɢɹ: ln 0 = 0 tg γ ≈ 1.04 ⋅ 10 3 0 tg γ , (6.24) rmin I 2m I [ ɦȺ] ɝɞɟ ɱɢɫɥɟɧɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɞɚɧ ɞɥɹ ɷɥɟɤɬɪɨɧɧɨɝɨ ɩɭɱɤɚ. ɉɪɢ ɷɬɨɦ ɧɟ ɛɵɥɚ ɭɱɬɟɧɚ ɫɢɥɚ Ʌɨɪɟɧɰɚ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɞɜɢɠɭɳɭɸɫɹ ɡɚɪɹɠɟɧɧɭɸ ɱɚɫɬɢɰɭ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ. ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɷɬɚ ɮɨɤɭɫɢɪɭɸɳɚɹ ɫɢɥɚ ɜ ɫɨɛɫɬɜɟɧɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɬɨɤɚ ɩɭɱɤɚ ɛɭɞɟɬ ɫɭɳɟɫɬɜɟɧɧɚ ɬɨɥɶɤɨ ɩɪɢ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɢɯ ɫɤɨɪɨɫɬɹɯ ɱɚɫɬɢɰ. Ɋɚɫɯɨɠɞɟɧɢɟ ɩɭɱɤɨɜ ɨɝɪɚɧɢɱɟɧɧɵɯ ɩɨɩɟɪɟɱɧɵɯ ɪɚɡɦɟɪɨɜ ɫɥɟɞɭɟɬ ɭɱɢɬɵɜɚɬɶ ɧɟ ɬɨɥɶɤɨ ɜ ɩɪɨɥɟɬɧɵɯ ɩɪɨɦɟɠɭɬɤɚɯ, ɧɨ ɢ ɜ ɷɥɟɤɬɪɨɧɧɵɯ ɢɥɢ ɢɨɧɧɵɯ ɩɭɲɤɚɯ. ɉɢɪɫɨɦ ɛɵɥɨ ɩɨɤɚɡɚɧɨ, ɱɬɨ ɦɨɠɧɨ ɩɨɞɨɛɪɚɬɶ ɮɨɪɦɭ ɨɤɚɣɦɥɹɸɳɢɯ ɩɭɱɨɤ ɩɪɨɦɟɠɭɬɨɱɧɵɯ ɷɥɟɤɬɪɨɞɨɜ ɬɚɤ, ɱɬɨɛɵ ɤɨɦɩɟɧɫɢɪɨɜɚɬɶ ɪɚɫɬɚɥɤɢɜɚɸɳɟɟ ɞɟɣɫɬɜɢɟ ɨɛɴɟɦɧɨɝɨ ɡɚɪɹɞɚ ɩɭɱɤɚ ɢ ɫɨɯɪɚɧɢɬɶ ɩɪɹɦɨɥɢɧɟɣɧɨɫɬɶ ɟɝɨ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ (ɩɭɲɤɢ ɉɢɪɫɚ). Ⱦɥɹ ɷɬɨɝɨ ɧɟɨɛɯɨɞɢɦɨ, ɱɬɨɛɵ ɞɥɹ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɜɧɟ ɩɭɱɤɚ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɟɝɨ ɜ ɫɥɭɱɚɟ ɩɥɨɫɤɨɣ ɝɟɨɦɟɬɪɢɢ ɭɪɚɜɧɟɧɢɸ d 2U d 2U Ɋɢɫ. 6.5. Ƚɟɨɦɟɬɪɢɹ ɷɤɜɢɩɨɬɟɧɰɢɚɥɟɣ ɜ ɩɭɲɤɟ Ʌɚɩɥɚɫɚ: ɧɚ + = 0, 2 2 ɉɢɪɫɚ, ɮɨɪɦɢɪɭɸɳɟɣ ɩɚɪɚɥɥɟɥɶɧɵɣ ɩɭɱɨɤ dx dy ɝɪɚɧɢɰɟ ɩɭɱɤɚ ɜɵɩɨɥɧɹɥɨɫɶ ɭɫɥɨɜɢɟ dU/dy = 0. Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɟ Ʌɚɩɥɚɫɚ ɫ x ɭɱɟɬɨɦ ɷɬɨɝɨ ɭɫɥɨɜɢɹ ɢ ɡɚɜɢɫɢɦɨɫɬɢ ɩɨɬɟɧɰɢɚɥɚ ɧɚ ɨɫɢ U ( x) = U (a)( ) 4 / 3 d ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ ɬɪɟɛɭɟɦɭɸ ɝɟɨɦɟɬɪɢɸ ɷɥɟɤɬɪɨɞɨɜ, ɤɨɬɨɪɚɹ ɞɥɹ ɩɥɨɫɤɨɝɨ ɫɥɭɱɚɹ ɡɚɞɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ: 4 ( x 2 + y 2 ) 2 / 3 cos( arctg ( y / x)) = U . 3
(6.25)
ɍɝɨɥ ɧɚɤɥɨɧɚ ɩɥɨɫɤɨɫɬɢ ɤɚɬɨɞɚ (U = 0) ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɩɭɱɤɚ arctg(y/x) = 3π/8 = 67.5ɨ. ȼ ɫɥɭɱɚɟ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɝɟɨɦɟɬɪɢɢ ɱɢɫɥɟɧɧɵɣ ɪɚɫɱɟɬ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɭɝɨɥ ɧɚɤɥɨɧɚ ɷɥɟɤɬɪɨɞɚ, ɩɪɢɥɟɝɚɸɳɟɝɨ ɤ ɤɚɬɨɞɭ, ɬɚɤɠɟ ɫɨɫɬɚɜɥɹɟɬ 67.5ɨ (ɪɢɫ .6.5).
ȽɅȺȼȺ 7 ɗɆɂɋɋɂɈɇɇȺə ɗɅȿɄɌɊɈɇɂɄȺ §44. Ɍɟɪɦɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɂɫɩɭɫɤɚɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɧɚɝɪɟɬɵɦɢ ɩɪɨɜɨɞɹɳɢɦɢ ɦɚɬɟɪɢɚɥɚɦɢ ɧɚɡɵɜɚɟɬɫɹ ɬɟɪɦɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɟɣ. ɗɬɨ ɹɜɥɟɧɢɟ ɛɵɥɨ ɨɛɧɚɪɭɠɟɧɨ ɜ 1883 ɝ. ɗɞɢɫɨɧɨɦ. Ⱥɧɚɥɢɬɢɱɟɫɤɢɣ ɪɚɫɱɟɬ ɩɥɨɬɧɨɫɬɢ ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɨɝɨ ɬɨɤɚ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢɫɯɨɞɹ ɢɡ ɦɨɞɟɥɢ Ɂɨɦɦɟɪɮɟɥɶɞɚ ɨ ɧɚɯɨɠɞɟɧɢɢ ɷɥɟɤɬɪɨɧɨɜ ɜ ɦɟɬɚɥɥɟ ɤɚɤ ɜ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɹɦɟ. ɗɥɟɤɬɪɨɧɵ ɜ ɦɟɬɚɥɥɟ, ɤɚɠɞɵɣ ɢɡ ɤɨɬɨɪɵɯ ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɟɣ:
ψk( r& ) =
&& 1 exp( i k r), L3 / 2
(7.1)
ɝɞɟ L3 = V – ɨɛɴɟɦ ɦɟɬɚɥɥɚ, ɜɨɥɧɨɜɨɣ ɜɟɤɬɨɪ k = 2π/L, ɩɨɞɱɢɧɹɸɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɸ Ɏɟɪɦɢ-Ⱦɢɪɚɤɚ, ɬ. ɟ. ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɱɚɫɬɢɰ ɜ ɨɞɧɨɦ ɫɨɫɬɨɹɧɢɢ f(E) =
1 . E − EF 1 + exp( ) k BT
(7.2)
ɉɪɢ Ɍ = 0 ɜɫɟ ɷɥɟɤɬɪɨɧɵ ɧɚɯɨɞɹɬɫɹ ɜɧɭɬɪɢ ɫɮɟɪɵ Ɏɟɪɦɢ. ɋ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ «ɩɥɨɬɧɨɫɬɶ» ɷɥɟɤɬɪɨɧɨɜ ɪɚɜɧɚ 1/h3, ɚ ɬɚɤɠɟ ɩɪɢɧɰɢɩɚ ɉɚɭɥɢ ɨ ɞɜɭɯ ɜɨɡɦɨɠɧɵɯ ɨɪɢɟɧɬɚɰɢɹɯ ɫɩɢɧɚ, ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ, «ɧɚɯɨɞɹɳɢɯɫɹ» ɜ ɩɪɟɞɟɥɚɯ ɫɮɟɪɵ Ɏɟɪɦɢ ɫ ɪɚɞɢɭɫɨɦ kF: N = 2(1/h3)(4/3)πpF3V. ɂɦɩɭɥɶɫ, ɤɨɬɨɪɵɣ ɢɦɟɸɬ ɷɥɟɤɬɪɨɧɵ ɧɚ ɫɮɟɪɟ Ɏɟɪɦɢ: pF = h(3n/8π)1/3, ɝɞɟ n = N/V – ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ ɜ 1 ɫɦ3. ɗɧɟɪɝɢɹ Ɏɟɪɦɢ EF = pF2/(2m) =
!2 (3π 2 n) 2 / 3 . 2m
(7.3)
Ʉɨɥɢɱɟɫɬɜɨ ɱɚɫɬɢɰ ɫ ɷɧɟɪɝɢɟɣ ɦɟɧɶɲɟ E: n(E) =
1 3π
2
(
2mE 3 / 2 ) , !2
(7.4)
ɬɨɝɞɚ ɩɥɨɬɧɨɫɬɶ ɱɚɫɬɢɰ (ɱɢɫɥɨ ɱɚɫɬɢɰ, ɢɦɟɸɳɢɯ ɷɧɟɪɝɢɸ ɨɬ E ɞɨ E + dE)
ρ(E) = dn =
1 2π
2
(
2m 3 / 2 1 / 2 ) E dE . !2
ɋ ɭɱɟɬɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ɏɟɪɦɢ-Ⱦɢɪɚɤɚ:
Ɋɢɫ. 7.1. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɜ ɦɟɬɚɥɥɟ ɩɨ ɷɧɟɪɝɢɹɦ
ρ(E) =
1 2π 2
(
2m 3 / 2 ) !2
E 1 / 2 dE . E − EF 1 + exp( ) k BT
(7.5)
ɉɪɢ ɚɛɫɨɥɸɬɧɨɦ ɧɭɥɟ ɬɟɦɩɟɪɚɬɭɪɵ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɨɜ ɦɟɬɚɥɥɚ ɧɟ ɦɨɠɟɬ ɛɵɬɶ ɛɨɥɶɲɟ ɷɧɟɪɝɢɢ Ɏɟɪɦɢ, ɩɨɷɬɨɦɭ ɧɢ ɨɞɢɧ ɷɥɟɤɬɪɨɧ ɧɟ ɦɨɠɟɬ ɜɵɣɬɢ ɢɡ ɦɟɬɚɥɥɚ, ɚ ɮɭɧɤɰɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɨɛɪɵɜɚɟɬɫɹ ɩɪɢ EF (ɪɢɫ. 7.1). ɉɪɢ Ɍ > 0 ɨɛɪɵɜ ɫɝɥɚɠɢɜɚɟɬɫɹ, ɩɨɹɜɥɹɟɬɫɹ «ɯɜɨɫɬ» ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɫ ɷɧɟɪɝɢɹɦɢ ɛɨɥɶɲɟ EF, ɢɦɟɧɧɨ ɭ ɷɬɢɯ ɷɥɟɤɬɪɨɧɨɜ, ɤɨɥɢɱɟɫɬɜɨ ɤɨɬɨɪɵɯ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ ɪɚɫɬɟɬ ɫ ɪɨɫɬɨɦ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨɜɟɪɯɧɨɫɬɢ, ɩɨɹɜɥɹɟɬɫɹ ɧɟɧɭɥɟɜɚɹ ɜɟɪɨɹɬɧɨɫɬɶ ɩɪɟɨɞɨɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ ɧɚ ɝɪɚɧɢɰɟ ɦɟɬɚɥɥɚ. ɉɨɷɬɨɦɭ ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɵɣ ɬɨɤ ɡɚɦɟɬɟɧ ɬɨɥɶɤɨ ɞɥɹ ɧɚɝɪɟɬɵɯ ɬɟɥ. ȿɝɨ ɜɟɥɢɱɢɧɚ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟɦ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨ ɧɨɪɦɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɷɧɟɪɝɢɢ Wx ɜ ɩɪɟɞɟɥɚɯ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɨɬ Wa ɞɨ ∞ , ɝɞɟ Wa - ɜɵɫɨɬɚ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ. ɋ ɭɱɟɬɨɦ ɜɟɪɨɹɬɧɨɫɬɢ ɩɪɟɨɞɨɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ, ɚ ɬɚɤɠɟ ɫ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ ɞɥɹ ɬɟɪɦɨɷɥɟɤɬɪɨɧɨɜ Wx - EF >> kBT , ɩɥɨɬɧɨɫɬɶ ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɨɝɨ ɬɨɤɚ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɚ ɮɨɪɦɭɥɨɣ Ɋɢɱɚɪɞɫɨɧɚ-Ⱦɷɲɦɚɧɚ: j t = AT 2 exp( −
eϕ a ), kT
(7.6)
ɝɞɟ ϕa = Wa - EF – ɪɚɛɨɬɚ ɜɵɯɨɞɚ ɷɥɟɤɬɪɨɧɚ ɢɡ ɦɚɬɟɪɢɚɥɚ ɤɚɬɨɞɚ, ɪɚɜɧɚɹ ɧɚɢɦɟɧɶɲɟɣ ɷɧɟɪɝɢɢ, ɤɨɬɨɪɭɸ ɧɭɠɧɨ ɫɨɨɛɳɢɬɶ ɷɥɟɤɬɪɨɧɚɦ ɞɥɹ ɢɯ ɷɦɢɫɫɢɢ, kB – ɩɨɫɬɨɹɧɧɚɹ Ȼɨɥɶɰɦɚɧɚ. ȼɟɥɢɱɢɧɭ A = A0D , ɭɱɢɬɵɜɚɸɳɭɸ ɩɪɨɡɪɚɱɧɨɫɬɶ ɛɚɪɶɟɪɚ ɦɟɠɞɭ ɦɟɬɚɥɥɨɦ ɢ ɜɚɤɭɭɦɨɦ D = (1 - r ), r – ɤɨɷɮɮɢɰɢɟɧɬ ɨɬɪɚɠɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɨɬ ɛɚɪɶɟɪɚ, ɭɫɪɟɞɧɟɧɧɵɣ ɩɨ ɷɧɟɪɝɢɹɦ ɷɥɟɤɬɪɨɧɨɜ, ɢɧɨɝɞɚ ɧɚɡɵɜɚɸɬ «ɩɨɫɬɨɹɧɧɨɣ Ɋɢɱɚɪɞɫɨɧɚ», ɝɞɟ 2
A0 [
4π mek B Ⱥ ]= = 120 .4 2 2 h3 ɫɦ Ʉ
(7.7)
- ɭɧɢɜɟɪɫɚɥɶɧɚɹ ɩɨɫɬɨɹɧɧɚɹ. ɋɥɟɞɭɟɬ ɭɱɟɫɬɶ, ɱɬɨ ɪɚɛɨɬɚ ɜɵɯɨɞɚ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ (ɜɫɥɟɞɫɬɜɢɟ ɬɟɩɥɨɜɨɝɨ ɪɚɫɲɢɪɟɧɢɹ), ɨɛɵɱɧɨ ɷɬɚ ɡɚɜɢɫɢɦɨɫɬɶ ɥɢɧɟɣɧɚɹ:
ϕa = ϕ0 + α(T-T0),
(7.8)
α = dϕ/dT|T=To = 10-5 ÷ 10-4 ɷȼ/ɝɪɚɞ – ɬɟɦɩɟɪɚɬɭɪɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ, ɤɨɬɨɪɵɣ ɦɨɠɟɬ ɛɵɬɶ ɤɚɤ ɩɨɥɨɠɢɬɟɥɶɧɵɦ, ɬɚɤ ɢ ɨɬɪɢɰɚɬɟɥɶɧɵɦ. Ɂɧɚɱɟɧɢɟ ɩɨɫɬɨɹɧɧɨɣ Ɋɢɱɚɪɞɫɨɧɚ Ⱥ ɞɥɹ ɪɚɡɧɵɯ ɦɟɬɚɥɥɨɜ ɢɡɦɟɧɹɸɬɫɹ ɨɬ 15 ɞɨ 350 Ⱥ/(ɫɦ2⋅Ʉ2). ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɪɚɛɨɬɵ ɜɵɯɨɞɚ ϕa ɢ «ɩɨɫɬɨɹɧɧɨɣ» Ɋɢɱɚɪɞɫɨɧɚ Ⱥ ɦɨɠɧɨ ɩɪɨɜɟɫɬɢ ɩɨ ɦɟɬɨɞɭ «ɩɪɹɦɨɣ Ɋɢɱɚɪɞɫɨɧɚ», ɫɬɪɨɹ ɩɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɞɚɧɧɵɦ ɡɚɜɢɫɢɦɨɫɬɶ ln(jT/T2) ɨɬ 1/T. ɉɨ ɬɚɧɝɟɧɫɭ ɭɝɥɚ ɧɚɤɥɨɧɚ ɩɨɥɭɱɟɧɧɨɣ ɩɪɹɦɨɣ ɨɩɪɟɞɟɥɹɸɬ ɪɚɛɨɬɭ ɜɵɯɨɞɚ ϕa, ɚ ɬɨɱɤɚ ɩɟɪɟɫɟɱɟɧɢɹ ɩɪɹɦɨɣ ɫ ɨɫɶɸ ɨɪɞɢɧɚɬ ɞɚɟɬ ɡɧɚɱɟɧɢɟ ln(A) .
Ɂɚɜɢɫɢɦɨɫɬɶ ɩɥɨɬɧɨɫɬɢ ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɨɝɨ ɬɨɤɚ (7.6) ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢɡ ɭɫɥɨɜɢɹ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ, ɟɫɥɢ ɪɚɫɫɱɢɬɚɬɶ ɩɨɬɨɤ ɷɥɟɤɬɪɨɧɨɜ ɜ ɜɚɤɭɭɦ: jɌ = enevɫɪ/4, ɝɞɟ
n e = 2(
me k B T 3 / 2 eϕ ) exp(− a ) k BT 2π!
(7.9) (7.10)
8kTe - ɫɪɟɞɧɹɹ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɚɹ ɫɤɨɪɨɫɬɶ. πm e ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ (ɢɥɢ ɩɪɟɧɟɛɪɟɠɢɦɨ ɦɚɥɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ) ɭɫɤɨɪɹɸɳɟɝɨ ɷɥɟɤɬɪɨɧɵ ɜɧɟɲɧɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɷɦɢɬɢɪɨɜɚɧɧɵɟ ɷɥɟɤɬɪɨɧɵ ɫɨɡɞɚɸɬ ɨɤɨɥɨ ɩɨɜɟɪɯɧɨɫɬɢ ɨɬɪɢɰɚɬɟɥɶɧɵɣ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɣ ɡɚɪɹɞ, ɨɝɪɚɧɢɱɢɜɚɸɳɢɣ ɬɨɤ ɬɟɪɦɨɷɦɢɫɫɢɢ. ɉɨɷɬɨɦɭ, ɜ ɫɥɭɱɚɟ ɦɚɥɵɯ ɧɚɩɪɹɠɟɧɢɣ ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɵɣ ɬɨɤ ɦɨɠɧɨ ɩɪɢɪɚɜɧɹɬɶ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ j3/2, 3/2 ɡɚɜɢɫɢɦɨɫɬɶ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ jɌ ɨɬ ɧɚɩɪɹɠɟɧɢɹ jɌ ∼ Ua . ɉɪɢ ɞɚɥɶɧɟɣɲɟɦ ɭɜɟɥɢɱɟɧɢɢ Ua ɨɛɴɟɦɧɵɣ ɡɚɪɹɞ ɭ ɤɚɬɨɞɚ ɢɫɱɟɡɚɟɬ ɢ, ɤɚɡɚɥɨɫɶ ɛɵ, ɬɨɤ ɞɨɥɠɟɧ ɜɵɣɬɢ ɧɚ ɧɚɫɵɳɟɧɢɟ, ɤɨɝɞɚ ɜɫɟ ɷɦɢɬɢɪɨɜɚɧɧɵɟ ɷɥɟɤɬɪɨɧɵ ɭɯɨɞɹɬ ɧɚ ɚɧɨɞ, ɢ ɧɟ ɡɚɜɢɫɟɬɶ ɨɬ Ua. Ɉɞɧɚɤɨ, ɤɚɤ ɩɨɤɚɡɚɥɢ ɷɤɫɩɟɪɢɦɟɧɬɵ, ɩɪɢ ɞɚɥɶɧɟɣɲɟɦ ɭɜɟɥɢɱɟɧɢɢ Ua ɬɨɤ ɷɦɢɫɫɢɢ ɩɪɨɞɨɥɠɚɟɬ ɦɟɞɥɟɧɧɨ ɪɚɫɬɢ. Ɋɨɫɬ ɷɥɟɤɬɪɨɧɧɨɝɨ ɬɨɤɚ ɷɦɢɫɫɢɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜɫɥɟɞɫɬɜɢɟ ɫɧɢɠɟɧɢɹ ɪɚɛɨɬɵ ɜɵɯɨɞɚ ɷɥɟɤɬɪɨɧɚ ɢɡ ɬɜɟɪɞɨɝɨ ɬɟɥɚ (ɩɨɧɢɠɟɧɢɹ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ)
- ɩɥɨɬɧɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ, v ɫɪ =
ϕȿ = ϕa - ∆ϕɲ
(7.11)
ɧɚɡɵɜɚɟɬɫɹ ɷɮɮɟɤɬɨɦ ɒɨɬɬɤɢ (ɪɢɫ. 7.2). ɉɨɬɟɧɰɢɚɥ ɩɨɥɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ x ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ ɦɟɬɚɥɥɚ ɫ ɭɱɟɬɨɦ ɫɢɥ ɡɟɪɤɚɥɶɧɨɝɨ ɨɬɨɛɪɚɠɟɧɢɹ ɡɚɪɹɞɚ ɢ ɜɧɟɲɧɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ E ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɜ ɜɢɞɟ: U(x) = EF + ϕa - e2/4x – eEx.
(7.12)
ɋɧɢɠɟɧɢɟ ɪɚɛɨɬɵ ɜɵɯɨɞɚ ɦɨɠɧɨ ɨɰɟɧɢɬɶ ɢɡ ɫɨɨɬɧɨɲɟɧɢɹ, ɩɪɢɪɚɜɧɢɜɚɹ ɧɚ ɜɟɪɲɢɧɟ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɯɨɥɦɚ ɫɢɥɵ ɬɨɪɦɨɠɟɧɢɹ ɜɧɭɬɪɶ ɦɟɬɚɥɥɚ ɢ ɫɢɥɵ ɭɫɤɨɪɟɧɢɹ ɜɨ ɜɧɟ: eE = e2/4x2m, ɬɨɝɞɚ ɩɨɥɨɠɟɧɢɟ ɦɚɤɫɢɦɭɦɚ xm= e / 4 E ,
(7.13)
ɚ ɩɨɬɟɧɰɢɚɥ ɜ ɦɚɤɫɢɦɭɦɟ Um = EF + ϕa - e3/2E1/2.
(7.14)
ɋɧɢɠɟɧɢɟ ɪɚɛɨɬɵ ɜɵɯɨɞɚ: e∆ϕɲ[ɷȼ] = e3/2E1/2 = 3.79⋅E1/2 [ȼ/ɫɦ]. ɉɥɨɬɧɨɫɬɶ ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɨɝɨ ɬɨɤɚ ɫ ɭɱɟɬɨɦ ɷɮɮɟɤɬɚ ɒɨɬɬɤɢ:
(7.15)
jɌɒ = jTexp(e3/2E1/2/kBT) = jTexp(4.39E1/2[ȼ/ɫɦ]/T[K]).
(7.16)
§45. Ⱥɜɬɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ
ȼ ɩɪɢɫɭɬɫɬɜɢɢ ɜɧɟɲɧɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜɵɫɨɤɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ E (106÷107 ȼ/ɫɦ), ɩɨɦɢɦɨ ɭɜɟɥɢɱɟɧɢɹ ɬɨɤɚ ɷɦɢɫɫɢɢ ɡɚ ɫɱɟɬ ɫɧɢɠɟɧɢɹ ɪɚɛɨɬɵ ɜɵɯɨɞɚ (ɷɮɮɟɤɬɚ ɒɨɬɬɤɢ), ɢɡ-ɡɚ ɨɝɪɚɧɢɱɟɧɧɨɫɬɢ ɬɨɥɳɢɧɵ ɛɚɪɶɟɪɚ ɩɨɹɜɥɹɟɬɫɹ ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɞɛɚɪɶɟɪɧɨɝɨ ɩɟɪɟɯɨɞɚ – «ɬɭɧɟɥɶɧɨɝɨ» ɷɮɮɟɤɬɚ. ɂɫɩɭɫɤɚɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɨɛɭɫɥɨɜɥɟɧɨɟ ɜɟɪɨɹɬɧɨɫɬɶɸ ɩɨɞɛɚɪɶɟɪɧɨɝɨ ɩɟɪɟɯɨɞɚ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ, ɢɦɟɸɳɟɝɨ ɜɨ ɜɧɟɲɧɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ɨɝɪɚɧɢɱɟɧɧɭɸ ɲɢɪɢɧɭ, ɧɚɡɵɜɚɟɬɫɹ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɟɣ. Ʉɨɷɮɮɢɰɢɟɧɬ ɩɪɨɯɨɠɞɟɧɢɹ (ɩɪɨɡɪɚɱɧɨɫɬɢ) ɛɚɪɶɟɪɚ ɡɚɜɢɫɢɬ ɨɬ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ Wx, ɜɵɫɨɬɵ Ɋɢɫ. 7.2 ɉɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ ɧɚ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ Wa, ɢ ɞɥɹ ɝɪɚɧɢɰɟ ɦɟɬɚɥɥ – ɜɚɤɭɭɦ ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɛɚɪɶɟɪɚ ɲɢɪɢɧɵ h ɜɵɪɚɠɚɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ: D(W x ) = exp(−4π 2m e (Wa − W x ) / h) .
(7.17)
Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɩɪɨɡɪɚɱɧɨɫɬɢ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ ɧɟɩɪɹɦɨɭɝɨɥɶɧɨɣ ɮɨɪɦɵ ɦɨɠɧɨ ɟɝɨ ɪɚɡɞɟɥɢɬɶ ɧɚ ɪɹɞ ɩɪɹɦɨɭɝɨɥɶɧɵɯ ɛɚɪɶɟɪɨɜ ɲɢɪɢɧɵ dx, ɢ ɩɪɨɢɧɬɟɝɪɢɪɨɜɚɬɶ ɩɨ ɲɢɪɢɧɟ ɛɚɪɶɟɪɚ. ȼ ɢɬɨɝɟ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ ɜɵɪɚɠɚɟɬɫɹ ɮɨɪɦɭɥɨɣ: D(W x ) = exp[−
8π 2m e 3he
⋅(
Wa − W x 3 / 2 ) ⋅ θ (ζ )] , E
(7.18)
ɝɞɟ θ(ζ) – ɮɭɧɤɰɢɹ ɇɨɪɞɝɟɣɦɚ, ɜɵɪɚɠɚɸɳɚɹɫɹ ɱɟɪɟɡ ɷɥɥɢɩɬɢɱɟɫɤɢɟ ɢɧɬɟɝɪɚɥɵ, ∆ϕ ɲ ∆ϕ ɲ e3 / 2 E1/ 2 . ɇɟɤɨɬɨɪɵɟ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ ɇɨɪɞɝɟɣɦɚ = = ɝɞɟ ζ = ϕ a (W x ) Wa − W x Wa − W x ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɬɚɛɥɢɰɟ 7.1. Ɍɚɛɥɢɰɚ 7.1. 0 ∆ϕɲ/ ϕa 1 θ
0.1 0.98
0.2 0.94
0.3 0.87
0.4 0.79
0.5 0.69
0.6 0.58
0.7 0.45
0.8 0.31
0.9 0.16
1.0 0
Ⱦɥɹ 0 < ζ < 1 θ(ζ) ≈ 0.955 – 1.03ζ 2. ɉɥɨɬɧɨɫɬɶ ɬɨɤɚ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɮɨɪɦɭɥɨɣ Ɏɚɭɥɟɪɚ-ɇɨɪɞɝɟɣɦɚ:
j Ⱥɗ [
(eϕ a ) 3 / 2 θ (∆ϕ ɲ / ϕ a ) Ⱥ E2 = ⋅ ⋅ − )= ] exp( B 0 eϕ a E / E0 ɫɦ 2
= 6.2 ⋅ 10
−6
⋅
E F / eϕ a E 2 [ ȼ / ɫɦ] E F + eϕ a
6.85 ⋅ 10 7 ⋅ (eϕ a ) 3 / 2 θ (∆ϕ ɲ / ϕ a ) ⋅ exp(− ), E[ ȼ / ɫɦ]
(7.19)
ɝɞɟ EF – ɷɧɟɪɝɢɹ Ɏɟɪɦɢ, B0=e2/(8πh), E0=8π 2me /(3he). ȼɥɢɹɧɢɟ ɦɧɨɠɢɬɟɥɹ E2, ɩɨɞɨɛɧɨ ɜɥɢɹɧɢɸ ɦɧɨɠɢɬɟɥɹ T2 ɜ ɮɨɪɦɭɥɟ Ɋɢɱɚɪɞɫɨɧɚ-Ⱦɷɲɦɚɧɚ, ɧɟɡɧɚɱɢɬɟɥɶɧɨ. Ȼɨɥɟɟ ɫɭɳɟɫɬɜɟɧɧɨ ɜɥɢɹɧɢɟ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɪɚɛɨɬɵ ɜɵɯɨɞɚ ɷɥɟɤɬɪɨɧɚ eϕa. Ⱥɜɬɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɫ ɦɢɤɪɨɫɤɨɩɢɱɟɫɤɢɯ ɨɫɬɪɢɣ ɱɚɳɟ ɜɫɟɝɨ ɹɜɥɹɟɬɫɹ ɩɪɢɱɢɧɨɣ ɩɪɨɛɨɹ ɜɚɤɭɭɦɧɵɯ ɩɪɨɦɟɠɭɬɤɨɜ. Ⱥɜɬɨɷɥɟɤɬɪɨɧɧɵɟ ɤɚɬɨɞɵ ɢɡɝɨɬɨɜɥɹɸɬɫɹ ɜ ɜɢɞɟ ɢɝɥ (ɨɫɬɪɢɣ) ɫ ɛɨɥɶɲɨɣ ɤɪɢɜɢɡɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɨɤɨɥɨ ɤɨɬɨɪɵɯ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɟ ɩɨɥɟ ɞɨɫɬɢɝɚɟɬ ɛɨɥɟɟ 106 ȼ/ɫɦ. §46. ɂɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɷɦɢɬɬɟɪɚ ɩɪɢ ɬɟɪɦɨ- ɢ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ
ɋɪɟɞɧɹɹ ɷɧɟɪɝɢɹ, ɭɧɨɫɢɦɚɹ ɷɥɟɤɬɪɨɧɨɦ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɩɪɢ ɬɟɪɦɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ, ɦɨɠɟɬ ɛɵɬɶ ɜɵɱɢɫɥɟɧɚ ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ ɦɚɤɫɜɟɥɥɨɜɫɤɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɩɨ ɷɧɟɪɝɢɹɦ, ɫ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ ɷɧɟɪɝɢɹ ɜɵɲɟɞɲɢɯ ɢɡ ɦɟɬɚɥɥɚ ɷɥɟɤɬɪɨɧɨɜ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɫɨɨɬɧɨɲɟɧɢɣ ɦɟɠɞɭ ɤɨɦɩɨɧɟɧɬɚɦɢ ɫɤɨɪɨɫɬɢ ɷɥɟɤɬɪɨɧɚ ɜ ɦɟɬɚɥɥɟ v ɢ ɜ ɜɚɤɭɭɦɟ u : mu x 2 / 2 = mv x 2 − Wa ° , (7.20) ®u y = v y ° ¯u z = v z ɝɞɟ ɨɫɶ x ɧɚɩɪɚɜɥɟɧɚ ɩɨ ɧɨɪɦɚɥɢ ɤ ɩɨɜɟɪɯɧɨɫɬɢ. ɑɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɩɨ ɧɨɪɦɚɥɢ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɦɟɬɚɥɥɚ ɫɨ ɫɤɨɪɨɫɬɹɦɢ ɜ ɩɪɟɞɟɥɚɯ ɨɬ ux ɞɨ ux + dux ɡɚɞɚɟɬɫɹ ɦɨɞɢɮɢɰɢɪɨɜɚɧɧɵɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ Ɇɚɤɫɜɟɥɥɚ : 2
2mWa + m 2 u x 4πm 2 dN = exp( / ) exp( )u x du x = − k T E k T B F B 2mk B T h3 2
2
mu x mu x mN 4πm 2 k B T exp(−eϕ a / k B T ) exp(− exp(− )u x du x = )u x du x = 3 k BT 2k B T 2k B T h W N exp(− x )dW x , (7.21) = k BT k BT
=
ɝɞɟ N = jT/e – ɱɢɫɥɨ ɬɟɪɦɨɷɥɟɤɬɪɨɧɨɜ ɫ ɟɞɢɧɢɰɵ ɩɥɨɳɚɞɢ ɜ ɫɟɤɭɧɞɭ. ɋɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɩɨ ɧɨɪɦɚɥɢ ɤ ɩɨɜɟɪɯɧɨɫɬɢ: u x =∞
Wx =
³
u x =0
∞
Wx
dN = k B T ³ ε exp(−ε )dε =k B T , N 0
(7.22)
ɝɞɟ ε = Wx/kBT. Ⱦɥɹ ɞɜɭɯ ɞɪɭɝɢɯ ɧɚɩɪɚɜɥɟɧɢɣ ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɤɚɤ ɞɥɹ ɨɛɵɱɧɨɝɨ 1 1 ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ: W y = k B T ɢ W z = k B T . ȼ ɢɬɨɝɟ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ 2 2 ɩɨɥɧɨɣ ɷɧɟɪɝɢɢ ɜɵɥɟɬɚɸɳɟɝɨ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɷɦɢɬɬɟɪɚ ɬɟɦɩɟɪɚɬɭɪɵ Ɍs: W = W x + W y + W z = 2 k B TS . (7.23)
ȿɫɥɢ ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ ɩɨɞɚɬɶ ɬɨɪɦɨɡɹɳɭɸ ɪɚɡɧɨɫɬɶ ɩɨɬɟɧɰɢɚɥɨɜ, ɬɨ ɭɫɥɨɜɢɟ ɩɨɩɚɞɚɧɢɹ ɷɥɟɤɬɪɨɧɚ ɧɚ ɤɚɬɨɞ: mev2/2 ≥ -eUa, ɝɞɟ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɚɧɨɞɟ Ua < 0. Ɍɨɤ ɧɚ ɚɧɨɞ: ∞
Ia = Sa
³
−
2 eU a me
ux Ne
eU me mu x2 exp(− )du x = I ɷ exp( a ) , k BT 2k B T k BT
(7.24)
ɝɞɟ Iɷ – ɬɨɤ ɫ ɷɦɢɬɬɟɪɚ. Ɇɟɧɹɹ Ua, ɦɨɠɧɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɨɩɪɟɞɟɥɹɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɩɨ ɷɧɟɪɝɢɹɦ. ɗɤɫɩɟɪɢɦɟɧɬɵ ɩɨɞɬɜɟɪɠɞɚɸɬ ɬɨ, ɱɬɨ ɷɦɢɬɢɪɨɜɚɧɧɵɟ ɷɥɟɤɬɪɨɧɵ ɢɦɟɸɬ ɪɚɫɩɪɟɞɟɥɟɧɢɟ Ɇɚɤɫɜɟɥɥɚ, ɩɪɢɱɟɦ ɬɟɦɩɟɪɚɬɭɪɚ ɷɥɟɤɬɪɨɧɨɜ ɩɨ ɦɚɤɫɜɟɥɥɨɜɫɤɨɦɭ ɪɚɫɩɪɟɞɟɥɟɧɢɸ ɪɚɜɧɚ ɬɟɦɩɟɪɚɬɭɪɟ ɷɦɢɬɬɟɪɚ. ɉɨɷɬɨɦɭ ɧɚɱɚɥɶɧɵɟ ɷɧɟɪɝɢɢ ɷɦɢɬɬɢɪɨɜɚɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ (ɫ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ 1 ɷȼ ≈ 11600 Ʉ) ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɧɭɥɟɜɵɦɢ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɷɧɟɪɝɢɹɦɢ, ɩɪɢɨɛɪɟɬɚɟɦɵɦɢ ɜ ɭɫɤɨɪɹɸɳɟɣ ɪɚɡɧɨɫɬɢ ɩɨɬɟɧɰɢɚɥɨɜ ɭɠɟ ɜ ɧɟɫɤɨɥɶɤɨ ɜɨɥɶɬ. Ɉɞɧɚɤɨ ɞɥɹ ɨɯɥɚɠɞɟɧɢɹ ɩɨɜɟɪɯɧɨɫɬɢ ɷɦɢɬɬɟɪɚ ɷɬɚ ɷɧɟɪɝɢɹ ɫɭɳɟɫɬɜɟɧɧɚ, ɤ ɬɨɦɭ ɠɟ ɤɚɠɞɵɣ ɷɥɟɤɬɪɨɧ ɩɨɦɢɦɨ ɬɟɩɥɨɜɨɣ ɷɧɟɪɝɢɢ ɭɧɨɫɢɬ ɢɡ ɦɟɬɚɥɥɚ ɷɧɟɪɝɢɸ, ɪɚɜɧɭɸ ɪɚɛɨɬɟ ɜɵɯɨɞɚ. Ɇɨɳɧɨɫɬɶ ɩɨɜɟɪɯɧɨɫɬɧɨɝɨ ɨɯɥɚɠɞɟɧɢɹ w = (jT/e)(2kBTS+eϕa). ɉɪɢ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɡɚ ɫɱɟɬ «ɬɭɧɧɟɥɶɧɨɝɨ» ɷɮɮɟɤɬɚ ɷɦɢɬɢɪɭɸɬɫɹ ɷɥɟɤɬɪɨɧɵ, ɨɛɥɚɞɚɸɳɢɟ ɷɧɟɪɝɢɟɣ, ɦɟɧɶɲɟɣ ɷɧɟɪɝɢɢ Ɏɟɪɦɢ: E < EF. ɋɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɷɦɢɬɢɪɨɜɚɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɜ ɷɬɨɦ ɫɥɭɱɚɟ W = - ϕa – (EF-E), ɦɨɳɧɨɫɬɶ ɩɨɜɟɪɯɧɨɫɬɧɨɝɨ ɧɚɝɪɟɜɚ ɩɨɜɟɪɯɧɨɫɬɢ ɡɚ ɫɱɟɬ ɩɪɢɯɨɞɚ ɛɨɥɟɟ ɜɵɫɨɤɨɷɧɟɪɝɟɬɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɢɡ ɨɛɴɟɦɚ ɦɟɬɚɥɥɚ: w = (jT/e)( EF-E). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɬɟɪɦɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɨɯɥɚɠɞɟɧɢɟɦ ɩɨɜɟɪɯɧɨɫɬɢ, ɚ ɚɜɬɨɷɥɟɤɬɪɨɧɧɚɹ – ɧɚɝɪɟɜɨɦ (ɷɮɮɟɤɬ ɇɨɬɬɢɧɝɟɦɚ). §47. Ɏɨɬɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ
ɂɫɩɭɫɤɚɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɩɚɞɚɸɳɟɝɨ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɢɡɥɭɱɟɧɢɹ ɧɚɡɵɜɚɟɬɫɹ ɮɨɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɟɣ (Ɏɗɗ). ɉɨɬɨɤ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɢɡɥɭɱɟɧɢɹ ɱɚɫɬɶɸ ɨɬɪɚɠɚɟɬɫɹ, ɚ ɱɚɫɬɶɸ ɩɪɨɧɢɤɚɟɬ ɜɧɭɬɪɶ ɬɟɥɚ ɢ ɬɚɦ ɩɨɝɥɨɳɚɟɬɫɹ, ɨɬɞɚɜɚɹ ɷɧɟɪɝɢɸ ɷɥɟɤɬɪɨɧɚɦ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɩɪɟɨɞɨɥɟɬɶ ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ ɢ ɜɵɣɬɢ ɢɡ ɬɟɥɚ. Ɏɗɗ ɛɵɥɚ ɨɛɧɚɪɭɠɟɧɚ Ƚɟɪɰɟɦ 1887 ɝ. Ɉɫɧɨɜɧɵɟ ɡɚɤɨɧɵ Ɏɗɗ, ɭɫɬɚɧɨɜɥɟɧɧɵɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɡɚɞɨɥɝɨ ɞɨ ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ ɨɛɨɫɧɨɜɚɧɢɹ, ɫɜɨɞɹɬɫɹ ɤ ɫɥɟɞɭɸɳɟɦɭ: 1. Ɏɨɬɨɷɥɟɤɬɪɨɧɧɵɣ ɬɨɤ ɜ ɪɟɠɢɦɟ ɧɚɫɵɳɟɧɢɹ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɩɚɞɚɸɳɟɦɭ ɧɚ ɷɦɢɬɬɟɪ ɩɥɨɬɧɨɫɬɢ ɩɨɬɨɤɚ ɦɨɳɧɨɫɬɢ (ɢɥɢ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɨɛɥɭɱɟɧɢɹ I [ȼɬ/ɫɦ2])
jɎɗ ∼ I (ɡɚɤɨɧ ɋɬɨɥɟɬɨɜɚ – 1889 ɝ.).
(7.25)
2. Ɍɟɨɪɟɬɢɱɟɫɤɨɟ ɨɛɨɫɧɨɜɚɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɨɬɤɪɵɬɨɣ Ʌɟɧɚɪɞɨɦ (1899 ɝ.) ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ – ɦɚɤɫɢɦɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɮɨɬɨɷɥɟɤɬɪɨɧɨɜ ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɱɚɫɬɨɬɟ ɩɚɞɚɸɳɟɝɨ ɢɡɥɭɱɟɧɢɹ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɟɝɨ ɢɧɬɟɧɫɢɜɧɨɫɬɢ – ɜɩɟɪɜɵɟ ɞɚɥ ɗɣɧɲɬɟɣɧ, ɜɜɟɞɹ ɜ ɮɢɡɢɤɭ ɩɨɧɹɬɢɟ ɨ ɤɜɚɧɬɚɯ ɫɜɟɬɚ (ɮɨɬɨɧɚɯ): 2 mv max = hν − eϕ a (ɡɚɤɨɧ ɗɣɧɲɬɟɣɧɚ). (7.26) 2 Ɉɬɤɥɨɧɟɧɢɟ ɨɬ ɡɚɤɨɧɚ ɗɣɧɲɬɟɣɧɚ ɜɨɡɧɢɤɚɟɬ ɩɪɢ ɛɨɥɶɲɢɯ ɢɧɬɟɧɫɢɜɧɨɫɬɹɯ ɢɡɥɭɱɟɧɢɹ, ɤɨɝɞɚ ɷɥɟɤɬɪɨɧ ɦɨɠɟɬ ɩɨɝɥɨɳɚɬɶ ɧɟɫɤɨɥɶɤɨ n ɮɨɬɨɧɨɜ: 2 mv max = nhν − eϕ a 2
(7.27)
3. ɋɥɟɞɫɬɜɢɟɦ ɡɚɤɨɧɚ ɗɣɧɲɬɟɣɧɚ ɹɜɥɹɟɬɫɹ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɞɥɢɧɨɜɨɥɧɨɜɨɣ (ɤɪɚɫɧɨɣ) ɝɪɚɧɢɰɵ λ ɨɛɥɚɫɬɢ ɫɩɟɤɬɪɚ ɩɚɞɚɸɳɟɝɨ ɢɡɥɭɱɟɧɢɹ, ɤɨɬɨɪɨɟ ɦɨɠɟɬ ɜɵɡɵɜɚɬɶ ɮɨɬɨɷɦɢɫɫɢɸ ɷɥɟɤɬɪɨɧɨɜ:
λ < λɝɪ, ɢɥɢ ν > νɝɪ = c/λɝɪ = eϕa/h,
(7.28)
ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɝɪɚɧɢɱɧɚɹ ɞɥɢɧɚ ɜɨɥɧɵ ɜɵɪɚɠɚɟɬɫɹ ɱɟɪɟɡ ɪɚɛɨɬɭ ɜɵɯɨɞɚ:
λɝɪ=12300/( eϕa[ɷȼ]) ɩɪɢ Ɍ = 0 Ʉ. ɉɪɢ Ɍ ≠ 0 Ʉ ɜ ɦɟɬɚɥɥɟ ɢɦɟɸɬɫɹ ɷɥɟɤɬɪɨɧɵ
ɫ ɷɧɟɪɝɢɹɦɢ, ɛɨɥɶɲɢɦɢ EF, ɞɥɹ ɧɢɯ ɝɪɚɧɢɱɧɚɹ ɱɚɫɬɨɬɚ ɫɧɢɠɚɟɬɫɹ. ɇɨ ɜ ɯɨɥɨɞɧɨɦ ɦɟɬɚɥɥɟ ɞɨɥɹ ɬɚɤɢɯ ɷɥɟɤɬɪɨɧɨɜ ɤɪɚɣɧɟ ɦɚɥɚ. Ʉɪɨɦɟ ɬɨɝɨ, ɪɚɛɨɬɚ ɜɵɯɨɞɚ, ɚ ɡɧɚɱɢɬ, ɢ ɝɪɚɧɢɱɧɚɹ ɱɚɫɬɨɬɚ ɡɚɜɢɫɢɬ ɨɬ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ (ɷɮɮɟɤɬ ɒɨɬɬɤɢ).
4. Ɏɨɬɨɷɮɮɟɤɬ ɨɛɥɚɞɚɟɬ ɫɜɨɣɫɬɜɨɦ ɛɟɡɵɧɟɪɰɢɚɥɶɧɨɫɬɢ - ɮɨɬɨɬɨɤ ɩɨɹɜɥɹɟɬɫɹ ɢ ɢɫɱɟɡɚɟɬ ɜɦɟɫɬɟ ɫ ɨɫɜɟɳɟɧɢɟɦ, ɡɚɩɚɡɞɵɜɚɹ ɧɟ ɛɨɥɟɟ ɱɟɦ ɧɚ 10-9 ɫ. Ɏɨɬɨɷɮɮɟɤɬ ɦɨɠɧɨ ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɥɢɛɨ ɤɜɚɧɬɨɜɵɦ ɜɵɯɨɞɨɦ Y – ɱɢɫɥɨɦ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɨɞɢɧ ɮɨɬɨɧ (Y = 10-3÷10-1), ɥɢɛɨ ɩɥɨɬɧɨɫɬɶɸ ɮɨɬɨɬɨɤɚ jɮ. Ɉɬɧɨɲɟɧɢɟ ɮɨɬɨɬɨɤɚ ɤ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɩɨɬɨɤɚ ɦɨɧɨɯɪɨɦɚɬɢɱɟɫɤɨɝɨ ɢɡɥɭɱɟɧɢɹ ɜɵɪɚɠɚɟɬ ɫɩɟɤɬɪɚɥɶɧɭɸ ɱɭɜɫɬɜɢɬɟɥɶɧɨɫɬɶ ɮɨɬɨɤɚɬɨɞɨɜ, ɚ ɤ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɩɨɬɨɤɚ ɢɡɥɭɱɟɧɢɹ ɫɬɚɧɞɚɪɬɧɨɝɨ ɢɫɬɨɱɧɢɤɚ ɫɜɟɬɚ – ɢɧɬɟɝɪɚɥɶɧɭɸ ɱɭɜɫɬɜɢɬɟɥɶɧɨɫɬɶ. Ƚɥɭɛɢɧɚ ɜɵɯɨɞɚ ɷɥɟɤɬɪɨɧɨɜ ɢɡ ɦɟɬɚɥɥɨɜ ɫɨɫɬɚɜɥɹɟɬ ɧɚɫɤɨɥɶɤɨ ɚɬɨɦɧɵɯ ɫɥɨɟɜ, ɩɨɷɬɨɦɭ, ɬɟɪɹɹ ɧɚ ɫɜɨɟɦ ɩɭɬɢ ɱɚɫɬɶ ɷɧɟɪɝɢɢ, ɮɨɬɨɷɥɟɤɬɪɨɧɵ ɧɚ ɜɵɯɨɞɟ ɢɡ ɦɟɬɚɥɥɨɜ ɢɦɟɸɬ ɧɟɤɨɬɨɪɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨ ɷɧɟɪɝɢɹɦ ɨɬ ɧɭɥɹ ɞɨ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ, ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɩɨ ɡɚɤɨɧɭ ɗɣɧɲɬɟɣɧɚ. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɮɨɬɨɷɥɟɤɬɪɨɧɨɜ ɩɨ ɷɧɟɪɝɢɹɦ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɦɟɬɨɞɨɦ ɡɚɞɟɪɠɢɜɚɸɳɟɝɨ ɩɨɬɟɧɰɢɚɥɚ. Ⱦɥɹ ɫɛɨɪɚ ɧɚ ɚɧɨɞ ɜɫɟɯ ɮɨɬɨɷɥɟɤɬɪɨɧɨɜ ɜ ɨɩɵɬɚɯ Ʌɭɤɢɪɫɤɨɝɨ ɢ ɉɪɟɥɢɠɚɟɜɚ ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɤɚɬɨɞ ɜ ɜɢɞɟ ɲɚɪɚ ɢ ɚɧɨɞ ɜ ɜɢɞɟ ɤɨɧɰɟɧɬɪɢɱɟɫɤɨɣ ɤɚɬɨɞɭ ɫɮɟɪɵ, ɱɟɪɟɡ ɭɡɤɨɟ ɨɬɜɟɪɫɬɢɟ ɤɨɬɨɪɨɣ ɧɚ ɤɚɬɨɞ ɩɨɞɚɜɚɥɫɹ ɥɭɱ ɫɜɟɬɚ. Ɋɚɡɧɨɫɬɶ ɡɧɚɱɟɧɢɣ ɬɨɤɚ ɩɪɢ ɞɜɭɯ ɡɚɞɟɪɠɢɜɚɸɳɢɯ ɩɨɬɟɧɰɢɚɥɚɯ -U ɢ -(U + ∆U) ɞɚɟɬ ɱɢɫɥɨ ɮɨɬɨɷɥɟɤɬɪɨɧɨɜ, ɷɧɟɪɝɢɹ ɤɨɬɨɪɵɯ ɩɪɢ ɜɵɥɟɬɟ ɫ ɤɚɬɨɞɚ ɥɟɠɢɬ ɜ ɩɪɟɞɟɥɚɯ ɨɬ eU ɞɨ e(U + ∆U). ɗɬɨɬ ɠɟ ɦɟɬɨɞ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɪɚɫɧɨɣ ɝɪɚɧɢɰɵ
ɮɨɬɨɷɮɮɟɤɬɚ. Ɂɚɞɟɪɠɢɜɚɸɳɢɣ ɩɨɬɟɧɰɢɚɥ, ɩɪɢ ɤɨɬɨɪɨɦ ɮɨɬɨɬɨɤ ɫɬɚɧɨɜɢɬɫɹ ɪɚɜɧɵɦ ɧɭɥɸ, ɨɩɪɟɞɟɥɹɟɬ ɪɚɡɧɨɫɬɶ ɦɟɠɞɭ ɱɚɫɬɨɬɨɣ ɝɚɦɦɚ-ɤɜɚɧɬɚ ν ɢ ɝɪɚɧɢɱɧɨɣ ɱɚɫɬɨɬɨɣ ɮɨɬɨɷɮɮɟɤɬɚ νɝɪ ɞɥɹ ɞɚɧɧɨɝɨ ɦɚɬɟɪɢɚɥɚ: U0 = h(ν - νɝɪ)/e. Ɂɧɚɱɟɧɢɹ U0, ɨɩɪɟɞɟɥɹɟɦɵɟ ɞɥɹ ɪɚɡɧɵɯ ɱɚɫɬɨɬ ɨɛɥɭɱɟɧɢɹ ν, ɥɟɠɚɬ ɧɚ ɩɪɹɦɨɣ, ɬɨɱɤɚ ɩɟɪɟɫɟɱɟɧɢɹ ɤɨɬɨɪɨɣ ɫ ɨɫɶɸ ɚɛɫɰɢɫɫ ɞɚɟɬ ɝɪɚɧɢɱɧɭɸ ɱɚɫɬɨɬɭ νɝɪ. Ɉɫɧɨɜɧɵɟ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ Ɏɗɗ ɦɟɬɚɥɥɨɜ ɯɨɪɨɲɨ ɨɩɢɫɵɜɚɸɬɫɹ ɬɟɨɪɢɟɣ Ɏɚɭɥɟɪɚ, ɫɨɝɥɚɫɧɨ ɤɨɬɨɪɨɣ ɩɨɫɥɟ ɩɨɝɥɨɳɟɧɢɹ ɜ ɦɟɬɚɥɥɟ ɮɨɬɨɧɚ ɟɝɨ ɷɧɟɪɝɢɹ ɩɟɪɟɯɨɞɢɬ ɷɥɟɤɬɪɨɧɚɦ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɱɟɝɨ ɷɥɟɤɬɪɨɧɧɵɣ ɝɚɡ ɜ ɦɟɬɚɥɥɟ ɨɤɨɥɨ ɟɝɨ ɩɨɜɟɪɯɧɨɫɬɢ ɫɨɫɬɨɢɬ ɢɡ ɫɦɟɫɢ ɝɚɡɨɜ ɫ ɧɨɪɦɚɥɶɧɵɦ (ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ Ɏɟɪɦɢ) ɢ ɜɨɡɛɭɠɞɟɧɧɵɦ (ɫɞɜɢɧɭɬɵɦ ɧɚ hν) ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ ɩɨ ɷɧɟɪɝɢɹɦ (ɪɢɫ. 7.3). Ⱦɥɹ ɩɨɞɫɱɟɬɚ ɱɢɫɥɚ ɮɨɬɨɷɥɟɤɬɪɨɧɨɜ ɦɨɠɧɨ ɩɪɨɜɟɫɬɢ ɬɚɤɨɟ ɠɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɱɬɨ ɢ ɩɪɢ ɩɨɞɫɱɟɬɟ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ ɬɟɪɦɨɷɦɢɫɫɢɢ, Ɋɢɫ. 7.3. Ɏɨɬɨɷɦɢɫɫɢɨɧɧɵɣ ɬɨɤ ɷɥɟɤɬɪɨɧɨɜ ɢɡ ɢɡɦɟɧɢɜ ɧɢɠɧɢɣ ɩɪɟɞɟɥ «ɯɜɨɫɬɚ» ɜɨɡɦɭɳɟɧɧɨɣ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɫ Wa ɧɚ Wa - hν, ɩɪɟɨɞɨɥɟɜɚɸɳɢɯ ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ ɬɟɦ ɫɚɦɵɦ ɜɤɥɸɱɢɜ ɜ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɷɥɟɤɬɪɨɧɵ, ɤɨɬɨɪɵɟ ɩɪɢɨɛɪɟɬɚɸɬ ɧɟɞɨɫɬɚɸɳɭɸ ɞɥɹ ɩɪɟɨɞɨɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ ɷɧɟɪɝɢɸ ɡɚ ɫɱɟɬ ɩɨɝɥɨɳɟɧɧɵɯ ɤɜɚɧɬɨɜ. Ɍɚɤ ɠɟ, ɤɚɤ ɢ ɞɥɹ ɬɟɪɦɨɷɥɟɤɬɪɨɧɨɜ, ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ ɜɟɪɨɹɬɧɨɫɬɶ ɩɪɨɯɨɠɞɟɧɢɹ ɛɚɪɶɟɪɚ, ɬɚɤ ɤɚɤ ɱɚɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɩɪɢ ɞɜɢɠɟɧɢɢ ɢɡ ɦɟɬɚɥɥɚ ɦɨɠɟɬ ɛɵɬɶ ɨɬɪɚɠɟɧɚ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɡɞɟɥɚ ɦɟɬɚɥɥ - ɜɚɤɭɭɦ. Ʉɪɨɦɟ ɷɬɨɝɨ, ɧɟɨɛɯɨɞɢɦɨ ɭɱɟɫɬɶ ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɝɥɨɳɟɧɢɹ ɮɨɬɨɧɚ. ɗɬɚ ɜɟɪɨɹɬɧɨɫɬɶ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɡɚɜɢɫɢɬ ɨɬ ɷɧɟɪɝɢɢ ɩɨɝɥɨɳɚɸɳɟɝɨ ɷɥɟɤɬɪɨɧɚ ɢ ɷɧɟɪɝɢɢ ɝɚɦɦɚɤɜɚɧɬɚ. ȼ ɬɟɨɪɢɢ Ɏɚɭɥɟɪɚ ɷɬɚ ɜɟɪɨɹɬɧɨɫɬɶ ɫɱɢɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ ɜɟɥɢɱɢɧɨɣ, ɱɬɨ, ɤɚɤ Ɋɢɫ. 7.4. Ɉɩɪɟɞɟɥɟɧɢɟ ɤɪɚɫɧɨɣ ɝɪɚɧɢɰɵ ɨɤɚɡɚɥɨɫɶ, ɜ ɢɧɬɟɪɜɚɥɟ ɱɚɫɬɨɬ ɨɬ νɝɪ ɞɨ ɫ ɩɨɦɨɳɶɸ ɮɭɧɤɰɢɢ Ɏɚɭɥɟɪɚ. 1.5νɝɪ ɜɵɩɨɥɧɹɟɬɫɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɩɥɨɬɧɨɫɬɶ ɮɨɬɨɬɨɤɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ Ɏɚɭɥɟɪɚ:
hν − hν ɝɪ 2 ),ν ≤ ν ɝɪ = eϕ a / h ° B1T exp( kT ° jɎ = ® , 2 ° B T 2 ( (hν − hν ɝɪ ) + B ),ν > ν 3 ɝɪ °¯ 2 k 2T 2
(7.29)
ɝɞɟ B1, B2, B3 – ɩɨɫɬɨɹɧɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɟ A0. Ɂɚɜɢɫɢɦɨɫɬɶ hγ jɮ( ) ɦɨɠɧɨ ɬɚɤɠɟ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ ɪɹɞɨɜ [32]. ɂɡ ɮɨɪɦɭɥɵ Ɏɚɭɥɟɪɚ ɜɢɞɧɨ, kT ɱɬɨ ɩɪɢ Ɍ ≈0 jɮ → 0 ɢ νɝɪ ɞɟɣɫɬɜɢɬɟɥɶɧɨ ɹɜɥɹɟɬɫɹ ɤɪɚɫɧɨɣ ɝɪɚɧɢɰɟɣ. ɉɪɢ Ɍ ≠ 0 ɧɟ ɫɭɳɟɫɬɜɭɟɬ ɪɟɡɤɨɣ ɝɪɚɧɢɰɵ ɮɨɬɨɷɮɮɟɤɬɚ, ɮɨɬɨɬɨɤ ɩɚɞɚɟɬ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ ɩɪɢ ν < νɝɪ, ɩɪɢ ν > νɝɪ ɩɥɨɬɧɨɫɬɶ ɮɨɬɨɬɨɤɚ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɤɜɚɞɪɚɬɭ ɱɚɫɬɨɬɵ ɩɚɞɚɸɳɟɝɨ ɢɡɥɭɱɟɧɢɹ jɎ ∼ ν 2. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɩɨɥɨɠɟɧɢɟ νɝɪ ɨɩɪɟɞɟɥɹɸɬ ɩɨ ɢɡɦɟɪɟɧɧɨɣ ɫɩɟɤɬɪɚɥɶɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɮɨɬɨɬɨɤɚ ɩɪɢ ɡɚɞɚɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ Ɍ > 0. ɗɬɚ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬɤɥɚɞɵɜɚɟɬɫɹ ɧɚ ɝɪɚɮɢɤɟ ɜ ɤɨɨɪɞɢɧɚɬɚɯ x = hν/kT ɢ y = ln( jɎ/T2). ɉɨɥɭɱɟɧɧɚɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɚɹ ɤɪɢɜɚɹ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɡɚɜɢɫɢɦɨɫɬɢ: ln( jɎ/T2) = B + F((hν- hνɝɪ)/kT) = B + F(x- hνɝɪ/kT).
(7.30)
Ⱦɚɧɧɚɹ ɤɪɢɜɚɹ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɤɪɢɜɨɣ ɮɭɧɤɰɢɢ Ɏɚɭɥɟɪɚ F = F(hν/kT) ɫɞɜɢɝɨɦ ɩɨ ɨɫɢ y ɧɚ ɤɨɧɫɬɚɧɬɭ B ɢ ɩɨ ɨɫɢ x ɧɚ hνɝɪ/kT (ɪɢɫ. 7.4). ɂɦɟɧɧɨ ɨɩɪɟɞɟɥɟɧɢɟ ɫɞɜɢɝɚ ɩɨ ɨɫɢ x ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɤɪɢɜɨɣ ɞɥɹ ɟɟ ɫɨɜɦɟɳɟɧɢɹ ɫ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɤɪɢɜɨɣ Ɏɚɭɥɟɪɚ ɩɨɡɜɨɥɹɟɬ ɧɚɣɬɢ ɝɪɚɧɢɱɧɭɸ ɱɚɫɬɨɬɭ νɝɪ. §48. ȼɬɨɪɢɱɧɚɹ ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ȼɬɨɪɢɱɧɚɹ ɷɥɟɤɬɪɨɧ-ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ
ɗɦɢɫɫɢɹ ɷɥɟɤɬɪɨɧɨɜ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɬɜɟɪɞɨɝɨ ɬɟɥɚ, ɛɨɦɛɚɪɞɢɪɭɟɦɨɣ ɩɨɬɨɤɨɦ ɷɥɟɤɬɪɨɧɨɜ, ɧɚɡɵɜɚɟɬɫɹ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɟɣ. ɇɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɚɹ ɫɯɟɦɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɦɟɬɨɞɨɦ ɡɚɞɟɪɠɢɜɚɸɳɟɝɨ ɩɨɥɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɫɮɟɪɢɱɟɫɤɨɝɨ ɤɨɥɥɟɤɬɨɪɚ Ʌɭɤɢɪɫɤɨɝɨ ɢ ɉɪɟɥɢɠɚɟɜɚ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 7.5. Ɂɚɞɟɪɠɢɜɚɸɳɟɟ ɩɨɥɟ ɩɪɢɤɥɚɞɵɜɚɟɬɫɹ ɦɟɠɞɭ Ɋɢɫ. 7.5. ɋɯɟɦɚ ɨɩɵɬɚ ɩɨ ɢɫɫɥɟɞɨɜɚɧɢɸ ɜɬɨɪɢɱɧɨɣ ɦɢɲɟɧɶɸ ɢ ɤɨɥɥɟɤɬɨɪɨɦ. ȿɫɥɢ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɩɨɬɟɧɰɢɚɥ ɤɨɥɥɟɤɬɨɪɚ ɛɭɞɟɬ ɛɨɥɶɲɟ, ɱɟɦ ɧɚ ɦɢɲɟɧɢ, ɬɨ ɧɚ ɤɨɥɥɟɤɬɨɪ ɩɪɢɞɟɬ ɩɨɥɧɵɣ ɬɨɤ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ Is. ȼɬɨɪɢɱɧɚɹ ɷɦɢɫɫɢɢ ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɤɨɥɢɱɟɫɬɜɨɦ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɨɞɧɭ ɩɟɪɜɢɱɧɭɸ ɱɚɫɬɢɰɭ: γe = Ns/Np. ɂɧɬɟɝɪɚɥɶɧɨ ɷɬɨ ɤɨɥɢɱɟɫɬɜɨ ɪɚɜɧɨ ɨɬɧɨɲɟɧɢɸ ɬɨɤɨɜ Ɋɢɫ. 7.6. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɩɨ ɷɧɟɪɝɢɹɦ
ɜɬɨɪɢɱɧɵɯ ɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ Is/Ip. Ȼɨɥɟɟ ɬɨɱɧɵɦ ɦɟɬɨɞɨɦ ɨɩɪɟɞɟɥɟɧɢɹ ɫɤɨɪɨɫɬɟɣ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɹɜɥɹɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɞɢɫɩɟɪɫɢɨɧɧɵɯ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɢɥɢ ɦɚɝɧɢɬɧɨɝɨ ɷɧɟɪɝɨɚɧɚɥɢɡɚɬɨɪɚ ɫ ɩɨɥɭɤɪɭɝɨɜɨɣ ɬɪɚɟɤɬɨɪɢɟɣ, ɨɩɢɫɚɧɧɨɝɨ ɜ ɝɥɚɜɟ 5. ɉɨɥɭɱɟɧɧɨɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɟ ɷɧɟɪɝɟɬɢɱɟɫɤɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ (ɪɢɫ. 7.6) ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɦɚɬɟɪɢɚɥɚ ɢ ɷɧɟɪɝɢɢ Ɋɢɫ. 7.7. Ɂɚɜɢɫɢɦɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɚ ɢɫɬɢɧɧɨɣ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɨɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɞɥɹ W, Mo, C, Be ɫɨɞɟɪɠɢɬ ɞɜɚ ɜɵɫɨɤɢɯ ɦɚɤɫɢɦɭɦɚ. ɉɟɪɜɵɣ ɜ ɨɛɥɚɫɬɢ ɦɚɥɵɯ ɷɧɟɪɝɢɣ (< 50 ɷȼ) ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɢɫɬɢɧɧɵɦ ɜɬɨɪɢɱɧɵɦ ɷɥɟɤɬɪɨɧɚɦ, ɤɨɬɨɪɵɟ ɜɵɯɨɞɹɬ ɢɡ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɡɚ ɫɱɟɬ ɩɨɝɥɨɳɟɧɢɹ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ. Ⱦɚɥɟɤɨ ɧɟ ɜɫɟ ɷɥɟɤɬɪɨɧɵ, ɩɨɥɭɱɢɜɲɢɟ ɞɨɩɨɥɧɢɬɟɥɶɧɭɸ ɷɧɟɪɝɢɸ, ɞɨɛɢɪɚɸɬɫɹ ɞɨ ɩɨɜɟɪɯɧɨɫɬɢ, ɪɚɫɬɪɚɱɢɜɚɹ ɷɧɟɪɝɢɸ ɩɨ ɩɭɬɢ ɧɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɫ ɢɨɧɚɦɢ ɪɟɲɟɬɤɢ ɢ ɞɪɭɝɢɦɢ ɷɥɟɤɬɪɨɧɚɦɢ. ɉɪɟɨɞɨɥɟɜɲɢɟ ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ ɢɫɬɢɧɧɵɟ ɜɬɨɪɢɱɧɵɟ ɷɥɟɤɬɪɨɧɵ ɧɚ ɜɵɯɨɞɟ ɢɦɟɸɬ ɷɧɟɪɝɢɢ, ɧɟ ɡɚɜɢɫɹɳɢɟ ɨɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ. Ɋɚɛɨɬɚ ɜɵɯɨɞɚ ɦɚɬɟɪɢɚɥɚ ɬɚɤɠɟ ɧɟ ɨɤɚɡɵɜɚɟɬ ɫɭɳɟɫɬɜɟɧɧɨɝɨ ɜɥɢɹɧɢɹ ɧɚ ɷɦɢɫɫɢɸ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, ɬɚɤ ɤɚɤ, ɜɨ-ɩɟɪɜɵɯ, ɷɧɟɪɝɢɹ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, ɤɚɤ ɩɪɚɜɢɥɨ, ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ ɪɚɛɨɬɵ ɜɵɯɨɞɚ, ɜɨ-ɜɬɨɪɵɯ, ɷɦɢɫɫɢɹ ɩɪɨɢɫɯɨɞɢɬ ɧɟ ɢɡ ɩɨɜɟɪɯɧɨɫɬɧɵɯ ɫɥɨɟɜ, ɚ ɢɡ ɝɥɭɛɢɧɵ ɦɟɬɚɥɥɚ, ɩɨɷɬɨɦɭ ɛɨɥɟɟ ɜɚɠɧɵɦ ɹɜɥɹɟɬɫɹ ɩɨɬɟɪɹ ɷɧɟɪɝɢɢ ɩɪɢ ɞɜɢɠɟɧɢɢ ɷɥɟɤɬɪɨɧɚ ɤ ɩɨɜɟɪɯɧɨɫɬɢ. ȼɬɨɪɨɣ, ɝɨɪɚɡɞɨ ɛɨɥɟɟ ɭɡɤɢɣ ɦɚɤɫɢɦɭɦ ɧɚɯɨɞɢɬɫɹ ɜ ɨɛɥɚɫɬɢ ɜɵɫɨɤɢɯ ɷɧɟɪɝɢɣ ɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɭɩɪɭɝɨ ɨɬɪɚɠɟɧɧɵɦ ɩɟɪɜɢɱɧɵɦ ɷɥɟɤɬɪɨɧɚɦ, ɩɪɚɤɬɢɱɟɫɤɢ ɩɨɥɧɨɫɬɶɸ ɫɨɯɪɚɧɢɜɲɢɦ ɫɜɨɸ ɫɤɨɪɨɫɬɶ ɩɨɫɥɟ ɨɬɪɚɠɟɧɢɹ. ɉɨɥɨɠɟɧɢɟ ɷɬɨɝɨ ɦɚɤɫɢɦɭɦɚ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ. Ɉɛɥɚɫɬɶ ɷɧɟɪɝɢɣ ɦɟɠɞɭ ɷɬɢɦɢ ɞɜɭɦɹ ɦɚɤɫɢɦɭɦɚɦɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɟ ɭɩɪɭɝɨ ɨɬɪɚɠɟɧɧɵɦ ɜɬɨɪɢɱɧɵɦ ɷɥɟɤɬɪɨɧɚɦ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɧɟɪɝɟɬɢɱɟɫɤɢɣ ɫɩɟɤɬɪ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɫɨɫɬɨɢɬ ɢɡ ɲɢɪɨɤɨɝɨ ɩɢɤɚ ɜ ɨɛɥɚɫɬɢ ɧɢɡɤɢɯ ɷɧɟɪɝɢɣ ɫ ɦɚɤɫɢɦɭɦɨɦ ɩɪɢ Wmax, ɤɨɬɨɪɵɣ ɩɪɢɧɚɞɥɟɠɢɬ ɢɫɬɢɧɧɨɜɬɨɪɢɱɧɵɦ ɷɥɟɤɬɪɨɧɚɦ, ɜɵɯɨɞɹɳɢɦ ɫ ɝɥɭɛɢɧɵ 5 - 100 Α ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ, ɢ ɨɱɟɧɶ ɭɡɤɨɝɨ ɩɢɤɚ ɨɬɪɚɠɟɧɧɵɯ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ ɜ ɨɛɥɚɫɬɢ ɜɵɫɨɤɢɯ ɷɧɟɪɝɢɣ ɫ ɦɚɤɫɢɦɭɦɨɦ ɩɪɢ ɷɧɟɪɝɢɢ, ɪɚɜɧɨɣ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ. Ⱦɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɢɫɬɢɧɧɨɣ ɷɥɟɤɬɪɨɧ-ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɜɜɨɞɹɬ ɤɨɷɮɮɢɰɢɟɧɬ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ δe= Ɋɢɫ. 7.8. Ɂɚɜɢɫɢɦɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɚ Ns/Np , ɝɞɟ Ns – ɱɢɫɥɨ ɢɫɬɢɧɧɨ ɨɬɪɚɠɟɧɢɹ ɨɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, Ns - ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, ɩɚɞɚɸɳɢɯ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ. Ⱦɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɷɦɢɫɫɢɢ ɨɬɪɚɠɟɧɧɵɯ ɨɬ
ɩɨɜɟɪɯɧɨɫɬɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɢɫɩɨɥɶɡɭɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬ ɨɬɪɚɠɟɧɢɹ ηe = (Ne+Nu)/Np, ɝɞɟ Ne ɢ Nu - ɭɩɪɭɝɨ ɢ ɧɟɭɩɪɭɝɨ ɨɬɪɚɠɟɧɧɵɟ ɷɥɟɤɬɪɨɧɵ. ɋɭɦɦɚɪɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ γe = δe + ηe. Ɂɚɜɢɫɢɦɨɫɬɶ δe ɨɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ Wp ɡɚɞɚɟɬɫɹ ɷɦɩɢɪɢɱɟɫɤɨɣ ɮɨɪɦɭɥɨɣ (Kollath):
δ e (W p ) Wp Wp = (2.72) 2 exp(−2 ), δ e max Wmax Wmax
(7.31)
ɝɞɟ δemax= 0.35eϕ a , Wmax – ɡɧɚɱɟɧɢɟ ɢ ɩɨɥɨɠɟɧɢɟ ɦɚɤɫɢɦɭɦɚ. ɉɨɥɨɠɟɧɢɟ ɦɚɤɫɢɦɭɦɚ ɡɚɜɢɫɢɦɨɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬɚ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɞɥɹ ɪɚɡɧɵɯ ɦɚɬɟɪɢɚɥɨɜ ɩɪɟɞɫɬɚɜɥɟɧɨ ɜ ɬɚɛɥɢɰɟ 7.2. Ɋɨɫɬ δe ɫ ɷɧɟɪɝɢɟɣ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɫɦɟɧɹɟɬɫɹ ɫɩɚɞɨɦ (ɪɢɫ. 7.7), ɬɚɤ ɤɚɤ ɩɪɢ ɞɚɥɶɧɟɣɲɟɦ ɪɨɫɬɟ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɨɛɪɚɡɨɜɚɧɢɟ ɜɬɨɪɢɱɧɵɯ ɩɪɨɢɫɯɨɞɢɬ ɜɫɟ ɝɥɭɛɠɟ ɢ ɝɥɭɛɠɟ, ɪɚɫɬɭɬ ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɜ ɦɟɬɚɥɥɟ ɢ ɢɯ ɜɵɯɨɞ ɫɬɚɧɨɜɢɬɫɹ ɜɫɟ ɛɨɥɟɟ ɡɚɬɪɭɞɧɟɧɧɵɦ. ɗɬɢɦ ɠɟ ɨɛɴɹɫɧɹɟɬɫɹ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɫɞɜɢɝɚ ɦɚɤɫɢɦɭɦɚ Wmax ɜ ɷɧɟɪɝɟɬɢɱɟɫɤɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɞɥɹ ɦɚɬɟɪɢɚɥɨɜ ɫ ɜɵɫɨɤɢɦ ɚɬɨɦɧɵɦ ɱɢɫɥɨɦ (ɧɚɩɪɢɦɟɪ, ɞɥɹ ɜɨɥɶɮɪɚɦɚ) ɜ ɫɬɨɪɨɧɭ ɧɢɡɤɢɯ ɷɧɟɪɝɢɣ ɢɡ-ɡɚ ɫɧɢɠɟɧɢɹ ɞɥɢɧɵ ɩɪɨɛɟɝɚ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɜ ɬɜɟɪɞɨɦ ɬɟɥɟ (ɷɥɟɤɬɪɨɧɚɦ, ɩɨɥɭɱɢɜɲɢɦ ɷɧɟɪɝɢɸ ɨɬ ɩɟɪɜɢɱɧɵɯ ɜɛɥɢɡɢ ɩɨɜɟɪɯɧɨɫɬɢ, ɥɟɝɱɟ ɜɵɣɬɢ ɢɡ ɬɜɟɪɞɨɝɨ ɬɟɥɚ). Ɂɚɜɢɫɢɦɨɫɬɶ δe ɨɬ ɭɝɥɚ ɩɚɞɟɧɢɹ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ α (ɭɝɨɥ ɫ ɧɨɪɦɚɥɶɸ ɤ ɩɨɜɟɪɯɧɨɫɬɢ) ɞɥɹ α < 60ɨ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ:
δ e (α ) = δ e (0) / cos β α ,
(7.32)
ɝɞɟ β = 1.3 ÷1.5. ɑɟɦ ɛɨɥɶɲɟ α, ɬɟɦ ɦɟɧɶɲɟ ɝɥɭɛɢɧɚ, ɤɨɬɨɪɭɸ ɧɭɠɧɨ ɩɪɟɨɞɨɥɟɬɶ ɜɬɨɪɢɱɧɨɦɭ ɷɥɟɤɬɪɨɧɭ ɞɥɹ ɜɵɯɨɞɚ. ɗɦɩɢɪɢɱɟɫɤɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɚ ɨɬɪɚɠɟɧɢɹ ηe ɞɥɹ ɧɨɪɦɚɥɶɧɨɝɨ ɩɚɞɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɨɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ Wp (ɪɢɫ.7.8) ɢ ɚɬɨɦɧɨɝɨ ɧɨɦɟɪɚ z:
η e (W p , z ) = W pm ( z ) exp(C ( z )) ,
(7.33)
m(z)=0.1382–0.9211z-0.5, C(z)=0.1904–0.2236lnz+0.1292ln2z–0.01491ln3z ɝɞɟ (Hunger). Ɂɚɜɢɫɢɦɨɫɬɶ ηe ɨɬ ɭɝɥɚ ɩɚɞɟɧɢɹ α:
η e (α ) = 0.891(
η e ( 0) 0.891
) cos α (Darlington).
(7.34)
Ɍɚɛɥɢɰɚ 7.2.
δemax
Wmax[ɷȼ]
Al
Be
1.0 300
0.5 200
C (ɚɥɦɚɡ) 2.8 750
ɋ (ɝɪɚɮɢɬ)
Cu
Fe
Mo
Ni
Ta
Ti
W
1.0 300
1.3 600
1.3 400
1.25 375
1.3 550
1.3 600
0.9 280
1.4 650
ɇɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɦ ɩɪɢɦɟɧɟɧɢɟɦ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɹɜɥɹɸɬɫɹ ɷɥɟɤɬɪɨɧɧɵɟ ɭɦɧɨɠɢɬɟɥɢ, ɩɪɢɧɰɢɩ ɞɟɣɫɬɜɢɹ ɤɨɬɨɪɵɯ ɩɪɟɞɫɬɚɜɥɟɧ
ɫɯɟɦɨɣ ɧɚ ɪɢɫ. 7.9. Ɇɚɤɫɢɦɚɥɶɧɨ ɩɨɥɧɨɟ ɩɨɩɚɞɚɧɢɹ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɫɥɟɞɭɸɳɢɣ ɷɦɢɬɬɟɪ ɦɨɠɟɬ ɨɛɟɫɩɟɱɢɜɚɬɶɫɹ ɦɚɝɧɢɬɧɨɣ ɢɥɢ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɮɨɤɭɫɢɪɨɜɤɨɣ. ȼɬɨɪɢɱɧɚɹ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ
ɉɪɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɢɨɧɨɜ ɫ ɩɨɜɟɪɯɧɨɫɬɶɸ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɧɚɛɥɸɞɚɟɬɫɹ ɷɦɢɫɫɢɹ ɷɥɟɤɬɪɨɧɨɜ, ɯɚɪɚɤɬɟɪɢɡɭɟɦɚɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ: γi = ne/ni, ɝɞɟ ne - ɱɢɫɥɨ ɷɦɢɬɢɪɨɜɚɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, ni ɱɢɫɥɨ ɢɨɧɨɜ, ɭɩɚɜɲɢɯ ɧɚ ɬɭ ɠɟ ɩɨɜɟɪɯɧɨɫɬɶ ɡɚ ɬɨ ɠɟ ɜɪɟɦɹ. Ⱦɥɹ ɨɞɧɨɡɚɪɹɞɧɵɯ ɢɨɧɨɜ γi = ne/ni = je/ji, ɩɪɢ ɷɦɢɫɫɢɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɢɨɧɨɜ ɡɚɪɹɞɨɦ Z γi = Zje/ji. ɗɦɢɫɫɢɹ ɷɥɟɤɬɪɨɧɨɜ ɦɨɠɟɬ Ɋɢɫ. 7.9. ɋɯɟɦɚ ɷɥɟɤɬɪɨɧɧɨɝɨ ɭɦɧɨɠɢɬɟɥɹ ɩɪɨɢɫɯɨɞɢɬɶ ɜ ɪɟɡɭɥɶɬɚɬɟ ɞɜɭɯ ɩɪɨɰɟɫɫɨɜ: ɩɟɪɜɵɣ ɩɪɨɰɟɫɫ, ɫɜɹɡɚɧ ɫ ɜɨɡɛɭɠɞɟɧɢɟɦ ɷɥɟɤɬɪɨɧɨɜ ɬɟɥɚ ɡɚ ɫɱɟɬ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɨɜ ɷɦɢɬɬɟɪɚ ɜ ɩɨɥɟ ɩɪɢɯɨɞɹɳɟɝɨ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ ɬɟɥɚ ɢɨɧɚ – ɬɚɤɭɸ ɷɦɢɫɫɢɸ ɧɚɡɵɜɚɸɬ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɫ γɩ; ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɷɦɢɫɫɢɢ ɜɬɨɪɨɣ ɩɪɨɰɟɫɫ ɫɜɹɡɚɧ ɫ ɜɨɡɛɭɠɞɟɧɢɟɦ ɷɥɟɤɬɪɨɧɧɨɣ ɫɢɫɬɟɦɵ ɬɟɥɚ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɟɣ ɢɨɧɚ – ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɷɦɢɫɫɢɸ ɧɚɡɵɜɚɸɬ ɤɢɧɟɬɢɱɟɫɤɨɣ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɷɦɢɫɫɢɢ γɤ. ȿɫɥɢ ɩɪɢɫɭɬɫɬɜɭɸɬ ɨɛɚ ɩɪɨɰɟɫɫɚ, ɬɨ γi = γɩ + γɤ. ɉɨɬɟɧɰɢɚɥɶɧɚɹ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɛɵɥɚ ɨɬɤɪɵɬɚ ɉɟɧɧɢɧɝɨɦ ɜ 1928 ɝ. ɉɪɢ ɢɫɫɥɟɞɨɜɚɧɢɢ ɡɚɜɢɫɢɦɨɫɬɢ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɨɬ ɷɧɟɪɝɢɢ ɩɚɞɚɸɳɢɯ ɢɨɧɨɜ ɨɧ ɨɛɧɚɪɭɠɢɥ, ɱɬɨ ɷɦɢɫɫɢɹ ɨɫɬɚɟɬɫɹ ɢ ɩɪɢ ɨɱɟɧɶ ɦɚɥɵɯ, ɩɪɚɤɬɢɱɟɫɤɢ ɧɭɥɟɜɵɯ, ɷɧɟɪɝɢɹɯ ɢɨɧɨɜ. ɂɡ ɷɬɨɝɨ ɦɨɠɧɨ Ɋɢɫ. 7.10. ɋɯɟɦɚ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɢɨɧɧɨɛɵɥɨ ɫɞɟɥɚɬɶ ɜɵɜɨɞ, ɱɬɨ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɢɫɩɭɫɤɚɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɧɟ ɫɜɹɡɚɧɨ ɫ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɟɣ ɢɨɧɨɜ. ȼ ɷɤɫɩɟɪɢɦɟɧɬɚɯ ɛɵɥɨ ɜɵɹɜɥɟɧɨ, ɱɬɨ ɬɚɤɚɹ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɩɪɨɢɫɯɨɞɢɬ ɬɨɥɶɤɨ ɞɥɹ ɢɨɧɨɜ, ɩɨɬɟɧɰɢɚɥ ɢɨɧɢɡɚɰɢɢ ɤɨɬɨɪɵɯ Vi ɜ ɞɜɚ ɪɚɡɚ ɛɨɥɶɲɟ ɪɚɛɨɬɵ ɜɵɯɨɞɚ ɦɚɬɟɪɢɚɥɚ ɷɦɢɬɬɟɪɚ ϕa: Vi >2ϕa.
(7.35)
ɗɬɨ ɧɚɯɨɞɢɬ ɨɛɴɹɫɧɟɧɢɟ ɜ ɦɨɞɟɥɢ ɨɠɟ-ɧɟɣɬɪɚɥɢɡɚɰɢɢ ɢɨɧɚ. ɉɪɢɛɥɢɠɚɹɫɶ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɦɟɬɚɥɥɚ, ɢɨɧ ɢɡɦɟɧɹɟɬ ɫɜɨɢɦ ɩɨɥɟɦ ɩɨɜɟɪɯɧɨɫɬɧɵɣ ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ, ɩɨɧɢɠɚɹ ɟɝɨ. Ɉɞɢɧ ɷɥɟɤɬɪɨɧ, ɢɦɟɹ ɜ ɦɟɬɚɥɥɟ ɷɧɟɪɝɢɸ E1, ɫɨɜɟɪɲɚɟɬ ɬɭɧɧɟɥɶɧɵɣ ɩɟɪɟɯɨɞ ɢ ɧɟɣɬɪɚɥɢɡɭɟɬ ɢɨɧ (ɪɢɫ. 7.10). ɉɪɢ ɷɬɨɦ
ɜɵɞɟɥɹɟɦɚɹ ɷɧɟɪɝɢɹ Vi – E1 ɦɨɠɟɬ ɛɵɬɶ ɩɟɪɟɞɚɧɚ ɜɬɨɪɨɦɭ ɷɥɟɤɬɪɨɧɭ, ɢɦɟɸɳɟɦɭ ɜ ɦɟɬɚɥɥɟ ɷɧɟɪɝɢɸ E2. Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɜɬɨɪɨɣ ɷɥɟɤɬɪɨɧ ɜɵɲɟɥ ɢɡ ɦɟɬɚɥɥɚ, ɟɝɨ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɞɨɥɠɧɚ ɛɵɬɶ ɛɨɥɶɲɟ ɧɭɥɹ: mv2/2 = Vi – E1 – E2 > 0. ɋ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ ɩɪɢ ɧɢɡɤɢɯ ɬɟɦɩɟɪɚɬɭɪɚɯ E1 ɢ E2 ɦɟɧɶɲɟ ϕa, Vi >2ϕa. Ɉɩɵɬ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɤɨɷɮɮɢɰɢɟɧɬ γɩ ɥɢɧɟɣɧɨ ɪɚɫɬɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɪɚɡɧɨɫɬɢ Vi -2ϕa ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɩɚɪ ɦɢɲɟɧɶ – ɢɨɧ. Ⱦɥɹ ɱɢɫɬɵɯ ɩɨɜɟɪɯɧɨɫɬɟɣ ɷɬɭ ɡɚɜɢɫɢɦɨɫɬɶ ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɷɦɩɢɪɢɱɟɫɤɨɣ ɮɨɪɦɭɥɨɣ:
γɩ ≈ 0.016(Vi -2ϕa)[ɷȼ].
(7.36)
Ʉɨɷɮɮɢɰɢɟɧɬ γɩ ɬɟɦ ɛɨɥɶɲɟ, ɱɟɦ ɛɨɥɶɲɟ ɡɚɪɹɞ ɢɨɧɚ (ɤɪɚɬɧɨɫɬɶ ɢɨɧɢɡɚɰɢɢ): γɩ(A+) < γɩ(A++) < γɩ(A+++). Ⱦɥɹ ɦɢɲɟɧɟɣ, ɩɨɜɟɪɯɧɨɫɬɶ ɤɨɬɨɪɵɯ ɞɨɫɬɚɬɨɱɧɨ ɱɢɫɬɚɹ, γɩ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɷɧɟɪɝɢɢ ɩɚɞɚɸɳɢɯ ɢɨɧɨɜ Ep: dγɩ/dEp ≈ 0. ɉɪɢ ɛɨɥɶɲɨɣ ɜɟɥɢɱɢɧɟ ɪɚɡɧɨɫɬɢ Vi -2ϕa >> kBT ɤɨɷɮɮɢɰɢɟɧɬ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɢɨɧɧɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨɜɟɪɯɧɨɫɬɢ ɦɢɲɟɧɢ. ɉɪɢ ɦɚɥɨɣ ɜɟɥɢɱɢɧɟ ɷɬɨɣ ɪɚɡɧɨɫɬɢ: Vi -2ϕa ≈ kBT ɬɟɪɦɢɱɟɫɤɨɟ ɭɜɟɥɢɱɟɧɢɟ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɨɜ ɩɨɜɵɲɚɟɬ ɜɟɪɨɹɬɧɨɫɬɶ ɷɦɢɫɫɢɢ ɢ γɩ ɪɚɫɬɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɬɟɦɩɟɪɚɬɭɪɵ, ɩɪɢ ɷɬɨɦ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɦɢɫɫɢɹ ɜɨɡɦɨɠɧɚ ɢ ɩɪɢ Vi < 2ϕa. ɉɪɢ ɜɵɫɨɤɢɯ ɷɧɟɪɝɢɹɯ ɩɚɞɚɸɳɢɯ ɢɨɧɨɜ ɤɢɧɟɬɢɱɟɫɤɚɹ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɩɪɟɨɛɥɚɞɚɟɬ ɧɚɞ ɩɨɬɟɧɰɢɚɥɶɧɨɣ. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɛɵɥɨ ɨɛɧɚɪɭɠɟɧɨ, ɱɬɨ ɫɭɳɟɫɬɜɭɟɬ ɩɨɪɨɝɨɜɨɟ ɡɧɚɱɟɧɢɟ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɢɨɧɨɜ (Ep)ɝɪ ∼1.5 ɤɷȼ, ɦɟɧɶɲɟ ɤɨɬɨɪɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬ ɷɦɢɫɫɢɢ γɤ ≈ 0. ȼ ɩɪɢɩɨɪɨɝɨɜɨɣ ɨɛɥɚɫɬɢ ɷɧɟɪɝɢɣ ɢɨɧɨɜ (Ep < 10 ɤɷȼ) ɤɨɷɮɮɢɰɢɟɧɬ ɷɦɢɫɫɢɢ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɷɧɟɪɝɢɢ: γɤ = ɋ(Ep - (Ep)ɝɪ), ɝɞɟ ɋ = const. Ⱦɥɹ ɱɢɫɬɵɯ ɦɟɬɚɥɥɨɜ ɋ ≤ 0.2⋅10-2 ɷȼ-1. ɉɪɢ ɛɨɥɟɟ ɜɵɫɨɤɢɯ ɷɧɟɪɝɢɹɯ γɤ ∼ Ep1/2 . ɉɪɢ ɨɛɥɭɱɟɧɢɢ ɦɨɧɨɤɪɢɫɬɚɥɥɨɜ ɤɨɷɮɮɢɰɢɟɧɬ γɤ ɡɚɜɢɫɢɬ ɨɬ ɭɝɥɚ ɩɚɞɟɧɢɹ ɢɨɧɨɜ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ, ɩɪɢɱɟɦ ɷɬɚ ɡɚɜɢɫɢɦɨɫɬɶ ɧɨɫɢɬ ɩɟɪɢɨɞɢɱɟɫɤɢɣ ɯɚɪɚɤɬɟɪ: ɩɨɥɨɠɟɧɢɹ ɦɚɤɫɢɦɭɦɨɜ ɫɨɜɩɚɞɚɸɬ ɫ ɧɚɩɪɚɜɥɟɧɢɹɦɢ ɩɚɞɚɸɳɢɯ ɢɨɧɨɜ ɜɞɨɥɶ ɤɪɢɫɬɚɥɥɨɝɪɚɮɢɱɟɫɤɢɯ ɧɚɩɪɚɜɥɟɧɢɣ ɜ ɦɨɧɨɤɪɢɫɬɚɥɥɟ. ɋɨɜɪɟɦɟɧɧɵɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨ ɤɢɧɟɬɢɱɟɫɤɨɣ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ (ɦɨɞɟɥɶ ɉɚɪɢɥɢɫɚ, ɉɟɬɪɨɜɚ, Ʉɢɲɢɧɟɜɫɤɨɝɨ) ɨɫɧɨɜɵɜɚɸɬɫɹ ɧɚ ɞɜɭɯɷɬɚɩɧɨɫɬɢ ɩɪɨɰɟɫɫɚ. ɇɚ ɩɟɪɜɨɦ ɷɬɚɩɟ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɢɨɧɚ ɩɟɪɟɞɚɟɬɫɹ ɷɥɟɤɬɪɨɧɧɨɣ ɫɢɫɬɟɦɟ ɦɟɬɚɥɥɚ ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ «ɞɵɪɨɤ» (ɩɨɥɭɱɚɹ ɷɧɟɪɝɢɸ, ɷɥɟɤɬɪɨɧɵ ɚɬɨɦɨɜ ɫɨɜɟɪɲɚɸɬ ɦɟɠɡɨɧɧɵɣ ɩɟɪɟɯɨɞ ɜ ɡɨɧɭ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɨɛɪɚɡɭɹ ɞɵɪɤɢ). ɇɚ ɜɬɨɪɨɦ ɷɬɚɩɟ ɩɪɨɢɫɯɨɞɢɬ ɪɟɤɨɦɛɢɧɚɰɢɹ ɞɵɪɤɢ ɢ ɷɥɟɤɬɪɨɧɚ ɩɪɨɜɨɞɢɦɨɫɬɢ ɦɟɬɚɥɥɚ ɫ ɩɟɪɟɞɚɱɟɣ ɜɵɞɟɥɹɸɳɟɣɫɹ ɷɧɟɪɝɢɢ ɡɚ ɫɱɟɬ ɨɠɟ-ɩɪɨɰɟɫɫɚ ɞɪɭɝɨɦɭ ɷɥɟɤɬɪɨɧɭ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɤɨɬɨɪɵɣ ɷɦɢɬɢɪɭɟɬɫɹ ɢɡ ɦɢɲɟɧɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɬɨɪɨɣ ɷɬɚɩ ɤɢɧɟɬɢɱɟɫɤɨɣ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɛɥɢɡɨɤ ɩɨ ɩɪɢɪɨɞɟ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɦɢɫɫɢɢ. ɉɨɜɟɪɯɧɨɫɬɧɚɹ ɢɨɧɢɡɚɰɢɹ
ɂɨɧɧɚɹ ɷɦɢɫɫɢɹ ɜ ɪɟɡɭɥɶɬɚɬɟ ɬɟɪɦɢɱɟɫɤɨɣ ɞɟɫɨɪɛɰɢɢ ɱɚɫɬɢɰ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɧɚɡɵɜɚɟɬɫɹ ɩɨɜɟɪɯɧɨɫɬɧɨɣ ɢɨɧɢɡɚɰɢɟɣ. ȼ ɜɢɞɟ ɢɨɧɨɜ ɦɨɝɭɬ ɢɫɩɚɪɹɬɶɫɹ ɤɚɤ ɚɬɨɦɵ ɫɚɦɨɝɨ ɧɚɝɪɟɬɨɝɨ ɬɟɥɚ (ɧɚɩɪɢɦɟɪ, ɦɟɬɚɥɥɚ), ɬɚɤ ɢ ɚɬɨɦɵ ɢ ɦɨɥɟɤɭɥɵ, ɤɨɬɨɪɵɟ ɩɨɩɚɥɢ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ ɢɡ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ. ɑɚɫɬɶ ɢɡ ɧɢɯ ɩɨɫɥɟ ɚɞɫɨɪɛɢɪɨɜɚɧɢɹ ɢɫɩɚɪɹɸɬɫɹ ɨɛɪɚɬɧɨ ɜ ɝɚɡ, ɧɨ ɭɠɟ ɜ ɜɢɞɟ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢɥɢ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ. ɉɨɜɟɪɯɧɨɫɬɧɚɹ ɢɨɧɢɡɚɰɢɹ ɛɵɥɚ ɨɬɤɪɵɬɚ Ʌɟɧɝɦɸɪɨɦ ɢ Ʉɢɧɝɞɨɧɨɦ (1923 ɝ.), ɤɨɬɨɪɵɟ ɨɛɧɚɪɭɠɢɥɢ ɜ ɰɢɥɢɧɞɪɢɱɟɫɤɨɦ ɞɢɨɞɟ, ɡɚɩɨɥɧɟɧɧɨɦ ɩɚɪɚɦɢ ɰɟɡɢɹ, ɬɨɤ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢɨɧɨɜ. ɋɬɟɩɟɧɶ ɩɨɜɟɪɯɧɨɫɬɧɨɣ
ɢɨɧɢɡɚɰɢɢ α = ni/na, ɝɞɟ ni - ɩɥɨɬɧɨɫɬɶ ɢɨɧɨɜ, ɨɬɥɟɬɚɸɳɢɯ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ, na ɩɥɨɬɧɨɫɬɶ ɢɫɩɚɪɹɸɳɢɯɫɹ ɚɬɨɦɨɜ, ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɡɚɪɹɞɨɜɨɟ ɪɚɜɧɨɜɟɫɢɟ ɜ ɢɫɩɚɪɹɸɳɟɦɫɹ ɩɨɬɨɤɟ ɱɚɫɬɢɰ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɫɩɨɫɨɛɚ ɩɨɫɬɭɩɥɟɧɢɹ ɱɚɫɬɢɰ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ. Ⱦɪɭɝɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɩɨɜɟɪɯɧɨɫɬɧɨɣ ɢɨɧɢɡɚɰɢɢ ɹɜɥɹɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬ ɩɨɜɟɪɯɧɨɫɬɧɨɣ ɢɨɧɢɡɚɰɢɢ β = ni/n = ni/(ni+na) (β=α/(1+α)). Ʉ ɨɩɢɫɚɧɢɸ ɩɪɨɰɟɫɫɚ ɢɨɧɢɡɚɰɢɢ ɢɫɩɚɪɹɸɳɢɯɫɹ ɚɬɨɦɨɜ Ʌɟɧɝɦɸɪ ɩɪɢɦɟɧɢɥ ɮɨɪɦɭɥɭ ɋɚɯɚ ɞɥɹ ɬɟɪɦɢɱɟɫɤɨɣ ɢɨɧɢɡɚɰɢɢ ɝɚɡɚ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɪɢ ɨɛɪɚɡɨɜɚɧɢɢ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢɨɧɨɜ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢ ɪɚɜɧɨɜɟɫɧɵɣ ɢɨɧɢɡɚɰɢɨɧɧɵɣ ɫɨɫɬɚɜ ɭ ɩɨɜɟɪɯɧɨɫɬɢ ɬɟɥɚ ɦɨɠɧɨ ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɫɬɟɩɟɧɶɸ ɢɨɧɢɡɚɰɢɢ α, ɤɨɬɨɪɚɹ ɜɵɱɢɫɥɹɟɬɫɹ ɢɡ ɭɪɚɜɧɟɧɢɹ ɋɚɯɚ-Ʌɟɧɝɦɸɪɚ:
α=
gi e(ϕ a − U i ) exp( ), ga kT
(7.37)
ɝɞɟ Ui – ɩɨɬɟɧɰɢɚɥ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ, eϕa – ɪɚɛɨɬɚ ɜɵɯɨɞɚ ɷɥɟɤɬɪɨɧɨɜ ɢɡ ɦɟɬɚɥɥɚ, gi/ga – ɨɬɧɨɲɟɧɢɟ ɫɬɚɬɢɫɬɢɱɟɫɤɢɯ ɜɟɫɨɜ ɢɨɧɧɨɝɨ ɢ ɚɬɨɦɧɨɝɨ ɫɨɫɬɨɹɧɢɣ ɢɨɧɢɡɢɪɭɸɳɢɯɫɹ ɱɚɫɬɢɰ ɪɚɜɧɨ ½ ɞɥɹ ɨɞɧɨɜɚɥɟɧɬɧɨɝɨ ɚɞɫɨɪɛɢɪɭɸɳɟɝɨ ɦɟɬɚɥɥɚ ɢ 2 - ɞɥɹ ɞɜɭɯɜɚɥɟɧɬɧɨɝɨ. ȿɫɥɢ ɷɧɟɪɝɢɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɩɨɤɪɵɬɢɹ (ɧɚɩɪɢɦɟɪ, Cs, K, Na ɧɚ W) ɦɟɧɶɲɟ ɪɚɛɨɬɵ ɜɵɯɨɞɚ ɷɥɟɤɬɪɨɧɨɜ ɢɡ ɦɟɬɚɥɥɢɱɟɫɤɨɣ ɩɨɞɥɨɠɤɢ, ɬɨ ɩɪɚɤɬɢɱɟɫɤɢ ɜɫɟ ɢɫɩɚɪɹɸɳɢɟɫɹ ɫ ɩɨɤɪɵɬɢɹ ɚɬɨɦɵ ɩɨɤɢɞɚɸɬ ɩɨɜɟɪɯɧɨɫɬɶ ɜ ɜɢɞɟ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢɨɧɨɜ. Ⱥɬɨɦɵ ɧɟɤɨɬɨɪɵɯ ɷɥɟɦɟɧɬɨɜ ɦɨɝɭɬ ɩɨɤɢɞɚɬɶ ɩɨɜɟɪɯɧɨɫɬɶ, ɩɪɢɫɨɟɞɢɧɹɹ ɤ ɫɟɛɟ ɷɥɟɤɬɪɨɧ ɢ ɩɪɟɜɪɚɳɚɹɫɶ ɜ ɨɬɪɢɰɚɬɟɥɶɧɵɣ ɢɨɧ. Ⱦɥɹ ɪɚɡɪɭɲɟɧɢɹ ɨɬɪɢɰɚɬɟɥɶɧɨɝɨ ɢɨɧɚ ɬɪɟɛɭɟɬɫɹ ɫɨɜɟɪɲɢɬɶ ɧɟɤɨɬɨɪɭɸ ɪɚɛɨɬɭ, ɤɨɬɨɪɭɸ ɚɬɨɦɨɜ ɧɚɡɵɜɚɸɬ ɪɚɛɨɬɨɣ ɫɪɨɞɫɬɜɚ eS. ɑɚɫɬɶ ɬɚɤɢɯ ɚɞɫɨɪɛɢɪɨɜɚɧɧɵɯ ɢɫɩɚɪɹɸɬɫɹ ɜ ɜɢɞɟ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɬɟɩɟɧɢ ɢɨɧɢɡɚɰɢɢ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɭɪɚɜɧɟɧɢɟ, ɚɧɚɥɨɝɢɱɧɨɟ ɭɪɚɜɧɟɧɢɸ ɋɚɯɚ-Ʌɟɧɝɦɸɪɚ:
α− =
e( S − ϕ a ) g− exp( ). ga kT
(7.38)
ȽɅȺȼȺ 8 ɗɅȿɄɌɊɂɑȿɋɄɂɃ ɌɈɄ ȼ ȽȺɁȺɏ ɂ ȽȺɁɈȼɕɃ ɊȺɁɊəȾ Ƚɚɡɨɜɵɣ ɪɚɡɪɹɞ − ɷɬɨ ɩɪɨɰɟɫɫ ɩɪɨɬɟɤɚɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ ɱɟɪɟɡ ɝɚɡ. Ɋɚɡɥɢɱɚɸɬ ɧɟɫɚɦɨɫɬɨɹɬɟɥɶɧɵɟ ɢ ɫɚɦɨɫɬɨɹɬɟɥɶɧɵɟ ɪɚɡɪɹɞɵ. ɇɟɫɚɦɨɫɬɨɹɬɟɥɶɧɵɣ ɪɚɡɪɹɞ ɜɨɡɦɨɠɟɧ ɩɪɢ ɢɧɠɟɤɰɢɢ ɷɥɟɤɬɪɨɧɨɜ ɜ ɪɚɡɪɹɞɧɵɣ ɩɪɨɦɟɠɭɬɨɤ (ɧɚɩɪɢɦɟɪ, ɬɟɪɦɨɷɦɢɫɫɢɹ ɫ ɤɚɬɨɞɚ) ɢɥɢ ɩɪɢ ɢɨɧɢɡɚɰɢɢ ɝɚɡɚ ɤɚɤɢɦɥɢɛɨ ɜɧɟɲɧɢɦ ɢɫɬɨɱɧɢɤɨɦ. ɇɟɫɚɦɨɫɬɨɹɬɟɥɶɧɵɟ ɪɚɡɪɹɞɵ ɢɫɩɨɥɶɡɭɸɬ ɞɨɜɨɥɶɧɨ ɲɢɪɨɤɨ: ɷɬɨ ɢ ɢɨɧɢɡɚɰɢɨɧɧɵɟ ɤɚɦɟɪɵ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɢ ɞɨɡɢɦɟɬɪɢɱɟɫɤɨɝɨ ɧɚɡɧɚɱɟɧɢɹ ɧɚ ɚɬɨɦɧɵɯ ɪɟɚɤɬɨɪɚɯ, ɝɚɡɨɬɪɨɧɵ ɜ ɜɵɩɪɹɦɢɬɟɥɶɧɵɯ ɭɫɬɚɧɨɜɤɚɯ ɫɟɬɟɣ ɩɢɬɚɧɢɹ ɩɨɫɬɨɹɧɧɵɦ ɬɨɤɨɦ, ɩɥɚɡɦɨɬɪɨɧɵ ɫ ɧɚɤɚɥɢɜɚɟɦɵɦ ɤɚɬɨɞɨɦ ɢ ɬ.ɞ. Ɏɢɡɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ, ɩɪɨɬɟɤɚɸɳɢɟ ɜ ɪɚɡɧɵɯ ɧɟɫɚɦɨɫɬɨɹɬɟɥɶɧɵɯ ɪɚɡɪɹɞɚɯ, ɟɫɬɟɫɬɜɟɧɧɨ, ɪɚɡɥɢɱɚɸɬɫɹ, ɧɨ ɧɟ ɜɫɟ ɨɧɢ ɯɚɪɚɤɬɟɪɧɵ ɞɥɹ ɫɨɛɫɬɜɟɧɧɨ ɝɚɡɨɜɵɯ ɪɚɡɪɹɞɨɜ, ɤɚɤ ɨɛɵɱɧɨ ɩɨɧɢɦɚɸɬ ɷɬɨɬ ɬɟɪɦɢɧ. ȼ ɧɢɯ ɫ ɩɨɦɨɳɶɸ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɩɪɨɫɬɨ ɫɨɛɢɪɚɸɬ ɨɛɪɚɡɭɸɳɢɟɫɹ ɜ ɨɛɴɟɦɟ ɡɚɪɹɞɵ (ɱɬɨ ɜɨɨɛɳɟ-ɬɨ ɧɟ ɫɨɜɫɟɦ "ɩɪɨɫɬɨ"!), ɜ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɯ ɫɱɟɬɱɢɤɚɯ ɢɫɩɨɥɶɡɭɸɬ ɨɝɪɚɧɢɱɟɧɧɨɟ ɨɛɪɚɡɨɜɚɧɢɟ ɷɥɟɤɬɪɨɧɧɵɯ ɥɚɜɢɧ, ɜ ɝɟɣɝɟɪɨɜɫɤɢɯ ɫɱɟɬɱɢɤɚɯ ɩɪɨɢɫɯɨɞɢɬ ɤɨɪɨɧɧɵɣ ɪɚɡɪɹɞ, ɜ ɝɚɡɨɬɪɨɧɚɯ ɢ ɬɢɪɚɬɪɨɧɚɯ «ɨɛɯɨɞɹɬ» ɡɚɤɨɧ «3/2», ɤɚɤ ɛɵ ɩɪɢɛɥɢɠɚɹ ɚɧɨɞ ɤ ɤɚɬɨɞɭ, ɜ ɞɭɝɨɜɵɯ ɥɚɦɩɚɯ ɞɧɟɜɧɨɝɨ ɫɜɟɬɚ ɬɟɪɦɨɷɦɢɫɫɢɹ ɫ ɩɨɞɨɝɪɟɜɧɵɯ ɤɚɬɨɞɨɜ ɬɨɥɶɤɨ ɨɛɟɫɩɟɱɢɜɚɟɬ ɡɚɠɢɝɚɧɢɟ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɣ ɞɭɝɢ. Ɉɞɧɚɤɨ ɧɚɢɛɨɥɟɟ ɲɢɪɨɤɨ ɩɪɢɦɟɧɹɸɬɫɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɵɟ ɪɚɡɪɹɞɵ, ɨ ɧɢɯ ɢ ɛɭɞɟɬ ɪɟɱɶ. ɋɚɦɨɫɬɨɹɬɟɥɶɧɵɣ ɬɥɟɸɳɢɣ ɪɚɡɪɹɞ ɡɚɠɢɝɚɟɬɫɹ ɬɨɝɞɚ, ɤɨɝɞɚ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɟɝɨ ɚɤɬɢɜɧɵɯ ɭɱɚɫɬɤɚɯ ɞɨɫɬɢɝɚɟɬ "ɧɚɩɪɹɠɟɧɢɹ ɩɪɨɛɨɹ", ɞɥɹ ɞɭɝɨɜɨɝɨ ɪɚɡɪɹɞɚ ɧɟɨɛɯɨɞɢɦɨ ɫɨɡɞɚɬɶ ɭɫɥɨɜɢɹ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɬɟɪɦɨɷɦɢɫɫɢɢ ɫ ɤɚɬɨɞɚ. Ʉɨɪɨɧɧɵɟ ɪɚɡɪɹɞɵ ɜɨɡɧɢɤɚɸɬ ɬɨɥɶɤɨ ɩɪɢ ɧɚɥɢɱɢɢ ɭɱɚɫɬɤɨɜ ɫ ɨɱɟɧɶ ɛɨɥɶɲɨɣ ɧɟɨɞɧɨɪɨɞɧɨɫɬɶɸ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɚ ɢɫɤɪɨɜɵɟ ɪɚɡɪɹɞɵ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɢɦɩɭɥɶɫɧɵɟ. ȼɫɟ ɷɬɨ ɫɩɪɚɜɟɞɥɢɜɨ ɞɥɹ ɩɨɫɬɨɹɧɧɵɯ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ, ɭ ɩɨɥɟɣ ȼɑ ɢ ɋȼɑ, ɤɨɬɨɪɵɟ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɸɬɫɹ ɜ ɬɟɯɧɨɥɨɝɢɹɯ, ɟɫɬɶ ɫɜɨɹ ɫɩɟɰɢɮɢɤɚ, ɨɫɨɛɟɧɧɨ ɭ ɩɨɥɟɣ ɥɚɡɟɪɧɨɣ ɢɫɤɪɵ. §49. ɗɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ ɜ ɝɚɡɚɯ ɋɬɨɥɤɧɨɜɟɧɢɹ ɱɚɫɬɢɰ ɦɨɝɭɬ ɢɦɟɬɶ ɭɩɪɭɝɢɣ ɢ ɧɟɭɩɪɭɝɢɣ ɯɚɪɚɤɬɟɪ. ɉɪɢ ɭɩɪɭɝɨɦ ɫɬɨɥɤɧɨɜɟɧɢɢ ɦɟɧɹɟɬɫɹ ɧɚɩɪɚɜɥɟɧɢɟ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ, ɩɪɨɢɫɯɨɞɢɬ ɨɛɦɟɧ ɢɦɩɭɥɶɫɚɦɢ ɢ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɟɣ. ɉɪɢ ɧɟɭɩɪɭɝɨɦ ɫɬɨɥɤɧɨɜɟɧɢɢ ɜɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ ɢ ɫɨɫɬɨɹɧɢɟ ɨɞɧɨɣ ɢɡ ɱɚɫɬɢɰ (ɪɟɞɤɨ ɤɨɝɞɚ ɨɛɨɢɯ) ɢɡɦɟɧɹɟɬɫɹ. ɂɨɧɢɡɚɰɢɹ ɚɬɨɦɚ ɩɪɢ ɭɞɚɪɟ ɷɥɟɤɬɪɨɧɨɦ ɩɪɨɢɫɯɨɞɢɬ ɡɚ ɫɱɟɬ ɩɟɪɟɞɚɱɢ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ ɚɬɨɦɭ. Ɂɧɚɱɟɧɢɟ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ, ɞɨɫɬɚɬɨɱɧɨɟ ɞɥɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚ ɧɚɡɵɜɚɟɬɫɹ ɩɨɬɟɧɰɢɚɥɨɦ ɢɨɧɢɡɚɰɢɢ Ui. ɉɪɢ ɦɧɨɝɨɤɪɚɬɧɨɣ ɢɨɧɢɡɚɰɢɢ ɷɧɟɪɝɢɹ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɨɬɪɵɜɚ ɤɚɠɞɨɝɨ ɫɥɟɞɭɸɳɟɝɨ ɷɥɟɤɬɪɨɧɚ ɜɨɡɪɚɫɬɚɟɬ. ɉɢɨɧɟɪɚɦɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɝɨ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɚ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɛɵɥɢ Ɏɪɚɧɤ ɢ Ƚɟɪɰ. Ɇɟɬɨɞ ɨɩɪɟɞɟɥɟɧɢɹ ɨɫɧɨɜɵɜɚɥɫɹ ɧɚ ɬɨɦ, ɱɬɨ ɡɚɜɢɫɢɦɨɫɬɶ ɬɨɤɚ, ɩɪɨɬɟɤɚɸɳɟɝɨ ɱɟɪɟɡ ɞɢɨɞ ɜ ɩɚɪɚɯ ɪɬɭɬɢ, ɨɬ ɭɫɤɨɪɹɸɳɟɝɨ ɷɥɟɤɬɪɨɧɵ ɧɚɩɪɹɠɟɧɢɹ ɧɨɫɢɬ ɧɟ ɦɨɧɨɬɨɧɧɵɣ ɜɨɡɪɚɫɬɚɸɳɢɣ ɯɚɪɚɤɬɟɪ, ɚ ɢɦɟɟɬ ɩɪɨɜɚɥɵ ɢɡ-ɡɚ ɩɨɬɟɪɶ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɜɨɡɛɭɠɞɟɧɢɟ ɢ ɢɨɧɢɡɚɰɢɸ ɚɬɨɦɨɜ ɪɬɭɬɢ. Ɂɚɜɢɫɢɦɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɢ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɥɸɛɨɝɨ ɝɚɡɚ ɨɬ ɷɧɟɪɝɢɢ ɱɚɫɬɢɰ U ɡɚɞɚɟɬɫɹ ɮɭɧɤɰɢɟɣ ɢɨɧɢɡɚɰɢɢ: fi = a(U-Ui)exp(-(U-Ui)/b),
(8.1)
ɝɞɟ a ɢ b − ɷɦɩɢɪɢɱɟɫɤɢɟ ɤɨɧɫɬɚɧɬɵ ɞɥɹ ɤɨɧɤɪɟɬɧɨɝɨ ɝɚɡɚ. ȼɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ, ɩɪɢɜɨɞɹɳɢɦɢ ɤ ɢɨɧɢɡɚɰɢɢ, ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɱɚɫɬɨɬɟ ɢɨɧɢɡɚɰɢɢ τi = 1/νi. ɑɢɫɥɨ ɢɨɧɢɡɚɰɢɣ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɩɥɨɬɧɨɫɬɢ ɱɚɫɬɢɰ ɝɚɡɚ n, ɫɤɨɪɨɫɬɢ ɧɚɥɟɬɚɸɳɟɣ ɱɚɫɬɢɰɵ v ɢ ɫɟɱɟɧɢɸ ɢɨɧɢɡɚɰɢɢ σi : νi = nvσi. (8.2) ɂɨɧɢɡɚɰɢɨɧɧɵɣ ɩɪɨɛɟɝ λi (ɞɥɢɧɚ, ɧɚ ɤɨɬɨɪɨɣ ɱɚɫɬɢɰɚ ɦɨɠɟɬ ɢɨɧɢɡɨɜɚɬɶ) ɪɚɜɟɧ λi = vτi = v/νi = 1/(nσi) = 1/Si,
(8.3)
ɝɞɟ Si = nσi ɧɚɡɵɜɚɟɬɫɹ ɫɭɦɦɚɪɧɵɦ ɫɟɱɟɧɢɟɦ ɢɨɧɢɡɚɰɢɢ. ɋɭɦɦɚɪɧɨɟ ɫɟɱɟɧɢɟ ɢɨɧɢɡɚɰɢɢ ɬɚɤ ɠɟ ɯɨɪɨɲɨ ɚɩɩɪɨɤɫɢɦɢɪɭɟɬɫɹ ɩɨɞɨɛɧɨɣ (8.1) ɡɚɜɢɫɢɦɨɫɬɶɸ ɨɬ ɷɧɟɪɝɢɢ ɱɚɫɬɢɰɵ U: Si = a (U - Ui) exp(- b(U - Ui) ) (ɮɨɪɦɭɥɚ Ɇɨɪɝɭɥɢɫɚ),
(8.4)
ɝɞɟ a ɢ b – ɷɦɩɢɪɢɱɟɫɤɢɟ ɤɨɧɫɬɚɧɬɵ ɞɥɹ ɤɨɧɤɪɟɬɧɨɝɨ ɝɚɡɚ. Ɂɚɜɢɫɢɦɨɫɬɶ ɫɭɦɦɚɪɧɨɝɨ ɫɟɱɟɧɢɹ ɜɨɡɛɭɠɞɟɧɢɹ ɢɦɟɟɬ ɩɨɯɨɠɢɣ ɜɢɞ: S r = S max
U −Ur U −Ur exp(1 − ) (ɮɨɪɦɭɥɚ Ɏɚɛɪɢɤɚɧɬɚ), (8.5) U max − U r U max − U r
ɝɞɟ Ur – ɩɨɬɟɧɰɢɚɥ ɜɨɡɛɭɠɞɟɧɧɨɝɨ ɭɪɨɜɧɹ, Umax ɢ Smax – ɷɧɟɪɝɢɹ ɢ ɫɟɱɟɧɢɟ ɜɨɡɛɭɠɞɟɧɢɹ ɜ ɦɚɤɫɢɦɭɦɟ ɮɭɧɤɰɢɢ ɜɨɡɛɭɠɞɟɧɢɹ, ɡɧɚɱɟɧɢɹ ɤɨɬɨɪɵɯ ɦɨɠɧɨ ɧɚɣɬɢ ɜ ɫɩɪɚɜɨɱɧɵɯ ɬɚɛɥɢɰɚɯ ɞɥɹ ɤɨɧɤɪɟɬɧɨɝɨ ɝɚɡɚ. ȼɪɟɦɹ ɩɪɟɛɵɜɚɧɢɹ ɚɬɨɦɚ ɜ ɜɨɡɛɭɠɞɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ ɦɨɠɧɨ ɫɜɹɡɚɬɶ ɫ ɱɢɫɥɨɦ ɩɟɪɟɯɨɞɨɜ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ N, ɬɨɝɞɚ ɡɚ ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ dt ɱɢɫɥɨ ɩɟɪɟɯɨɞɨɜ: Ndt = wnadt, ɝɞɟ w – ɜɟɪɨɹɬɧɨɫɬɶ ɞɚɧɧɨɝɨ ɩɟɪɟɯɨɞɚ na - ɤɨɧɰɟɧɬɪɚɰɢɹ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ. ɑɢɫɥɨ ɚɤɬɨɜ ɢɡɥɭɱɟɧɢɹ ɪɚɜɧɨ ɭɛɵɥɢ ɱɢɫɥɚ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ: Ndt = -dna, ɬɨɝɞɚ dna = - wnadt. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɢɫɥɨ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ ɢɡɦɟɧɹɟɬɫɹ ɜɨ ɜɪɟɦɟɧɢ ɩɨ ɡɚɤɨɧɭ: na(t) = na0exp(-wt),
(8.6)
ɝɞɟ na0 – ɤɨɧɰɟɧɬɪɚɰɢɹ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ. Ɂɚ ɜɪɟɦɹ t0 = 1/w ɤɨɧɰɟɧɬɪɚɰɢɹ ɭɦɟɧɶɲɚɟɬɫɹ ɜ «ɟ» ɪɚɡ. ɗɬɨ ɜɪɟɦɹ ɢ ɩɨɥɚɝɚɸɬ ɜɪɟɦɟɧɟɦ ɩɪɟɛɵɜɚɧɢɹ ɚɬɨɦɚ ɜ ɜɨɡɛɭɠɞɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ. ɇɟɫɦɨɬɪɹ ɧɚ ɦɚɥɨɫɬɶ ɷɬɨɣ ɜɟɥɢɱɢɧɵ t0 ∼ 10-8 ÷ 10-7 ɫ, ɞɚɠɟ ɡɚ ɫɬɨɥɶ ɤɨɪɨɬɤɨɟ ɜɪɟɦɹ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɜɨɡɛɭɠɞɟɧɧɨɝɨ ɚɬɨɦɚ ɜɨɡɦɨɠɧɨ ɩɨɥɭɱɟɧɢɟ ɧɨɜɨɣ ɩɨɪɰɢɢ ɷɧɟɪɝɢɢ, ɞɨɫɬɚɬɨɱɧɨɣ ɞɥɹ ɩɟɪɟɯɨɞɚ ɚɬɨɦɚ ɧɚ ɫɥɟɞɭɸɳɢɣ ɭɪɨɜɟɧɶ ɜɨɡɛɭɠɞɟɧɢɹ, ɥɢɛɨ ɞɥɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚ, ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɝɨɜɨɪɹɬ ɨ ɫɬɭɩɟɧɱɚɬɨɣ ɢɨɧɢɡɚɰɢɢ. ɂɦɟɧɧɨ ɬɚɤɨɣ ɩɪɨɰɟɫɫ ɫɬɭɩɟɧɱɚɬɨɣ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɪɬɭɬɢ ɧɚɛɥɸɞɚɥɫɹ ɜ ɨɩɵɬɚɯ Ɏɪɚɧɤɚ ɢ Ƚɟɪɰɚ. ɋɪɟɞɢ ɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɚɬɨɦɨɜ ɢ ɦɨɥɟɤɭɥ ɫɭɳɟɫɬɜɭɸɬ ɦɟɬɚɫɬɚɛɢɥɶɧɵɟ ɫɨɫɬɨɹɧɢɹ, ɜɪɟɦɟɧɚ ɠɢɡɧɢ ɤɨɬɨɪɵɯ ɨɬ 10-4 ɞɨ ɧɟɫɤɨɥɶɤɢɯ ɫɟɤɭɧɞ. ɋɚɦɵɣ ɧɢɠɧɢɣ ɦɟɬɚɫɬɚɛɢɥɶɧɵɣ ɭɪɨɜɟɧɶ ɧɚɡɵɜɚɟɬɫɹ ɪɟɡɨɧɚɧɫɧɵɦ. Ⱦɥɹ ɪɬɭɬɢ ɪɟɡɨɧɚɧɫɧɵɣ ɭɪɨɜɟɧɶ ɜɨɡɛɭɠɞɟɧɢɹ ɪɚɜɟɧ 4.7 ɷȼ, ɩɪɢ ɩɪɟɜɵɲɟɧɢɢ ɷɧɟɪɝɢɟɣ ɷɥɟɤɬɪɨɧɨɜ ɷɬɨɝɨ ɡɧɚɱɟɧɢɹ ɧɚɛɥɸɞɚɥɫɹ ɩɟɪɜɵɣ ɩɪɨɜɚɥ ɜ ɡɚɜɢɫɢɦɨɫɬɢ
ɬɨɤɚ ɨɬ ɭɫɤɨɪɹɸɳɟɝɨ ɷɥɟɤɬɪɨɧɵ ɩɨɬɟɧɰɢɚɥɚ. Ɇɟɬɚɫɬɚɛɢɥɶɧɚɹ ɱɚɫɬɢɰɚ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɫ ɷɥɟɤɬɪɨɧɨɦ ɦɨɠɟɬ ɢ ɞɟɡɚɤɬɢɜɢɪɨɜɚɬɶɫɹ, ɬɨ ɟɫɬɶ ɩɟɪɟɣɬɢ ɜ ɨɫɧɨɜɧɨɟ ɫɨɫɬɨɹɧɢɟ, ɷɬɨɬ ɩɪɨɰɟɫɫ ɧɚɡɵɜɚɟɬɫɹ ɧɟɭɩɪɭɝɢɦ ɫɨɭɞɚɪɟɧɢɟɦ ɜɬɨɪɨɝɨ ɪɨɞɚ. Ʉɪɨɦɟ ɨɛɪɚɡɨɜɚɧɢɹ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢɨɧɨɜ ɩɪɢ ɩɪɨɬɟɤɚɧɢɢ ɬɨɤɚ ɜ ɝɚɡɟ ɜɨɡɦɨɠɧɨ ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ. Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɨɬɪɢɰɚɬɟɥɶɧɵɣ ɢɨɧ ɫɭɳɟɫɬɜɨɜɚɥ ɢ ɛɵɥ ɭɫɬɨɣɱɢɜ, ɟɝɨ ɜɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ Ei ɞɨɥɠɧɚ ɛɵɬɶ ɦɟɧɶɲɟ, ɱɟɦ ɷɧɟɪɝɢɹ ɧɨɪɦɚɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɩɚɪɵ ɚɬɨɦ – ɫɜɨɛɨɞɧɵɣ ɷɥɟɤɬɪɨɧ E0. Ɋɚɡɧɨɫɬɶ A = E0 – Ei ɧɚɡɵɜɚɟɬɫɹ ɫɪɨɞɫɬɜɨɦ ɚɬɨɦɚ ɤ ɷɥɟɤɬɪɨɧɭ. ȼ ɚɬɨɦɚɯ ɫ ɡɚɩɨɥɧɟɧɧɨɣ ɜɧɟɲɧɟɣ ɷɥɟɤɬɪɨɧɧɨɣ ɨɛɨɥɨɱɤɨɣ (ɢɧɟɪɬɧɵɟ ɝɚɡɵ He, Ne, Ar, Xe, Kr,..) ɷɥɟɤɬɪɨɧɧɚɹ ɨɛɨɥɨɱɤɚ ɷɤɪɚɧɢɪɭɟɬ ɹɞɪɨ ɢ ɜɟɪɨɹɬɧɨɫɬɶ ɨɛɪɚɡɨɜɚɧɢɹ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ ɦɚɥɚ. Ⱥɬɨɦɵ ɫ ɧɟɩɨɥɧɵɦɢ ɜɧɟɲɧɢɦɢ ɨɛɨɥɨɱɤɚɦɢ (F, Cl, K, Na…), ɭ ɤɨɬɨɪɵɯ ɨɛɨɥɨɱɤɢ ɛɥɢɠɟ ɜɫɟɝɨ ɤ ɡɚɩɨɥɧɟɧɢɸ, ɨɛɪɚɡɭɸɬ ɧɚɢɛɨɥɟɟ ɭɫɬɨɣɱɢɜɵɟ ɨɬɪɢɰɚɬɟɥɶɧɵɟ ɢɨɧɵ. ɋɪɨɞɫɬɜɨ ɷɬɢɯ ɚɬɨɦɨɜ ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɨ: AF − = 3.4 ÷ 3.6 ɷȼ, ACl − = 3.82 ɷȼ. ȿɫɥɢ ɷɥɟɤɬɪɨɧ ɞɨ ɫɬɨɥɤɧɨɜɟɧɢɹ ɢɦɟɥ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ Ek, ɬɨ ɩɪɢ ɟɝɨ ɡɚɯɜɚɬɟ ɞɨɥɠɧɚ ɨɫɜɨɛɨɠɞɚɬɶɫɹ ɷɧɟɪɝɢɹ A + Ek. ɗɬɚ ɷɧɟɪɝɢɹ ɦɨɠɟɬ ɨɫɜɨɛɨɠɞɚɬɶɫɹ ɱɟɪɟɡ ɢɡɥɭɱɟɧɢɟ: e + a → a- + hγ, ɧɨ ɛɨɥɟɟ ɜɟɪɨɹɬɟɧ ɩɪɨɰɟɫɫ ɨɛɪɚɡɨɜɚɧɢɹ ɨɬɪɢɰɚɬɟɥɶɧɨɝɨ ɢɨɧɚ ɜ ɪɟɡɭɥɶɬɚɬɟ ɫɬɨɥɤɧɨɜɟɧɢɹ ɬɪɟɯ ɬɟɥ X + Y + e → X+ + Y- + e ɢɥɢ X + Y → X+ + Y- . Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ ɜ ɝɚɡɚɯ ɧɟɞɨɫɬɚɬɨɱɧɨ ɪɚɫɫɦɨɬɪɟɧɢɹ ɩɪɨɰɟɫɫɨɜ ɢɨɧɢɡɚɰɢɢ ɢ ɪɟɤɨɦɛɢɧɚɰɢɢ. ɇɟɨɛɯɨɞɢɦɨ ɨɩɢɫɚɧɢɟ ɞɜɢɠɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɢ ɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ, ɩɪɢɱɟɦ ɫɬɚɬɢɫɬɢɱɟɫɤɨɟ, ɬ. ɟ. ɭɫɪɟɞɧɟɧɧɨɟ ɩɨ ɦɧɨɝɨɱɢɫɥɟɧɧɵɦ ɫɬɨɥɤɧɨɜɟɧɢɹɦ. ɉɪɢ ɧɚɥɢɱɢɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɧɚ ɯɚɨɬɢɱɟɫɤɨɟ ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰ ɧɚɤɥɚɞɵɜɚɟɬɫɹ ɧɚɩɪɚɜɥɟɧɧɨɟ ɞɜɢɠɟɧɢɟ ɜɞɨɥɶ ɩɨɥɹ. Ⱦɥɹ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɩɪɨɰɟɫɫɚ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɬɨɤɚ ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɢ ɫɪɟɞɧɹɹ ɫɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɞɨɥɠɧɵ ɨɫɬɚɜɚɬɶɫɹ ɩɨɫɬɨɹɧɧɵɦɢ, ɧɟɫɦɨɬɪɹ ɧɚ ɩɪɢɫɭɬɫɬɜɢɟ ɭɫɤɨɪɹɸɳɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. ɗɬɨ ɜɨɡɦɨɠɧɨ, ɟɫɥɢ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɫɢɥɚ ɤɨɦɩɟɧɫɢɪɭɟɬɫɹ ɫɢɥɨɣ ɬɪɟɧɢɹ (ɷɥɟɤɬɪɨɧɵ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɹɯ ɨɬɞɚɸɬ ɱɚɫɬɶ ɫɜɨɟɣ ɷɧɟɪɝɢɢ). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɪɟɞɧɹɹ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɨɬ ɨɞɧɨɝɨ ɷɥɟɤɬɪɨɞɚ ɤ ɞɪɭɝɨɦɭ, ɤɨɬɨɪɭɸ ɧɚɡɵɜɚɸɬ ɫɤɨɪɨɫɬɶɸ ɞɪɟɣɮɚ ud, ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ. Ɉɬɧɨɲɟɧɢɟ ɫɤɨɪɨɫɬɢ ɧɚɩɪɚɜɥɟɧɧɨɝɨ ɞɜɢɠɟɧɢɹ (ɫɤɨɪɨɫɬɢ ɞɪɟɣɮɚ) ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɤ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɧɚɡɵɜɚɟɬɫɹ ɩɨɞɜɢɠɧɨɫɬɶɸ:
b[ɫɦ2/(ȼ⋅ɫɦ)] = ud/E.
(8.7)
ɋɤɨɪɨɫɬɶ ɞɪɟɣɮɚ ɦɨɠɧɨ ɨɰɟɧɢɬɶ ɢɡ ɩɪɟɞɩɨɥɨɠɟɧɢɹ, ɱɬɨ ɨɧɚ ɦɧɨɝɨ ɦɟɧɶɲɟ ɬɟɩɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɫɬɨɥɤɧɨɜɟɧɢɹ ɱɚɫɬɢɰɚ ɬɟɪɹɟɬ ɜɫɸ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ. Ɂɚ ɜɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ τɫɬ ɡɚɪɹɠɟɧɧɚɹ eE τ ɫɬ , ud = S/τɫɬ, ɬɨɝɞɚ: ɱɚɫɬɢɰɚ ɩɪɨɣɞɟɬ ɩɭɬɶ S = 2me
be =
eλɫɬ , 2mvɌ
(8.8)
ɝɞɟ λ ɫɬ - ɫɪɟɞɧɹɹ ɞɥɢɧɚ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ, vɌ - ɬɟɩɥɨɜɚɹ ɫɤɨɪɨɫɬɶ. Ⱦɥɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ɇɚɤɫɜɟɥɥɥɚ ɭɫɪɟɞɧɟɧɧɚɹ ɩɨ ɫɤɨɪɨɫɬɹɦ ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ (ɮɨɪɦɭɥɚ Ʌɚɧɠɟɜɟɧɚ):
u d [ɫɦ / ɫ] =
eλ 2me eE eλ E[ ȼ / ɫɦ] λ ɫɬ = 0.64 ɫɬ E = 0.64 1 ⋅ , πkT 2me mvɌ mvɌ p[ ɦɦ. ɪɬ.ɫɬ.]
(8.9)
ɝɞɟ λ1 = pλɫɬ - ɫɪɟɞɧɢɣ ɩɪɨɛɟɝ ɩɪɢ ɞɚɜɥɟɧɢɢ 1 ɦɦ.ɪɬ.ɫɬ. Ⱦɥɹ ɫɪɟɞɧɟɣ ɫɤɨɪɨɫɬɢ ɞɪɟɣɮɚ ɢɨɧɨɜ ɮɨɪɦɭɥɚ Ʌɚɧɠɟɜɟɧɚ ɢɦɟɟɬ ɜɢɞ:
u d = ai
eλi1 m E 1+ i ⋅ , mi viɌ mµ p
(8.10)
ai – ɤɨɷɮɮɢɰɢɟɧɬ, ɪɚɜɧɵɣ 0.5 ÷1, mµ - ɦɚɫɫɚ ɦɨɥɟɤɭɥɵ ɢɨɧɚ. ɗɥɟɤɬɪɨɧɵ ɧɚ ɫɜɨɟɦ ɩɭɬɢ ɢɨɧɢɡɭɸɬ ɚɬɨɦɵ, «ɢɨɧɢɡɭɸɳɭɸ» ɫɩɨɫɨɛɧɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɚɧɝɥɢɱɚɧɢɧ Ɍɚɭɧɫɟɧɞ ɩɪɟɞɥɨɠɢɥ ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɤɨɷɮɮɢɰɢɟɧɬɨɦ α, ɧɚɡɜɚɧɧɵɦ ɜɩɨɫɥɟɞɫɬɜɢɢ ɩɟɪɜɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ Ɍɚɭɧɫɟɧɞɚ, ɪɚɜɧɵɦ ɱɢɫɥɭ ɷɥɟɤɬɪɨɧɨɜ, ɫɨɡɞɚɜɚɟɦɵɯ ɷɥɟɤɬɪɨɧɨɦ ɧɚ ɟɞɢɧɢɰɟ ɞɥɢɧɵ ɩɪɨɛɟɝɚ. ɉɪɢ ɬɚɤɨɦ ɨɩɢɫɚɧɢɢ ɩɪɢɪɨɫɬ ɤɨɥɢɱɟɫɬɜɚ ɷɥɟɤɬɪɨɧɨɜ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ α ɢ ɤɨɥɢɱɟɫɬɜɭ ɚɬɨɦɨɜ n: dn(x) = αndx. Ɍɨɝɞɚ ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɪɚɫɫɬɨɹɧɢɢ x:
ne(x)=n0exp(αx),
(8.11)
ɚ ɩɟɪɜɵɣ ɤɨɷɮɮɢɰɢɟɧɬ Ɍɚɭɧɫɟɧɞɚ:
α = (1/n)(dn/dx).
(8.12)
ɉɪɨɰɟɫɫ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɦɨɠɧɨ ɬɚɤɠɟ ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɱɚɫɬɨɬɨɣ ɢɨɧɢɡɚɰɢɢ Yi – ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ, ɫɨɡɞɚɜɚɟɦɵɯ ɨɞɧɢɦ ɷɥɟɤɬɪɨɧɨɦ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ:
Yi = (1/n)(dn/dt).
(8.13)
Ɍɨɝɞɚ ɱɚɫɬɨɬɚ ɢɨɧɢɡɚɰɢɢ ɫɜɹɡɚɧɚ ɫ ɩɟɪɜɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ Ɍɚɭɧɫɟɧɞɚ ɱɟɪɟɡ ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ:
Yi/α = ud ȼɫɟ ɬɪɢ ɜɟɥɢɱɢɧɵ α, Yi, ud ɡɚɜɢɫɹɬ ɨɬ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ȿ. ɋɪɚɡɭ ɨɬɦɟɬɢɦ, ɱɬɨ α(E), Yi(E), ud(E) ɜɟɫɶɦɚ ɫɥɨɠɧɵɟ ɡɚɜɢɫɢɦɨɫɬɢ, ɦɟɧɹɸɬɫɹ ɫ ɢɡɦɟɧɟɧɢɟɦ ɭɫɥɨɜɢɣ ɪɚɡɪɹɞɚ, ɧɨ ɞɥɹ Yi(E) ɢ α(E) ɜɫɟɝɞɚ ɜɟɫɶɦɚ ɫɢɥɶɧɵɟ (ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɵɟ, ɫɬɟɩɟɧɧɵɟ). §50. Ɍɟɨɪɢɹ ɷɥɟɤɬɪɨɧɧɵɯ ɥɚɜɢɧ
ȼ ɤɨɧɰɟ 80-ɯ ɝ. ɩɪɨɲɥɨɝɨ ɜɟɤɚ ɧɟɦɟɰ Ɏ. ɉɚɲɟɧ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɭɫɬɚɧɨɜɢɥ, ɱɬɨ ɧɚɩɪɹɠɟɧɢɟ ɡɚɠɢɝɚɧɢɹ ɪɚɡɪɹɞɚ Uɡ ɡɚɜɢɫɢɬ ɨɬ ɩɪɨɢɡɜɟɞɟɧɢɹ pd (ɝɞɟ p – ɞɚɜɥɟɧɢɟ ɝɚɡɚ, d – ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɷɥɟɤɬɪɨɞɚɦɢ) ɢ ɢɦɟɟɬ ɧɟɤɨɟ ɦɢɧɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɞɥɹ ɞɚɧɧɨɝɨ ɝɚɡɚ ɢ ɜɟɥɢɱɢɧɵ ɜɬɨɪɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ
Ɍɚɭɧɫɟɧɞɚ γ, (ɤɪɢɜɵɟ ɉɚɲɟɧɚ ɧɚ ɪɢɫ. 8.1). Ⱦɥɹ ɨɛɴɹɫɧɟɧɢɹ ɷɬɨɝɨ ɮɚɤɬɚ ɩɨɬɪɟɛɨɜɚɥɨɫɶ ɤɨɥɢɱɟɫɬɜɟɧɧɨɟ ɨɩɢɫɚɧɢɟ ɩɪɨɰɟɫɫɚ ɪɚɡɦɧɨɠɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɪɚɡɪɹɞɟ. ɉɟɪɜɨɣ ɤɨɥɢɱɟɫɬɜɟɧɧɨɣ ɬɟɨɪɢɟɣ ɝɚɡɨɜɨɝɨ ɪɚɡɪɹɞɚ ɛɵɥɚ ɬɟɨɪɢɹ ɷɥɟɤɬɪɨɧɧɵɯ ɥɚɜɢɧ, ɩɪɟɞɥɨɠɟɧɧɚɹ Ɍɚɭɧɫɟɧɞɨɦ ɜ ɫɚɦɨɦ ɧɚɱɚɥɟ 20-ɝɨ ɜɟɤɚ. Ɋɢɫ 8.1. Ʉɪɢɜɵɟ ɉɚɲɟɧɚ
ȼɨɡɧɢɤɧɨɜɟɧɢɟ, ɪɚɡɜɢɬɢɟ ɢ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɪɚɡɪɹɞɚ ɜɨ ɜɪɟɦɟɧɢ ɢ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ
1) Ɋɚɡɜɢɬɢɟ ɜɨ ɜɪɟɦɟɧɢ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɪɟɚɥɶɧɨ, ɩɨɦɢɦɨ ɪɨɠɞɟɧɢɹ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ ɧɚ ɨɞɢɧ ɩɟɪɜɢɱɧɵɣ ɷɥɟɤɬɪɨɧ Yi ɷɥɟɤɬɪɨɧɨɜ, ɧɟɤɨɟ ɤɨɥɢɱɟɫɬɜɨ ɷɥɟɤɬɪɨɧɨɜ ɨɞɧɨɜɪɟɦɟɧɧɨ ɝɢɛɧɟɬ: ɚ)ɩɪɢɥɢɩɚɟɬ ɤ ɚɬɨɦɚɦ ɢ ɦɨɥɟɤɭɥɚɦ ɫ ɱɚɫɬɨɬɨɣ Ya, ɛ) ɞɢɮɮɭɧɞɢɪɭɟɬ ɧɚ ɫɬɟɧɤɢ ɭɫɬɚɧɨɜɤɢ ɫ ɱɚɫɬɨɬɨɣ Yd, ɜ) ɪɟɤɨɦɛɢɧɢɪɭɟɬ ɫ ɢɨɧɚɦɢ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɪɟɤɨɦɛɢɧɚɰɢɢ β. Ɉɛɵɱɧɨ ɪɟɤɨɦɛɢɧɚɰɢɸ ɧɟ ɭɱɢɬɵɜɚɸɬ, ɬɚɤ ɱɬɨ ɭɫɥɨɜɢɟɦ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɢ ɪɚɡɜɢɬɢɹ ɪɚɡɪɹɞɚ:
Yi(E) > Yd + Ya
(8.14)
ɚ ɝɨɪɟɧɢɹ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɪɚɡɪɹɞɚ:
Yi(E) = Yd + Ya
(8.15)
ɗɬɨ ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ "ɫɬɚɰɢɨɧɚɪɧɵɣ ɤɪɢɬɟɪɢɣ ɩɪɨɛɨɹ". ɉɨ ɨɩɪɟɞɟɥɟɧɢɸ, Yd = 1/τd, ɝɞɟ ɜɪɟɦɹ ɞɢɮɮɭɡɢɢ τd ɡɚɜɢɫɢɬ ɨɬ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ D ɢ ɯɚɪɚɤɬɟɪɧɚɹ ɞɢɮɮɭɡɢɨɧɧɚɹ ɞɥɢɧɚ ɩɪɨɛɟɝɚ ɷɥɟɤɬɪɨɧɨɜ ɤ ɫɬɟɧɤɚɦ λd : τd = λd2/D. Ⱦɥɹ ɰɢɥɢɧɞɪɚ 1/λd2 = (2.4/R)2 + (π/L)2 (R ɢ L − ɪɚɞɢɭɫ ɢ ɞɥɢɧɚ ɰɢɥɢɧɞɪɚ); ɞɥɹ ɩɚɪɚɥɥɟɩɢɩɟɞɚ: 1/λd2 = (π/L1)2 + (π/L2)2 + (π/L3)2 (L1, L2, L3 − ɥɢɧɟɣɧɵɟ ɪɚɡɦɟɪɵ ɩɚɪɚɥɥɟɩɢɩɟɞɚ). ɂɡ ɜɵɪɚɠɟɧɢɣ ɞɥɹ ɱɚɫɬɨɬɵ ɢɨɧɢɡɚɰɢɢ (8.13) ɢ ɭɫɥɨɜɢɹ (8.14) ɦɨɠɧɨ ɫɨɫɬɚɜɢɬɶ ɮɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɨɟ ɫɨɨɬɧɨɲɟɧɢɟ ɛɚɥɚɧɫɚ ɞɥɹ ɩɥɨɬɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ:
dne/dt = ne(Yi(E) - Yd - Ya),
(8.16)
ne = ne0exp((Yi(E) - Yd - Ya)t) = ne0exp(t/θ),
(8.17)
ɨɬɤɭɞɚ
ɝɞɟ θ - ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɥɚɜɢɧɵ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɪɚɡɜɢɜɚɬɶɫɹ ɥɚɜɢɧɚ ɦɨɠɟɬ ɬɨɥɶɤɨ, ɟɫɥɢ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟ (8.14), ɢ ɩɪɢ ɧɟɨɝɪɚɧɢɱɟɧɧɨɦ t ɥɚɜɢɧɚ ɦɨɠɟɬ ɪɚɡɜɢɜɚɬɶɫɹ ɩɪɨɢɡɜɨɥɶɧɨ ɞɨɥɝɨ. ɇɨ ɟɫɬɶ ɫɢɬɭɚɰɢɢ, ɤɨɝɞɚ t ɨɱɟɧɶ ɦɚɥɨ (ɨɫɨɛɟɧɧɨ ɜ ɥɚɡɟɪɧɨɣ ɢɫɤɪɟ), ɬɨɝɞɚ ɧɟɨɛɯɨɞɢɦɨ ɛɨɥɶɲɨɟ ɩɪɟɜɵɲɟɧɢɟ ɪɨɠɞɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɧɚɞ ɝɢɛɟɥɶɸ, ɬ. ɟ. ɛɨɥɶɲɨɟ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ȿ (ɚ ɜ ɥɚɡɟɪɧɨɣ ɢɫɤɪɟ ɩɪɨɫɬɨ ɝɢɝɚɧɬɫɤɨɟ!). ɂɡ ɨɛɨɛɳɟɧɧɨɝɨ ɤɪɢɬɟɪɢɹ ɩɪɨɛɨɹ (8.17):
θ -1(E(t)) = Yi(E) - Yd - Ya = ln(n(t)/n0)/t
(8.18)
ɜɢɞɧɨ, ɱɬɨ ɪɚɡɪɹɞ ɩɪɢɯɨɞɢɬ ɤ ɫɬɚɰɢɨɧɚɪɧɨɦɭ ɩɪɢ t → ∞. ɇɚ ɫɚɦɨɦ ɞɟɥɟ ɷɬɨɬ ɩɟɪɟɯɨɞ ɩɪɨɢɫɯɨɞɢɬ ɪɚɧɶɲɟ. ɇɚɪɚɫɬɚɧɢɟ ɬɨɤɚ ɧɟ ɛɟɡɝɪɚɧɢɱɧɨ, ɤɚɤ ɷɬɨ ɞɨɥɠɧɨ ɛɵɥɨ ɛɵɬɶ ɩɨ ɬɟɨɪɢɢ ɷɥɟɤɬɪɨɧɧɵɯ ɥɚɜɢɧ, ɚ ɨɝɪɚɧɢɱɢɜɚɟɬɫɹ ɨɛɴɟɦɧɵɦ ɡɚɪɹɞɨɦ. Ɍɚɤ ɤɚɤ ɫ ɪɨɫɬɨɦ ɩɨɫɥɟɞɧɟɝɨ ɩɪɢ ɜɨɡɧɢɤɧɨɜɟɧɢɢ ɜɢɪɬɭɚɥɶɧɨɝɨ ɤɚɬɨɞɚ ɷɮɮɟɤɬɢɜɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɞɨ ɚɧɨɞɚ ɫɨɤɪɚɳɚɟɬɫɹ, ɬɨ ɧɚ ɛɨɥɟɟ ɤɨɪɨɬɤɨɣ ɞɥɢɧɟ ɩɪɨɥɟɬɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ ɭɦɟɧɶɲɚɟɬɫɹ ɜɟɪɨɹɬɧɨɫɬɶ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɢ ɦɨɥɟɤɭɥ ɝɚɡɚ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɪɚɡɪɹɞ ɩɟɪɟɯɨɞɢɬ ɤ ɫɬɚɰɢɨɧɚɪɧɨɦɭ. 2) Ɋɚɡɜɢɬɢɟ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ. ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɢɡ ɤɚɬɨɞɚ ɜɵɥɟɬɟɥ ɨɞɢɧ ɷɥɟɤɬɪɨɧ. ȼ ɫɢɥɶɧɨɦ ɩɨɥɟ ɩɪɢɤɚɬɨɞɧɨɝɨ ɫɥɨɹ ɨɧ ɛɵɫɬɪɨ ɧɚɛɟɪɟɬ ɷɧɟɪɝɢɸ, ɞɨɫɬɚɬɨɱɧɭɸ ɞɥɹ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɚ (ɦɨɥɟɤɭɥɵ) ɝɚɡɚ, ɩɨɫɥɟ ɢɨɧɢɡɚɰɢɢ ɛɭɞɟɬ ɞɜɚ ɦɟɞɥɟɧɧɵɯ ɷɥɟɤɬɪɨɧɚ (ɢ ɨɞɢɧ ɢɨɧ). ɗɥɟɤɬɪɨɧɵ ɬɚɤ ɠɟ ɭɫɤɨɪɹɬɫɹ, ɤɚɠɞɵɣ ɩɪɨɢɡɜɟɞɟɬ ɢɨɧɢɡɚɰɢɸ ɫɬɚɧɟɬ ɢɯ ɱɟɬɵɪɟ - ɬɨɠɟ ɭɫɤɨɪɹɬɫɹ, ɢɨɧɢɡɭɸɬ, ɫɬɚɧɟɬ ɜɨɫɟɦɶ ɢ ɬ.ɞ.ɜɨɡɧɢɤɚɟɬ ɥɚɜɢɧɚ, ɢɞɟɬ Ɋɢɫ. 8.2. ɋɯɟɦɵ (ɚ) ɥɚɜɢɧɧɨɝɨ ɪɚɡɦɧɨɠɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɰɟɩɧɨɣ ɩɪɨɰɟɫɫ (ɪɢɫ. 8.2). ɜ ɩɪɨɦɟɠɭɬɤɟ ɦɟɠɞɭ ɤɚɬɨɞɨɦ Ʉ ɢ ɚɧɨɞɨɦ Ⱥ ɢ (ɛ) ɇɚ ɪɚɫɫɬɨɹɧɢɢ x ɩɟɪɜɵɣ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɪɚɫɩɥɵɜɚɧɢɹ ɷɥɟɤɬɪɨɧɧɨɣ ɥɚɜɢɧɵ, ɷɥɟɤɬɪɨɧ ɫɨɡɞɚɫɬ (ɟαx -1) ɤɨɬɨɪɚɹ ɪɨɠɞɚɟɬɫɹ ɨɬ ɷɥɟɤɬɪɨɧɚ, ɜɵɲɟɞɲɟɝɨ ɢɡ ɷɥɟɤɬɪɨɧɧɵɯ ɩɚɪ. ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɦɟɫɬɚ ɤɚɬɨɞɚ ȼɨɡɧɢɤɚɸɳɢɟ ɜ ɩɪɨɦɟɠɭɬɤɟ ɷɥɟɤɬɪɨɧɵ ɞɪɟɣɮɭɸɬ ɤ ɚɧɨɞɭ, ɢɨɧɵ – ɤ ɤɚɬɨɞɭ. ɉɪɢɯɨɞɹɳɢɟ ɧɚ ɤɚɬɨɞ ɢɨɧɵ ɫɩɨɫɨɛɧɵ ɜɵɛɢɜɚɬɶ ɢɡ ɤɚɬɨɞɚ ɜɬɨɪɢɱɧɵɟ ɷɥɟɤɬɪɨɧɵ. Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɩɪɨɰɟɫɫɚ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ Ɍɚɭɧɫɟɧɞɨɦ ɛɵɥ ɩɪɟɞɥɨɠɟɧ ɜɬɨɪɨɣ ɤɨɷɮɮɢɰɢɟɧɬ γ, ɪɚɜɧɵɣ ɱɢɫɥɭ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɨɞɢɧ ɩɪɢɯɨɞɹɳɢɣ ɧɚ ɤɚɬɨɞ ɢɨɧ (ɜɬɨɪɨɣ ɤɨɷɮɮɢɰɢɟɧɬ Ɍɚɭɧɫɟɧɞɚ) ɢ ɡɚɜɢɫɹɳɢɣ ɨɬ ɦɚɬɟɪɢɚɥɚ ɤɚɬɨɞɚ, ɱɢɫɬɨɬɵ ɟɝɨ ɩɨɜɟɪɯɧɨɫɬɢ ɢ ɞɪ., ɨɛɵɱɧɨ γ = 10-4 ÷ 10-2. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɢɨɧɵ ɩɨɣɞɭɬ ɤ ɤɚɬɨɞɭ, ɭɫɤɨɪɹɬɫɹ ɢ ɜɵɛɶɸɬ ɢɡ ɤɚɬɨɞɚ γ(ɟαx -1) ɷɥɟɤɬɪɨɧɨɜ. Ⱦɚɠɟ ɟɫɥɢ ɷɬɨ ɛɭɞɟɬ ɜɫɟɝɨ ɨɞɢɧ ɜɬɨɪɢɱɧɵɣ ɷɥɟɤɬɪɨɧ, ɬɨ ɩɪɨɰɟɫɫ ɩɨɜɬɨɪɢɬɫɹ, ɬɚɤ ɱɬɨ ɭɫɥɨɜɢɟɦ ɝɨɪɟɧɢɹ ɪɚɡɪɹɞɚ ɛɭɞɟɬ:
γ(ɟαx -1) ≥ 1.
(8.19)
Ʉɚɠɞɵɣ ɜɬɨɪɢɱɧɵɣ ɷɥɟɤɬɪɨɧ ɬɚɤɠɟ ɢɨɧɢɡɭɟɬ ɚɬɨɦɵ ɢ ɪɨɠɞɚɟɬ ɷɥɟɤɬɪɨɧɵ (ɟαx 1). ɇɟɬɪɭɞɧɨ ɩɨɤɚɡɚɬɶ, ɟɫɥɢ ɱɢɫɥɨ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ n0, ɞɥɢɧɚ ɩɪɨɦɟɠɭɬɤɚ
ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ d, ɬɨ ɩɨɫɥɟ ɫɭɦɦɢɪɨɜɚɧɢɹ ɜɫɟɯ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ γ(ɟαx -1) < 1, ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ, ɩɪɢɯɨɞɹɳɢɯ ɧɚ ɚɧɨɞ, ɛɭɞɟɬ ɪɚɜɧɨ:
n = n0 ⋅
exp(αd ) . 1 − γ (exp(αd ) − 1)
(8.20)
ȼɟɥɢɱɢɧɚ
µ = γ(exp(αd)-1)
(8.21)
ɧɚɡɵɜɚɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɢɨɧɢɡɚɰɢɨɧɧɨɝɨ ɧɚɪɚɫɬɚɧɢɹ. ɉɪɢ µ < 1 ɬɨɤ ɛɭɞɟɬ ɡɚɬɭɯɚɬɶ, ɭɫɥɨɜɢɟ µ = 1 ɹɜɥɹɟɬɫɹ ɭɫɥɨɜɢɟɦ ɩɟɪɟɯɨɞɚ ɤ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɦɭ ɪɚɡɪɹɞɭ (ɭɫɥɨɜɢɟ ɡɚɠɢɝɚɧɢɹ ɪɚɡɪɹɞɚ) ɢ ɭɫɥɨɜɢɟɦ ɫɬɚɰɢɨɧɚɪɧɨɫɬɢ ɪɚɡɪɹɞɚ. Ʉɚɪɬɢɧɚ ɭɩɪɨɳɟɧɚ ɢ ɢɞɟɚɥɢɡɢɪɨɜɚɧɚ, ɪɟɚɥɶɧɨ ɷɥɟɤɬɪɨɧɵ ɝɢɛɧɭɬ (ɩɪɢɥɢɩɚɸɬ, ɪɟɤɨɦɛɢɧɢɪɭɸɬ, ɞɢɮɮɭɧɞɢɪɭɸɬ ɤ ɫɬɟɧɤɚɦ), ɧɨ ɢ ɫɨɡɞɚɸɬɫɹ ɧɚ ɤɚɬɨɞɟ ɧɟ ɬɨɥɶɤɨ ɢɨɧɧɨɣ ɛɨɦɛɚɪɞɢɪɨɜɤɨɣ, ɞɚ ɢ α = const ɬɨɥɶɤɨ ɩɪɢ E = const ɧɚ ɜɫɟɣ ɩɪɨɬɹɠɟɧɧɨɫɬɢ d, ɧɨ ɜ ɞɟɣɫɬɜɢɬɟɥɶɧɨɫɬɢ ȿ ɜ ɤɚɬɨɞɧɨɦ ɫɥɨɟ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɹɟɬɫɹ. ȼ ɤɨɧɰɟ ɩɪɨɲɥɨɝɨ ɫɬɨɥɟɬɢɹ Ɍɚɭɧɞɫɟɧɞ, ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɜ ɨɝɪɨɦɧɨɟ ɱɢɫɥɨ ɨɩɵɬɨɜ, ɭɫɬɚɧɨɜɢɥ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ:
α/ɪ =Ⱥexp(-Bp/E),
(8.22ɚ)
ɝɞɟ Ⱥ ɢ ȼ ɩɨɫɬɨɹɧɧɵɟ ɞɥɹ ɞɚɧɧɨɝɨ ɝɚɡɚ ɢ ɤɚɬɨɞɚ, ɪ - ɞɚɜɥɟɧɢɟ, ȿ - ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. Ɍɚɤɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɦɨɠɟɬ ɛɵɬɶ ɤɚɱɟɫɬɜɟɧɧɨ ɨɛɴɹɫɧɟɧɚ ɬɟɦ, ɱɬɨ ɜɟɪɨɹɬɧɨɫɬɶ ɩɪɨɣɬɢ ɷɥɟɤɬɪɨɧɭ ɛɟɡ ɫɬɨɥɤɧɨɜɟɧɢɣ ɩɭɬɶ λi, ɧɚ ɤɨɬɨɪɨɦ ɷɥɟɤɬɪɨɧ ɧɚɛɢɪɚɟɬ ɧɟɨɛɯɨɞɢɦɭɸ ɞɥɹ ɢɨɧɢɡɚɰɢɢ ɷɧɟɪɝɢɸ, ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ exp(-λi/ λ ɫɬ ). Ʉɨɷɮɮɢɰɢɟɧɬ Ɍɚɭɧɫɟɧɞɚ α = Nexp(-λi/ λ ɫɬ ),ɝɞɟ N = 1/ λ ɫɬ - ɱɢɫɥɨ ɫɨɭɞɚɪɟɧɢɣ ɧɚ 1 ɫɦ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɟ ɞɚɜɥɟɧɢɸ: N = N0p, N0 – ɱɢɫɥɨ ɫɬɨɥɤɧɨɜɟɧɢɣ ɷɥɟɤɬɪɨɧɚ ɧɚ 1 ɫɦ ɩɭɬɢ ɩɪɢ ɞɚɜɥɟɧɢɢ, ɪɚɜɧɨɦ ɟɞɢɧɢɰɟ. ɋ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ λi = Ui/E ɩɨɥɭɱɢɦ ɫɨɨɬɧɨɲɟɧɢɟ, ɩɨɞɨɛɧɨɟ (8.22ɚ):
α/ɪ =N0exp(-N0Uip/E),
(8.22ɛ)
ɉɨɞɫɬɚɧɨɜɤɚ ɱɢɫɥɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɞɚɟɬ ɩɪɚɜɢɥɶɧɵɣ ɩɨɪɹɞɨɤ ɜɟɥɢɱɢɧ Ⱥ ɢ ȼ. Ʉɨɷɮɮɢɰɢɟɧɬɵ Ɍɚɭɧɫɟɧɞɚ α ɢ γ ɨɛɥɚɞɚɸɬ ɬɟɦ ɫɜɨɣɫɬɜɨɦ, ɱɬɨ ɨɬɧɨɲɟɧɢɟ α/p ɢ γ ɧɟ ɹɜɥɹɸɬɫɹ ɮɭɧɤɰɢɟɣ ɩɨ ɨɬɞɟɥɶɧɨɫɬɢ ɨɬ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ E ɢ ɞɚɜɥɟɧɢɹ ɝɚɡɚ p, ɚ ɡɚɜɢɫɢɬ ɨɬ ɢɯ ɨɬɧɨɲɟɧɢɹ: α /p=f1(E/p) ɢ γ =f2(E/p). ɍɫɥɨɜɢɟ ɡɚɠɢɝɚɧɢɹ ɪɚɡɪɹɞɚ, ɢɥɢ ɭɫɥɨɜɢɟ, ɩɨɡɜɨɥɹɸɳɟɟ ɨɩɪɟɞɟɥɢɬɶ ɧɚɩɪɹɠɟɧɢɟ ɡɚɠɢɝɚɧɢɹ Uɡ ɢɦɟɟɬ ɜɢɞ: f1 (
Uɡ U )(exp( f 2 ( ɡ )) − 1) = 1 . pd pd
(8.23)
ɂɡ (8.23) ɜɢɞɧɨ, ɱɬɨ ɧɚɩɪɹɠɟɧɢɟ ɡɚɠɢɝɚɧɢɹ Uɡ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɩɪɨɢɡɜɟɞɟɧɢɹ pd, ɢ ɩɪɢ pd = const ɧɚɩɪɹɠɟɧɢɟ ɡɚɠɢɝɚɧɢɹ ɧɟ ɦɟɧɹɟɬɫɹ. ɗɬɚ ɡɚɤɨɧɨɦɟɪɧɨɫɬɶ ɧɨɫɢɬ ɧɚɡɜɚɧɢɟ ɡɚɤɨɧ ɉɚɲɟɧɚ. Ʉɪɢɜɭɸ ɉɚɲɟɧɚ (ɫɦ. ɪɢɫ. 8.1), ɨɬɪɚɠɚɸɳɭɸ
ɡɚɜɢɫɢɦɨɫɬɶ Uɡ ɨɬ pd, ɧɚɡɵɜɚɸɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɡɚɠɢɝɚɧɢɹ ɪɚɡɪɹɞɚ. ȼɵɪɚɠɚɹ α ɢɡ ɭɫɥɨɜɢɹ ɡɚɠɢɝɚɧɢɹ ɪɚɡɪɹɞɚ (µ = 1) ɫ ɭɱɟɬɨɦ (8.21) ɢ ɩɨɞɫɬɚɜɥɹɹ ɜ ɜɵɪɚɠɟɧɢɟ (8.22ɚ), ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ: E/p =B/(C + ln(pd)), ɝɞɟ C = ln(Ⱥ/(ln(1/γ+1))). ɉɪɢɧɹɜ Uɡ = Ed, ɧɚɣɞɟɦ ɡɚɜɢɫɢɦɨɫɬɶ ɧɚɩɪɹɠɟɧɢɟ
ɡɚɠɢɝɚɧɢɹ ɨɬ pd:
Uɡ =Bpd/(C + ln(pd)), ɤɨɬɨɪɚɹ ɢ ɨɩɢɫɵɜɚɟɬɫɹ ɤɪɢɜɵɦɢ ɉɚɲɟɧɚ. ȼɚɠɧɨ, ɱɬɨ ɫɭɳɟɫɬɜɟɧɧɵ ɧɟ p, d, E "ɨɬɞɟɥɶɧɨ", ɚ "ɤɨɦɛɢɧɚɰɢɢ" pd (ɬ.ɤ. p = ngTg, ɝɞɟ ng ɢ Tg - ɩɥɨɬɧɨɫɬɶ ɢ ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ, ɟɫɥɢ Tg = const, ɬɨ pd ɨɩɪɟɞɟɥɹɟɬ ɱɢɫɥɨ ɢɨɧɢɡɭɸɳɢɯ ɫɬɨɥɤɧɨɜɟɧɢɣ ɧɚ ɩɪɨɛɟɝɟ d), ɢ, ɨɫɨɛɟɧɧɨ, ȿ/ɪ, ɬ.ɟ. ɤɚɤ ɛɵ "ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɩɨɥɹ ɧɚ ɨɞɧɭ ɱɚɫɬɢɰɭ ɝɚɡɚ". Ɇɢɧɢɦɭɦ Uɡ ɫɨɨɬɜɟɬɫɬɜɭɟɬ (pd)min : (pd)min = ( e /A)ln(1/γ + 1),
(8.24)
ɝɞɟ e ≈ 2.72 - ɧɟ ɡɚɪɹɞ ɷɥɟɤɬɪɨɧɚ, ɚ ɨɫɧɨɜɚɧɢɟ ɧɚɬɭɪɚɥɶɧɨɝɨ ɥɨɝɚɪɢɮɦɚ. ɋɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɦɢɧɢɦɚɥɶɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɡɚɠɢɝɚɧɢɹ Uɡmin = B(1-C) ɡɚɜɢɫɢɬ ɬɨɥɶɤɨ ɨɬ ɫɨɪɬɚ ɝɚɡɚ ɢ ɦɚɬɟɪɢɚɥɚ ɤɚɬɨɞɚ, ɦɢɧɢɦɭɦ ɨɬɧɨɲɟɧɢɹ (ȿ/ɪ)min = ȼ ɡɚɜɢɫɢɬ ɬɨɥɶɤɨ ɨɬ ɫɨɪɬɚ ɝɚɡɚ. ɋɬɨɥɟɬɨɜ, ɢɫɫɥɟɞɭɹ ɮɨɬɨɷɥɟɤɬɪɨɧɧɭɸ ɷɦɢɫɫɢɸ, ɫɬɪɟɦɢɥɫɹ ɩɨɞɨɛɪɚɬɶ ɞɚɜɥɟɧɢɟ ɝɚɡɚ ɞɥɹ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɮɨɬɨɬɨɤɚ. Ɉɧ ɨɛɧɚɪɭɠɢɥ, ɱɬɨ ɟɫɥɢ ɭɦɟɧɶɲɚɬɶ ɞɚɜɥɟɧɢɟ, ɬɨ ɫɢɥɚ ɬɨɤɚ ɫɧɚɱɚɥɚ ɭɜɟɥɢɱɢɜɚɟɬɫɹ, ɚ ɡɚɬɟɦ ɭɦɟɧɶɲɚɟɬɫɹ, ɬ. ɟ. ɫɭɳɟɫɬɜɭɟɬ ɦɚɤɫɢɦɭɦ ɬɨɤɚ ɩɨ ɞɚɜɥɟɧɢɸ. ȿɫɥɢ ɩɪɢ ɷɬɨɦ ɦɟɧɹɬɶ ɨɬ ɨɩɵɬɚ ɤ ɨɩɵɬɭ ɪɚɡɧɨɫɬɶ ɩɨɬɟɧɰɢɚɥɨɜ ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ, ɬɨ ɦɚɤɫɢɦɭɦ ɬɨɤɚ ɜɫɟɝɞɚ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɞɧɨɦɭ ɢ ɬɨɦɭ ɠɟ E/p. ɉɪɨɞɟɥɚɜ ɩɪɢɜɟɞɟɧɧɵɟ ɜɵɲɟ ɪɚɫɫɭɠɞɟɧɢɹ, Ɍɚɭɧɫɟɧɞ ɞɚɥ ɨɛɴɹɫɧɟɧɢɟ ɷɬɨɦɭ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɦɭ ɮɚɤɬɭ ɢ ɧɚɡɜɚɥ ɷɬɨ ɷɮɮɟɤɬɨɦ ɋɬɨɥɟɬɨɜɚ, ɚ ɡɧɚɱɟɧɢɟ (ȿ/ɪ)min ɜɩɨɫɥɟɞɫɬɜɢɢ ɧɚɡɜɚɥɢ ɤɨɧɫɬɚɧɬɨɣ ɋɬɨɥɟɬɨɜɚ. Ɋɚɫɱɟɬɵ ɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɨ ɫɨɜɩɚɞɚɸɬ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɤɪɢɜɵɦɢ ɉɚɲɟɧɚ (ɫɦ. ɪɢɫ.8.1). Ɉɩɢɫɚɬɟɥɶɧɨ ɤɪɢɜɵɟ ɉɚɲɟɧɚ ɦɨɠɧɨ ɩɨɧɹɬɶ ɬɚɤ: ɫ ɭɦɟɧɶɲɟɧɢɟɦ (pd) ɦɟɞɥɟɧɧɨ ɪɚɫɬɟɬ ȿ/ɪ (ɩɪɚɜɚɹ ɜɟɬɜɶ ɧɚ ɪɢɫ.8.1), ɡɧɚɱɢɬ, ɪɚɫɬɟɬ Yi ɢ ɞɥɹ ɩɪɨɛɨɹ ɞɨɫɬɚɬɨɱɧɨ ɦɟɧɶɲɢɯ Uɡ, ɢ ɬɚɤ ɞɨ Uɡmin. Ⱦɚɥɶɧɟɣɲɟɟ ɭɦɟɧɶɲɟɧɢɟ pd (ɥɟɜɚɹ ɜɟɬɜɶ) ɩɪɢɜɨɞɢɬ ɤ ɛɵɫɬɪɨɦɭ ɭɯɨɞɭ ɷɥɟɤɬɪɨɧɨɜ (ɦɚɥɨ ɫɬɨɥɤɧɨɜɟɧɢɣ) ɢ ɞɥɹ ɤɨɦɩɟɧɫɚɰɢɢ ɷɬɨɝɨ ɧɟɨɛɯɨɞɢɦ ɛɵɫɬɪɵɣ ɪɨɫɬ ȿ/ɪ, ɬ.ɟ. ɩɨɬɟɧɰɢɚɥɚ ɩɪɨɛɨɹ Uɡ. Ɇɨɠɧɨ ɞɚɬɶ ɨɩɢɫɚɧɢɟ ɷɬɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɨɦ ɡɧɚɱɟɧɢɢ ɨɞɧɨɣ ɢɡ ɜɟɥɢɱɢɧ p ɢɥɢ d. ɉɭɫɬɶ ɞɚɜɥɟɧɢɟ ɭɦɟɧɶɲɚɟɬɫɹ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ d. Ɍɨɝɞɚ ɫ ɭɦɟɧɶɲɟɧɢɟɦ ɞɚɜɥɟɧɢɹ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɞɥɢɧɚ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ, ɬ.ɟ. ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɧɚɛɢɪɚɟɦɚɹ ɷɥɟɤɬɪɨɧɨɦ ɷɧɟɪɝɢɹ, ɚ ɡɧɚɱɢɬ ɪɚɫɬɟɬ α. Ⱦɚɥɟɟ ɫ ɭɦɟɧɶɲɟɧɢɟɦ p ɪɟɡɤɨ ɫɧɢɠɚɟɬɫɹ ɱɢɫɥɨ ɫɬɨɥɤɧɨɜɟɧɢɣ ɢ α ɭɦɟɧɶɲɚɟɬɫɹ. ɉɪɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ ɫ ɭɦɟɧɶɲɟɧɢɟɦ ɪɚɫɫɬɨɹɧɢɹ d ɭɜɟɥɢɱɢɜɚɟɬɫɹ α, ɬɚɤ ɤɚɤ ɪɚɫɬɟɬ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ. Ɂɚɬɟɦ ɫ ɭɦɟɧɶɲɟɧɢɟɦ d ɤɨɷɮɮɢɰɢɟɧɬ Ɍɚɭɧɫɟɧɞɚ ɫɧɢɠɚɟɬɫɹ ɢɡ-ɡɚ ɭɦɟɧɶɲɟɧɢɹ ɞɥɢɧɵ ɪɚɡɜɢɬɢɹ ɥɚɜɢɧɵ. Ɍɚɤɠɟ ɨɩɢɫɚɬɟɥɶɧɨ ɦɨɠɧɨ ɩɨɧɹɬɶ ɷɦɩɢɪɢɱɟɫɤɭɸ ɡɚɜɢɫɢɦɨɫɬɶ Ɍɚɭɧɫɟɧɞɚ (8.22) ɢ ɤɪɢɜɵɟ ɉɚɲɟɧɚ (ɪɢɫ.8.1).
Ɍɟɦɧɵɣ (ɬɚɭɧɫɟɧɞɨɜɫɤɢɣ) ɪɚɡɪɹɞ
Ɍɟɦɧɵɣ (ɬɚɭɧɫɟɧɞɨɜɫɤɢɣ) ɪɚɡɪɹɞ – ɷɬɨ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɪɚɡɪɹɞ ɜ ɝɚɡɚɯ ɩɪɢ ɧɢɡɤɨɦ ɞɚɜɥɟɧɢɢ (ɩɨɪɹɞɤɚ ɧɟɫɤɨɥɶɤɢɯ Ɍɨɪɪ) ɢ ɨɱɟɧɶ ɦɚɥɵɯ ɬɨɤɚɯ (ɦɟɧɟɟ 10-5 Ⱥ). ɗɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɜ ɪɚɡɪɹɞɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɨɞɧɨɪɨɞɧɨ ɢɥɢ ɫɥɚɛɨ ɧɟɨɞɧɨɪɨɞɧɨ, ɢ ɧɟ ɢɫɤɚɠɚɟɬɫɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɦ ɡɚɪɹɞɨɦ, ɤɨɬɨɪɵɣ ɩɪɟɧɟɛɪɟɠɢɦɨ ɦɚɥ. ɇɚɡɜɚɧ ɩɨ ɢɦɟɧɢ Ɍɚɭɧɫɟɧɞɚ, ɤɨɬɨɪɵɣ ɜ 1900 ɝ. ɫɨɡɞɚɥ ɬɟɨɪɢɸ ɷɥɟɤɬɪɨɧɧɵɯ ɥɚɜɢɧ, ɩɨ ɤɨɬɨɪɨɣ ɩɪɢ ɭɫɥɨɜɢɢ ɜɵɩɨɥɧɟɧɢɹ ɪɚɡɜɢɬɢɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɚɡɪɹɞɚ (8.19) ɬɨɤ ɪɚɡɪɹɞɚ ɞɨɥɠɟɧ ɧɟɨɝɪɚɧɢɱɟɧɧɨ ɜɨɡɪɚɫɬɚɬɶ ɫɨ ɜɪɟɦɟɧɟɦ. Ɋɟɚɥɶɧɨ ɠɟ ɬɨɤ ɨɝɪɚɧɢɱɟɧ ɩɚɪɚɦɟɬɪɚɦɢ ɰɟɩɢ. Ɉɱɟɧɶ ɦɚɥɵɣ ɬɨɤ ɬɚɭɧɫɟɧɞɨɜɫɤɨɝɨ ɪɚɡɪɹɞɚ ɨɛɭɫɥɨɜɥɟɧ ɛɨɥɶɲɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ ɜɧɟɲɧɟɣ ɰɟɩɢ. ȿɫɥɢ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɧɟɲɧɟɣ ɰɟɩɢ ɫɧɢɠɚɬɶ, ɭɜɟɥɢɱɢɜɚɹ ɬɨɤ, ɬɨ ɬɚɭɧɫɟɧɞɨɜɫɤɢɣ ɪɚɡɪɹɞ ɩɟɪɟɯɨɞɢɬ ɜ ɬɥɟɸɳɢɣ. §51. Ɍɥɟɸɳɢɣ ɪɚɡɪɹɞ
Ɍɥɟɸɳɢɣ ɪɚɡɪɹɞ – ɷɬɨ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɪɚɡɪɹɞ ɜ ɝɚɡɟ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɣɫɹ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɣ ɧɟɪɚɜɧɨɜɟɫɧɨɫɬɶɸ ɢ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɶɸ, ɜɨɡɧɢɤɚɸɳɟɣ ɜ ɪɚɡɪɹɞɟ ɩɥɚɡɦɵ. ɗɮɮɟɤɬɢɜɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɷɥɟɤɬɪɨɧɨɜ ɫɭɳɟɫɬɜɟɧɧɨ ɜɵɲɟ ɬɟɦɩɟɪɚɬɭɪɵ ɝɚɡɚ ɢ ɷɥɟɤɬɪɨɞɨɜ. Ɍɟɪɦɨɷɦɢɫɫɢɹ ɩɪɚɤɬɢɱɟɫɤɢ ɨɬɫɭɬɫɬɜɭɟɬ (ɷɥɟɤɬɪɨɞɵ ɯɨɥɨɞɧɵɟ). ɋɜɨɟ ɧɚɡɜɚɧɢɟ ɪɚɡɪɹɞ ɩɨɥɭɱɢɥ ɢɡ-ɡɚ ɧɚɥɢɱɢɹ ɨɤɨɥɨ ɤɚɬɨɞɚ ɬɚɤ ɧɚɡɵɜɚɟɦɨɝɨ ɬɥɟɸɳɟɝɨ ɫɜɟɱɟɧɢɹ. Ȼɥɚɝɨɞɚɪɹ ɫɜɟɱɟɧɢɸ ɝɚɡɚ ɬɥɟɸɳɢɣ ɪɚɡɪɹɞ ɧɚɲɟɥ ɲɢɪɨɤɨɟ ɩɪɢɦɟɧɟɧɢɟ ɜ ɥɚɦɩɚɯ ɞɧɟɜɧɨɝɨ ɫɜɟɬɚ, ɪɚɡɥɢɱɧɵɯ ɨɫɜɟɬɢɬɟɥɶɧɵɯ ɩɪɢɛɨɪɚɯ ɢ ɬ.ɩ. Ʉɥɚɫɫɢɱɟɫɤɚɹ ɫɯɟɦɚ ɭɫɬɚɧɨɜɤɢ ɞɥɹ ɢɡɭɱɟɧɢɹ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ ɢɡɨɛɪɚɠɟɧɚ ɧɚ ɪɢɫ. 8.3, ɝɞɟ 1- ɫɬɟɤɥɹɧɧɵɣ ɛɚɥɥɨɧ, ɞɢɚɦɟɬɪɨɦ 1-3 ɫɦ, ɞɥɢɧɧɨɣ ɞɨ 1 ɦ; 2 - ɤɚɬɨɞ; 3 - ɚɧɨɞ; 4 - ɛɚɥɥɚɫɬɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ (ɨɛɹɡɚɬɟɥɶɧɵɣ ɷɥɟɦɟɧɬ); Ⱥ – ɦɢɤɪɨ-, ɦɢɥɥɢ-, ɢɥɢ ɩɪɨɫɬɨ ɚɦɩɟɪɦɟɬɪ. Ȼɚɥɥɨɧ 1 ɦɨɠɧɨ ɨɬɤɚɱɚɬɶ ɢ ɡɚɬɟɦ Ɋɢɫ. 8.3. Ʉɥɚɫɫɢɱɟɫɤɚɹ ɫɯɟɦɚ ɞɥɹ ɢɡɭɱɟɧɢɹ ɝɚɡɨɜɨɝɨ ɪɚɡɪɹɞɚ ɡɚɩɨɥɧɢɬɶ ɜɵɛɪɚɧɧɵɦ ɝɚɡɨɦ ɞɨ ɡɚɞɚɧɧɨɝɨ ɞɚɜɥɟɧɢɹ. Ɉɛɵɱɧɨ ɜ ɪɚɡɪɹɞɟ ɧɚɛɥɸɞɚɸɬɫɹ ɬɪɢ ɜɢɡɭɚɥɶɧɨ ɪɚɡɥɢɱɢɦɵɟ ɨɛɥɚɫɬɢ: ɚ) ɩɪɢɤɚɬɨɞɧɚɹ ɨɛɥɚɫɬɶ, ɧɚ ɧɟɣ ɩɚɞɚɟɬ ɧɚɩɪɹɠɟɧɢɟ Uk, ɨɛɵɱɧɨ 200 ÷ 700 ȼ; ɛ) ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ - ɜ ɮɢɡɢɤɟ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ ɩɚɫɫɢɜɧɵɣ ɷɥɟɦɟɧɬ: ɫɛɥɢɠɚɹ ɚɧɨɞ ɢ ɤɚɬɨɞ ɦɨɠɧɨ ɥɢɤɜɢɞɢɪɨɜɚɬɶ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ, ɪɚɡɪɹɞ ɛɭɞɟɬ ɝɨɪɟɬɶ; ɨɞɧɚɤɨ ɜ ɬɟɯɧɢɤɟ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ - ɩɨɥɟɡɧɵɣ ɷɥɟɦɟɧɬ: ɨɧ ɫɜɟɬɢɬɫɹ ɜ ɪɟɤɥɚɦɧɵɯ ɬɪɭɛɤɚɯ, ɨɧ ɢ ɟɫɬɶ ɚɤɬɢɜɧɚɹ ɫɪɟɞɚ ɜ ɝɚɡɨɜɵɯ ɥɚɡɟɪɚɯ, ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɧɟɦ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɦɟɧɧɨ ɬɟɯɧɢɱɟɫɤɢɦɢ ɬɪɟɛɨɜɚɧɢɹɦɢ, ɧɚɩɪɢɦɟɪ, ɞɥɢɧɨɣ ɪɟɤɥɚɦɧɵɯ ɬɪɭɛɨɤ; ɜ) ɩɪɢɚɧɨɞɧɵɣ ɫɥɨɣ ɨɛɵɱɧɨ ɨɱɟɧɶ ɬɨɧɤɢɣ, ɫɨɫɬɨɢɬ ɢɡ ɫɜɟɬɹɳɟɣɫɹ "ɩɥɟɧɤɢ", ɢ ɬɨɧɤɨɝɨ ɬɟɦɧɨɝɨ ɭɱɚɫɬɤɚ. Ⱦɨɥɝɨ ɫɱɢɬɚɥɢ, ɱɬɨ ɨɧ ɬɨɠɟ "ɩɚɫɫɢɜɧɵɣ", ɨɞɧɚɤɨ ɬɟɩɟɪɶ ɞɨɤɚɡɚɧɨ, ɱɬɨ ɧɟɤɨɬɨɪɵɟ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɪɹɦɨ ɫɜɹɡɚɧɵ ɫ ɧɢɦ. ɉɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ
ɚɧɨɞɧɨɦ ɫɥɨɟ Ua ɧɟɜɟɥɢɤɨ (10 ÷ 20 ȼ) ɢ ɨɛɵɱɧɨ ɛɥɢɡɤɨ ɤ ɩɨɬɟɧɰɢɚɥɭ ɢɨɧɢɡɚɰɢɢ ɝɚɡɚ (ɨɱɟɧɶ ɱɭɜɫɬɜɢɬɟɥɶɧɨ ɤ ɫɨɫɬɨɹɧɢɸ ɩɨɜɟɪɯɧɨɫɬɢ ɚɧɨɞɚ). ɉɪɢɤɚɬɨɞɧɚɹ ɨɛɥɚɫɬɶ
ɉɪɢɤɚɬɨɞɧɚɹ ɨɛɥɚɫɬɶ ɮɢɡɢɱɟɫɤɢ ɧɚɢɛɨɥɟɟ ɜɚɠɧɵɣ ɷɥɟɦɟɧɬ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ: ɢɦɟɧɧɨ ɜ ɧɟɦ ɨɛɪɚɡɭɟɬɫɹ ɷɥɟɤɬɪɨɧɧɚɹ ɥɚɜɢɧɚ. ȼ ɞɚɧɧɨɦ ɝɚɡɟ ɩɪɢ ɞɚɧɧɨɦ ɞɚɜɥɟɧɢɢ ɮɨɪɦɢɪɭɟɬɫɹ ɞɥɢɧɚ ɩɪɢɤɚɬɨɞɧɨɣ ɨɛɥɚɫɬɢ dk, ɪɚɜɧɚɹ ɧɟɫɤɨɥɶɤɢɦ ɞɥɢɧɚɦ ɢɨɧɢɡɚɰɢɢ. ɍɫɬɚɧɨɜɢɜɲɚɹɫɹ ɞɥɢɧɚ dk, ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚɹ ɞɚɜɥɟɧɢɸ p, ɬɚɤɨɜɚ, ɱɬɨɛɵ ɜɟɥɢɱɢɧɚ pdk ɫɨɨɬɜɟɬɫɬɜɨɜɚɥɚ ɦɢɧɢɦɚɥɶɧɨɦɭ ɡɧɚɱɟɧɢɸ Uk (ɩɪɢɪɨɞɚ ɷɤɨɧɨɦɧɚ!). Ɉɫɧɨɜɧɨɣ ɯɚɪɚɤɬɟɪɧɨɣ ɨɫɨɛɟɧɧɨɫɬɶ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ ɹɜɥɹɟɬɫɹ ɛɨɥɶɲɨɟ ɩɚɞɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɢɤɚɬɨɞɧɨɣ ɨɛɥɚɫɬɢ Uk. – ɫɨɬɧɢ ɜɨɥɶɬ. ɂɡ ɤɚɬɨɞɧɨɝɨ ɫɥɨɹ ɜ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ ɭɯɨɞɢɬ ɧɟɤɨɬɨɪɨɟ ɤɨɥɢɱɟɫɬɜɨ ɷɥɟɤɬɪɨɧɨɜ ɫ ɬɚɤɨɣ ɷɧɟɪɝɢɟɣ, ɱɬɨɛɵ ɢɨɧɢɡɨɜɚɬɶ ɜ ɫɬɨɥɛɟ ɞɨɫɬɚɬɨɱɧɨ ɚɬɨɦɨɜ (ɦɨɥɟɤɭɥ) ɞɥɹ ɤɨɦɩɟɧɫɚɰɢɢ ɬɟɪɹɟɦɵɯ ɷɥɟɤɬɪɨɧɨɜ, ɬɨ ɟɫɬɶ Uk ɞɨɥɠɧɨ ɛɵɬɶ ɦɧɨɝɨ ɛɨɥɶɲɟ ɩɨɬɟɧɰɢɚɥɚ ɢɨɧɢɡɚɰɢɢ ɚɬɨɦɨɜ ɝɚɡɚ. Ʉɚɬɨɞɧɚɹ ɨɛɥɚɫɬɶ ɤɚɤ ɛɵ "ɩɪɢɤɥɟɟɧɚ" ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɤɚɬɨɞɚ: ɟɫɥɢ ɩɪɨɜɨɞɹɳɟɣ ɹɜɥɹɟɬɫɹ ɬɨɥɶɤɨ ɨɞɧɚ ɟɝɨ ɩɨɜɟɪɯɧɨɫɬɶ, ɬɨ ɩɪɢ ɥɸɛɨɦ ɩɨɜɨɪɨɬɟ ɤɚɬɨɞɚ ɪɚɡɪɹɞ ɩɪɢɯɨɞɢɬ ɬɨɥɶɤɨ ɧɚ ɧɟɟ - ɞɚɠɟ ɟɫɥɢ ɟɟ ɩɨɜɟɪɧɭɬɶ ɧɚ 180°, ɤɚɤ ɛɵ ɫɩɢɧɨɣ ɤ ɚɧɨɞɭ. ɋɜɟɱɟɧɢɟ ɤɚɬɨɞɧɨɣ ɨɛɥɚɫɬɢ "ɫɥɨɢɫɬɨɟ" (ɪɢɫ. 8.4). ɍ ɫɚɦɨɝɨ ɤɚɬɨɞɚ ɧɚɯɨɞɢɬɫɹ ɬɟɦɧɨɟ "ɚɫɬɨɧɨɜɨ ɩɪɨɫɬɪɚɧɫɬɜɨ", ɫɜɹɡɚɧɧɨɟ ɫ ɬɟɦ, ɱɬɨ ɷɥɟɤɬɪɨɧɵ, ɜɵɲɟɞɲɢɟ ɫ ɤɚɬɨɞɚ, ɟɳɟ ɧɟ ɧɚɛɪɚɥɢ ɞɨɫɬɚɬɨɱɧɨɣ ɷɧɟɪɝɢɢ ɞɥɹ ɜɨɡɛɭɠɞɟɧɢɹ ɚɬɨɦɨɜ ɢ ɦɨɥɟɤɭɥ ɝɚɡɚ. Ɂɚɬɟɦ ɪɚɫɩɨɥɚɝɚɟɬɫɹ ɨɛɥɚɫɬɶ ɤɚɬɨɞɧɨɝɨ ɫɜɟɱɟɧɢɹ, ɜ ɤɨɬɨɪɨɣ ɩɪɨɢɫɯɨɞɢɬ ɢɧɬɟɧɫɢɜɧɨɟ ɜɨɡɛɭɠɞɟɧɢɟ ɪɚɡɥɢɱɧɵɯ ɭɪɨɜɧɟɣ. Ʉɚɬɨɞɧɨɟ ɬɟɦɧɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ, ɜɨɡɧɢɤɚɟɬ ɬɚɦ, ɝɞɟ ɷɧɟɪɝɢɹ ɭɫɤɨɪɟɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ «ɩɟɪɟɜɚɥɢɜɚɟɬ» ɱɟɪɟɡ ɡɧɚɱɟɧɢɟ ɜ ɦɚɤɫɢɦɭɦɟ ɮɭɧɤɰɢɢ ɜɨɡɛɭɠɞɟɧɢɹ, ɫɟɱɟɧɢɹ ɜɨɡɛɭɠɞɟɧɢɹ ɭɦɟɧɶɲɚɸɬɫɹ, ɤɨɥɢɱɟɫɬɜɨ ɜɨɡɛɭɠɞɟɧɧɵɯ ɚɬɨɦɨɜ ɩɚɞɚɟɬ. Ⱦɚɥɟɟ ɷɥɟɤɬɪɨɧɵ ɩɪɟɢɦɭɳɟɫɬɜɟɧɧɨ ɢɨɧɢɡɭɸɬ ɚɬɨɦɵ, ɩɪɨɢɫɯɨɞɢɬ ɥɚɜɢɧɨɨɛɪɚɡɧɨɟ ɪɚɡɦɧɨɠɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ, ɤɨɬɨɪɵɟ ɭɫɤɨɪɹɹɫɶ ɜɧɨɜɶ ɜɵɡɵɜɚɸɬ ɜɨɡɛɭɠɞɟɧɢɟ ɚɬɨɦɨɜ. ɉɨɹɜɥɹɟɬɫɹ «ɬɥɟɸɳɟɟ ɨɬɪɢɰɚɬɟɥɶɧɨɟ ɫɜɟɱɟɧɢɟ», ɛɥɚɝɨɞɚɪɹ ɤɨɬɨɪɨɦɭ ɬɥɟɸɳɢɣ ɪɚɡɪɹɞ ɢ ɩɨɥɭɱɢɥ ɫɜɨɟ ɧɚɡɜɚɧɢɟ. ȼ ɜɨɡɧɢɤɚɸɳɟɣ ɜ ɪɚɡɪɹɞɟ ɩɥɚɡɦɟ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɪɟɡɤɨ ɩɚɞɚɟɬ, ɷɥɟɤɬɪɨɧɵ, ɪɚɫɬɪɚɱɢɜɚɹ ɫɜɨɸ ɷɧɟɪɝɢɸ, ɧɟ ɩɪɢɨɛɪɟɬɚɸɬ ɜ ɫɥɚɛɨɦ ɩɨɥɟ ɞɨɫɬɚɬɨɱɧɨɣ ɞɥɹ ɜɨɡɛɭɠɞɟɧɢɹ ɚɬɨɦɨɜ, ɜɨɡɧɢɤɚɟɬ ɬɟɦɧɨɟ "ɮɚɪɚɞɟɟɜɨ ɩɪɨɫɬɪɚɧɫɬɜɨ". ȼ ɨɛɥɚɫɬɢ ɬɥɟɸɳɟɝɨ ɫɜɟɱɟɧɢɹ (ρ ≈ 0) ɧɚɢɛɨɥɟɟ ɢɞɟɚɥɶɧɚɹ ɩɥɚɡɦɚ. Ɍɚɤ ɤɚɤ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ E ≈ 0 ɷɥɟɤɬɪɨɧɵ ɩɟɪɟɯɨɞɹɬ ɢɡ ɨɛɥɚɫɬɢ ɬɥɟɸɳɟɝɨ ɫɜɟɱɟɧɢɹ ɜ ɮɚɪɚɞɟɟɜɨ ɩɪɨɫɬɪɚɧɫɬɜɨ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɡɚ ɫɱɟɬ ɞɢɮɮɭɡɢɢ. ɂɨɧɵ ɩɨɩɚɞɚɸɬ ɜ ɩɪɢɤɚɬɨɞɧɭɸ ɨɛɥɚɫɬɶ ɬɚɤɠɟ ɡɚ ɫɱɟɬ ɞɢɮɮɭɡɢɢ. ɍɫɤɨɪɟɧɧɵɟ ɤ ɤɚɬɨɞɭ ɢɨɧɵ ɜɵɛɢɜɚɸɬ ɜɬɨɪɢɱɧɵɟ ɷɥɟɤɬɪɨɧɵ. Ɍɟɦɧɨɟ ɮɚɪɚɞɟɟɜɨ ɩɪɨɫɬɪɚɧɫɬɜɨ – ɷɬɨ ɩɟɪɟɯɨɞɧɚɹ ɨɛɥɚɫɬɶ, ɜ ɤɨɬɨɪɨɣ ɧɟɬ ɢɨɧɢɡɚɰɢɢ ɢ ɜɨɡɛɭɠɞɟɧɢɹ. ɉɨ ɦɟɪɟ ɩɪɢɛɥɢɠɟɧɢɹ ɤ ɩɨɥɨɠɢɬɟɥɶɧɨɦɭ ɫɬɨɥɛɭ ɛɟɫɩɨɪɹɞɨɱɧɨɟ ɬɟɩɥɨɜɨɟ ɞɜɢɠɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɜɫɟ ɛɨɥɟɟ ɩɪɟɨɛɥɚɞɚɟɬ ɧɚɞ ɧɚɩɪɚɜɥɟɧɧɵɦ ɞɜɢɠɟɧɢɟɦ. Ɉɩɢɫɚɧɢɟ ɜɫɟɯ ɩɪɨɰɟɫɫɨɜ, ɨɛɴɹɫɧɹɸɳɢɯ ɷɬɭ "ɫɥɨɢɫɬɨɫɬɶ" (ɢ ɧɟɤɨɬɨɪɵɟ ɛɨɥɟɟ ɬɨɧɤɢɟ ɷɮɮɟɤɬɵ) ɢ ɫɟɣɱɚɫ ɹɜɥɹɟɬɫɹ ɞɚɥɟɤɨ ɧɟ ɩɨɥɧɵɦ. ɇɟɩɨɧɹɬɧɨ ɢ ɟɳɟ ɨɞɧɨ ɹɜɥɟɧɢɟ: ɩɥɨɳɚɞɶ ɬɨɤɨɜɨɝɨ ɩɹɬɧɚ Sɩ ɧɚ ɤɚɬɨɞɟ ɜ ɧɨɪɦɚɥɶɧɨɦ ɪɟɠɢɦɟ ɜɫɟɝɞɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɫɨɨɬɧɨɲɟɧɢɹ Sɩ = I/jɩ, ɝɞɟ: I ɩɨɥɧɵɣ ɬɨɤ, ɚ jɩ – ɧɟɤɨɬɨɪɚɹ «ɧɨɪɦɚɥɶɧɚɹ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ», ɩɨɫɬɨɹɧɧɚɹ ɞɥɹ ɞɚɧɧɨɝɨ ɪɚɡɪɹɞɚ. ɗɬɨ ɜɚɠɧɨɟ ɫɜɨɣɫɬɜɨ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ ɧɚɡɵɜɚɟɬɫɹ ɡɚɤɨɧɨɦ ɧɨɪɦɚɥɶɧɨɣ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ. ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ I (ɧɚɩɪɢɦɟɪ, ɩɪɢ ɫɧɢɠɟɧɢɢ ɜɧɟɲɧɟɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R ɢɥɢ ɩɨɜɵɲɟɧɢɢ ɗȾɋ ɢɫɬɨɱɧɢɤɚ
ε)
Sɩ ɪɚɫɬɟɬ
ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɬɨɤɭ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɬɨɤɨɜɨɟ ɩɹɬɧɨ ɧɟ ɡɚɣɦɟɬ ɜɫɸ ɩɪɨɜɨɞɹɳɭɸ ɩɨɜɟɪɯɧɨɫɬɶ ɤɚɬɨɞɚ (ɢ ɩɨɞɜɨɞɹɳɢɯ ɝɨɥɵɯ ɩɪɨɜɨɞɨɜ). ɉɪɢ ɷɬɨɦ ɤɚɬɨɞɧɨɟ ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɟ Uk ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ. Ⱦɚɥɶɧɟɣɲɟɟ ɩɨɜɵɲɟɧɢɟ I ɩɪɢɜɨɞɢɬ ɤ ɪɨɫɬɭ Uk - ɷɬɨ "ɚɧɨɦɚɥɶɧɵɣ ɪɟɠɢɦ" ɫ ɚɧɨɦɚɥɶɧɵɦ ɤɚɬɨɞɧɵɦ ɩɚɞɟɧɢɟɦ ɩɨɬɟɧɰɢɚɥɚ, ɚ ɫɚɦ ɪɚɡɪɹɞ ɩɟɪɟɯɨɞɢɬ ɤ ɚɧɨɦɚɥɶɧɨɦɭ ɬɥɟɸɳɟɦɭ ɪɚɡɪɹɞɭ. ɉɨɱɟɦɭ jɩ = const ɨɫɬɚɟɬɫɹ ɧɟɢɡɜɟɫɬɧɵɦ. ɉɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ
ȿɫɥɢ ɜ ɭɫɬɚɧɨɜɤɟ ɧɚ ɪɢɫ. 8.3 ɩɨɜɵɲɚɬɶ ɬɨɤ, ɬɨ ɜ ɤɚɤɨɣ-ɬɨ ɦɨɦɟɧɬ ɡɚɝɨɪɢɬɫɹ ɪɚɡɪɹɞ, ɩɪɢɱɟɦ ɦɟɠɞɭ ɤɚɬɨɞɧɨɣ ɨɛɥɚɫɬɶɸ ɢ ɚɧɨɞɨɦ ɩɨɹɜɢɬɫɹ ɫɜɟɱɟɧɢɟ ɫ ɞɥɢɧɨɣ ɜɨɥɧɵ, ɯɚɪɚɤɬɟɪɧɨɣ ɞɥɹ ɞɚɧɧɨɝɨ ɝɚɡɚ, ɢ ɡɚɧɢɦɚɸɳɟɟ ɜɫɟ ɫɟɱɟɧɢɟ ɬɪɭɛɤɢ. ɗɬɨ ɢ ɟɫɬɶ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ, ɩɪɢɱɟɦ ɧɚ ɧɟɦ ɛɭɞɟɬ ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ, Uɩɫ =
ε
- IR – Uk - Ua. ɗɬɨ ɟɞɢɧɫɬɜɟɧɧɚɹ ɨɛɥɚɫɬɶ ɪɚɡɪɹɞɚ, ɤɨɬɨɪɚɹ ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɢɡɜɨɥɶɧɨɣ ɞɥɢɧɵ. ɉɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɥɚɡɦɭ ɫ ɤɨɧɰɟɧɬɪɚɰɢɟɣ ɱɚɫɬɢɰ, ɭɛɵɜɚɸɳɢɯ ɨɬ ɨɫɢ ɤ ɫɬɟɧɤɚɦ, ɜ ɧɟɦ ɢɞɟɬ ɢɧɬɟɧɫɢɜɧɵɣ ɩɪɨɰɟɫɫ ɢɨɧɢɡɚɰɢɢ ɢ ɩɨɬɟɪɢ ɱɚɫɬɢɰ ɧɚ ɫɬɟɧɤɢ, ɩɪɢ ɷɬɨɦ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɞɚɟɬ ɢɨɧɨɜ ɜ ɤɚɬɨɞɧɭɸ ɨɛɥɚɫɬɶ. ɍɯɨɞɹɳɢɟ ɧɚ ɫɬɟɧɤɭ ɷɥɟɤɬɪɨɧɵ ɡɚɪɹɠɚɸɬ ɢɯ ɨɬɪɢɰɚɬɟɥɶɧɨ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ, ɢ ɢɨɧɵ ɭɫɤɨɪɹɸɬɫɹ ɧɚ ɫɬɟɧɤɭ, ɬ. ɟ. ɩɪɨɢɫɯɨɞɢɬ ɚɦɛɢɩɨɥɹɪɧɚɹ ɞɢɮɮɭɡɢɹ. ȼ ɢɬɨɝɟ ɷɥɟɤɬɪɨɧɵ ɢ ɢɨɧɵ ɧɚ ɫɬɟɧɤɚɯ ɪɟɤɨɦɛɢɧɢɪɭɸɬ. ɇɚɥɢɱɢɟ ɪɚɞɢɚɥɶɧɨɝɨ ɝɪɚɞɢɟɧɬɚ ɩɪɢɜɨɞɢɬ ɤ ɬɨɦɭ,
Ɋɢɫ. 8.4. Ʉɚɪɬɢɧɚ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ ɜ ɬɪɭɛɤɟ ɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɫɜɟɱɟɧɢɹ J, ɩɨɬɟɧɰɢɚɥɚ U, ɩɪɨɞɨɥɶɧɨɝɨ ɩɨɥɹ ȿ, ɩɥɨɬɧɨɫɬɟɣ ɷɥɟɤɬɪɨɧɧɨɝɨ ɢ ɢɨɧɧɨɝɨ ɬɨɤɨɜ je, j+, ɤɨɧɰɟɧɬɪɚɰɢɣ ne, n+ ɢ ɨɛɴɟɦɧɨɝɨ ɡɚɪɹɞɚ ρ = e(ne - n+)
ɱɬɨ ɷɤɜɢɩɨɬɟɧɰɢɚɥɢ ɢɦɟɸɬ ɜɵɩɭɤɥɭɸ ɮɨɪɦɭ.
Ɉɫɨɛɟɧɧɨ ɨɬɱɟɬɥɢɜɨ ɷɬɨ ɜɢɞɧɨ ɩɪɢ ɜɨɡɧɢɤɧɨɜɟɧɢɢ ɜ ɩɨɥɨɠɢɬɟɥɶɧɨɦ ɫɬɨɥɛɟ ɡɚ ɫɱɟɬ ɤɨɥɟɛɚɬɟɥɶɧɵɯ ɩɪɨɰɟɫɫɨɜ ɫɬɨɹɱɢɯ ɢɥɢ ɛɟɝɭɳɢɯ ɫɬɪɚɬ. ɉɪɨɰɟɫɫ ɨɛɪɚɡɨɜɚɧɢɹ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɫɬɨɥɛɚ ɞɨɜɨɥɶɧɨ ɫɥɨɠɧɵɣ, ɯɨɬɹ ɟɝɨ "ɧɚɡɧɚɱɟɧɢɟ" – ɫɨɟɞɢɧɢɬɶ ɤɚɬɨɞɧɵɣ ɢ ɚɧɨɞɧɵɣ ɫɥɨɢ. ɋɬɨɥɛ ɷɥɟɤɬɪɢɱɟɫɤɢ ɧɟɣɬɪɚɥɟɧ, ɬɚɤ ɱɬɨ ɩɥɨɬɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ (ɨɞɧɨɡɚɪɹɞɧɵɯ) ɪɚɜɧɵ, ɚ ɬɨɤɢ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɫɢɥɶɧɨ ɪɚɡɥɢɱɚɸɬɫɹ. Ɍɟɦɩɟɪɚɬɭɪɚ ɨɫɧɨɜɧɨɣ ɦɚɫɫɵ ɷɥɟɤɬɪɨɧɨɜ Ɍe = 1 ÷ 2 ɷȼ, ɚ ɢɨɧɨɜ ɩɪɚɤɬɢɱɟɫɤɢ ɪɚɜɧɚ ɬɟɦɩɟɪɚɬɭɪɟ ɫɬɟɧɨɤ (ɢɨɧɵ ɛɵɫɬɪɨ ɨɛɦɟɧɢɜɚɸɬɫɹ ɩɨɫɬɭɩɚɬɟɥɶɧɨɣ ɷɧɟɪɝɢɟɣ ɫ ɝɚɡɨɦ), ɬɚɤ ɱɬɨ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢ ɫɢɥɶɧɨ ɧɟɪɚɜɧɨɜɟɫɟɧ. Ɉɧ ɨɱɟɧɶ ɧɟɪɚɜɧɨɜɟɫɟɧ ɢ ɜ ɢɨɧɢɡɚɰɢɨɧɧɨɦ ɨɬɧɨɲɟɧɢɢ – ɞɥɹ ɧɟɝɨ ɫɩɪɚɜɟɞɥɢɜɚ ɮɨɪɦɭɥɚ ɗɥɶɜɟɪɬɚ. ɋɛɥɢɠɚɹ ɤɚɬɨɞ ɢ ɚɧɨɞ, ɦɨɠɧɨ ɥɢɤɜɢɞɢɪɨɜɚɬɶ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ, ɧɨ ɪɚɡɪɹɞ ɛɭɞɟɬ ɝɨɪɟɬɶ. Ȼɨɥɟɟ ɬɨɝɨ, ɚɧɨɞɧɵɦ ɫɥɨɟɦ ɦɨɠɧɨ ɩɪɨɣɬɢ ɬɟɦɧɨɟ ɮɚɪɚɞɟɟɜɨ ɩɪɨɫɬɪɚɧɫɬɜɨ, ɧɨ ɤɚɤ ɬɨɥɶɤɨ ɨɧ ɫɨɩɪɢɤɨɫɧɟɬɫɹ ɫ ɬɥɟɸɳɢɦ ɫɥɨɟɦ – ɨɬɪɢɰɚɬɟɥɶɧɨɟ ɬɥɟɸɳɟɟ ɫɜɟɱɟɧɢɟ ɪɚɡɪɹɞɚ ɩɨɝɚɫɧɟɬ. ɋɪɚɜɧɢɬɟɥɶɧɨ ɧɟɞɚɜɧɨ ɛɵɥɨ ɞɨɤɚɡɚɧɨ, ɱɬɨ ɫɜɟɱɟɧɢɟ ɫɬɨɥɛɚ ɩɨɞɞɟɪɠɢɜɚɸɬ ɨɬɧɨɫɢɬɟɥɶɧɨ ɛɵɫɬɪɵɟ ɷɥɟɤɬɪɨɧɵ (20 ÷ 30 ɷȼ), ɭɫɤɨɪɟɧɧɵɟ ɜ ɤɚɬɨɞɧɨɣ ɨɛɥɚɫɬɢ ɢ ɩɨɫɬɭɩɚɸɳɢɟ ɢɡ ɤɚɬɨɞɧɨɝɨ ɫɬɨɥɛɚ ɜ ɤɨɥɢɱɟɫɬɜɟ, ɤɚɤ ɪɚɡ ɞɨɫɬɚɬɨɱɧɨɦ ɞɥɹ ɤɨɦɩɟɧɫɚɰɢɢ ɩɨɬɟɪɶ ɷɥɟɤɬɪɨɧɨɜ ɜ ɧɟɦ ɢ ɨɛɟɫɩɟɱɟɧɢɹ ɜɨɡɛɭɠɞɟɧɢɹ ɝɚɡɚ. ȼ ɪɟɤɥɚɦɧɵɯ ɬɪɭɛɤɚɯ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ ɫɥɟɞɭɟɬ ɡɚ ɜɫɟɦɢ ɢɯ ɢɡɝɢɛɚɦɢ, ɱɬɨ ɨɛɴɹɫɧɹɟɬɫɹ ɨɛɪɚɡɨɜɚɧɢɟɦ ɩɨɜɟɪɯɧɨɫɬɧɵɯ ɡɚɪɹɞɨɜ ɧɚ ɜɧɭɬɪɟɧɧɢɯ ɫɬɟɧɤɚɯ ɬɪɭɛɨɤ ɢ ɩɨɹɜɥɟɧɢɟɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɩɨɩɟɪɟɱɧɵɯ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ. ȿɫɥɢ ɭɜɟɥɢɱɢɜɚɬɶ ɞɚɜɥɟɧɢɟ, ɬɨ ɩɪɨɢɫɯɨɞɢɬ ɫɠɚɬɢɟ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɲɧɭɪɚ, ɬɟɦɩɟɪɚɬɭɪɚ ɢ ɩɪɨɜɨɞɢɦɨɫɬɶ ɜɨɡɪɚɫɬɚɸɬ, ɬɨɤ ɪɚɫɬɟɬ, ɜɵɡɵɜɚɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɣ ɪɚɡɨɝɪɟɜ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɪɨɫɬɚ ɬɟɦɩɟɪɚɬɭɪɵ ɦɨɠɟɬ ɧɚɱɚɬɶɫɹ ɬɟɪɦɢɱɟɫɤɚɹ ɢɨɧɢɡɚɰɢɹ ɢ ɬɥɟɸɳɢɣ ɪɚɡɪɹɞ ɦɨɠɟɬ ɩɟɪɟɣɬɢ ɜ ɞɭɝɨɜɨɣ. Ɍɚɤ ɤɚɤ ɷɬɨ ɨɱɟɧɶ ɜɚɠɧɚɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ, ɪɚɫɫɦɨɬɪɢɦ ɟɟ ɦɟɯɚɧɢɡɦ, ɩɪɚɜɞɚ, ɧɟɫɤɨɥɶɤɨ ɭɩɪɨɳɟɧɧɨ. ɇɟɭɫɬɨɣɱɢɜɨɫɬɢ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɫɬɨɥɛɚ
ɑɚɫɬɨ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ "ɫɬɪɚɬɢɮɢɰɢɪɨɜɚɧ" – ɫɨɫɬɨɢɬ ɢɡ ɫɜɟɬɥɵɯ ɢ ɬɟɦɧɵɯ ɩɨɥɨɫ, ɨɛɵɱɧɨ ɛɟɝɭɳɢɯ ɫ ɬɚɤɨɣ ɫɤɨɪɨɫɬɶɸ, ɱɬɨ ɜɢɡɭɚɥɶɧɨ ɫɬɨɥɛ ɜɨɫɩɪɢɧɢɦɚɟɬɫɹ ɫɩɥɨɲɧɵɦ. ɗɬɨ ɨɞɧɚ ɢɡ ɧɟɭɫɬɨɣɱɢɜɨɫɬɟɣ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɫɬɨɥɛɚ, ɧɨ ɧɟ ɫɚɦɚɹ ɧɟɩɪɢɹɬɧɚɹ. ɇɚɢɛɨɥɟɟ ɜɚɠɧɚɹ – ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ "ɤɨɧɬɪɚɤɰɢɹ" ɢɥɢ "ɲɧɭɪɨɜɚɧɢɟ". ɉɪɢ ɧɟɤɨɬɨɪɨɦ ɩɪɟɞɟɥɶɧɨɦ ɡɧɚɱɟɧɢɢ ɬɨɤɚ (ɩɪɟɞɟɥ ɡɚɜɢɫɢɬ ɨɬ ɦɧɨɝɢɯ ɤɨɧɤɪɟɬɧɵɯ ɭɫɥɨɜɢɣ) ɪɚɡɪɹɞ ɜ ɬɪɭɛɤɟ ɫɨɛɢɪɚɟɬɫɹ ɜ ɬɨɧɤɢɣ ɹɪɤɨ ɫɜɟɬɹɳɟɣɫɹ ɲɧɭɪ, ɨɱɟɧɶ ɩɨɯɨɠɢɣ ɧɚ ɲɧɭɪ ɞɭɝɨɜɨɝɨ ɪɚɡɪɹɞɚ (ɜ ɚɧɝɥɨɹɡɵɱɧɨɣ ɥɢɬɟɪɚɬɭɪɟ ɧɚɡɵɜɚɸɬ arcing, "ɞɭɝɨɜɚɧɢɟ"), ɧɨ ɷɬɨ ɟɳɟ ɧɟ ɞɭɝɚ, ɯɨɬɹ ɬɟɦɩɟɪɚɬɭɪɚ ɢɨɧɨɜ Ti ɩɨɞɧɢɦɚɟɬɫɹ ɞɨ ɞɟɫɹɬɵɯ ɞɨɥɟɣ ɷɥɟɤɬɪɨɧ-ɜɨɥɶɬ, ɬɚɤ ɱɬɨ ɨɬɪɵɜ Ɍɟ ɨɬ Ti ɫɭɳɟɫɬɜɟɧɧɨ ɭɦɟɧɶɲɚɟɬɫɹ. ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɮɥɭɤɬɭɚɬɢɜɧɨ ɩɪɨɢɡɨɲɥɨ ɦɟɫɬɧɨɟ ɩɨɜɵɲɟɧɢɟ ɩɥɨɬɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ δne↑, ɤɚɤ ɫɥɟɞɫɬɜɢɟ ɜɵɪɚɫɬɚɟɬ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ δj↑ (j = neev), ɩɪɨɜɨɞɢɦɨɫɬɶ δσ↑ (σ = nee2/τ) ɢ ɷɧɟɪɝɨɜɵɞɟɥɟɧɢɟ δw↑ (w = j2/σ). ȼ ɪɟɡɭɥɶɬɚɬɟ ɜɨɡɪɚɫɬɟɬ ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ δɌg↑, ɭɦɟɧɶɲɢɬɫɹ ɟɝɨ ɩɥɨɬɧɨɫɬɶ δng↓ (ɬɚɤ ɤɚɤ ɞɚɜɥɟɧɢɟ pg = ngTg ɜɵɪɚɜɧɢɜɚɟɬɫɹ ɛɵɫɬɪɨ ɢ ɟɝɨ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɩɨɫɬɨɹɧɧɵɦ), ɜɨɡɪɚɫɬɚɟɬ ɨɬɧɨɲɟɧɢɟ δE/ng↑, ɜɵɪɚɫɬɚɟɬ ɱɚɫɬɨɬɚ ɢɨɧɢɡɚɰɢɢ δYi↑, ɜɨɡɪɚɫɬɚɟɬ δne↑ – ɰɟɩɨɱɤɚ ɡɚɦɤɧɭɥɚɫɶ:
δne↑ → δj↑ → δw↑ → δɌg↑ → δng↓ → δE/ng↑ → δYi↑ → δne↑ → …
(8.25)
ɢɞɟɬ ɪɨɫɬ j ɢ Ɍg, ɨɛɪɚɡɭɟɬɫɹ ɲɧɭɪ. ɇɟɭɫɬɨɣɱɢɜɨɫɬɶ ɧɚɡɵɜɚɸɬ "ɢɨɧɢɡɚɰɢɨɧɧɨɩɟɪɟɝɪɟɜɧɨɣ" (ɰɟɩɨɱɤɚ ɦɨɠɟɬ ɧɚɱɚɬɶɫɹ ɢ ɫɨ ɫɥɭɱɚɣɧɨɝɨ ɥɨɤɚɥɶɧɨɝɨ ɜɨɡɪɚɫɬɚɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɝɚɡɚ δTg↑). Ⱥɧɨɞɧɵɣ ɫɥɨɣ
Ⱥɧɨɞɧɵɣ ɫɥɨɣ, ɜɫɟɝɞɚ ɨɱɟɧɶ ɬɨɧɤɢɣ. ɗɥɟɤɬɪɨɧɵ ɭɫɤɨɪɹɸɬɫɹ ɤ ɚɧɨɞɭ ɢ 1 ɢɨɧɢɡɭɸɬ ɝɚɡ. ȿɫɥɢ ɬɨɤ ɧɚ ɚɧɨɞ Ia = ne ev e S ɛɨɥɶɲɟ ɪɚɡɪɹɞɧɨɝɨ ɬɨɤɚ ɜ ɰɟɩɢ (Ia 4 > I), ɬɨ ɚɧɨɞ ɡɚɪɹɠɚɟɬɫɹ ɨɬɪɢɰɚɬɟɥɶɧɨ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɫɬɨɥɛɚ, ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ (Ia < I) ɩɨɥɨɠɢɬɟɥɶɧɨ. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜ ɥɚɡɟɪɧɵɯ ɫɪɟɞɚɯ (ɩɪɢ ɛɨɥɶɲɢɯ p ɢ j) ɩɪɢ ɩɨɜɵɲɟɧɢɢ ɞɚɜɥɟɧɢɹ ɪɚɫɬɟɬ ɚɧɨɞɧɨɟ ɩɚɞɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ, ɧɨ ɫɨɯɪɚɧɹɟɬɫɹ ɧɨɪɦɚɥɶɧɚɹ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ, ɫɪɚɜɧɢɦɚɹ ɫ ɧɨɪɦɚɥɶɧɨɣ ɩɥɨɬɧɨɫɬɶɸ ɬɨɤɚ ɤɚɬɨɞɚ. Ƚɚɡɨɜɵɟ ɥɚɡɟɪɵ ɢ ɬɥɟɸɳɢɣ ɪɚɡɪɹɞ
ɉɨɹɜɥɟɧɢɟ ɝɚɡɨɜɵɯ ɥɚɡɟɪɨɜ, ɭɧɢɜɟɪɫɚɥɶɧɨɫɬɶ ɢɯ ɩɪɢɦɟɧɟɧɢɹ ɢ ɫɬɪɟɦɥɟɧɢɟ ɩɨɜɵɫɢɬɶ ɷɧɟɪɝɨɫɨɞɟɪɠɚɧɢɟ ɥɚɡɟɪɧɨɝɨ ɥɭɱɚ ɩɪɢɜɟɥɢ ɤ ɩɨɫɬɚɧɨɜɤɟ ɢ ɪɚɡɪɟɲɟɧɢɸ ɦɧɨɝɢɯ ɧɨɜɵɯ ɮɢɡɢɤɨ-ɬɟɯɧɢɱɟɫɤɢɯ ɩɪɨɛɥɟɦ. ȿɫɥɢ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ ɜ ɦɚɥɨɦɨɳɧɵɯ ɥɚɡɟɪɚɯ (ɟɫɬɶ ɥɚɡɟɪɵ ɦɨɳɧɨɫɬɢ ɜ ɞɨɥɢ ɦɢɥɥɢɜɚɬɬɚ, ɧɚɩɪɢɦɟɪ, ɞɥɹ ɯɢɪɭɪɝɢɢ ɝɥɚɡɚ ɫ ɰɟɥɶɸ ɩɪɢɜɚɪɢɜɚɧɢɹ ɫɟɬɱɚɬɤɢ) ɩɨɬɪɟɛɨɜɚɥɨ ɥɢɲɶ ɧɟɡɧɚɱɢɬɟɥɶɧɨ ɢɡɦɟɧɢɬɶ ɤɨɧɫɬɪɭɤɰɢɸ ɤɚɬɨɞɚ ɢ ɚɧɨɞɚ (ɨɧɢ ɫɬɚɥɢ ɩɪɨɜɨɞɹɳɢɦɢ ɤɨɥɶɰɚɦɢ ɧɚ ɜɧɭɬɪɟɧɧɢɯ ɤɨɧɰɚɯ ɬɪɭɛɤɢ (ɪɢɫ. 8.5), ɩɨɹɜɢɥɢɫɶ ɡɟɪɤɚɥɚ), ɬɨ ɤɨɧɫɬɪɭɤɰɢɹ ɦɨɳɧɵɯ ɥɚɡɟɪɨɜ ɫɬɚɥɚ Ɋɢɫ. 8.5. ɋɯɟɦɚ ɋ02 - ɥɚɡɟɪɚ ɧɟɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɢ ɫ ɞɢɮɮɭɡɢɨɧɧɵɦ ɨɯɥɚɠɞɟɧɢɟɦ: 1 – ɪɚɡɪɹɞɧɚɹ ɬɪɭɛɤɚ, 2 – ɫɨɜɟɪɲɟɧɧɨ ɢɧɨɣ. ɉɪɢ ɬɟɦɩɟɪɚɬɭɪɟ ɤɨɥɶɰɟɜɵɟ ɷɥɟɤɬɪɨɞɵ, 3 – ɦɟɞɥɟɧɧɚɹ ɩɪɨɤɚɱɤɚ ɥɚɡɟɪɧɨɣ ɚɤɬɢɜɧɨɣ ɝɚɡɨɜɨɣ ɫɪɟɞɵ ɫɦɟɫɢ, 4 – ɪɚɡɪɹɞɧɚɹ ɩɥɚɡɦɚ, 5 – ɜɧɟɲɧɹɹ ɬɪɭɛɤɚ, 6 – ɨɯɥɚɠɞɚɸɳɚɹ ɩɪɨɬɨɱɧɚɹ ɜɨɞɚ, 7 – ɝɥɭɯɨɟ ɡɟɪɤɚɥɨ, 8 – ɜɵɲɟ ~ 450 ÷ 500Ʉ ɜɵɯɨɞɧɨɟ ɩɨɥɭɩɪɨɡɪɚɱɧɨɟ ɡɟɪɤɚɥɨ, 9 – ɜɵɯɨɞɹɳɟɟ ɢɡɥɭɱɟɧɢɟ ɷɧɟɪɝɢɹ ɤɨɥɟɛɚɬɟɥɶɧɵɯ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɝɟɧɟɪɚɰɢɸ ɤɨɝɟɪɟɧɬɧɨɝɨ ɢɡɥɭɱɟɧɢɹ, ɧɚɱɢɧɚɟɬ ɨɱɟɧɶ ɛɵɫɬɪɨ ɩɟɪɟɯɨɞɢɬɶ ɜ ɩɨɫɬɭɩɚɬɟɥɶɧɵɟ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ, ɬ.ɟ. ɜ ɬɟɩɥɨ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɧɟɞɨɩɭɫɬɢɦ ɧɚɝɪɟɜ ɛɨɥɟɟ ɱɟɦ ɧɚ 300 ɝɪɚɞɭɫɨɜ, ɧɭɠɟɧ ɨɱɟɧɶ ɢɧɬɟɧɫɢɜɧɵɣ ɬɟɩɥɨɨɬɜɨɞ. Ɍɟɩɥɨɨɬɜɨɞ ɢɡ ɛɨɥɶɲɢɯ ɨɛɴɟɦɨɜ ɡɚ ɫɱɟɬ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ ɝɚɡɚ ɨɛɟɫɩɟɱɢɬɶ ɧɟɥɶɡɹ. Ɋɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɩɨɥɭɱɢɥɚ ɢɞɟɹ ɧɟɩɪɟɪɵɜɧɨɣ ɫɦɟɧɵ ɝɚɡɚ, ɩɨɹɜɢɥɢɫɶ ɛɵɫɬɪɨɩɪɨɬɨɱɧɵɟ ɥɚɡɟɪɵ, ɚ ɪɚɛɨɱɢɣ ɨɛɴɟɦ ɜ ɧɢɯ ɫɨɡɞɚɸɬ ɞɜɟ ɩɚɪɚɥɥɟɥɶɧɵɟ ɩɥɚɫɬɢɧɵ, ɞɥɢɧɨɣ ɢ ɲɢɪɢɧɨɣ ɜ ɧɟɫɤɨɥɶɤɨ ɞɟɫɹɬɤɨɜ ɫɚɧɬɢɦɟɬɪɨɜ. Ɋɚɡɪɹɞ ɨɪɝɚɧɢɡɭɸɬ ɢɥɢ ɜɞɨɥɶ ɩɨɬɨɤɚ ɝɚɡɚ, ɢɥɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɟɦɭ (ɪɢɫ. 8.6). Ɍɚɤ ɤɚɤ ɜ ɥɚɡɟɪɧɵɣ ɥɭɱ ɩɟɪɟɯɨɞɢɬ ɧɟ ɛɨɥɟɟ 30% ɜɤɥɚɞɵɜɚɟɦɨɣ ɜ ɪɚɡɪɹɞ ɷɧɟɪɝɢɢ, ɧɟ ɦɟɧɟɟ 70% ɞɨɥɠɟɧ ɭɧɨɫɢɬɶ ɝɚɡ, ɩɨɷɬɨɦɭ ɞɥɹ ɦɨɳɧɵɯ ɥɚɡɟɪɨɜ ɧɭɠɧɵ ɨɱɟɧɶ ɛɨɥɶɲɢɟ ɩɨɬɨɤɢ ɝɚɡɚ. Ɋɚɫɱɟɬɵ (ɢ ɨɩɵɬ) ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɜ ɧɚɢɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɵɯ CO2 ɥɚɡɟɪɚɯ ɧɚ 10 ɤȼɬ ɦɨɳɧɨɫɬɢ
ɢɡɥɭɱɟɧɢɹ ɧɚɞɨ "ɢɡɪɚɫɯɨɞɨɜɚɬɶ" ɛɨɥɟɟ 80 – 100 ɝ/ɫ. əɫɧɨ, ɱɬɨ ɫɢɫɬɟɦɚ ɝɚɡɨɨɬɜɨɞɚ ɞɨɥɠɧɚ ɛɵɬɶ ɡɚɦɤɧɭɬɚɹ ɫ ɨɯɥɚɠɞɟɧɢɟɦ ɝɚɡɚ (ɫɢɫɬɟɦɵ ɩɪɨɤɚɱɤɢ ɢ ɯɨɥɨɞɢɥɶɧɢɤɨɜ): ɧɟɛɨɥɶɲɚɹ ɚɤɬɢɜɧɚɹ ɡɨɧɚ "ɨɛɪɚɫɬɚɟɬ" ɨɝɪɨɦɧɵɦ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɦ, ɧɨ ɧɟɢɡɛɟɠɧɵɦ ɨɛɨɪɭɞɨɜɚɧɢɟɦ. ȼɬɨɪɚɹ ɨɫɨɛɟɧɧɨɫɬɶ – ɛɨɪɶɛɚ ɫ ɤɨɧɬɪɚɤɰɢɟɣ: ɟɫɥɢ ɜɦɟɫɬɨ ɪɚɜɧɨɦɟɪɧɨ ɫɜɟɬɹɳɟɝɨɫɹ ɩɨɥɧɨɝɨ ɨɛɴɟɦɚ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ "ɫɬɨɥɛɚ" ɨɛɪɚɡɭɟɬɫɹ ɨɞɢɧ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɲɧɭɪɨɜ ɫ ɢɨɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ Ti ɜ ɞɟɫɹɬɵɟ ɞɨɥɢ ɷȼ, ɬɨ ɧɚ ɬɚɤɨɣ ɩɥɚɡɦɟ ɢɧɜɟɪɫɧɨɣ ɡɚɫɟɥɟɧɧɨɫɬɢ ɤɨɥɟɛɚɬɟɥɶɧɵɯ ɭɪɨɜɧɟɣ ɛɵɬɶ ɧɟ ɦɨɠɟɬ. Ɉɞɧɢɦ ɢɡ ɨɫɧɨɜɧɵɯ ɦɟɬɨɞɨɜ, ɩɪɢɦɟɧɹɟɦɵɯ ɩɪɚɤɬɢɱɟɫɤɢ ɜɨ ɜɫɟɯ ɦɨɳɧɵɯ ɥɚɡɟɪɚɯ, ɹɜɥɹɟɬɫɹ ɪɚɡɞɟɥɟɧɢɟ ɤɚɬɨɞɨɜ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɱɟɪɟɡ ɤɚɠɞɵɣ ɲɟɥ ɬɨɤ, ɦɟɧɶɲɢɣ, ɱɟɦ ɧɭɠɧɨ ɞɥɹ ɤɨɧɬɪɚɤɰɢɢ. ɍ ɤɚɠɞɨɝɨ ɤɚɬɨɞɚ ɫɜɨɟ ɛɚɥɥɚɫɬɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ R (ɫɦ. ɪɢɫ. 8.3), ɬɚɤ ɱɬɨ ɟɫɥɢ ɞɚɠɟ ɧɚ ɤɚɤɨɦ-ɥɢɛɨ ɢɡ ɧɢɯ ɢ ɛɭɞɟɬ
Ɋɢɫ.8.6. Ɍɢɩɢɱɧɚɹ ɝɟɨɦɟɬɪɢɹ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ ɜ ɷɥɟɤɬɪɨɪɚɡɪɹɞɧɵɯ ɥɚɡɟɪɚɯ ɧɚ ɋɈ2; ɚ - ɩɨɩɟɪɟɱɧɵɣ ɪɚɡɪɹɞ (ɬɨɤ ɢɞɟɬ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɝɚɡɨɜɨɦɭ ɩɨɬɨɤɭ ɧɚɩɪɚɜɥɟɧɢɹ ɫɤɨɪɨɫɬɢ); ɜɟɪɯɧɹɹ ɩɥɚɬɚ ɭɫɟɹɧɚ ɤɚɬɨɞɧɵɦɢ ɷɥɟɦɟɧɬɚɦɢ Ʉ, ɧɢɠɧɹɹ ɫɥɭɠɢɬ ɚɧɨɞɨɦ Ⱥ; ɛ - ɩɪɨɞɨɥɶɧɵɣ ɪɚɡɪɹɞ, ɤɚɬɨɞɧɵɟ ɷɥɟɦɟɧɬɵ Ʉ ɪɚɫɩɨɥɨɠɟɧɵ ɜɜɟɪɯ ɩɨ ɩɨɬɨɤɭ, ɚɧɨɞɨɦ Ⱥ ɫɥɭɠɢɬ ɬɪɭɛɤɚ
ɤɨɧɬɪɚɤɰɢɹ, ɬɨ ɷɬɨ ɧɟ ɫɭɳɟɫɬɜɟɧɧɨ: ɤɚɬɨɞɨɜ ɬɵɫɹɱɢ. ȿɫɬɶ ɢ ɞɪɭɝɢɟ ɦɟɬɨɞɵ, ɧɚɩɪɢɦɟɪ, ɫɞɟɥɚɬɶ ɢɦɩɭɥɶɫɧɵɣ ɪɚɡɪɹɞ ɧɟɫɚɦɨɫɬɨɹɬɟɥɶɧɵɦ ɢ ɜɨɡɛɭɠɞɚɬɶ ɩɭɱɤɨɦ ɛɵɫɬɪɵɯ (ȿ ~ 100 ɤɷȼ) ɷɥɟɤɬɪɨɧɨɜ, ɤɨɦɛɢɧɢɪɨɜɚɬɶ ɩɨɫɬɨɹɧɧɵɟ ɢ ȼɑ, ɩɨɫɬɨɹɧɧɵɟ ɢ ɢɦɩɭɥɶɫɧɵɟ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ. ɉɪɢɦɟɧɟɧɢɟ ȼɑ ɢ, ɨɫɨɛɟɧɧɨ, ɢɦɩɭɥɶɫɧɵɯ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ ɛɨɥɶɲɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɩɨɡɜɨɥɢɥɨ ɪɟɡɤɨ ɭɜɟɥɢɱɢɬɶ ɷɧɟɪɝɨɫɴɟɦ ɫ ɟɞɢɧɢɰɵ ɪɚɛɨɱɟɝɨ ɨɛɴɟɦɚ ɚɤɬɢɜɧɨɣ ɫɪɟɞɵ. §52. Ⱦɭɝɨɜɵɟ ɪɚɡɪɹɞɵ
ɗɥɟɤɬɪɢɱɟɫɤɨɣ ɞɭɝɨɣ ɧɚɡɵɜɚɸɬ ɭɫɬɚɧɨɜɢɜɲɢɣɫɹ (ɢɥɢ ɩɨɱɬɢ ɭɫɬɚɧɨɜɢɜɲɢɣɫɹ) ɪɚɡɪɹɞ, ɤɨɬɨɪɵɣ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɧɢɡɤɢɦ ɤɚɬɨɞɧɵɦ ɩɚɞɟɧɢɟɦ ɩɨɬɟɧɰɢɚɥɚ ɢ ɜɵɫɨɤɨɣ ɩɥɨɬɧɨɫɬɶɸ ɬɨɤɚ ɧɚ ɤɚɬɨɞɟ (jk ≥ 10 ÷ 102 Ⱥ/ɫɦ2). Ɍɚɤɢɟ ɮɨɪɦɵ ɪɚɡɪɹɞɚ ɢɡɜɟɫɬɧɵ ɫ 1802ɝ. (ɉɟɬɪɨɜ ȼ.ȼ.), ɧɨ ɪɹɞ ɨɫɨɛɟɧɧɨɫɬɟɣ ɧɟ ɩɨɧɹɬɟɧ ɢ ɞɨ ɫɢɯ ɩɨɪ. ɇɟ ɭɫɬɚɧɨɜɢɥɚɫɶ ɟɳɟ ɞɚɠɟ ɨɛɳɟɩɪɢɧɹɬɚɹ ɤɥɚɫɫɢɮɢɤɚɰɢɹ ɞɭɝɨɜɵɯ ɪɚɡɪɹɞɨɜ, ɤɨɬɨɪɵɟ ɞɟɥɹɬɫɹ ɩɨ ɬɢɩɭ ɤɚɬɨɞɨɜ ɢ ɩɨ ɞɚɜɥɟɧɢɸ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ. Ɍɚɤ, ɩɨ ɬɢɩɭ ɤɚɬɨɞɚ ɪɚɡɥɢɱɚɸɬ: ɚ) ɩɨɞɨɝɪɟɜɧɵɟ; ɛ) ɝɨɪɹɱɢɟ; ɜ) ɯɨɥɨɞɧɵɟ; ɝ) ɭɝɨɥɶɧɵɟ; ɩɨ ɞɚɜɥɟɧɢɸ: ɚ) ɧɢɡɤɨɝɨ ɞɚɜɥɟɧɢɹ (p ≤ 10-3 ÷ 1 ɚɬɦ); ɛ) ɜɵɫɨɤɨɝɨ (ɪ ∼ 1 ÷ 5 ɚɬɦ); ɝ) ɫɜɟɪɯɜɵɫɨɤɨɝɨ (ɪ > 10 ɚɬɦ). ȼ ɞɭɝɨɜɨɦ ɪɚɡɪɹɞɟ ɦɨɠɧɨ ɪɚɡɥɢɱɢɬɶ:
1) ɩɪɢɤɚɬɨɞɧɵɣ ɫɥɨɣ – ɬɨɧɤɢɣ, ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɩɨɪɹɞɤɚ ɩɨɬɟɧɰɢɚɥɚ ɢɨɧɢɡɚɰɢɢ (ɛɵɜɚɟɬ ɞɚɠɟ ɦɟɧɶɲɟ) ɚɬɨɦɨɜ ɝɚɡɚ; 2) ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ, ɫɨɫɬɨɹɧɢɟ ɢ ɩɨɜɟɞɟɧɢɟ ɩɥɚɡɦɵ ɜ ɤɨɬɨɪɨɦ ɨɩɪɟɞɟɥɹɟɬɫɹ ɛɚɥɚɧɫɨɦ ɷɧɟɪɝɢɢ; (ɬɟɦɩɟɪɚɬɭɪɵ ɢɨɧɨɜ Ti ɢ ɷɥɟɤɬɪɨɧɨɜ Ɍɟ ɜ ɰɟɧɬɪɚɥɶɧɨɣ ɱɚɫɬɢ ɫɬɨɥɛɚ ɪɚɜɧɵ); ɜ) ɚɧɨɞɧɵɣ, ɬɨɠɟ ɬɨɧɤɢɣ ɫɥɨɣ ɢ ɬɨɠɟ ɫ ɦɚɥɵɦ ɩɚɞɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɧɟɦ. Ⱦɭɝɢ ɫ ɩɨɞɨɝɪɟɜɧɵɦ ɤɚɬɨɞɨɦ
Ⱦɭɝɢ ɫ ɩɨɞɨɝɪɟɜɧɵɦ ɤɚɬɨɞɨɦ ɷɬɨ ɧɟɫɚɦɨɫɬɨɹɬɟɥɶɧɵɟ ɪɚɡɪɹɞɵ, ɢɫɩɨɥɶɡɭɸɬɫɹ ɜ ɨɫɧɨɜɧɨɦ ɤɚɤ ɜɵɩɪɹɦɢɬɟɥɢ, ɭɩɪɚɜɥɹɟɦɵɟ ɜɤɥɸɱɟɧɢɟɦ - ɜɵɤɥɸɱɟɧɢɟɦ ɪɚɡɪɹɞɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ (ɝɚɡɨɬɪɨɧɵ) ɢɥɢ ɢɡɦɟɧɟɧɢɟɦ ɮɚɡɨɜɨɝɨ ɫɞɜɢɝɚ ɧɚɩɪɹɠɟɧɢɣ ɚɧɨɞɚ (ɢɥɢ ɤɚɬɨɞɚ) ɢ ɫɟɬɤɢ (ɬɢɪɚɬɪɨɧɵ). ȼ ɞɭɝɟ ɤɚɬɨɞɧɵɣ ɫɥɨɣ ɬɨɥɶɤɨ ɭɫɤɨɪɹɟɬ ɷɥɟɤɬɪɨɧɵ ɬɟɪɦɨɷɦɢɫɫɢɢ ɧɚɫɬɨɥɶɤɨ, ɱɬɨɛɵ ɨɧɢ ɩɨɞɞɟɪɠɢɜɚɥɢ ɧɭɠɧɭɸ ɢɨɧɢɡɚɰɢɸ ɝɚɡɚ. Ɉɛɪɚɡɭɸɳɚɹɫɹ ɩɥɚɡɦɚ ɤɚɤ ɛɵ "ɩɪɢɛɥɢɠɚɟɬ" ɚɧɨɞ ɤ ɤɚɬɨɞɭ, ɬɚɤ ɱɬɨ ɨɝɪɚɧɢɱɟɧɢɟ ɬɨɤɚ ɨɛɴɟɦɧɵɦ ɡɚɪɹɞɨɦ ("ɡɚɤɨɧ 3/2" ɞɥɹ ɜɚɤɭɭɦɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ) ɜ ɞɭɝɟ ɧɟɬ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɪɢ ɧɚɩɪɹɠɟɧɢɢ ɦɟɠɞɭ ɚɧɨɞɨɦ ɢ ɤɚɬɨɞɨɦ 10-20 ȼ ɬɨɤ ɧɚ ɩɨɪɹɞɤɢ ɛɨɥɶɲɟ, ɱɟɦ ɛɵɥ ɛɵ ɜ ɜɚɤɭɭɦɟ. Ⱦɭɝɢ ɫ ɝɨɪɹɱɢɦɢ ɤɚɬɨɞɚɦɢ
Ⱦɭɝɢ ɫ ɝɨɪɹɱɢɦɢ ɤɚɬɨɞɚɦɢ ɨɱɟɧɶ ɪɚɫɩɪɨɫɬɪɚɧɟɧɵ. Ɉɧɢ ɛɵɜɚɸɬ ɨɬ ɞɟɫɹɬɤɨɜ ɦɢɥɥɢɚɦɩɟɪ (ɥɚɦɩɵ ɞɧɟɜɧɨɝɨ ɫɜɟɬɚ) ɞɨ ɦɟɝɚɚɦɩɟɪ (ɜ ɷɥɟɤɬɪɨɥɢɬɢɱɟɫɤɢɯ ɜɚɧɧɚɯ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɚɥɸɦɢɧɢɹ ɢ ɦɚɝɧɢɹ). ɉɪɢɤɚɬɨɞɧɚɹ ɨɛɥɚɫɬɶ ɝɨɪɹɱɟɝɨ ɞɭɝɨɜɨɝɨ ɪɚɡɪɹɞɚ ɧɟ ɩɪɨɳɟ ɩɪɢɤɚɬɨɞɧɨɣ ɨɛɥɚɫɬɢ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ, ɞɚ ɢ ɢɡɭɱɟɧɚ ɹɜɧɨ ɯɭɠɟ. ɍɫɤɨɪɟɧɧɵɟ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɜɛɥɢɡɢ ɤɚɬɨɞɚ ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɵɟ ɷɥɟɤɬɪɨɧɵ ɜ ɩɪɢɤɚɬɨɞɧɨɣ ɨɛɥɚɫɬɢ ɫɨɡɞɚɸɬ ɢɨɧ-ɷɥɟɤɬɪɨɧɧɵɟ ɩɚɪɵ. ɂɨɧɵ ɭɫɤɨɪɹɸɬɫɹ ɤ ɤɚɬɨɞɭ, ɧɚ ɤɨɬɨɪɨɦ ɩɪɨɢɡɜɨɞɹɬɫɹ 2 ÷ 9 ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɨɞɢɧ ɢɨɧ. ɉɪɨɢɡɜɨɞɫɬɜɨ ɷɥɟɤɬɪɨɧɨɜ ɢɨɧɚɦɢ ɧɚ ɤɚɬɨɞɟ ɱɟɪɟɡ ɬɟɩɥɨ (ɬɟɪɦɨɷɦɢɫɫɢɹ) ɷɧɟɪɝɟɬɢɱɟɫɤɢ ɡɧɚɱɢɬɟɥɶɧɨ ɜɵɝɨɞɧɟɟ, ɱɟɦ ɩɪɹɦɚɹ ɢɨɧɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ (ɤɚɤ ɜ ɬɥɟɸɳɟɦ ɪɚɡɪɹɞɟ), ɧɨ ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ ɩɪɢ ɛɨɥɶɲɨɣ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ. Ʉɚɬɨɞɨɦ ɨɛɵɱɧɨ ɫɥɭɠɢɬ ɢɥɢ ɜɵɫɨɤɨɬɟɦɩɟɪɚɬɭɪɧɵɣ ɦɟɬɚɥɥ (ɱɚɫɬɨ ɜɨɥɶɮɪɚɦ) ɢɥɢ ɪɚɫɩɥɚɜ ɦɟɬɚɥɥɚ (ɜɚɧɧɵ ɩɪɢ ɩɪɨɢɡɜɨɞɫɬɜɟ Al, Mg). ɇɟɫɦɨɬɪɹ ɧɚ ɧɢɡɤɨɟ ɩɚɞɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ, ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɨɤɨɥɨ ɤɚɬɨɞɚ ɜ ɞɭɝɟ ɛɨɥɶɲɨɟ, ɬɚɤ ɤɚɤ ɩɥɚɡɦɚ ɩɨɞɠɢɦɚɟɬ ɩɪɢɤɚɬɨɞɧɵɣ ɫɥɨɣ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɤɚɬɨɞɚ. Ɍɚɤ, ɞɥɹ ɩɥɨɬɧɨɫɬɟɣ ɬɨɤɚ j ∼ 103 Ⱥ/ɫɦ2 ɬɨɤ ɬɟɪɦɨɷɦɢɫɫɢɢ ɜɨɡɪɚɫɬɚɟɬ ɡɚ ɫɱɟɬ ɷɮɮɟɤɬɚ ɒɨɬɬɤɢ ɜ ∼ 3 ɪɚɡɚ (Ek ∼ 106 ȼ/ɫɦ). Ɉɞɧɚɤɨ ɬɨɤɢ ɜ 108 Ⱥ/ɫɦ2 ɨɛɴɹɫɧɢɬɶ ɬɟɪɦɨɷɥɟɤɬɪɨɧɧɨɣ ɢ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɟɣ ɤɚɬɨɞɚ ɧɟɜɨɡɦɨɠɧɨ, ɩɪɢɯɨɞɢɬɫɹ ɞɟɥɚɬɶ ɩɪɟɞɩɨɥɨɠɟɧɢɹ ɨ ɜɡɪɵɜɧɨɣ ɷɦɢɫɫɢɢ ɦɢɤɪɨɨɫɬɪɢɣ ɢ ɨ ɪɚɫɩɥɚɜɥɟɧɢɢ ɩɨɜɟɪɯɧɨɫɬɢ ɤɚɬɨɞɚ ɢ ɜɵɛɪɨɫɟ ɪɚɫɩɥɚɜɥɟɧɧɨɝɨ ɦɟɬɚɥɥɚ ɜ ɪɚɡɪɹɞɧɵɣ ɩɪɨɦɟɠɭɬɨɤ ɫ ɩɨɫɥɟɞɭɸɳɟɣ ɟɝɨ ɢɨɧɢɡɚɰɢɟɣ. Ⱦɭɝɢ ɫ ɯɨɥɨɞɧɵɦɢ ɤɚɬɨɞɚɦɢ
Ⱦɭɝɢ ɫ ɯɨɥɨɞɧɵɦɢ ɤɚɬɨɞɚɦɢ − ɷɬɨ ɩɨ ɫɭɳɟɫɬɜɭ ɞɭɝɢ ɫ ɥɨɤɚɥɶɧɵɦɢ ɬɟɪɦɨɷɦɢɬɬɟɪɚɦɢ: ɧɚ ɤɚɬɨɞɟ ɨɛɪɚɡɭɸɬɫɹ ɬɨɤɨɜɵɟ ɩɹɬɧɚ, ɩɪɢ ɱɟɦ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ ɞɨɥɠɧɚ ɛɵɬɶ ɛɨɥɶɲɟ ɤɪɢɬɢɱɟɫɤɨɣ (ɞɥɹ ɞɚɧɧɨɝɨ ɦɟɬɚɥɥɚ), ɢɧɚɱɟ ɞɭɝɚ ɝɚɫɧɟɬ. ɗɬɨ ɨɛɴɹɫɧɹɟɬɫɹ ɧɟɨɛɯɨɞɢɦɨɫɬɶɸ ɤɨɧɰɟɧɬɪɚɰɢɢ ɷɧɟɪɝɢɢ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɫ ɤɚɬɨɞɚ. ɉɥɨɬɧɨɫɬɢ ɬɨɤɚ ɨɱɟɧɶ ɛɨɥɶɲɢɟ (ɭ ɦɟɞɢ ɞɨ 108 Ⱥ/ɫɦ2!), ɞɚɧɧɵɟ ɨɩɵɬɨɜ ɫɢɥɶɧɨ ɪɚɡɥɢɱɚɸɬɫɹ, ɚ ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ ɧɟɬ. ɉɹɬɧɚ ɯɚɨɬɢɱɟɫɤɢ ɛɟɝɚɸɬ ɩɨ ɤɚɬɨɞɭ, ɩɨɩɵɬɤɢ ɭɩɨɪɹɞɨɱɢɬɶ ɢɯ ɞɜɢɠɟɧɢɹ ɩɨɤɚ ɧɟ ɞɚɥɢ ɪɟɡɭɥɶɬɚɬɚ. ɋ 1903ɝ.
ɢɡɜɟɫɬɧɨ, ɱɬɨ ɟɫɥɢ ɩɹɬɧɨ ɩɨɦɟɫɬɢɬɶ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɇ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɟ ɬɨɤɭ & & j, ɬɨ ɩɹɬɧɨ ɩɨɛɟɠɢɬ ɧɚɜɫɬɪɟɱɭ (!) ɜɟɤɬɨɪɭ j × H ...Ɉɛɴɹɫɧɟɧɢɹ ɞɨ ɫɢɯ ɩɨɪ ɧɟɬ. ɇɟɬ ɩɨɥɧɨɝɨ ɩɨɧɢɦɚɧɢɹ ɢ ɦɟɯɚɧɢɡɦɨɜ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ: ɟɫɥɢ ɞɥɹ ɫɪɟɞɧɢɯ ɡɧɚɱɟɧɢɣ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ (j ∼ 106 Ⱥ/ɫɦ2), ɪɚɫɱɟɬɧɨɟ ɩɨɥɟ ȿ ∼ 107 ȼ/ɫɦ (ɭ ɫɚɦɨɝɨ ɤɚɬɨɞɚ) - ɬɟɨɪɢɹ ɢ ɷɤɫɩɟɪɢɦɟɧɬ ɩɪɢɦɟɪɧɨ ɫɨɜɩɚɞɚɸɬ, ɬɨ ɧɢ ɞɥɹ ɦɚɥɵɯ, ɧɢ ɞɥɹ ɫɚɦɵɯ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ j ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɡɧɚɱɟɧɢɹ ȿ ɨɤɚɡɵɜɚɸɬɫɹ ɧɟɩɪɚɜɞɨɩɨɞɨɛɧɨ ɛɨɥɶɲɢɦɢ. ɂɧɨɝɞɚ ɩɹɬɧɚ ɨɫɬɚɧɚɜɥɢɜɚɸɬɫɹ (ɛɵɜɚɟɬ ɧɚɞɨɥɝɨ), ɜ ɬɚɤɨɦ ɦɟɫɬɟ ɢɞɟɬ ɫɢɥɶɧɚɹ ɷɪɨɡɢɹ (ɞɨ ɞɵɪ ɢ ɩɪɟɤɪɚɳɟɧɢɹ ɪɚɡɪɹɞɚ). ɒɢɪɨɤɨ ɩɪɢɦɟɧɹɸɬɫɹ ɤɚɬɨɞɵ ɢɡ ɪɬɭɬɢ ɜ ɜɵɩɪɹɦɢɬɟɥɹɯ - ɢɝɧɢɬɪɨɧɚɯ. ɉɪɢ ɩɚɞɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɧɢɠɟ ɩɨɬɟɧɰɢɚɥɚ ɡɚɠɢɝɚɧɢɹ ɪɚɡɪɹɞ ɞɨɥɠɟɧ ɩɨɝɚɫɧɭɬɶ (ɧɟɬ ɬɟɩɥɨɜɨɣ "ɢɧɟɪɰɢɢ" ɝɨɪɹɱɢɯ ɤɚɬɨɞɨɜ), ɟɝɨ ɧɚɞɨ ɩɨɞɠɢɝɚɬɶ. Ⱦɥɹ ɷɬɨɝɨ ɜɜɨɞɹɬ ɫɩɟɰɢɚɥɶɧɵɣ ɞɨɩɨɥɧɢɬɟɥɶɧɵɣ ɚɧɨɞ"ɢɝɧɚɣɬɨɪ", ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɤɨɬɨɪɵɣ ɩɨɞɚɸɬ ɫ ɧɭɠɧɵɦ ɫɞɜɢɝɨɦ ɩɨ ɮɚɡɟ. Ʉɚɠɞɵɣ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɩɨɥɭɩɟɪɢɨɞ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦ ɢɝɧɢɬɪɨɧɟ ɫɨɡɞɚɸɬɫɹ "ɡɚɬɪɚɜɨɱɧɵɟ" ɩɚɪɵ ɪɬɭɬɢ, ɢɧɢɰɢɢɪɭɸɳɢɟ ɪɚɡɪɹɞ. ɉɨ ɬɟɪɦɢɧɨɥɨɝɢɢ [33] ɢɝɧɢɬɪɨɧ, ɩɨɠɚɥɭɣ, ɧɚɞɨ ɨɬɧɟɫɬɢ ɤ "ɜɚɤɭɭɦɧɵɦ ɞɭɝɚɦ" − ɛɟɡ ɩɚɪɨɜ ɦɟɬɚɥɥɚ ɤɚɬɨɞɚ ɪɚɡɪɹɞ ɧɟ ɝɨɪɢɬ. "ȼɚɤɭɭɦɧɵɟ" ɞɭɝɢ ɝɨɪɹɬ ɜɫɟɝɞɚ ɫ ɭɱɚɫɬɢɟɦ ɩɚɪɨɜ ɦɚɬɟɪɢɚɥɚ ɤɚɬɨɞɚ ɢ ɢɦɟɸɬ ɜɨɡɪɚɫɬɚɸɳɭɸ ɜɨɥɶɬ-ɚɦɩɟɪɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ (ȼȺɏ) (ɨɛɵɱɧɨ ȼȺɏ ɩɚɞɚɸɳɚɹ). ɉɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ ɞɭɝɨɜɨɝɨ ɪɚɡɪɹɞɚ
ɉɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ ɞɭɝɨɜɨɝɨ ɪɚɡɪɹɞɚ ɫɢɥɶɧɨ ɡɚɜɢɫɢɬ ɨɬ ɪɨɞɚ ɝɚɡɚ, ɞɚɜɥɟɧɢɹ, ɫɢɥɵ ɬɨɤɚ. ɉɪɢ ɦɚɥɵɯ ɞɚɜɥɟɧɢɹɯ (p ≤ 0.1 ɚɬɦ) ɢ ɫɢɥɟ ɬɨɤɚ (I ∼ 1Ⱥ) ɫɬɨɥɛ ɧɟɪɚɜɧɨɜɟɫɟɧ (Te > Ti) ɢ ɫɢɥɶɧɨ ɧɚɩɨɦɢɧɚɟɬ ɤɨɧɬɪɚɝɢɪɨɜɚɧɧɵɣ ɲɧɭɪ ɬɥɟɸɳɟɝɨ ɪɚɡɪɹɞɚ. ɉɥɚɡɦɚ ɩɚɪɨɜ ɦɟɬɚɥɥɚ, ɦɨɥɟɤɭɥɹɪɧɵɯ ɝɚɡɨɜ, ɩɪɢ ɞɚɜɥɟɧɢɢ p ≥ 1 ɚɬɦ ɜɫɟɝɞɚ ɪɚɜɧɨɜɟɫɧɚ, ɯɚɪɚɤɬɟɪɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ (ɩɨ ɪɚɞɢɭɫɭ ɫɬɨɥɛɚ) ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɩɪɨɜɨɞɢɦɨɫɬɢ ɩɪɟɞɫɬɚɜɥɟɧɨ ɧɚ ɪɢɫ. 8.7. ɉɪɢ ɨɛɵɱɧɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɢ ɬɨɤɚ ɬɟɦɩɟɪɚɬɭɪɚ ɛɭɞɟɬ ɢɦɟɬɶ ɤɨɥɨɤɨɨɛɪɚɡɧɭɸ ɮɨɪɦɭ, ɪɚɜɧɨɦɟɪɧɨ ɭɦɟɧɶɲɚɹɫɶ ɨɬ T ~ (10 ÷ 12)⋅103 Ʉ ɜ ɰɟɧɬɪɟ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ ɫɬɟɧɤɢ. ɉɥɨɬɧɨɫɬɶ Ɋɢɫ. 8.7. ɋɯɟɦɚɬɢɱɟɫɤɢɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ɍ ɢ ɷɥɟɤɬɪɨɧɨɜ ɩɨ ɪɚɞɢɭɫɭ ɫɩɚɞɚɟɬ ɩɪɨɜɨɞɢɦɨɫɬɢ σ ɩɨ ɪɚɞɢɭɫɭ ɫɬɨɥɛɚ ɞɭɝɢ. ɨɱɟɧɶ ɛɵɫɬɪɨ − ɜ ɪɚɜɧɨɜɟɫɧɨɣ ɒɬɪɢɯɨɜɚɹ ɥɢɧɢɹ - ɡɚɦɟɧɚ σ (r) ɫɬɭɩɟɧɶɤɨɣ ɜ ɤɚɧɚɥɨɜɨɣ ɦɨɞɟɥɢ ɩɥɚɡɦɟ ne ~ exp(-r/r0) (ɚ ɫ ɧɟɣ ɢ ɩɪɨɜɨɞɢɦɨɫɬɶ (σ ~ ne)), ɬɚɤ ɱɬɨ ɬɨɤɨɩɪɨɜɨɞɹɳɢɣ ɤɚɧɚɥ ɫɨɫɪɟɞɨɬɨɱɟɧ ɭ ɨɫɢ. ɇɚ ɪɚɞɢɭɫɟ, ɛɨɥɶɲɟɦ rɨ (ɪɢɫ. 8.7), ɩɪɨɜɨɞɢɦɨɫɬɶɸ ɩɥɚɡɦɵ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ. Ɉɞɧɚɤɨ ɫɜɹɡɚɬɶ ɤɨɥɢɱɟɫɬɜɟɧɧɨ ɬɨɤ I, ɪɚɞɢɭɫɵ r0 ɢ R, ɦɨɳɧɨɫɬɶ w ɭɞɚɥɨɫɶ ɒɬɟɧɛɟɤɭ, ɬɨɥɶɤɨ ɜɜɟɞɹ ɩɪɢɧɰɢɩ ɦɢɧɢɦɭɦɚ ɦɨɳɧɨɫɬɢ "min w". ɉɪɢ ɡɚɞɚɧɧɨɦ ɬɨɤɟ I ɢ ɪɚɞɢɭɫɟ R ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ
r0 ɬɚɤɨɟ, ɱɬɨɛɵ ɜɵɞɟɥɹɸɳɚɹɫɹ ɜ ɪɚɡɪɹɞɟ ɦɨɳɧɨɫɬɶ ɛɵɥɚ ɦɢɧɢɦɚɥɶɧɨɣ (ɩɨɡɠɟ ɞɨɤɚɡɚɥɢ, ɱɬɨ ɩɪɢɧɰɢɩ " min w " ɫɩɪɚɜɟɞɥɢɜ ɧɟ ɜɫɟɝɞɚ, ɧɨ ɜ ɞɭɝɟ ɫɩɪɚɜɟɞɥɢɜ). ɋɭɳɟɫɬɜɟɧɧɨ, ɱɬɨ ɦɚɤɫɢɦɚɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ Ɍɤ (ɫɦ. ɪɢɫ.8.7) ɜɟɫɶɦɚ ɫɥɚɛɨ ɡɚɜɢɫɢɬ ɨɬ ɨɯɥɚɠɞɟɧɢɹ ɞɭɝɢ (ɜɚɠɟɧ ɬɨɥɶɤɨ ɬɟɩɥɨɨɬɜɨɞ ɨɬ ɤɚɬɨɞɚ) ɢ ɪɚɫɬɟɬ ɫ ɜɤɥɚɞɵɜɚɟɦɨɣ ɦɨɳɧɨɫɬɶɸ ɧɟɫɤɨɥɶɤɨ ɦɟɞɥɟɧɧɟɟ, ɱɟɦ ɤɨɪɟɧɶ ɤɜɚɞɪɚɬɧɵɣ ɢɡ ɦɨɳɧɨɫɬɢ. ɉɪɢ ɜɵɫɨɤɨɦ ɞɚɜɥɟɧɢɢ (p ≥ 10 ɚɬɦ) ɢ ɜɵɫɨɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ (Ɍ ≥ 12000Ʉ) ɨɱɟɧɶ ɫɭɳɟɫɬɜɟɧɧɵɦ ɨɤɚɡɵɜɚɟɬɫɹ ɨɯɥɚɠɞɟɧɢɟ ɢɡɥɭɱɟɧɢɟɦ, ɨɧɨ ɭɧɨɫɢɬ ɞɨ 90% ɦɨɳɧɨɫɬɢ. ȼ ɩɨɫɥɟɞɧɢɟ ɝɨɞɵ ɜɵɫɨɤɢɣ ɫɜɟɬɨɜɨɣ ɄɉȾ ɞɭɝ ɜɵɫɨɤɨɝɨ ɞɚɜɥɟɧɢɹ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɸɬ ɞɥɹ ɨɫɜɟɳɟɧɢɹ ɞɨɪɨɝ. Ɉɛɥɚɫɬɶ ɚɧɨɞɚ
Ɉɛɥɚɫɬɶ ɚɧɨɞɚ ɬɚɤ-ɠɟ, ɤɚɤ ɢ ɩɪɢɤɚɬɨɞɧɚɹ, ɜɟɫɶɦɚ ɬɨɧɤɚɹ, ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɧɟɣ ɡɚɜɢɫɢɬ ɨɬ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɚɧɨɞɚ, ɚ ɢɯ ɞɜɚ. ɉɟɪɜɵɣ ɪɟɠɢɦ ɞɢɮɮɭɡɧɵɣ ɢɦɟɟɬ ɦɟɫɬɨ ɩɪɢ ɛɨɥɶɲɨɣ ɩɥɨɳɚɞɢ ɚɧɨɞɚ ɢ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ j ≤ 102Ⱥ/ɫɦ2 , ɬɨɤ ɪɚɫɩɪɟɞɟɥɟɧ ɩɨ ɜɫɟɦɭ ɚɧɨɞɭ ɢ ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɨɱɟɧɶ ɦɚɥɨ (1 ÷ 3 ȼ) (ɢ ɞɚɠɟ ɛɵɜɚɟɬ ɨɬɪɢɰɚɬɟɥɶɧɵɦ). ȼɬɨɪɨɣ ɪɟɠɢɦ: ɟɫɥɢ ɩɥɨɳɚɞɶ ɚɧɨɞɚ ɦɚɥɚ (ɬɨɤ ɜɵɯɨɞɢɬ ɧɚ ɤɪɚɹ ɢ ɬ.ɞ.), ɬɨ ɩɪɢ ɧɟɤɨɬɨɪɨɦ ɬɨɤɟ (ɡɚɜɢɫɢɬ ɨɬ ɦɧɨɝɢɯ ɩɪɢɱɢɧ) ɬɨɤ ɫɨɛɢɪɚɟɬɫɹ ɜ ɩɹɬɧɨ (ɢɥɢ ɩɹɬɧɚ) ɫ ɩɥɨɬɧɨɫɬɶɸ j = 102 Ⱥ/ɫɦ2. Ⱥɧɨɞɧɵɟ ɩɹɬɧɚ ɨɛɪɚɡɭɸɬ ɩɪɚɜɢɥɶɧɵɟ ɝɟɨɦɟɬɪɢɱɟɫɤɢɟ ɮɢɝɭɪɵ (!), ɢɧɨɝɞɚ ɛɟɝɚɸɬ, ɧɨ ɬɨɠɟ ɩɨ ɭɩɨɪɹɞɨɱɟɧɧɵɦ ɬɪɚɟɤɬɨɪɢɹɦ (ɤɪɭɝɢ, ɨɜɚɥɵ,...). Ɇɟɯɚɧɢɡɦɵ ɧɟ ɢɡɜɟɫɬɧɵ. Ɂɚɠɢɝɚɧɢɟ ɞɭɝɢ
Ɂɚɠɢɝɚɧɢɟ ɞɭɝɢ ɦɨɠɧɨ ɩɪɨɢɡɜɟɫɬɢ, ɫɨɟɞɢɧɹɹ ɷɥɟɤɬɪɨɞɵ (ɨɫɧɨɜɧɵɟ ɢɥɢ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɟ, ɤɚɤ ɜ ɢɝɧɢɬɪɨɧɟ), ɚ ɡɚɬɟɦ ɪɚɡɴɟɞɢɧɹɹ ɢɯ. ɉɪɨɰɟɫɫ ɡɚɠɢɝɚɧɢɹ ɞɭɝɢ ɩɪɢ ɪɚɡɦɵɤɚɧɢɢ ɰɟɩɢ (ɩɪɢ ɪɚɡɴɟɞɢɧɟɧɢɢ ɷɥɟɤɬɪɨɞɨɜ) ɨɛɴɹɫɧɹɟɬɫɹ ɥɨɤɚɥɶɧɵɦ ɪɚɡɨɝɪɟɜɨɦ ɷɥɟɤɬɪɨɞɨɜ ɜɫɥɟɞɫɬɜɢɟ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɦɟɠɞɭ ɧɢɦɢ ɩɥɨɯɨɝɨ ɤɨɧɬɚɤɬɚ, ɤɨɝɞɚ ɢɡ-ɡɚ ɛɨɥɶɲɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɪɨɢɫɯɨɞɢɬ ɧɚɝɪɟɜ ɦɟɫɬɚ ɤɨɧɬɚɤɬɚ ɞɨ ɬɟɪɦɨɷɦɢɫɫɢɢ ɢ ɪɚɡɪɹɞ ɡɚɠɢɝɚɟɬɫɹ. Ɍɚɤɨɣ ɠɟ ɩɪɨɰɟɫɫ ɩɪɨɢɫɯɨɞɢɬ ɢ ɩɪɢ ɪɚɡɦɵɤɚɧɢɢ ɬɨɤɚ ɜ ɫɢɥɶɧɨɬɨɱɧɵɯ ɜɵɤɥɸɱɚɬɟɥɹɯ ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ ɜɪɟɞɧɵɯ ɞɭɝ, ɤɨɬɨɪɵɟ ɜɵɠɢɝɚɸɬ ɷɥɟɤɬɪɨɞɵ. Ⱦɪɭɝɨɣ ɫɩɨɫɨɛ ɨɛɪɚɡɨɜɚɧɢɹ ɞɭɝɢ − ɷɬɨ ɢɨɧɢɡɚɰɢɹ ɜ ɦɟɠɷɥɟɤɬɪɨɞɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɩɪɢ ɩɨɞɚɱɟ ɩɨɜɵɲɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɢ ɜɵɛɨɪ ɮɨɪɦɵ ɷɥɟɤɬɪɨɞɨɜ, ɫɩɨɫɨɛɫɬɜɭɸɳɟɣ ɪɚɡɪɹɞɭ (ɨɛɵɱɧɨ ɨɫɬɪɢɟ). ȿɫɥɢ ɜ ɬɥɟɸɳɟɦ ɪɚɡɪɹɞɟ ɭɜɟɥɢɱɢɜɚɬɶ ɫɢɥɭ ɬɨɤɚ (ɩɭɬɟɦ ɫɧɢɠɟɧɢɹ ɜɧɟɲɧɟɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɢɥɢ ɩɨɜɵɲɚɹ ɗȾɋ ɢɫɬɨɱɧɢɤɚ ε), ɬɨ ɩɪɢ ɛɨɥɶɲɨɣ ɫɢɥɟ ɬɨɤɚ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɷɥɟɤɬɪɨɞɚɯ ɬɪɭɛɤɢ ɧɚɱɢɧɚɟɬ ɩɚɞɚɬɶ, ɪɚɡɪɹɞ ɛɵɫɬɪɨ ɪɚɡɜɢɜɚɟɬɫɹ, ɩɪɟɜɪɚɳɚɹɫɶ ɜ ɞɭɝɨɜɨɣ. ȼ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɩɟɪɟɯɨɞ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɫɤɚɱɤɨɦ ɢ ɧɟɪɟɞɤɨ ɜɟɞɟɬ ɤ ɤɨɪɨɬɤɨɦɭ ɡɚɦɵɤɚɧɢɸ. ɍɝɨɥɶɧɚɹ ɞɭɝɚ
ɍɝɨɥɶɧɚɹ ɞɭɝɚ ɢɫɬɨɪɢɱɟɫɤɢ ɢɡɜɟɫɬɧɚ ɫ 1802 ɝ., ɢɡɭɱɟɧɚ, ɩɨɠɚɥɭɣ, ɥɭɱɲɟ ɜɫɟɯ ɞɪɭɝɢɯ, ɩɪɢɱɟɦ ɤɨɧɤɪɟɬɧɨ ɜ ɜɨɡɞɭɯɟ. Ⱦɭɝɨɜɵɟ ɫɜɟɬɢɥɶɧɢɤɢ, ɫɜɟɱɚ əɛɥɨɱɤɨɜɚ, ɩɟɪɜɵɟ ɫɜɚɪɤɢ, ɧɚɜɚɪɢɜɚɧɢɟ ɦɟɬɚɥɥɨɜ ɜɟɥɢɫɶ ɫ ɭɝɨɥɶɧɵɦɢ ɞɭɝɚɦɢ. ɇɨ ɭ ɧɢɯ ɛɵɥ ɛɨɥɶɲɨɣ ɧɟɞɨɫɬɚɬɨɤ: ɨɞɢɧ ɢɡ ɷɥɟɤɬɪɨɞɨɜ ɫɝɨɪɚɥ ɛɵɫɬɪɟɟ ɞɪɭɝɨɝɨ. Ȼɵɥ ɢɡɨɛɪɟɬɟɧ ɪɹɞ ɭɫɬɪɨɣɫɬɜ, ɪɟɝɭɥɢɪɭɸɳɢɯ ɩɨɞɚɱɭ ɭɝɥɟɣ, ɢɯ ɜɵɩɭɫɤɚɥɚ ɩɪɨɦɵɲɥɟɧɧɨɫɬɶ. ɇɨ ɜ ɫɟɪɟɞɢɧɟ 19-ɝɨ ɜɟɤɚ əɛɥɨɱɤɨɜ ɩɪɟɞɥɨɠɢɥ ɩɟɪɟɣɬɢ ɨɬ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɤ ɩɟɪɟɦɟɧɧɨɦɭ: ɭ ɝɟɧɟɪɚɬɨɪɨɜ ɡɚɦɟɧɢɬɶ ɤɨɥɥɟɤɬɨɪ ɧɚ
ɬɨɤɨɫɴɟɦɧɵɟ ɤɨɥɶɰɚ. Ɍɨɤ ɛɭɞɟɬ ɦɟɧɹɬɶ ɡɧɚɤ, ɭɝɥɢ ɛɭɞɭɬ ɝɨɪɟɬɶ ɨɞɢɧɚɤɨɜɨ. ɋ ɷɬɨɝɨ ɦɨɦɟɧɬɚ "ɛɨɪɶɛɚ" ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ (ɨɧ ɢ ɞɨ ɫɢɯ ɩɨɪ ɧɭɠɟɧ ɨɱɟɧɶ ɦɧɨɝɢɦ ɩɨɬɪɟɛɢɬɟɥɹɦ − ɨɬ ɷɥɟɤɬɪɢɱɟɤ ɩɪɢ ɛɨɥɶɲɢɯ I, ɞɨ ɷɥɟɤɬɪɨɧɢɤɢ − ɩɪɢ ɦɚɥɵɯ I) ɫ ɩɟɪɟɦɟɧɧɵɦ (ɟɝɨ ɦɨɠɧɨ ɬɪɚɧɫɩɨɪɬɢɪɨɜɚɬɶ, ɡɧɚɱɢɬ, ɫɬɪɨɢɬɶ ɦɨɳɧɵɟ ɷɥɟɤɬɪɨɫɬɚɧɰɢɢ, ɱɬɨ ɜɵɝɨɞɧɟɟ) ɩɪɨɞɨɥɠɚɥɚɫɶ ɩɪɢɦɟɪɧɨ ɞɨ 20-ɯ ɝɝ. XX ɜ. Ʉɨɧɟɱɧɨ, ɩɨɛɟɞɢɥ ɩɟɪɟɦɟɧɧɵɣ. ɉɥɚɡɦɚ ɭɝɨɥɶɧɨɣ ɞɭɝɢ ɜ ɚɬɦɨɫɮɟɪɟ ɪɚɜɧɨɜɟɫɧɚɹ, ɯɨɬɹ ɩɨ ɟɟ ɞɥɢɧɟ ɬɟɦɩɟɪɚɬɭɪɚ ɦɟɧɹɟɬɫɹ ɛɨɥɟɟ ɱɟɦ ɜ ɞɜɚ ɪɚɡɚ (ɨɬ 12000 ɞɨ ~ 5000Ʉ). Ʉɚɬɨɞɧɨɟ ɩɚɞɟɧɢɟ ɫɧɢɠɚɟɬɫɹ ɜɩɥɨɬɶ ɞɨ 10 ȼ (!), ɚɧɨɞɧɨɟ ɬɨɠɟ ɩɨɪɹɞɤɚ 10 ȼ, ɨɫɬɚɥɶɧɨɟ (ɧɟɫɤɨɥɶɤɨ ɜɨɥɶɬ) ɩɪɢɯɨɞɢɬɫɹ ɧɚ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɫɬɨɥɛ. ȼȺɏ ɞɨ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɡɧɚɱɟɧɢɹ ɬɨɤɚ ɩɚɞɚɸɳɚɹ, ɡɚɬɟɦ ɧɚɩɪɹɠɟɧɢɟ ɫɤɚɱɤɨɦ ɭɦɟɧɶɲɚɟɬɫɹ, ɜɨɡɧɢɤɚɟɬ ɲɢɩɟɧɢɟ («ɲɢɩɹɳɚɹ ɞɭɝɚ»), ɢ ȼȺɏ ɫɬɚɧɨɜɢɬɫɹ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ. ɂɧɬɟɪɟɫɧɨ, ɱɬɨ ɤɚɬɨɞ (Ɍɤ ≈ 3500 Ʉ) ɯɨɥɨɞɧɟɟ ɚɧɨɞɚ (Ɍɚ ≈ 4200 Ʉ). §53. ɂɫɤɪɨɜɨɣ ɢ ɤɨɪɨɧɧɵɣ, ȼɑ- ɢ ɋȼɑ- ɪɚɡɪɹɞɵ ɂɫɤɪɨɜɨɣ ɪɚɡɪɹɞ
ɂɫɤɪɨɜɨɣ ɪɚɡɪɹɞ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɢɦɩɭɥɶɫɧɵɣ, ɟɝɨ ɢɡɭɱɚɥɢ ɢ ɞɨ ɩɨɹɜɥɟɧɢɹ ɢɫɬɨɱɧɢɤɨɜ ɬɨɤɚ: ɬɪɟɧɢɟɦ ɡɚɪɹɠɚɥɢ ɤɨɧɞɟɧɫɚɬɨɪɵ ("ɥɟɣɞɟɧɫɤɢɟ ɛɚɧɤɢ"), ɫɨɛɢɪɚɥɢ ɚɬɦɨɫɮɟɪɧɨɟ ɷɥɟɤɬɪɢɱɟɫɬɜɨ ɜ ɩɪɟɞɝɪɨɡɨɜɵɯ ɭɫɥɨɜɢɹɯ. ȼ Ɋɨɫɫɢɢ ɜ XVIII ɜ. ɪɚɛɨɬɚɥɢ Ɇ. Ʌɨɦɨɧɨɫɨɜ ɢ Ƚ. Ɋɢɯɦɚɧ, ɜ Ⱥɦɟɪɢɤɟ ȼ.Ɏɪɚɧɤɥɢɧ. Ɉɧ ɩɪɟɞɥɨɠɢɥ ɩɟɪɜɨɟ ɨɛɴɹɫɧɟɧɢɟ ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɹɜɥɟɧɢɹɦ: ɷɥɟɤɬɪɢɱɟɫɬɜɨ − "ɧɟɜɟɫɨɦɚɹ ɠɢɞɤɨɫɬɶ" (ɜɪɨɞɟ "ɬɟɩɥɨɪɨɞɚ"), ɟɟ ɢɡɛɵɬɨɤ − ɡɧɚɤ (+), ɧɟɞɨɫɬɚɬɨɤ − ɡɧɚɤ (-). ȿɫɥɢ ɫɨɟɞɢɧɢɬɶ ɢɯ ɩɪɨɜɨɞɧɢɤɨɦ, ɬɨ (+) ɩɨɬɟɱɟɬ ɤ (-)... Ɍɚɤ, ɜ ɷɥɟɤɬɪɨɬɟɯɧɢɤɟ ɬɨɤ ɢ ɞɨ ɫɢɯ ɩɨɪ ɬɟɱɟɬ ɨɬ (+) ɤ (-)!.. Ɋɟɚɥɶɧɨɟ ɢɡɭɱɟɧɢɟ ɨɱɟɧɶ ɛɵɫɬɪɨ ɩɪɨɬɟɤɚɸɳɢɯ ɢɫɤɪɨɜɵɯ ɪɚɡɪɹɞɨɜ ɫɬɚɥɨ ɜɨɡɦɨɠɧɨ ɫ ɩɨɹɜɥɟɧɢɟɦ ɤɚɦɟɪ ȼɢɥɶɫɨɧɚ, ɩɪɢɛɨɪɨɜ ɫɤɨɪɨɫɬɧɨɝɨ ɮɨɬɨɝɪɚɮɢɪɨɜɚɧɢɹ, ɤɚɬɨɞɧɵɯ ɨɫɰɢɥɥɨɝɪɚɮɨɜ. Ɉɤɚɡɚɥɨɫɶ, ɱɬɨ ɢɫɤɪɚ ɦɨɠɟɬ ɡɚɝɨɪɚɬɶɫɹ ɜ ɩɥɨɬɧɨɦ (ɞɚɜɥɟɧɢɟ ɩɨɪɹɞɤɚ ɚɬɦɨɫɮɟɪɵ ɢ ɛɨɥɶɲɟ) ɝɚɡɟ ɩɪɢ ɛɨɥɶɲɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ. ɉɟɪɜɢɱɧɚɹ ɥɚɜɢɧɚ ɛɵɫɬɪɨ ɩɨɥɹɪɢɡɭɟɬɫɹ − ɷɥɟɤɬɪɨɧɵ ɨɬɯɨɞɹɬ ɜ ɫɬɨɪɨɧɭ ɚɧɨɞɚ, ɚ ɢɨɧɵ ɩɪɚɤɬɢɱɟɫɤɢ ɫɬɨɹɬ. ɉɪɢ ɨɛɪɚɡɨɜɚɧɢɢ ɥɚɜɢɧɵ ɩɪɨɢɫɯɨɞɢɬ ɦɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɣ ɫ ɛɵɫɬɪɵɦ ɜɵɫɜɟɱɢɜɚɧɢɟɦ, ɮɨɬɨɷɮɮɟɤɬ ɫɨɡɞɚɟɬ ɧɨɜɵɟ ɷɥɟɤɬɪɨɧɵ, ɧɨɜɵɟ ɥɚɜɢɧɵ ɜɛɥɢɡɢ ɨɫɧɨɜɧɨɣ, ɨɧɢ ɜɬɹɝɢɜɚɸɬɫɹ ɜ ɨɫɧɨɜɧɭɸ ɥɚɜɢɧɭ, ɪɚɫɬɟɬ ɟɟ ɨɛɴɟɞɢɧɟɧɧɵɣ ɡɚɪɹɞ, ɪɚɫɬɟɬ ɫɨɡɞɚɜɚɟɦɨɟ ɢɦ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ E. Ʉɨɝɞɚ ɷɬɨ ɩɨɥɟ ȿ ɩɪɢɦɟɪɧɨ ɫɬɚɧɟɬ ɪɚɜɧɵɦ ɜɧɟɲɧɟɦɭ ȿ0, ɜɨɡɧɢɤɚɟɬ ɬɨɧɤɢɣ ɩɪɨɜɨɞɹɳɢɣ ɤɚɧɚɥ − ɫɬɪɢɦɟɪ, ɫɨɟɞɢɧɹɸɳɢɣ ɷɥɟɤɬɪɨɞɵ (ɫɬɪɢɦɟɪ ɦɨɠɟɬ ɛɵɬɶ ɧɚɩɪɚɜɥɟɧ ɤ ɥɸɛɨɦɭ ɷɥɟɤɬɪɨɞɭ ɢɥɢ ɫɪɚɡɭ ɤ ɨɛɨɢɦ). ɋɤɨɪɨɫɬɶ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɫɬɪɢɦɟɪɨɜ (ɛɨɥɟɟ 108 ɫɦ/ɫ) ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ ɫɤɨɪɨɫɬɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɷɥɟɤɬɪɨɧɧɵɯ ɥɚɜɢɧ, ɨɩɪɟɞɟɥɹɟɦɨɣ ɩɨɞɜɢɠɧɨɫɬɶɸ ɷɥɟɤɬɪɨɧɨɜ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɥɹ ɪɚɡɜɢɬɢɹ ɫɬɪɢɦɟɪɚ ɧɟɨɛɯɨɞɢɦɨ ɜɵɩɨɥɧɟɧɢɟ ɞɜɭɯ ɭɫɥɨɜɢɣ: 1) ɩɨɥɟ ɥɚɜɢɧɵ ɫɪɚɜɧɢɜɚɟɬɫɹ ɫ ɜɧɟɲɧɢɦ ɩɨɥɟɦ (E ∼ E0); 2) ɢɡɥɭɱɟɧɢɟ ɩɟɪɟɞɧɟɝɨ ɮɪɨɧɬɚ ɥɚɜɢɧɵ ɞɨɫɬɚɬɨɱɧɨ ɞɥɹ ɮɨɬɨɢɨɧɢɡɚɰɢɢ ɧɭɠɧɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɚɬɨɦɨɜ ɝɚɡɚ. ɋɨɛɫɬɜɟɧɧɨ ɫɬɪɢɦɟɪ ɫɥɚɛɨɩɪɨɜɨɞɹɳɢɣ, ɧɨ ɩɟɪɟɞ ɫɚɦɵɦ ɡɚɦɵɤɚɧɢɟɦ ɦɟɠɷɥɟɤɬɪɨɞɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ ɜɞɨɥɶ ɧɟɝɨ ɩɪɨɯɨɞɢɬ ɜɨɥɧɚ ɫɤɚɱɤɚ ɩɨɬɟɧɰɢɚɥɚ, ɨɛɪɚɡɭɟɬɫɹ ɯɨɪɨɲɨ ɩɪɨɜɨɞɹɳɢɣ ɤɚɧɚɥ, ɢ ɭɠɟ ɩɨ ɧɟɦɭ ɩɪɨɯɨɞɢɬ ɛɨɥɶɲɨɣ ɬɨɤ − ɫɨɛɫɬɜɟɧɧɨ ɢɫɤɪɚ. Ƚɚɡ ɜ ɤɚɧɚɥɟ ɫɢɥɶɧɨ ɧɚɝɪɟɜɚɟɬɫɹ, ɜɨɡɧɢɤɚɟɬ ɫɤɚɱɨɤ ɞɚɜɥɟɧɢɹ − ɡɜɭɤɨɜɚɹ ɜɨɥɧɚ (ɜ ɦɨɥɧɢɢ − ɝɪɨɦ). (ɂɡɥɨɠɟɧɢɟ ɜɟɫɶɦɚ ɭɩɪɨɳɟɧɧɨɟ, ɧɨ ɛɨɥɟɟ ɚɤɤɭɪɚɬɧɨɟ ɧɚɦɧɨɝɨ ɞɥɢɧɧɟɟ, ɚ ɩɨɥɧɨɣ ɹɫɧɨɫɬɢ ɜɫɟ ɪɚɜɧɨ ɧɟɬ...) ȿɫɥɢ ɦɟɠɷɥɟɤɬɪɨɞɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɛɨɥɶɲɨɟ, ɩɨɥɟ ȿ
ɧɟɨɞɧɨɪɨɞɧɨɟ, ɧɚ ɤɨɧɰɟ ɫɬɢɦɟɪɚ ɦɨɠɟɬ ɨɛɪɚɡɨɜɚɬɶɫɹ ɯɨɪɨɲɨ ɩɪɨɜɨɞɹɳɢɣ ɭɱɚɫɬɨɤ - ɥɢɞɟɪ (ɪɢɫ. 8.8), ɱɬɨ ɯɚɪɚɤɬɟɪɧɨ ɞɥɹ ɦɨɥɧɢɣ, ɝɞɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɨɛɪɚɡɭɟɬɫɹ ɧɟɫɤɨɥɶɤɨ ɥɢɞɟɪɨɜ, ɩɨ ɫɭɳɟɫɬɜɭ, ɧɟɫɤɨɥɶɤɨ ɪɚɡɪɹɞɨɜ ɫ ɜɪɟɦɟɧɧɵɦɢ ɫɞɜɢɝɚɦɢ ɜ ɞɟɫɹɬɤɢ ɦɢɥɥɢɫɟɤɭɧɞ. ɂɫɤɪɨɜɨɣ ɪɚɡɪɹɞ ɩɨɥɭɱɢɥ ɩɪɢɦɟɧɟɧɢɟ ɜ ɩɪɨɦɵɲɥɟɧɧɨɫɬɢ, ɷɬɨ ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ "ɷɥɟɤɬɪɨɷɪɨɡɢɨɧɧɵɣ" ɫɩɨɫɨɛ ɨɛɪɚɛɨɬɤɢ ɦɟɬɚɥɥɨɜ, ɡɚɩɚɬɟɧɬɨɜɚɧɧɵɣ ɜ ɪɹɞɟ ɫɬɪɚɧ. Ȼɨɥɟɟ ɩɨɞɪɨɛɧɨ ɨɛ ɢɫɤɪɨɜɨɦ ɪɚɡɪɹɞɟ ɫɦ. [34]. Ʉɨɪɨɧɧɵɣ ɪɚɡɪɹɞ.
Ʉɨɪɨɧɧɵɣ ɪɚɡɪɹɞ − ɫɚɦɨɫɬɨɹɬɟɥɶɧɵɣ ɪɚɡɪɹɞ, Ɋɢɫ. 8.8. ɋɯɟɦɚ ɥɢɞɟɪɚ, ɩɪɨɪɚɫɬɚɸɳɟɝɨ ɨɬ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɨɫɬɪɢɹ ɩɨ ɩɭɬɢ, ɩɪɨɥɨɠɟɧɧɨɦɭ ɤɨɬɨɪɵɣ ɜɨɡɧɢɤɚɟɬ ɬɨɥɶɤɨ ɩɪɢ ɫɬɪɢɦɟɪɚɦɢ, ɤɨɬɨɪɵɟ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɜɬɹɝɢɜɚɸɬ ɭɫɥɨɜɢɢ ɨɱɟɧɶ ɛɨɥɶɲɨɣ ɥɚɜɢɧɵ ɧɟɨɞɧɨɪɨɞɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɯɨɬɹ ɛɵ ɭ ɨɞɧɨɝɨ ɢɡ ɷɥɟɤɬɪɨɞɨɜ (ɨɫɬɪɢɟ − ɩɥɨɫɤɨɫɬɶ, ɧɢɬɶ − ɩɥɨɫɤɨɫɬɶ, ɞɜɟ ɧɢɬɢ, ɧɢɬɶ ɜ ɰɢɥɢɧɞɪɟ ɛɨɥɶɲɨɝɨ ɪɚɞɢɭɫɚ ɢ ɬ.ɞ.). ɍɫɥɨɜɢɹ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɢ ɪɚɡɜɢɬɢɹ ɤɨɪɨɧɵ ɪɚɡɥɢɱɧɵɟ ɩɪɢ ɪɚɡɧɨɣ ɩɨɥɹɪɧɨɫɬɢ "ɨɫɬɪɢɹ" (ɧɚɡɨɜɟɦ ɬɚɤ ɷɥɟɤɬɪɨɞ, ɜɛɥɢɡɢ ɤɨɬɨɪɨɝɨ ȿ ɫɢɥɶɧɨ ɧɟɨɞɧɨɪɨɞɧɨ). ȿɫɥɢ ɨɫɬɪɢɟ − ɤɚɬɨɞ (ɤɨɪɨɧɚ "ɨɬɪɢɰɚɬɟɥɶɧɚɹ"), ɬɨ ɡɚɠɢɝɚɧɢɟ ɤɨɪɨɧɵ ɩɨ ɫɭɳɟɫɬɜɭ ɩɪɨɢɫɯɨɞɢɬ ɬɚɤ ɠɟ, ɤɚɤ ɜ ɬɥɟɸɳɟɦ ɪɚɡɪɹɞɟ, ɬɨɥɶɤɨ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɟɪɜɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ Ɍɚɭɧɫɟɧɞɚ α (ɬɚɤ ɤɚɤ ɩɨɥɟ ȿ ɫɢɥɶɧɨ ɧɟɨɞɧɨɪɨɞɧɨɟ) ɜ ɜɨɡɞɭɯɟ (ɩɪɚɤɬɢɱɟɫɤɢ ɜɚɠɧɵɣ ɫɥɭɱɚɣ) ɧɚɞɨ ɭɱɢɬɵɜɚɬɶ ɩɪɢɥɢɩɚɧɢɟ (ɧɚɥɢɱɢɟ ɤɢɫɥɨɪɨɞɚ), ɬɚɤ ɱɬɨ x1
³ (α ( x) − a
n
( x))dx = ln(1 + γ −1 ) ,
(8.26)
0
ɝɞɟ x1 − ɪɚɫɫɬɨɹɧɢɟ ɞɨ ɬɨɱɤɢ, ɜ ɤɨɬɨɪɨɣ ȿ ɭɠɟ ɬɚɤ ɦɚɥɨ, ɱɬɨ ɢɨɧɢɡɚɰɢɹ ɧɟ ɩɪɨɢɫɯɨɞɢɬ: E ≈ 0. ȼ ɬɚɤɨɣ ɤɨɪɨɧɟ ɟɫɬɶ ɫɜɟɱɟɧɢɟ ɬɨɥɶɤɨ ɞɨ ɪɚɫɫɬɨɹɧɢɹ, ɬɨɠɟ ɩɪɢɦɟɪɧɨ, ɪɚɜɧɨɝɨ x1. ȿɫɥɢ "ɨɫɬɪɢɟ" - ɚɧɨɞ (ɤɨɪɨɧɚ "ɩɨɥɨɠɢɬɟɥɶɧɚɹ"), ɬɨ ɤɚɪɬɢɧɚ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɹɟɬɫɹ: ɨɤɨɥɨ ɨɫɬɪɢɹ ɧɚɛɥɸɞɚɸɬɫɹ ɫɜɟɬɹɳɢɟɫɹ ɧɢɬɢ, ɤɚɤ ɛɵ ɪɚɡɛɟɝɚɸɳɢɟɫɹ ɨɬ ɨɫɬɪɢɹ (ɪɢɫ. 8.9). ȼɟɪɨɹɬɧɨ, ɷɬɨ ɫɬɪɢɦɟɪɵ ɨɬ ɥɚɜɢɧ, ɡɚɪɨɠɞɟɧɧɵɯ ɜ ɨɛɴɟɦɟ ɮɨɬɨɷɥɟɤɬɪɨɧɚɦɢ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɢ ɤɪɢɬɟɪɢɣ ɡɚɠɢɝɚɧɢɹ ɞɪɭɝɨɣ − ɬɚɤɨɣ, ɤɚɤ ɞɥɹ ɨɛɪɚɡɨɜɚɧɢɹ ɫɬɪɢɦɟɪɚ. ȼ ɥɸɛɨɦ ɤɨɪɨɧɧɨɦ ɪɚɡɪɹɞɟ ɫɭɳɟɫɬɜɟɧɧɚ ɧɟɨɞɧɨɪɨɞɧɨɫɬɶ ȿ, ɬ.ɟ. ɤɨɧɤɪɟɬɧɚɹ ɝɟɨɦɟɬɪɢɹ ɷɥɟɤɬɪɨɞɨɜ. ɉɨɥɧɨɣ ɹɫɧɨɫɬɢ ɜ ɦɟɯɚɧɢɡɦɟ ɝɨɪɟɧɢɹ ɪɚɡɪɹɞɚ ɧɟɬ, ɧɨ ɷɬɨ ɧɟ ɦɟɲɚɟɬ ɩɪɢɦɟɧɟɧɢɸ ɤɨɪɨɧɧɵɯ ɪɚɡɪɹɞɨɜ ɜ ɩɪɨɦɵɲɥɟɧɧɨɫɬɢ (ɷɥɟɤɬɪɨɮɢɥɶɬɪɵ); ɜ ɫɱɟɬɱɢɤɚɯ Ƚɟɣɝɟɪ-Ɇɸɥɥɟɪɚ ɬɨɠɟ ɪɚɛɨɬɚɟɬ ɤɨɪɨɧɧɵɣ ɪɚɡɪɹɞ. ɇɨ ɨɧ ɛɵɜɚɟɬ ɢ ɜɪɟɞɟɧ, ɧɚɩɪɢɦɟɪ, ɧɚ ɜɵɫɨɤɨɜɨɥɶɬɧɵɯ ɥɢɧɢɹɯ (Ʌȿɉ) ɤɨɪɨɧɧɵɟ ɪɚɡɪɹɞɵ ɫɨɡɞɚɸɬ
ɡɚɦɟɬɧɵɟ ɩɨɬɟɪɢ. Ʉɨɪɨɧɵ ɛɵɜɚɸɬ ɩɪɟɪɵɜɢɫɬɵɦɢ ɫ ɪɚɡɥɢɱɧɵɦɢ − ɭ ɱɚɫɬɨɬɚɦɢ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɞɨ 104 Ƚɰ, ɭ ɨɬɪɢɰɚɬɟɥɶɧɵɯ − ɞɨ 106 Ƚɰ − ɚ ɷɬɨ ɪɚɞɢɨɞɢɚɩɚɡɨɧ, ɩɨɦɟɯɢ. Ɇɟɯɚɧɢɡɦ ɩɪɟɪɵɜɢɫɬɨɫɬɢ ɪɚɡɪɹɞɚ ɭ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɤɨɪɨɧɵ, ɜɢɞɢɦɨ, ɫɜɹɡɚɧ ɫ ɬɟɦ, ɱɬɨ ɷɥɟɤɬɪɨɧɵ Ɋɢɫ. 8.9. ɋɬɪɢɦɟɪ ɨɬ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɫɬɟɪɠɧɹ ɞɢɚɦɟɬɪɨɦ 2 ɫɦ ɧɚ ɩɥɨɫɤɨɫɬɶ ɧɚ ɪɚɫɫɬɨɹɧɢɢ 150 ɫɦ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɧɚɩɪɹɠɟɧɢɢ 125 ɫɬɪɢɦɟɪɨɜ ɜɬɹɝɢɜɚɸɬɫɹ ɜ ɚɧɨɞ, ɤȼɬ; ɫɩɪɚɜɚ - ɪɚɫɱɟɬ, ɩɪɨɜɟɞɟɧɵ ɷɤɜɢɩɨɬɟɧɰɢɚɥɶɧɵɟ ɩɨɜɟɪɯɧɨɫɬɢ, ɰɢɮɪɵ ɨɤɨɥɨ ɤɪɢɜɵɯ - ɞɨɥɢ ɨɬ ɩɪɢɥɨɠɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ, ɩɨɥɨɠɢɬɟɥɶɧɵɟ ɨɬɫɱɢɬɚɧɧɵɟ ɨɬ ɩɥɨɫɤɨɫɬɢ; ɫɥɟɜɚ - ɮɨɬɨɝɪɚɮɢɹ ɫɬɪɢɦɟɪɨɜ ɜ ɬɟɯ ɠɟ ɨɫɬɨɜɵ ɷɤɪɚɧɢɪɭɸɬ ɭɫɥɨɜɢɹɯ ɚɧɨɞ, ɧɨɜɵɟ ɫɬɪɢɦɟɪɵ ɧɟ ɦɨɝɭɬ ɫɨɡɞɚɜɚɬɶɫɹ, ɩɨɤɚ ɨɫɬɨɜɵ ɧɟ ɭɣɞɭɬ ɤ ɤɚɬɨɞɭ. Ɍɨɝɞɚ ɚɧɨɞ "ɨɬɤɪɨɟɬɫɹ" ɢ ɤɚɪɬɢɧɚ ɩɨɜɬɨɪɢɬɫɹ. Ⱦɥɹ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɤɨɪɨɧɵ ɫɭɳɟɫɬɜɟɧɧɨ ɧɚɥɢɱɢɟ ɜ ɜɨɡɞɭɯɟ ɤɢɫɥɨɪɨɞɚ − ɧɟɦɧɨɝɨ ɨɬɨɣɞɹ ɨɬ ɤɨɪɨɧɵ ɷɥɟɤɬɪɨɧɵ ɩɪɢɥɢɩɚɸɬ ɤ ɤɢɫɥɨɪɨɞɭ, ɨɬɪɢɰɚɬɟɥɶɧɵɟ ɢɨɧɵ ɷɤɪɚɧɢɪɭɸɬ ɨɫɬɪɢɟ, ɢ ɩɨɤɚ ɨɧɢ ɧɟ ɭɣɞɭɬ ɤ ɚɧɨɞɭ, ɪɚɡɪɹɞ ɩɪɟɤɪɚɳɚɟɬɫɹ. ɉɨɫɥɟ ɭɯɨɞɚ ɢɨɧɨɜ ɪɚɡɪɹɞ ɜɨɡɧɢɤɧɟɬ ɜɧɨɜɶ ɢ ɤɚɪɬɢɧɚ ɩɨɜɬɨɪɢɬɫɹ. ȼɵɫɨɤɨɱɚɫɬɨɬɧɵɟ (ȼɑ) ɪɚɡɪɹɞɵ
~ ~ ȼ ȼɑ-ɞɢɚɩɚɡɨɧɟ (10-1 ÷ 102 ɆȽɰ) ɩɪɢɧɹɬɨ ɪɚɡɥɢɱɚɬɶ E ɢ H ɬɢɩɵ ɪɚɡɪɹɞɨɜ − ɩɨ ɨɩɪɟɞɟɥɹɸɳɟɦɭ ɜɟɤɬɨɪɭ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȼ ɥɚɡɟɪɧɨɣ ɬɟɯɧɢɤɟ ~ ɢɫɩɨɥɶɡɭɸɬ E (ɟɦɤɨɫɬɧɵɟ) ɪɚɡɪɹɞɵ, ɩɨɦɟɳɚɹ ɪɚɛɨɱɢɣ ɨɛɴɟɦ ɜ ɤɨɧɞɟɧɫɚɬɨɪ, ɤ ɩɥɚɫɬɢɧɚɦ ɤɨɬɨɪɨɝɨ ɩɨɞɜɨɞɹɬ ȼɑ-ɧɚɩɪɹɠɟɧɢɟ (ɩɥɚɫɬɢɧɵ ɢɧɨɝɞɚ ɩɪɹɦɨ ɜɜɨɞɹɬ ɜ ɨɛɴɟɦ, ɢɧɨɝɞɚ ɢɡɨɥɢɪɭɸɬ ɞɢɷɥɟɤɬɪɢɤɨɦ − ɨɛɵɱɧɨ ɫɬɟɤɥɨɦ). Ɇɨɳɧɨɫɬɢ ɷɬɢɯ ɪɚɡɪɹɞɨɜ ɧɟɛɨɥɶɲɢɟ (ɢɯ ɡɚɞɚɱɚ ɩɨɞɞɟɪɠɚɬɶ ɢɨɧɢɡɚɰɢɸ), ɧɨ ~ E ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɜɟɥɢɤɢ − ɞɨ ɞɟɫɹɬɤɨɜ ɤɷȼ. ɉɪɢɦɟɧɟɧɢɟ ȼɑ ɢɧɞɭɤɰɢɨɧɧɵɯ ɩɨɥɟɣ Ɋɢɫ. 8.10. ɂɧɞɭɤɰɢɨɧɧɵɣ ɪɚɡɪɹɞ ɜ ɬɪɭɛɤɟ ɪɚɞɢɭɫɨɦ R, ɜɫɬɚɜɥɟɧɧɨɣ ɜ ɞɥɢɧɧɵɣ ɫɨɥɟɧɨɢɞ; r0 - ɪɚɞɢɭɫ ɩɥɚɡɦɵ, ɫɩɪɚɜɚ ~ ( H -ɩɨɥɟɣ) ɭɠɟ ɫ ɤɨɧɰɚ – ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨ ɪɚɞɢɭɫɭ 40-ɯ ɝ. ɫɬɚɥɨ ɜɟɫɶɦɚ ɲɢɪɨɤɢɦ, ɯɨɬɹ, ɜ ɨɫɧɨɜɧɨɦ, ɜ ɜɢɞɟ ȼɑ-ɩɟɱɟɣ. ȼɟɡɞɟ, ɝɞɟ ɧɭɠɧɨ ɱɢɫɬɨɟ ɬɟɩɥɨ ɢ
~ ɟɫɬɶ ɩɪɨɜɨɞɹɳɚɹ ɫɪɟɞɚ, H ɩɨɥɹ ɧɟɡɚɦɟɧɢɦɵ. ɗɬɨ ɢ ɩɪɨɢɡɜɨɞɫɬɜɨ ɩɨɥɭɩɪɨɜɨɞɧɢɤɨɜɵɯ ɦɚɬɟɪɢɚɥɨɜ, ɢ ɡɨɧɧɚɹ ɩɥɚɜɤɚ ɱɢɫɬɵɯ ɦɟɬɚɥɥɨɜ, ɢ ɫɜɟɪɯɱɢɫɬɵɟ ɯɢɦɢɱɟɫɤɢɟ ɫɨɟɞɢɧɟɧɢɹ ɢ ɞɚɠɟ ɛɵɬɨɜɵɟ ɩɟɱɢ. ɉɪɚɜɞɚ, ɜ ɷɬɢɯ ɭɫɬɪɨɣɫɬɜɚɯ ɩɨɱɬɢ ɧɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɫɨɝɥɚɫɨɜɚɧɢɹ ɝɟɧɟɪɚɬɨɪɚ ɢ ɧɚɝɪɭɡɤɢ − ɫɨɨɬɧɨɲɟɧɢɟ ɪɟɚɤɬɢɜɧɨɝɨ ɢ ɚɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɧɚɝɪɭɡɤɢ ɦɟɧɹɟɬɫɹ ɦɚɥɨ. Ⱥ ɜɨɬ ɜ ɪɚɡɪɹɞɚɯ ɞɟɥɨ ɫɥɨɠɧɟɟ: ɢɡɦɟɧɟɧɢɟ ɩɚɪɚɦɟɬɪɨɜ ɫɪɟɞɵ ɪɚɡɪɹɞɚ (ɫɨɩɪɨɬɢɜɥɟɧɢɟ, ɫɚɦɨɢɧɞɭɤɰɢɹ, ɜɡɚɢɦɨɢɧɞɭɤɰɢɹ − ɫɜɹɡɶ ɫ ɢɧɞɭɤɬɨɪɨɦ) ɦɨɝɭɬ ɦɟɧɹɬɶɫɹ ɜ ɲɢɪɨɤɢɯ ɩɪɟɞɟɥɚɯ. Ɉɛɵɱɧɨ ɢɧɞɭɤɬɨɪ − ɤɚɬɭɲɤɚ (ɛɵɜɚɟɬ ɢ ɨɞɢɧ ɜɢɬɨɤ!), ɜɧɭɬɪɢ ɤɨɬɨɪɨɣ ɢ ɩɪɨɢɫɯɨɞɢɬ ɪɚɡɪɹɞ (ɪɢɫ. 8.10). ~ ~ ɉɟɪɟɦɟɧɧɨɟ H ɩɨɥɟ ɧɚɩɪɚɜɥɟɧɨ ɜɞɨɥɶ ɨɫɢ ɤɚɬɭɲɤɢ, ɩɨɥɟ E ɚɤɫɢɚɥɶɧɨ ɤ ~ ɧɟɣ. Ⱦɥɹ ɩɨɞɞɟɪɠɚɧɢɹ ɪɚɡɪɹɞɚ ɧɭɠɧɨɟ E ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɶɲɟ, ɱɟɦ ɞɥɹ ɟɝɨ ɡɚɠɢɝɚɧɢɹ. ɉɨɷɬɨɦɭ ɨɛɵɱɧɨ ɜɜɨɞɹɬ ɜ ɨɛɴɟɦ ɬɨɧɤɢɣ ɦɟɬɚɥɥɢɱɟɫɤɢɣ ɷɥɟɤɬɪɨɞ, ɨɧ ɪɚɡɨɝɪɟɜɚɟɬɫɹ, ɞɚɟɬ ɬɟɪɦɨɷɥɟɤɬɪɨɧɵ (ɢɧɨɝɞɚ ɱɚɫɬɢɱɧɨ ɢɫɩɚɪɹɟɬɫɹ), ɢɧɢɰɢɢɪɭɟɬ ɪɚɡɪɹɞ, ɩɨɫɥɟ ɱɟɝɨ ɟɝɨ ɭɞɚɥɹɸɬ. ȼɨ ɜɪɟɦɹ ɪɚɛɨɬɵ ɦɨɳɧɨɫɬɶ ɜɜɨɞɢɬɫɹ ɩɨɬɨɤɨɦ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ: <S> = (ɫ/4π) ,
(8.27)
ɚ ɨɬɜɨɞɢɬɫɹ ɱɚɳɟ ɜɫɟɝɨ ɩɨɬɨɤɨɦ ɝɚɡɚ (ɨɧ ɢɨɧɢɡɭɟɬɫɹ ɢ ɭɧɨɫɢɬ ɷɧɟɪɝɢɸ). ɇɨ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɷɧɟɪɝɢɹ ɩɪɨɧɢɤɚɟɬ ɜ ɩɥɚɡɦɭ (ɩɪɨɜɨɞɧɢɤ) ɧɚ ɝɥɭɛɢɧɭ ɯ, ɫɩɚɞɚɹ ɩɨ ɷɤɫɩɨɧɟɧɬɟ ɟɯɪ(-ɯ/δ), ɝɞɟ δ − ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ ɫɤɢɧɫɥɨɣ, ɢ ɟɝɨ ɭɫɥɨɜɢɥɢɫɶ ɫɱɢɬɚɬɶ ɝɥɭɛɢɧɨɣ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɩɨɬɨɤɚ:
δ2 = ɫ2/(2πσω) ,
(8.28)
ɝɞɟ σ − ɩɪɨɜɨɞɢɦɨɫɬɶ ɩɪɨɜɨɞɧɢɤɚ, ω − ɱɚɫɬɨɬɚ ȼɑ ɩɨɥɹ. Ɉɱɟɜɢɞɧɨ, ɪɟɠɢɦ ɪɚɛɨɬɵ ɭɫɬɚɧɨɜɤɢ ɡɚɜɢɫɢɬ ɨɬ ɫɨɨɬɧɨɲɟɧɢɹ R ɢ ɜɟɥɢɱɢɧɵ δ. ȿɫɥɢ δ < R, ɬɨ ɷɧɟɪɝɢɹ ɩɨɝɥɨɳɚɟɬɫɹ, ɜ ɫɥɨɟ ɬɨɥɳɢɧɨɣ δ, ɨɛɪɚɡɭɹ ɩɪɨɜɨɞɹɳɢɣ ɰɢɥɢɧɞɪ. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨ ɪɚɞɢɭɫɭ ɬɟɦɩɟɪɚɬɭɪɵ Ɍ ɢ ɩɪɨɜɨɞɢɦɨɫɬɢ σ ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɚ ɪɢɫ. 8.11, ɩɨ ɫɭɳɟɫɬɜɭ, ɷɬɨ ɩɨɥɧɵɣ ɚɧɚɥɨɝ ɤɚɧɚɥɨɜɨɣ ɦɨɞɟɥɢ ɞɭɝɢ, ɟɟ ɧɚɡɵɜɚɸɬ "ɦɨɞɟɥɶɸ ɦɟɬɚɥɥɢɱɟɫɤɨɝɨ ɰɢɥɢɧɞɪɚ". ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɪɟɚɥɶɧɨ ɦɨɠɧɨ ɭɩɪɚɜɥɹɬɶ ɞɚɜɥɟɧɢɟɦ p (ɠɟɥɚɬɟɥɶɧɨ ɩɨɛɨɥɶɲɟ!) ɢ ɩɨɬɨɤɨɦ , ɨɩɪɟɞɟɥɹɟɦɵɦ
Ɋɢɫ. 8.11. ɋɯɟɦɚɬɢɱɟɫɤɢɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨ ɪɚɞɢɭɫɭ ɬɟɦɩɟɪɚɬɭɪɵ (ɚ), ɩɪɨɜɨɞɢɦɨɫɬɢ (ɛ) ɢ ɞɠɨɭɥɟɜɚ ɬɟɩɥɚ (ɜ) ɜ ɢɧɞɭɤɰɢɨɧɧɨɦ ɪɚɡɪɹɞɟ; ɲɬɪɢɯɨɜɚɹ ɥɢɧɢɹ - ɡɚɦɟɧɚ σ (r) ɫɬɭɩɟɧɶɤɨɣ ɜ ɦɨɞɟɥɢ ɦɟɬɚɥɥɢɱɟɫɤɨɝɨ ɰɢɥɢɧɞɪɚ, J – ɬɟɩɥɨɜɨɣ ɩɨɬɨɤ, S0 ɩɨɬɨɤ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ, δ - ɬɨɥɳɢɧɚ ɫɤɢɧɫɥɨɹ
ɚɦɩɟɪɜɢɬɤɚɦɢ: ~ IN (ɝɞɟ I − ɬɨɤ, N − ɱɢɫɥɨ ɜɢɬɤɨɜ ɧɚ ɟɞɢɧɢɰɭ ɞɥɢɧɵ ɢɧɞɭɤɬɨɪɚ). ɋȼɑ-ɪɚɡɪɹɞɵ
Ɍɚɤɢɟ ɪɚɡɪɹɞɵ ɧɚɱɚɥɢ ɩɪɢɦɟɧɹɬɶ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɜ ɦɨɞɟɥɹɯ ɬɟɪɦɨɹɞɟɪɧɵɯ ɭɫɬɚɧɨɜɨɤ (ɧɟ ɨɱɟɧɶ ɭɫɩɟɲɧɨ ɧɚ ɫɬɚɞɢɢ ɪɚɡɪɹɞɚ) ɢ ɜ ɩɥɚɡɦɨɯɢɦɢɱɟɫɤɢɯ ɭɫɬɚɧɨɜɤɚɯ. ɉɪɢ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬɚɯ (ɝɢɝɨɝɟɪɰɵ) ɫɭɳɟɫɬɜɟɧɧɵ ɝɟɨɦɟɬɪɢɱɟɫɤɢɟ ɫɨɨɬɧɨɲɟɧɢɹ, ɜɚɠɧɵ ɩɪɟɥɨɦɥɟɧɢɹ ɢ ɨɬɪɚɠɟɧɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɜɨɥɧɵ. ɋȼɑɷɧɟɪɝɢɹ ɜɟɫɶɦɚ ɞɨɪɨɝɚɹ, ɧɨ ɨɤɚɡɵɜɚɟɬɫɹ, ɱɬɨ ɢɫɩɨɥɶɡɭɹ ɪɚɡɪɹɞ ɜ ɋȼɑɩɥɚɡɦɨɬɪɨɧɚɯ ɦɨɠɧɨ ɜɜɟɫɬɢ ɜ ɩɥɚɡɦɭ ɞɨ 90% ɋȼɑ ɷɧɟɪɝɢɢ [35]. ɇɚɢɛɨɥɟɟ ɢɫɩɨɥɶɡɭɟɦɵɟ ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɫɯɟɦɵ ɋȼɑ-ɪɚɡɪɹɞɨɜ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 8.12. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜ ɫɯɟɦɟ (ɪɢɫ. 8.12) ɩɨɱɬɢ ɜɫɹ ɦɨɳɧɨɫɬɶ ɩɨɝɥɨɳɚɟɬɫɹ ɜ ɫɬɪɭɟ ɝɚɡɚ (ɩɪɟɜɪɚɳɚɸɳɟɣɫɹ ɜ ɩɥɚɡɦɭ): ɜɧɟɲɧɹɹ ɩɨɜɟɪɯɧɨɫɬɶ ɫɬɨɥɛɚ ɩɥɚɡɦɵ ɢ ɜɧɭɬɪɟɧɧɹɹ ɩɨɜɟɪɯɧɨɫɬɶ ɜɨɥɧɨɜɨɞɚ ɨɛɪɚɡɭɸɬ ɤɨɚɤɫɢɚɥɶɧɭɸ ɥɢɧɢɸ ɞɥɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɜɨɥɧɵ − ɷɧɟɪɝɢɹ ɜ ɫɬɨɥɛ ɜɬɟɤɚɟɬ ɩɨ ɪɚɞɢɭɫɭ (ɤɚɤ ɜ ȼɑ-ɪɚɡɪɹɞɟ). ɂɧɬɟɪɟɫɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɦɟɯɚɧɢɡɦ ɩɪɨɛɨɹ ɜ ɋȼɑ (ɧɨ ɧɟ ȼɑ!) ɞɢɚɩɚɡɨɧɟ ɩɨɯɨɠ ɧɚ ɦɟɯɚɧɢɡɦ ɩɪɨɛɨɹ ɜ ɬɥɟɸɳɟɦ ɪɚɡɪɹɞɟ (ɨɛɪɚɡɨɜɚɧɢɟ ɥɚɜɢɧ, ɫɬɚɰɢɨɧɚɪɧɵɣ ɤɪɢɬɟɪɢɣ ɩɪɨɛɨɹ (8.19), ɤɪɢɜɵɟ ɡɚɜɢɫɢɦɨɫɬɢ Ɋɢɫ. 8.12. ɋɯɟɦɚ ɪɚɡɪɹɞɚ ɜ ɜɨɥɧɨɜɨɞɟ, ɩɨɞɞɟɪɠɢɜɚɟɦɨɝɨ H01 ɜɨɥɧɨɣ: ɚ) ɫɟɱɟɧɢɟ ɜɨɥɧɨɜɨɞɚ E = f(p) - ɚɧɚɥɨɝɢ ɤɪɢɜɵɯ ɉɚɲɟɧɚ, ɞɢɚɦɟɬɪɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɶɸ ɬɪɭɛɤɢ, ɩɥɚɡɦɚ ɡɚɬɟɧɟɧɚ; ɫɪɚɜɧɢɦɨɫɬɶ ɩɨɪɨɝɨɜɵɯ ɡɧɚɱɟɧɢɣ ɛ) ɪɚɫɩɪɟɞɟɥɟɧɢɟ ȿ ɜɞɨɥɶ ɲɢɪɨɤɨɣ ɫɬɟɧɤɢ ɜɨɥɧɨɜɨɞɚ ȿ/p), ɨ ɧɟɦ ɩɨɞɪɨɛɧɨ ɦɨɠɧɨ ɩɪɨɱɢɬɚɬɶ ɜ [33]. Ɉɩɬɢɱɟɫɤɢɣ ɩɪɨɛɨɣ
Ɉɩɬɢɱɟɫɤɢɣ ɩɪɨɛɨɣ − ɥɚɡɟɪɧɚɹ ɢɫɤɪɚ, ɫɚɦɵɣ ɦɨɥɨɞɨɣ ɜɢɞ ɝɚɡɨɜɨɝɨ ɪɚɡɪɹɞɚ. ȼɩɟɪɜɵɟ ɧɚɛɥɸɞɚɥɫɹ ɜ 1963ɝ. ɜ ɮɨɤɭɫɟ ɥɭɱɚ ɝɢɝɚɧɬɫɤɨɝɨ ɪɭɛɢɧɨɜɨɝɨ ɥɚɡɟɪɚ ɫ ɦɨɳɧɨɫɬɶɸ 30 Ɇȼɬ ɞɥɢɬɟɥɶɧɨɫɬɶɸ ɢɦɩɭɥɶɫɚ 3⋅10-4 ɫ, ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ȿ ≈ 6⋅106 ȼ/ɫɦ. əɜɥɟɧɢɟ ɛɵɥɨ ɧɟɨɞɧɨɡɧɚɱɧɵɦ, ɩɪɢɜɥɟɤɥɨ ɲɢɪɨɤɨɟ ɜɧɢɦɚɧɢɟ ɢ ɭɠɟ ɢɡɭɱɟɧɨ ɧɟ ɯɭɠɟ ɞɪɭɝɢɯ ɪɚɡɪɹɞɨɜ. Ʉ ɥɚɡɟɪɧɨɣ ɢɫɤɪɟ ɩɪɢɦɟɧɢɦ ɧɟɫɬɚɰɢɨɧɚɪɧɵɣ ɤɪɢɬɟɪɢɣ ɩɪɨɛɨɹ (8.17), ɩɪɢɱɟɦ ɪɨɥɶ ɩɨɬɟɪɶ ɷɥɟɤɬɪɨɧɨɜ Ya ɢ Yd ɦɨɠɟɬ ɞɚɠɟ ɨɤɚɡɚɬɶɫɹ ɧɟ ɫɭɳɟɫɬɜɟɧɧɨɣ − ɜɪɟɦɹ ɨɱɟɧɶ ɦɚɥɨ, ɜɫɟ ɨɩɪɟɞɟɥɹɟɬ ɫɨɡɞɚɧɢɟ ɷɥɟɤɬɪɨɧɨɜ, ɥɚɜɢɧ. ɇɨ ɜɨɬ "ɡɚɬɪɚɜɨɱɧɵɣ" ɷɥɟɤɬɪɨɧ ɦɨɠɟɬ ɪɨɞɢɬɶɫɹ ɜ ɪɟɡɭɥɶɬɚɬɟ ɦɧɨɝɨɮɨɬɨɧɧɨɝɨ ɮɨɬɨɷɮɮɟɤɬɚ (ɩɨ ɫɭɳɟɫɬɜɭ ɤɜɚɧɬɨɜɨɝɨ ɹɜɥɟɧɢɹ). ɂɧɬɟɪɟɫɧɨ, ɱɬɨ ɟɫɬɶ ɛɨɥɶɲɨɟ ɫɯɨɞɫɬɜɨ ɩɪɨɰɟɫɫɨɜ ɩɪɨɛɨɹ ɜ ɨɩɬɢɱɟɫɤɨɦ ɢ ɋȼɑ ɞɢɚɩɚɡɨɧɚɯ − ɧɚɩɪɢɦɟɪ, ɪɚɫɱɟɬɵ ɩɨɪɨɝɨɜ ɩɪɨɛɨɹ ɢ ɫɪɚɜɧɟɧɢɟ ɢɯ ɫ ɷɤɫɩɟɪɢɦɟɧɬɨɦ. Ɋɚɡɜɢɬɢɟ ɥɚɡɟɪɨɜ ɢ ɩɨɜɵɲɟɧɢɟ ɢɯ ɦɨɳɧɨɫɬɢ ɩɪɢɜɟɥɨ ɤ ɬɨɦɭ, ɱɬɨ ɟɳɟ ɜ 1976ɝ. ɭ ɧɚɫ ɫɦɨɝɥɢ ɡɚɠɟɱɶ "ɢɫɤɪɭ" ɜ ɜɨɡɞɭɯɟ ɞɥɢɧɧɨɣ 8 ɦ, ɚ ɪɟɤɨɪɞɧɵɟ ɞɥɢɧɵ ɛɵɥɢ ɛɨɥɶɲɟ ɞɟɫɹɬɤɚ ɦɟɬɪɨɜ.
ɋɩɢɫɨɤ ɰɢɬɢɪɨɜɚɧɧɨɣ ɥɢɬɟɪɚɬɭɪɵ. 1. Ɋɨɦɚɧɨɜɫɤɢɣ Ɇ.Ʉ. ɗɥɟɦɟɧɬɚɪɧɵɟ ɩɪɨɰɟɫɫɵ ɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɱɚɫɬɢɰ ɜ ɩɥɚɡɦɟ. – Ɇ: ɂɡɞ. ɆɂɎɂ, 1984. 2. Zhdanov S.K., Kurnaev V.A., Pisarev A.A. Lectures on Plasma Physics. M: MEPhI, 1998. 3. Ⱥɥɟɤɫɚɧɞɪɨɜ Ⱥ.Ɏ., Ɋɭɯɚɞɡɟ Ⱥ.Ⱥ. Ʌɟɤɰɢɢ ɩɨ ɷɥɟɤɬɪɨɞɢɧɚɦɢɤɟ ɩɥɚɡɦɨɩɨɞɨɛɧɵɯ ɫɪɟɞ. Ɇ: ɂɡɞ. ɆȽɍ, 1999. 4. Ɏɨɪɬɨɜ ȼ.ȿ., əɤɭɛɨɜ ɂ.Ɍ. ɇɟɢɞɟɚɥɶɧɚɹ ɩɥɚɡɦɚ. Ɇ: ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1994. 5. Ɏɢɡɢɱɟɫɤɚɹ ɷɧɰɢɤɥɨɩɟɞɢɹ \ɩɨɞ ɪɟɞ. ɉɪɨɯɨɪɨɜɚ Ⱥ.Ɇ. \, ɬ.2. Ɇ: ɋɨɜɟɬɫɤɚɹ ɷɧɰɢɤɥɨɩɟɞɢɹ, 1990. 6. Ɏɢɡɢɱɟɫɤɢɟ ɜɟɥɢɱɢɧɵ. ɋɩɪɚɜɨɱɧɢɤ\ɩɨɞ ɪɟɞ. Ƚɪɢɝɨɪɶɟɜɚ ɂ.ɋ., Ɇɟɣɥɢɯɨɜɚ ȿ.Ɂ.\. Ɇ: ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1991. 7. ɋɦɢɪɧɨɜ Ȼ.Ⱥ. Ɏɢɡɢɤɚ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɵ. Ɇ.: ɇɚɭɤɚ, 1978, ɫ.132, ɡɚɞɚɱɚ 2.23. 8. Ⱥɥɟɤɫɟɟɜ Ȼ.ȼ., Ʉɨɬɟɥɶɧɢɤɨɜ ȼ.Ⱥ. Ɂɨɧɞɨɜɵɣ ɦɟɬɨɞ ɞɢɚɝɧɨɫɬɢɤɢ ɩɥɚɡɦɵ. Ɇ.: ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1988. 9. Ɏɪɚɧɰ-Ʉɚɦɟɧɟɰɤɢɣ Ⱦ.Ⱥ. Ʌɟɤɰɢɢ ɩɨ ɮɢɡɢɤɟ ɩɥɚɡɦɵ. - Ɇ.: Ⱥɬɨɦɢɡɞɚɬ, 1964. 10. Ⱥɪɰɢɦɨɜɢɱ Ʌ.Ⱥ. ɍɩɪɚɜɥɹɟɦɵɟ ɬɟɪɦɨɹɞɟɪɧɵɟ ɪɟɚɤɰɢɢ. - Ɇ.: Ɏɢɡɦɚɬɝɢɡ, 1961. 11. Ɍɪɭɛɧɢɤɨɜ Ȼ.Ⱥ. Ɍɟɨɪɢɹ ɩɥɚɡɦɵ. - Ɇ.:ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1996. 12. Ʌɭɤɶɹɧɨɜ ɋ.ɘ., Ʉɨɜɚɥɶɫɤɢɣ ɇ.Ƚ. Ƚɨɪɹɱɚɹ ɩɥɚɡɦɚ ɢ ɭɩɪɚɜɥɹɟɦɵɣ ɹɞɟɪɧɵɣ ɫɢɧɬɟɡ. Ɇ.:ɆɂɎɂ, 1997. 13. Ȼɪɚɝɢɧɫɤɢɣ ɋ.ɂ. ȼɨɩɪɨɫɵ ɬɟɨɪɢɢ ɩɥɚɡɦɵ. - Ɇ.: Ⱥɬɨɦɢɡɞɚɬ, 1963, ɬ.1, ɫ.208-209. 14. Ƚɚɥɟɟɜ Ⱥ.Ⱥ., ɋɚɝɞɟɟɜ Ɋ.Ɂ. ȼɨɩɪɨɫɵ ɬɟɨɪɢɢ ɩɥɚɡɦɵ. - Ɇ.: Ⱥɬɨɦɢɡɞɚɬ, 1973. 15. Ɍɚɦɦ ȿ.ɂ. Ɉɫɧɨɜɵ ɬɟɨɪɢɢ ɷɥɟɤɬɪɢɱɟɫɬɜɚ. - Ɇ.: Ƚɨɫɬɟɯɢɡɞɚɬ, 1946, ɫ.432. 16. Ʌɟɨɧɬɨɜɢɱ Ɇ.Ⱥ., Ɉɫɨɜɟɰ ɋ.Ɇ. - Ⱥɬɨɦɧɚɹ ɷɧɟɪɝɢɹ, 1956, ʋ3. 17. Ʉɚɞɨɦɰɟɜ Ȼ.Ȼ. Ʉɨɥɥɟɤɬɢɜɧɵɟ ɹɜɥɟɧɢɹ ɜ ɩɥɚɡɦɟ. - Ɇ: ɇɚɭɤɚ, 1976. 18. Ⱥɥɟɤɫɚɧɞɪɨɜ Ⱥ.Ɏ., Ȼɨɝɞɚɧɤɟɜɢɱ Ʌ.ɋ., Ɋɭɯɚɞɡɟ Ⱥ.Ⱥ. Ɉɫɧɨɜɵ ɷɥɟɤɬɪɨɞɢɧɚɦɢɤɢ ɩɥɚɡɦɵ. - Ɇ: ȼɵɫɲɚɹ ɲɤɨɥɚ, 1978. 19. ɂɜɚɧɨɜ Ⱥ.Ⱥ. Ɏɢɡɢɤɚ ɫɢɥɶɧɨɧɟɪɚɜɧɨɜɟɫɧɨɣ ɩɥɚɡɦɵ. - Ɇ.: Ⱥɬɨɦɢɡɞɚɬ, 1977, ɫ.11-23. 20. Ʌɢɮɲɢɰ ȿ.Ɇ., ɉɢɬɚɟɜɫɤɢɣ Ʌ.ɉ. Ɏɢɡɢɱɟɫɤɚɹ ɤɢɧɟɬɢɤɚ (ɋɟɪɢɹ: «Ɍɟɨɪɟɬɢɱɟɫɤɚɹ ɮɢɡɢɤɚ», ɬɨɦ ɏ). - Ɇ: ɇɚɭɤɚ, 1979. 21. Ʉɢɧɝɫɟɩ Ⱥ.ɋ. ȼɜɟɞɟɧɢɟ ɜ ɧɟɥɢɧɟɣɧɭɸ ɮɢɡɢɤɭ ɩɥɚɡɦɵ. - Ɇ: ɂɡɞ. ɆɎɌɂ, 1996. 22. Ʉɚɞɨɦɰɟɜ Ȼ.Ȼ. Ɏɢɡɢɤɚ ɩɥɚɡɦɵ ɢ ɩɪɨɛɥɟɦɚ ɭɩɪɚɜɥɹɟɦɵɯ ɬɟɪɦɨɹɞɟɪɧɵɯ ɪɟɚɤɰɢɣ. Ɇ.:ɂɡɞ.Ⱥɇ ɋɋɋɊ, 1958. 23. ɒɚɮɪɚɧɨɜ ȼ.Ⱦ. Ɏɢɡɢɤɚ ɩɥɚɡɦɵ ɢ ɩɪɨɛɥɟɦɚ ɭɩɪɚɜɥɹɟɦɵɯ ɬɟɪɦɨɹɞɟɪɧɵɯ ɪɟɚɤɰɢɣ. - Ɇ.: ɂɡɞ.Ⱥɇ ɋɋɋɊ, 1958, ɬ.2 24. Ɋɚɣɡɟɪ ɘ.ɉ. Ɉɫɧɨɜɵ ɫɨɜɪɟɦɟɧɧɨɣ ɮɢɡɢɤɢ ɝɚɡɨɪɚɡɪɹɞɧɵɯ ɩɪɨɰɟɫɫɨɜ, Ɇɨɫɤɜɚ, ɇɚɭɤɚ, 1980 25. Ⱦɢɦɢɬɪɨɜ ɋ.Ʉ., Ɏɟɬɢɫɨɜ ɂ.Ʉ., Ʌɚɛɨɪɚɬɨɪɧɵɣ ɩɪɚɤɬɢɤɭɦ ɩɨ ɮɢɡɢɤɟ ɝɚɡɨɪɚɡɪɹɞɧɨɣ ɩɥɚɡɦɵ ɢ ɩɭɱɤɪɜ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ, ɆɂɎɂ, 1989 26. Ⱥɪɰɢɦɨɜɢɱ Ʌ.Ⱥ., Ʌɭɤɶɹɧɨɜ ɋ.ɘ. Ⱦɜɢɠɟɧɢɟ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɢ ɦɚɝɧɢɬɧɵɯ ɩɨɥɹɯ, Ɇ. 1972. 27. Ƚɥɚɡɟɪ, Ɉɫɧɨɜɵ ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɢ, Ɇɨɫɤɜɚ, 1957, ɫɬɪ.64 28. Ʉɟɥɶɦɚɧ ȼ.Ɇ., əɜɨɪ ɋ.ə., ɗɥɟɤɬɪɨɧɧɚɹ ɨɩɬɢɤɚ, Ɇɨɫɤɜɚ, 1959, ɫ.125 29. Ʉɚɩɰɨɜ ɇ.Ⱥ., ɗɥɟɤɬɪɨɧɢɤɚ, Ɇɨɫɤɜɚ, 1956, ɫɬɪ.138 30. Ƚɪɚɧɨɜɫɤɢɣ ȼ.Ʌ. ɗɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ ɜ ɝɚɡɚɯ, Ɇɨɫɤɜɚ, 1971. 31. Ⱦɨɛɪɟɰɨɜ Ʌ.ɇ., Ƚɚɦɚɸɧɨɜɚ Ɇ.ȼ., ɗɦɢɫɫɢɨɧɧɚɹ ɷɥɟɤɬɪɨɧɢɤɚ, Ɇɨɫɤɜɚ, 1966. 32. ɉɪɨɬɚɫɨɜ ɘ.ɋ., ɑɭɜɚɲɟɜ ɋ.ɇ., Ɏɢɡɢɱɟɫɤɚɹ ɷɥɟɤɬɪɨɧɢɤɚ ɝɚɡɨɪɚɡɪɹɞɧɵɯ ɭɫɬɪɨɣɫɬɜ, Ɇɨɫɤɜɚ, 1992, ɫ.352 33. Ɋɚɣɡɟɪ ɘ.ɉ. Ɏɢɡɢɤɚ ɝɚɡɨɜɨɝɨ ɪɚɡɪɹɞɚ. Ɇ: ɇɚɭɤɚ, 1992. 34. Ʌɨɞɡɢɧɫɤɢɣ ɗ.Ⱦ., Ɏɢɪɫɨɜ Ɉ.Ȼ. Ɍɟɨɪɢɹ ɢɫɤɪɵ. Ɇ: Ⱥɬɨɦɢɡɞɚɬ, 1975. 35. Ɋɭɫɚɧɨɜ Ⱦ., Ɏɪɢɞɦɚɧ Ⱥ.Ⱥ. Ɏɢɡɢɤɚ ɯɢɦɢɱɟɫɤɢ ɚɤɬɢɜɧɨɣ ɩɥɚɡɦɵ. Ɇ: 1984.
