Жданов С.К Цветков И.В - Основы физических процессов в плазме и в плазменных установках (2000)
.pdf
Ⱦɥɹ ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ ɧɢɡɤɨɬɟɦɩɟɪɚɬɭɪɧɨɣ ɩɥɚɡɦɵ ɯɚɪɚɤɬɟɪɧɨ ɛɨɥɶɲɨɟ ɱɢɫɥɨ ɤɨɥɟɛɚɬɟɥɶɧɨ-ɜɪɚɳɚɬɟɥɶɧɨ ɜɨɡɛɭɠɞɟɧɧɵɯ ɦɨɥɟɤɭɥ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɱɢɫɥɨɦ ɷɥɟɤɬɪɨɧɧɨɜɨɡɛɭɠɞɟɧɧɵɯ. Ɂɚɫɟɥɟɧɢɟ ɤɨɥɟɛɚɬɟɥɶɧɨ-ɜɪɚɳɚɬɟɥɶɧɵɯ ɭɪɨɜɧɟɣ ɩɪɨɢɫɯɨɞɢɬ ɚɤɬɢɜɧɨ ɩɪɢ ɧɟɤɨɬɨɪɵɯ ɯɢɦɢɱɟɫɤɢɯ ɪɟɚɤɰɢɹɯ (ɧɚɩɪɢɦɟɪ, ɝɨɪɟɧɢɟ ɭɝɥɟɪɨɞɚ ɜ ɤɢɫɥɨɪɨɞɟ ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ ɋɈ - ɞɨ 90% ɷɧɟɪɝɢɢ ɚɫɫɨɰɢɚɰɢɢ ɋɈ ɢɞɟɬ ɧɚ ɜɨɡɛɭɠɞɟɧɢɟ), ɜ ɬɥɟɸɳɟɦ ɪɚɡɪɹɞɟ. Ɍɭɲɢɬɶ ɜɨɡɛɭɠɞɟɧɢɟ ɦɨɠɧɨ ɪɚɡɥɢɱɧɵɦɢ ɩɭɬɹɦɢ — ɢɡɥɭɱɟɧɢɟɦ (ɢɫɩɨɥɶɡɭɟɬɫɹ ɜ ɥɚɡɟɪɚɯ), ɱɚɫɬɢɱɧɵɦ ɩɟɪɟɯɨɞɨɦ ɷɧɟɪɝɢɢ ɜɨɡɛɭɠɞɟɧɢɹ ɜ ɷɧɟɪɝɢɸ ɯɢɦɢɱɟɫɤɢɯ ɫɜɹɡɟɣ (ɢɫɩɨɥɶɡɭɟɬɫɹ ɜ ɩɥɚɡɦɨɯɢɦɢɢ). ɉɨ ɦɟɪɟ ɩɨɜɵɲɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɝɚɡɚ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɱɢɫɥɨ ɱɚɫɬɢɰ ɫ ɷɥɟɤɬɪɨɧɧɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ.
ȼɨɛɵɱɧɵɯ ɭɫɥɨɜɢɹɯ ɷɥɟɤɬɪɨɧ ɧɚɯɨɞɢɬɫɹ ɜ ɚɬɨɦɟ, ɦɨɥɟɤɭɥɟ (ɢɥɢ ɢɨɧɟ) ɜ ɨɫɧɨɜɧɨɦ ɫɨɫɬɨɹɧɢɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦ ɦɢɧɢɦɭɦɭ ɟɝɨ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ. ɉɨɥɭɱɢɜ ɧɟɤɨɬɨɪɭɸ ɞɨɛɚɜɨɱɧɭɸ ɷɧɟɪɝɢɸ (ɨɬ ɮɨɬɨɧɚ ɢɥɢ ɞɪɭɝɨɣ ɱɚɫɬɢɰɵ), ɷɥɟɤɬɪɨɧ ɦɨɠɟɬ ɩɟɪɟɣɬɢ ɧɚ ɛɨɥɟɟ ɜɵɫɨɤɨ ɥɟɠɚɳɢɣ ɷɧɟɪɝɟɬɢɱɟɫɤɢɣ ɭɪɨɜɟɧɶ. ȼɟɪɨɹɬɧɨɫɬɶ ɬɚɤɨɝɨ ɩɪɨɰɟɫɫɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɫɟɱɟɧɢɹɦɢ ɜɨɡɛɭɠɞɟɧɢɹ ɢ ɫɢɥɶɧɨ ɡɚɜɢɫɢɬ ɨɬ ɫɩɨɫɨɛɚ ɜɨɡɛɭɠɞɟɧɢɹ.
ȼɨɡɛɭɠɞɟɧɢɟ ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ ɫ ɱɚɫɬɢɰɚɦɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɟɥɢɱɢɧɨɣ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɫɤɨɪɨɫɬɢ, ɡɚɪɹɞɨɜɵɦ ɫɨɫɬɨɹɧɢɟɦ ɫɨɭɞɚɪɹɸɳɢɯɫɹ ɱɚɫɬɢɰ ɢ ɢɦɟɟɬ ɪɟɡɨɧɚɧɫɧɵɣ ɯɚɪɚɤɬɟɪ.
ȼɨɡɛɭɠɞɟɧɢɟ ɮɨɬɨɧɚɦɢ ɢɦɟɟɬ ɱɟɬɤɢɣ ɪɟɡɨɧɚɧɫɧɵɣ ɯɚɪɚɤɬɟɪ ɞɥɹ ɚɬɨɦɨɜ ɢ ɚɬɨɦɚɪɧɵɯ ɢɨɧɨɜ ɢ ɛɨɥɟɟ "ɪɚɡɦɵɬɨ" ɞɥɹ ɦɨɥɟɤɭɥ.
ȼɨɛɳɟɦ ɫɥɭɱɚɟ ɨɰɟɧɤɭ ɜɟɪɨɹɬɧɨɫɬɢ ɩɪɨɰɟɫɫɚ ɜɨɡɛɭɠɞɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɚɬɨɦɧɨɣ ɱɚɫɬɢɰɵ (ɚɬɨɦɚ, ɦɨɥɟɤɭɥɵ, ɢɨɧɚ) ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ, ɫɪɚɜɧɢɜɚɹ ɜɪɟɦɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɱɚɫɬɢɰ ɢ ɜɪɟɦɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɩɟɪɟɯɨɞɚ. Ⱥɬɨɦɧɵɟ ɱɚɫɬɢɰɵ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɫɜɨɢɦɢ ɷɥɟɤɬɪɨɧɧɵɦɢ ɨɛɨɥɨɱɤɚɦɢ, ɢ ɟɫɥɢ ɫɛɥɢɠɟɧɢɟ ɩɪɨɢɫɯɨɞɢɬ ɦɟɞɥɟɧɧɨ (ɬ.ɟ. ɨɬɧɨɫɢɬɟɥɶɧɵɟ ɫɤɨɪɨɫɬɢ ɚɬɨɦɧɵɯ ɱɚɫɬɢɰ ɦɚɥɵ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫɨ ɫɤɨɪɨɫɬɶɸ ɷɥɟɤɬɪɨɧɨɜ ɜ ɚɬɨɦɟ), ɬɨ ɢɯ ɷɥɟɤɬɪɨɧɧɵɟ ɨɛɨɥɨɱɤɢ ɭɫɩɟɜɚɸɬ ɩɨɫɬɟɩɟɧɧɨ ɩɟɪɟɫɬɪɨɢɬɶɫɹ, ɚ ɡɚɬɟɦ ɜɟɪɧɭɬɶɫɹ ɜ ɢɫɯɨɞɧɨɟ
ɫɨɫɬɨɹɧɢɟ. ȿɫɥɢ ɠɟ ɜɪɟɦɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɚɥɨ, ɬɨ ɷɥɟɤɬɪɨɧɵ ɡɚ ɜɪɟɦɹ tɷ "ɩɟɪɟɛɪɚɫɵɜɚɸɬɫɹ" ɧɚ ɧɨɜɵɣ ɭɪɨɜɟɧɶ, ɩɪɨɢɫɯɨɞɢɬ ɜɨɡɛɭɠɞɟɧɢɟ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ,
ɜɨɡɛɭɠɞɟɧɢɟ ɧɟ ɩɪɨɢɫɯɨɞɢɬ, ɟɫɥɢ tɚɬ>>tɷ. ɉɨ ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧɵ tɚɬ=a/v, ɝɞɟ a - ɪɚɡɦɟɪ ɚɬɨɦɚ, a v - ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɫɤɨɪɨɫɬɶ. ɉɨ ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧɵ tɷ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɢɡ ɩɪɢɧɰɢɩɚ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɢ:
tɷ = !
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 |
- ɜɵɫɜɟɱɢɜɚɧɢɟ ɩɪɢ ɜɨɡɜɪɚɳɟɧɢɢ ɷɥɟɤɬɪɨɧɚ ɧɚ ɨɫɧɨɜɧɨɣ ɭɪɨɜɟɧɶ |
|
(ɜɨɡɦɨɠɧɨ ɫɬɭɩɟɧɱɚɬɨɟ ɩɭɬɟɦ ɢɫɩɭɫɤɚɧɢɹ ɪɹɞɚ ɮɨɬɨɧɨɜ); |
ɛ) Ⱥ* + ȼɋ → Ⱥ + ȼɋ |
- ɬɭɲɟɧɢɟ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɫ ɦɨɥɟɤɭɥɨɣ, ɷɧɟɪɝɢɹ ɜɨɡɛɭɠɞɟɧɢɹ |
Ⱥ + ȼ + ɋ |
ɩɟɪɟɯɨɞɢɬ ɢɥɢ ɜ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɱɚɫɬɢɰ, ɢɥɢ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ |
ɞɢɫɫɨɰɢɚɰɢɸ ɦɨɥɟɤɭɥɵ. Ɍɭɲɟɧɢɟ ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ ɫ ɚɬɨɦɨɦ |
|
ɜ) Ⱥ* + ȼ → Ⱥȼ+ + ɟ |
ɦɚɥɨɜɟɪɨɹɬɧɨ; |
- ɚɫɫɨɰɢɚɬɢɜɧɚɹ ɢɨɧɢɡɚɰɢɹ. ɗɧɟɪɝɢɹ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɢɨɧɢɡɚɰɢɸ. ȼɟɫɶɦɚ |
|
ɝ) Ⱥ* + ȼ → Ⱥ + ȼ+ + ɟ |
ɜɟɪɨɹɬɧɵɣ ɩɪɨɰɟɫɫ ɞɥɹ ɧɟɤɨɬɨɪɵɯ ɫɨɫɬɨɹɧɢɣ; |
- ɷɮɮɟɤɬ ɉɟɧɧɢɝɚ; ɩɪɨɰɟɫɫ ɩɪɨɢɫɯɨɞɢɬ, ɟɫɥɢ ɷɧɟɪɝɢɹ ɜɨɡɛɭɠɞɟɧɢɹ ɚɬɨɦɚ |
|
|
Ⱥ* ɜ ɦɟɬɚɫɬɚɛɢɥɶɧɨɟ ɫɨɫɬɨɹɧɢɟ ɛɨɥɶɲɟ ɩɨɬɟɧɰɢɚɥɚ ɢɨɧɢɡɚɰɢɢ ɱɚɫɬɢɰɵ ȼ. |
ɞ) Ⱥ* + ȼ → ȼ* + Ⱥ |
- 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
Ɋɢɫ.1.6. ɋɯɟɦɚ ɭɩɪɭɝɨɝɨ ɫɨɭɞɚɪɟɧɢɹ |
ɡɚɪɹɞɨɜ Z ɢ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɫɤɨɪɨɫɬɢ v: |
|
|||
|
tg(θ/2) = ρ /ρ, |
ρ = |
Z1 Z2 e2 |
(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
dσ |
|
ρ dρ |
§ |
ρ |
|
·2 |
|
||
|
= |
|
¨ |
|
|
|
¸ |
(1.18) |
|
|
|
|
2 |
|
|
||||
dΩ |
|
sinθ dθ |
© |
2 sin |
|
(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 = −2πnvdx³(1 − cosθ )ρdρ , |
|
||||||
ɩɨɞɫɬɚɜɥɹɹ (1.18) ɢ ɭɱɢɬɵɜɚɹ, ɱɬɨ |
|
||||||
sin2 (θ 2) = |
|
ρ 2 |
|
|
, |
|
|
ρ 2 |
+ ρ 2 |
|
|||||
|
|
|
|
||||
ɨɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɢɦ: |
|
|
|
|
|
||
|
|
∞ |
ρdρ |
|
|||
dv = −4πnvdxρ 2 ³ |
|
||||||
|
|
. |
(1.19) |
||||
ρ 2 |
+ ρ 2 |
||||||
|
|
0 |
|
|
|
|
|
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 |
|
2dxL , |
(1.20) |
ɝɞɟ |
c |
|
|
|
|
|
|
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 |
, |
|||
v |
|
λ |
||||
|
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):
σ |
|
~ |
1 |
|
1 |
. |
(1.23) |
c |
E 2 |
|
|||||
|
|
|
T 2 |
|
|||
ȼɜɨɞɹɬ ɢ ɩɨɧɹɬɢɟ ɜɪɟɦɟɧɢ ɪɚɫɫɟɹɧɢɹ ɢɥɢ ɤɭɥɨɧɨɜɫɤɨɝɨ ɜɪɟɦɟɧɢ, ɨɩɪɟɞɟɥɹɹ ɟɝɨ ɤɚɤ:
τc = |
λ |
= |
1 |
. |
|
v |
nσc v |
||||
|
|
|
Ʌɟɝɤɨ ɜɢɞɟɬɶ, ɱɬɨ ɜɪɟɦɹ ɪɚɫɫɟɹɧɢɹ ɛɵɫɬɪɨ ɪɚɫɬɟɬ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ
τc T3/2.
(1.24)
(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
Ɋɢɫ.1.7. |
Ɍɪɚɟɤɬɨɪɢɢ ɱɚɫɬɢɰ |
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.
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 |
= w |
− w . |
(1.26) |
|
|||
dt |
i |
r |
|
|
|
|
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 = |
|
ki |
|
= |
ne ni |
. |
|
|
|
(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) |
ɋɤɨɪɨɫɬɶ ɩɪɨɰɟɫɫɚ |
|
|||||||||||||
a+γ→i+e (ɢɨɧɢɡɚɰɢɹ) |
wi′ = ki′na j |
|
|
||||||||||||
i+e→a+γ |
|
(ɪɟɤɨɦɛɢɧɚɰɢɹ) |
w′ = k ′ n |
n |
e |
|
|||||||||
|
|
|
|
|
|
|
|
|
|
|
p |
p i |
|
|
|
Ɂɞɟɫɶ na, |
ni, |
ne - ɩɥɨɬɧɨɫɬɢ |
ɚɬɨɦɨɜ, ɢɨɧɨɜ ɢ |
ɷɥɟɤɬɪɨɧɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, k ′ j,k ′ |
- |
||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
i p |
|
ɤɨɷɮɮɢɰɢɟɧɬɵ ɫɤɨɪɨɫɬɢ ɮɨɬɨɢɨɧɢɡɚɰɢɢ ɢ ɢɡɥɭɱɚɬɟɥɶɧɨɣ ɪɟɤɨɦɛɢɧɚɰɢɢ. |
|
||||||||||||||
ȼ ɪɚɜɧɨɜɟɫɢɢ |
|
|
|
|
|
||||||||||
w′ = w′ , |
|
|
|
|
|
|
(1.28) |
||||||||
i |
|
p |
|
|
|
|
|
|
|
|
|
|
|
|
|
ɢ ɤɨɧɫɬɚɧɬɚ ɪɚɜɧɨɜɟɫɢɹ, ɨɩɪɟɞɟɥɟɧɧɚɹ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɫɥɭɱɚɟ, ɨɤɚɡɵɜɚɟɬɫɹ |
|
||||||||||||||
K = |
|
ki′ j |
= |
ni ne |
, |
|
|
|
(1.29) |
||||||
|
k′ |
|
|
|
|
||||||||||
|
|
|
|
|
n |
a |
|
|
|
|
|
||||
|
|
p |
|
|
|
|
|
|
|
|
|
||||
(ɩɨ ɩɪɢɧɰɢɩɭ ɞɟɬɚɥɶɧɨɝɨ ɪɚɜɧɨɜɟɫɢɹ), ɬɚɤ ɱɬɨ ɜ ɨɛɨɢɯ ɫɥɭɱɚɹɯ |
|
||||||||||||||
K = |
ni ne |
. |
|
|
|
|
|
|
(1.30) |
||||||
|
|
|
|
|
|
|
|||||||||
|
|
n |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
a |
|
|
|
|
|
|
|
|
|
|
|
|
|
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:
α = |
ni |
= |
ni |
, |
n |
= n + n , |
(1.31) |
|
|
||||||
|
ni + na |
|
no |
0 |
i a |
|
|
|
|
|
|
|
|||
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:
α = − |
K |
+ |
§ |
· |
2 |
K . |
(1.32) |
|
¨ |
K ¸ |
+ |
||||||
|
2no |
|
© |
2no ¹ |
|
n0 |
|
|
ɉɪɢ ɦɚɥɨɣ ɫɬɟɩɟɧɢ ɢɨɧɢɡɚɰɢɢ, ɤɨɝɞɚ ɤɨɧɰɟɧɬɪɚɰɢɹ ɢɨɧɨɜ ɦɚɥɚ, ni << no, ɧɚɯɨɞɢɦ ni ≈ |
Kn0 , ɬɚɤ |
|||||||
ɱɬɨ |
|
|
|
|
|
|
|
|
α = |
ni |
≈ |
|
K , |
|
|
|
(1.33) |
|
n0 |
|
no |
|
|
|
|
|
ɬ.ɟ. ɫɬɟɩɟɧɶ ɢɨɧɢɡɚɰɢɢ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɤɨɪɧɸ ɤɜɚɞɪɚɬɧɨɦɭ ɢɡ ɧɚɱɚɥɶɧɨɣ ɩɥɨɬɧɨɫɬɢ, ɬɚɤ ɤɚɤ ɤɨɧɫɬɚɧɬɚ ɪɚɜɧɨɜɟɫɢɹ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɬɨɥɶɤɨ ɬɟɦɩɟɪɚɬɭɪɵ ɝɚɡɚ.
ɉɪɢ ɛɨɥɶɲɨɣ ɫɬɟɩɟɧɢ ɢɨɧɢɡɚɰɢɢ, ɤɨɝɞɚ ɤɨɧɰɟɧɬɪɚɰɢɹ ɧɟɣɬɪɚɥɶɧɵɯ ɚɬɨɦɨɜ 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) |
ɋɤɨɪɨɫɬɶ ɩɪɨɰɟɫɫɚ |
||||||||||
a+e→i+2e (ɢɨɧɢɡɚɰɢɹ) |
wi |
= ki na ne |
|
||||||||
i+e→a+γ |
(ɪɟɤɨɦɛɢɧɚɰɢɹ) |
w′ |
= k ′ n |
n |
e |
||||||
|
|
|
|
|
|
|
|
p |
p i |
|
|
ɉɪɢɪɚɜɧɢɜɚɹ ɫɤɨɪɨɫɬɢ ɩɪɹɦɨɝɨ ɢ ɨɛɪɚɬɧɨɝɨ ɩɪɨɰɟɫɫɨɜ, ɩɨɥɭɱɢɦ ɮɨɪɦɭɥɭ |
|||||||||||
ɗɥɶɜɟɪɬɚ: |
|
|
|
|
|
|
|
|
|
|
|
K ′ = |
ni |
= |
|
ki |
, |
|
|
|
(1.34) |
||
|
|
|
|
|
|||||||
|
|
n |
a |
k′ |
|
|
|
|
|||
|
|
|
p |
|
|
|
|
||||
ɢɡ ɤɨɬɨɪɨɣ ɜɢɞɧɨ, ɱɬɨ ɫɬɟɩɟɧɶ ɢɨɧɢɡɚɰɢɢ |
|
|
|
|
|||||||
α = |
|
K ′ |
|
|
|
|
|
(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:
|
n |
n |
i |
|
g |
g |
e |
§ |
m′T |
· |
3/ 2 |
K = |
e |
|
= |
i |
|
¨ |
e |
¸ |
e− I / T , |
||
na |
|
ga |
|
2π!2 |
|||||||
|
|
|
|
© |
¹ |
|
|||||
ɝɞɟ gi, ge, ga — ɫɬɚɬɢɫɬɢɱɟɫɤɢɟ ɜɟɫɚ ɢɨɧɨɜ, ɷɥɟɤɬɪɨɧɨɜ ɢ ɚɬɨɦɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ; I - ɷɧɟɪɝɢɹ
ɢɨɧɢɡɚɰɢɢ |
ɚɬɨɦɚ, |
|
m′ = m m |
/ ( m + m ) |
- ɩɪɢɜɟɞɟɧɧɚɹ ɦɚɫɫɚ. Ɉɬɜɟɱɚɸɳɚɹ |
ɷɬɨɦɭ |
||||||||
|
|
|
|
|
|
|
|
e |
e i |
|
e |
i |
|
|
ɪɚɜɧɨɜɟɫɢɸ ɫɬɟɩɟɧɶ ɢɨɧɢɡɚɰɢɢ α, ɤɚɤ ɥɟɝɤɨ ɜɵɜɟɫɬɢ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ |
|
|||||||||||||
|
α |
2 |
|
g |
g |
e |
§ |
m′T |
·3/ 2 T |
|
|
|
|
|
|
|
|
= |
i |
|
¨ |
e |
¸ |
|
e− I / T , |
|
|
(1.36) |
|
|
1 − α 2 |
ga |
|
2π!2 |
p |
|
|
|||||||
|
|
|
© |
¹ |
|
|
|
|
||||||
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~10- 15ɫɦ2. ȼ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɫɪɟɞɧɹɹ ɞɥɢɧɚ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ λe,i ~ 1
naσe,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 |
|
|||||||||
< ∆u > |
eE |
τ |
, |
< ∆u |
> − |
eE |
τ |
|
. |
(1.39) |
m |
m |
|
||||||||
i |
i |
|
e |
|
|
e |
|
|
||
|
i |
|
|
|
|
e |
|
|
|
|
ȼ ɮɨɪɦɭɥɚɯ (1.39) ɜɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɫ ɧɟɣɬɪɚɥɶɧɵɦɢ ɱɚɫɬɢɰɚɦɢ