Жданов С.К Цветков И.В - Основы физических процессов в плазме и в плазменных установках (2000)
.pdfɢɨɧɢɡɚɰɢɢ 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 ɢɡɭɪɚɜɧɟɧɢɹ ɋɚɯɚ-Ʌɟɧɝɦɸɪɚ:
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e(ϕ a − Ui ) |
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(7.37) |
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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 ɧɚɡɵɜɚɸɬ ɪɚɛɨɬɨɣ ɫɪɨɞɫɬɜɚ eS. ɑɚɫɬɶ ɬɚɤɢɯ ɚɞɫɨɪɛɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ ɢɫɩɚɪɹɸɬɫɹ ɜ ɜɢɞɟ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɬɟɩɟɧɢ ɢɨɧɢɡɚɰɢɢ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɭɪɚɜɧɟɧɢɟ, ɚɧɚɥɨɝɢɱɧɨɟ ɭɪɚɜɧɟɧɢɸ ɋɚɯɚ-Ʌɟɧɝɦɸɪɚ:
α − = |
g − |
exp( |
e(S − ϕ a ) |
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(7.38) |
g a |
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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 |
|
U − U r |
exp(1 − |
U − U r |
) (ɮɨɪɦɭɥɚ Ɏɚɛɪɢɤɚɧɬɚ), (8.5) |
max U max − U r |
|
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|
|
|
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
ɱɚɫɬɢɰɚ ɩɪɨɣɞɟɬ ɩɭɬɶ S = |
eE |
τ ɫɬ , ud = S/τɫɬ, ɬɨɝɞɚ: |
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2me |
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ɫɬ |
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ɝɞɟ |
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ɫɬ |
- ɫɪɟɞɧɹɹ ɞɥɢɧɚ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ, |
vɌ - ɬɟɩɥɨɜɚɹ ɫɤɨɪɨɫɬɶ. Ⱦɥɹ |
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λ |
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ɪɚɫɩɪɟɞɟɥɟɧɢɹ |
Ɇɚɤɫɜɟɥɥɥɚ ɭɫɪɟɞɧɟɧɧɚɹ ɩɨ |
ɫɤɨɪɨɫɬɹɦ ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ |
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ud [ɫɦ/ ɫ] = |
2me eE λɫɬ |
= 0.64 eλɫɬ E = 0.64 |
eλ1 |
E[ȼ/ ɫɦ] |
, (8.9) |
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πkT 2me |
mvɌ |
mvɌ |
p[ɦɦ.ɪɬ.ɫɬ.] |
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ɝɞɟ λ1 = pλɫɬ - ɫɪɟɞɧɢɣ ɩɪɨɛɟɝ ɩɪɢ ɞɚɜɥɟɧɢɢ 1 ɦɦ.ɪɬ.ɫɬ. Ⱦɥɹ ɫɪɟɞɧɟɣ ɫɤɨɪɨɫɬɢ ɞɪɟɣɮɚ ɢɨɧɨɜ ɮɨɪɦɭɥɚ Ʌɚɧɠɟɜɟɧɚ ɢɦɟɟɬ ɜɢɞ:
u |
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eλi1 |
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mi |
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ai – ɤɨɷɮɮɢɰɢɟɧɬ, ɪɚɜɧɵɣ 0.5 1, m - 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: |
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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) |
ɨɬɤɭɞɚ |
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ne = ne0exp((Yi(E) - Yd - Ya)t) = ne0exp(t/θ), |
(8.17) |
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, |
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ɩɨɫɥɟ ɢɨɧɢɡɚɰɢɢ ɛɭɞɟɬ ɞɜɚ |
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ɦɟɞɥɟɧɧɵɯ |
ɷɥɟɤɬɪɨɧɚ |
(ɢ |
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ɨɞɢɧ ɢɨɧ). ɗɥɟɤɬɪɨɧɵ ɬɚɤ |
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ɠɟ |
ɭɫɤɨɪɹɬɫɹ, |
ɤɚɠɞɵɣ |
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ɩɪɨɢɡɜɟɞɟɬ |
ɢɨɧɢɡɚɰɢɸ |
- |
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ɫɬɚɧɟɬ ɢɯ ɱɟɬɵɪɟ - ɬɨɠɟ |
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ɭɫɤɨɪɹɬɫɹ, |
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ɢɨɧɢɡɭɸɬ, |
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ɫɬɚɧɟɬ ɜɨɫɟɦɶ ɢ ɬ.ɞ.- |
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ɜɨɡɧɢɤɚɟɬ |
ɥɚɜɢɧɚ, ɢɞɟɬ |
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Ɋɢɫ. 8.2. ɋɯɟɦɵ (ɚ) ɥɚɜɢɧɧɨɝɨ ɪɚɡɦɧɨɠɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ |
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ɰɟɩɧɨɣ ɩɪɨɰɟɫɫ (ɪɢɫ. 8.2). |
ɜ ɩɪɨɦɟɠɭɬɤɟ ɦɟɠɞɭ ɤɚɬɨɞɨɦ Ʉ ɢ ɚɧɨɞɨɦ Ⱥ ɢ (ɛ) |
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ɇɚ |
ɪɚɫɫɬɨɹɧɢɢ |
x ɩɟɪɜɵɣ |
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ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɪɚɫɩɥɵɜɚɧɢɹ ɷɥɟɤɬɪɨɧɧɨɣ ɥɚɜɢɧɵ, |
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ɷɥɟɤɬɪɨɧ ɫɨɡɞɚɫɬ (ɟαx -1) |
ɤɨɬɨɪɚɹ ɪɨɠɞɚɟɬɫɹ ɨɬ ɷɥɟɤɬɪɨɧɚ, ɜɵɲɟɞɲɟɝɨ ɢɡ |
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ɷɥɟɤɬɪɨɧɧɵɯ |
ɩɚɪ. |
ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɦɟɫɬɚ ɤɚɬɨɞɚ |
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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) |
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(8.20) |
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1 − γ (exp(αd) − 1) |
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ȼɟɥɢɱɢɧɚ |
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µ = γ(exp(αd)-1) |
(8.21) |
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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/ λɫɬ ). Ʉɨɷɮɮɢɰɢɟɧɬ Ɍɚɭɧɫɟɧɞɚ α = Nexp(-λi/ λɫɬ ),ɝɞɟ N = 1/ λɫɬ - 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:
f |
1 |
( |
U ɡ |
)(exp( f |
2 |
( |
U ɡ |
)) − 1) = 1. |
(8.23) |
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pd |
pd |
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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