Жданов С.К Цветков И.В - Основы физических процессов в плазме и в плазменных установках (2000)
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ɗɥɟɤɬɪɨɧɧɵɟ ɦɢɤɪɨɫɤɨɩɵ
ɉɪɟɢɦɭɳɟɫɬɜɨ
ɷɥɟɤɬɪɨɧɧɨɝɨ ɦɢɤɪɨɫɤɨɩɚ ɩɟɪɟɞ ɨɩɬɢɱɟɫɤɢɦ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɟɝɨ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟɣ ɪɚɡɪɟɲɚɸɳɟɣ ɫɩɨɫɨɛɧɨɫɬɢ. Ɋɚɡɪɟɲɚɸɳɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɨɩɬɢɱɟɫɤɨɝɨ ɦɢɤɪɨɫɤɨɩɚ ɨɝɪɚɧɢɱɟɧɚ ɧɟɜɨɡɦɨɠɧɨɫɬɶɸ ɫɧɢɠɟɧɢɹ ɞɢɮɮɪɚɤɰɢɢ ɥɭɱɟɣ ɩɭɬɟɦ ɭɦɟɧɶɲɟɧɢɹ ɞɥɢɧɵ ɜɨɥɧɵ ɢɡ-ɡɚ ɨɝɪɚɧɢɱɟɧɧɨɝɨ ɞɢɚɩɚɡɨɧɚ ɞɥɢɧ ɜɨɥɧ ɜɢɞɢɦɨɝɨ ɫɜɟɬɚ. ȼ ɷɥɟɤɬɪɨɧɧɵɯ
ɦɢɤɪɨɫɤɨɩɚɯ |
ɜɨɡɦɨɠɧɨ |
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ɭɦɟɧɶɲɚɬɶ ɞɥɢɧɭ ɜɨɥɧɵ |
ɚ) |
ɜ) |
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ɞɟ Ȼɪɨɣɥɹ λ = h/(mv) ɞɨ |
ɛ) |
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ɧɟɫɤɨɥɶɤɢɯ |
ɚɧɝɫɬɪɟɦ |
Ɋɢɫ. 5.14. ɋɯɟɦɵ ɨɩɬɢɱɟɫɤɨɝɨ (ɚ), ɦɚɝɧɢɬɧɨɝɨ (ɛ) ɢ |
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ɩɭɬɟɦ |
ɢɫɩɨɥɶɡɨɜɚɧɢɹ |
ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ (ɜ) ɷɥɟɤɬɪɨɧɧɨɝɨ ɦɢɤɪɨɫɤɨɩɚ: |
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ɭɫɤɨɪɹɸɳɢɯ |
ɷɥɟɤɬɪɨɧɵ |
Ʉ – ɢɫɬɨɱɧɢɤ ɷɥɟɤɬɪɨɧɨɜ, Ɉ – ɨɛɴɟɤɬ, D –ɞɢɚɮɪɚɝɦɚ, L1, L2, L3 – |
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ɜɵɫɨɤɢɯ ɧɚɩɪɹɠɟɧɢɣ (ɞɨ |
ɥɢɧɡɵ, I1, I2 – ɩɟɪɜɢɱɧɨɟ ɢ ɜɬɨɪɢɱɧɨɟ ɢɡɨɛɪɚɠɟɧɢɟ, S – ɷɤɪɚɧ. |
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ɧɟɫɤɨɥɶɤɢɯ |
ɞɟɫɹɬɤɨɜ ɢ |
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ɞɚɠɟ ɫɨɬɟɧ ɤɷȼ). ɋɯɟɦɵ ɷɥɟɤɬɪɨɧɧɵɯ ɦɢɤɪɨɫɤɨɩɨɜ ɫ ɦɚɝɧɢɬɧɨɣ ɢ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɣ ɮɨɤɭɫɢɪɨɜɤɨɣ ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɚ ɪɢɫ. 5.14. ɂɫɫɥɟɞɭɟɦɵɣ ɨɛɴɟɤɬ ɩɪɨɫɜɟɱɢɜɚɟɬɫɹ ɩɭɱɤɨɦ ɦɨɧɨɯɪɨɦɚɬɢɱɟɫɤɢɯ ɷɥɟɤɬɪɨɧɨɜ. ɉɟɪɜɢɱɧɨɟ ɢɡɨɛɪɚɠɟɧɢɟ ɨɛɴɟɤɬɚ ɩɨɩɚɞɚɟɬ ɜ ɮɨɤɚɥɶɧɭɸ ɩɥɨɫɤɨɫɬɶ ɩɪɨɟɤɰɢɨɧɧɨɣ ɥɢɧɡɵ, ɤɨɬɨɪɚɹ ɞɚɟɬ ɭɜɟɥɢɱɟɧɧɨɟ ɢɡɨɛɪɚɠɟɧɢɟ ɨɛɴɟɤɬɚ ɧɚ ɷɤɪɚɧɟ. Ɉɞɧɢɦ ɢɡ ɫɭɳɟɫɬɜɟɧɧɵɯ ɬɪɟɛɨɜɚɧɢɣ ɤ ɷɥɟɤɬɪɨɧɧɨɦɭ ɦɢɤɪɨɫɤɨɩɭ ɹɜɥɹɟɬɫɹ ɩɨɞɞɟɪɠɚɧɢɟ ɜ ɨɛɥɚɫɬɢ ɥɢɧɡ ɜɵɫɨɤɨɝɨ ɜɚɤɭɭɦɚ (ɩɨɪɹɞɤɚ 10-4 10-5 ɦɦ ɪɬ. ɫɬ.), ɬɚɤ ɤɚɤ ɩɪɢ ɬɚɤɢɯ ɜɵɫɨɤɢɯ ɧɚɩɪɹɠɟɧɢɹɯ ɜɨɡɦɨɠɧɨ ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɪɚɡɪɹɞɚ, ɧɚɪɭɲɚɸɳɟɝɨ ɧɟɨɛɯɨɞɢɦɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ. Ɋɚɡɪɟɲɚɸɳɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɷɥɟɤɬɪɨɧɧɨɝɨ ɦɢɤɪɨɫɤɨɩɚ ɨɝɪɚɧɢɱɢɜɚɟɬɫɹ ɩɪɟɠɞɟ ɜɫɟɝɨ ɯɪɨɦɚɬɢɱɟɫɤɨɣ ɢ ɫɮɟɪɢɱɟɫɤɨɣ ɚɛɟɪɪɚɰɢɹɦɢ. Ɇɨɧɨɯɪɨɦɚɬɢɱɧɨɫɬɶ ɷɥɟɤɬɪɨɧɧɨɝɨ ɩɭɱɤɚ ɧɚɪɭɲɚɟɬɫɹ ɢɡ-ɡɚ ɤɨɥɟɛɚɧɢɣ ɭɫɤɨɪɹɸɳɟɝɨ ɧɚɩɪɹɠɟɧɢɹ ɢ ɪɚɡɛɪɨɫɚ ɷɧɟɪɝɢɣ ɷɥɟɤɬɪɨɧɨɜ, ɢɡɥɭɱɚɟɦɵɯ ɧɚɤɚɥɟɧɧɵɦ ɤɚɬɨɞɨɦ. ȼ ɦɚɝɧɢɬɧɨɦ ɷɥɟɤɬɪɨɧɧɨɦ ɦɢɤɪɨɫɤɨɩɟ ɤɨɥɟɛɚɧɢɟ ɫɢɥɵ ɬɨɤɚ ɜ ɨɛɦɨɬɤɟ ɥɢɧɡ ɩɪɢɜɨɞɢɬ ɤ ɞɨɩɨɥɧɢɬɟɥɶɧɨɦɭ ɪɚɡɦɵɬɢɸ ɢɡɨɛɪɚɠɟɧɢɹ. Ʉɪɨɦɟ ɩɪɨɫɜɟɱɢɜɚɸɳɢɯ ɷɥɟɤɬɪɨɧɧɵɯ ɦɢɤɪɨɫɤɨɩɨɜ ɲɢɪɨɤɨɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɩɨɥɭɱɢɥɢ ɫɤɚɧɢɪɭɸɳɢɟ ɷɥɟɤɬɪɨɧɧɵɟ ɦɨɤɪɨɫɤɨɩɵ, ɜ ɤɨɬɨɪɵɯ ɢɡɨɛɪɚɠɟɧɢɟ ɮɨɪɦɢɪɭɟɬɫɹ ɨɬɪɚɠɟɧɧɵɦɢ ɨɬ ɢɫɫɥɟɞɭɟɦɨɝɨ ɨɛɪɚɡɰɚ ɢɥɢ ɜɬɨɪɢɱɧɵɦɢ ɷɥɟɤɬɪɨɧɚɦɢ.
ȽɅȺȼȺ 6
ȼɅɂəɇɂȿ ɉɊɈɋɌɊȺɇɋɌȼȿɇɇɈȽɈ ɁȺɊəȾȺ ɗɅȿɄɌɊɈɇɇɕɏ ɂ ɂɈɇɇɕɏ ɉɍɑɄɈȼ
§42. Ɉɝɪɚɧɢɱɟɧɢɟ ɬɨɤɚ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɦ ɡɚɪɹɞɨɦ ɜ ɞɢɨɞɟ
ȼ ɩɪɨɦɟɠɭɬɤɟ ɞɥɢɧɨɣ d ɦɟɠɞɭ ɩɥɨɫɤɢɦɢ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɜɚɤɭɭɦɟ ɥɢɧɟɣɧɨ: U(x)=U(a) dx (ɷɬɨ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɹɜɥɹɟɬɫɹ
ɪɟɲɟɧɢɟɦ ɭɪɚɜɧɟɧɢɹ Ʌɚɩɥɚɫɚ ∆U = 0). ɉɨ ɦɟɪɟ ɭɜɟɥɢɱɟɧɢɹ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ ɨɛɴɟɦɧɵɣ ɡɚɪɹɞ ρ(x) ɜ ɩɪɨɦɟɠɭɬɤɟ ɪɚɫɬɟɬ, ɢɡɦɟɧɹɹ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɢ ɩɪɢɜɨɞɹ ɤ ɜɨɡɧɢɤɧɨɜɟɧɢɸ ɜɛɥɢɡɢ ɩɨɜɟɪɯɧɨɫɬɢ ɤɚɬɨɞɚ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ - «ɜɢɪɬɭɚɥɶɧɨɝɨ ɤɚɬɨɞɚ», ɨɬ
ɤɨɬɨɪɨɝɨ ɷɥɟɤɬɪɨɧɵ ɨɬɪɚɠɚɸɬɫɹ ɨɛɪɚɬɧɨ ɧɚ ɤɚɬɨɞ (ɪɢɫ. 6.1). Ⱦɥɹ
ɨɩɪɟɞɟɥɟɧɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɦɟɠɭɬɤɟ
ɧɟɨɛɯɨɞɢɦɨ ɪɟɲɚɬɶ ɭɪɚɜɧɟɧɢɟ ɉɭɚɫɫɨɧɚ ∆U= -4πρ(x) ɫ ɭɱɟɬɨɦ
ɬɨɝɨ, ɱɬɨ ɩɥɨɬɧɨɫɬɶ ɬɨɤɚ ɜ ɩɪɨɦɟɠɭɬɤɟ j = - ρv. ȿɫɥɢ ɫɱɢɬɚɬɶ, ɱɬɨ ɷɥɟɤɬɪɨɧɵ ɷɦɢɬɢɪɭɸɬɫɹ ɫ
ɤɚɬɨɞɚ ɫ ɧɭɥɟɜɨɣ ɫɤɨɪɨɫɬɶɸ (ɬɟɩɥɨɜɚɹ ɷɧɟɪɝɢɹ ɷɦɢɫɫɢɨɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɦɧɨɝɨ ɦɟɧɶɲɟ ɷɧɟɪɝɢɢ, ɩɪɢɨɛɪɟɬɚɟɦɨɣ ɜ ɩɪɨɦɟɠɭɬɤɟ), ɬɨ ɭɫɬɨɣɱɢɜɵɦ ɹɜɥɹɟɬɫɹ ɪɟɠɢɦ, ɤɨɝɞɚ «ɜɢɪɬɭɚɥɶɧɵɣ ɤɚɬɨɞ» ɧɟ ɨɛɪɚɡɭɟɬɫɹ, ɚ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɤɚɬɨɞɚ ɪɚɜɧɨ
ɧɭɥɸ: E = dUdx x=0 = 0 . ɉɪɢ ɬɚɤɨɦ
Ɋɢɫ. 6.1. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɥɨɫɤɨɦ ɞɢɨɞɟ ɛɟɡ ɜɥɢɹɧɢɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɝɨ ɡɚɪɹɞɚ (I), ɜ ɪɟɠɢɦɟ ɨɝɪɚɧɢɱɟɧɢɹ ɬɨɤɚ ɨɛɴɟɦɧɵɦ ɡɚɪɹɞɨɦ (II) ɢ ɜ ɪɟɠɢɦɟ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɜɢɪɬɭɚɥɶɧɨɝɨ ɤɚɬɨɞɚ (III)
ɝɪɚɧɢɱɧɨɦ ɭɫɥɨɜɢɢ ɜ ɪɟɠɢɦɟ ɨɝɪɚɧɢɱɟɧɢɹ ɬɨɤɚ ɨɛɴɟɦɧɵɦ ɡɚɪɹɞɨɦ ɪɟɲɟɧɢɟɦ ɭɪɚɜɧɟɧɢɹ ɉɭɚɫɫɨɧɚ
d 2U |
= |
4πj |
1 |
(6.1) |
dx2 |
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2e / m |
U |
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(ɡɞɟɫɶ ɭɱɬɟɧɨ, ɱɬɨ ɩɪɢ ɧɚɱɚɥɶɧɨɣ ɧɭɥɟɜɨɣ ɫɤɨɪɨɫɬɢ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɨɜ mv2/2 = eU) ɹɜɥɹɟɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɦɟɠɭɬɤɟ ɜ ɜɢɞɟ:
U (x) =U (a)( |
x |
)4 / 3 . |
(6.2) |
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ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɥɨɬɧɨɫɬɶ ɷɥɟɤɬɪɨɧɧɨɝɨ ɬɨɤɚ, ɤɨɬɨɪɵɣ ɦɨɠɧɨ ɩɪɨɩɭɫɬɢɬɶ ɱɟɪɟɡ ɩɪɨɦɟɠɭɬɨɤ ɨɝɪɚɧɢɱɟɧɚ ɜɟɥɢɱɢɧɨɣ, ɡɚɜɢɫɹɳɟɣ ɨɬ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɚɧɨɞɟ Ua ɢ ɨɬ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɤɚɬɨɞɚɦ ɢ ɚɧɨɞɨɦ d:
j3 / 2 [Ⱥ/ ɫɦ |
2 |
] = |
2 e U a3 / 2 |
= 2.33 10 |
−6 |
U a3 / 2 [ȼ] |
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(6.3) |
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9π me |
d 2 |
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d 2 |
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ɗɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɩɨɥɭɱɢɥɨ ɧɚɡɜɚɧɢɟ ɡɚɤɨɧɚ ɑɚɣɥɶɞɚ-Ʌɟɧɝɦɸɪɚ, ɢɥɢ ɡɚɤɨɧɚ «3/2». Ⱦɥɹ ɢɨɧɧɨɝɨ ɬɨɤɚ:
ji [Ⱥ/ ɫɦ] = |
2 |
e |
U a3 / 2 |
= 5.46 |
U a3 / 2 [ȼ] |
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(6.4) |
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9π |
M i |
d 2 |
M i [ɚ.ɟ.ɦ.]d 2 |
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ȿɫɥɢ ɭɱɢɬɵɜɚɬɶ ɧɚɱɚɥɶɧɭɸ ɫɤɨɪɨɫɬɶ ɷɦɢɬɢɪɨɜɚɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ v0, ɬɨ ɭɪɚɜɧɟɧɢɟ ɉɭɚɫɫɨɧɚ ɩɪɢɦɟɬ ɜɢɞ:
d 2U = |
4πj |
, |
(6.5) |
dx2 |
v0 1 + 2eU /(mv02 ) |
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ɪɟɲɟɧɢɟɦ ɤɨɬɨɪɨɝɨ ɹɜɥɹɟɬɫɹ ɡɚɜɢɫɢɦɨɫɬɶ |
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U(x) = (mv02/2e)((±(x/xm-1))4/3-1), |
(6.6) |
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(ɡɞɟɫɶ “+” ɩɪɢ x > xm, “-“ ɩɪɢ x < xm). Ɉɤɨɥɨ ɤɚɬɨɞɚ ɜɨɡɧɢɤɚɟɬ «ɜɢɪɬɭɚɥɶɧɵɣ ɤɚɬɨɞ» (ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ) ɝɥɭɛɢɧɨɣ eUm=mv02/2 ɧɚ ɪɚɫɫɬɨɹɧɢɢ
xm = |
mv03 |
ɨɬ ɤɚɬɨɞɚ (ɪɢɫ.6.1). |
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18πej |
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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
ɨɩɢɫɵɜɚɟɬɫɹ ɫɩɟɰɢɚɥɶɧɨɣ ɮɭɧɤɰɢɟɣ Ȼɨɝɭɫɥɚɜɫɤɨɝɨ β (ra ) , ɝɞɟ ra ɢ rk – ɪɚɞɢɭɫɵ rk
ɚɧɨɞɚ ɢ ɤɚɬɨɞɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ:
J3 / 2 |
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U a3 / 2 |
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Ⱦɥɹ ɩɨɥɧɨɝɨ ɬɨɤɚ, ɩɪɢɯɨɞɹɳɟɝɨ ɧɚ ɚɧɨɞ, I3/2=J3/2Sa (Sa=2πrala – ɩɥɨɳɚɞɶ ɚɧɨɞɚ.):
J3 / 2 |
[Ⱥ] = |
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2e |
U a3 / 2 Sa |
= 2.33 |
10 |
−6 U a3 / 2 [ȼ]Sa |
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(6.8) |
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me r 2 |
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(ra ) |
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- ɮɨɪɦɭɥɚ Ʌɟɧɝɦɸɪɚ-Ȼɨɝɭɫɥɚɜɫɤɨɝɨ. Ɂɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ Ȼɨɝɭɫɥɚɜɫɤɨɝɨ ɞɥɹ ɲɢɪɨɤɨɝɨ ɞɢɚɩɚɡɨɧɚ ra/rk ɦɨɠɧɨ ɧɚɣɬɢ ɜ ɬɚɛɥɢɰɚɯ [29].
Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɦɟɠɭɬɤɟ ɨɩɢɫɵɜɚɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ:
U (r) = U |
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Ⱦɥɹ ɫɮɟɪɢɱɟɫɤɨɝɨ ɞɢɨɞɚ ɩɨɥɧɵɣ ɬɨɤ ɧɚ ɚɧɨɞ Ia: |
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I a [Ⱥ] = |
4 2e U a3 / 2 |
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−6 U a3 / 2 |
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(6.10) |
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ɝɞɟ α(ra/rk) – ɬɚɛɭɥɢɪɨɜɚɧɧɚɹ ɮɭɧɤɰɢɹ Ʌɟɧɝɦɸɪɚ [30]. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ:
U (r) = U (a)( |
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§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:
d 2U |
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ɍɫɬɨɣɱɢɜɨɟ ɪɟɲɟɧɢɟ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɩɪɢ ɝɪɚɧɢɱɧɵɯ ɭɫɥɨɜɢɹɯ U(0) = U(d) = 0
ɫɭɳɟɫɬɜɭɟɬ ɬɨɥɶɤɨ ɩɪɢ ɞɨɩɨɥɧɢɬɟɥɶɧɨɦ ɝɪɚɧɢɱɧɨɦ ɭɫɥɨɜɢɢ ɧɚ ɩɨɥɟ [31]:
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Mv 2 |
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ɩɭɱɤɚ. ɗɬɨ ɭɫɥɨɜɢɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɭɫɥɨɜɢɸ ɧɚ ɦɚɤɫɢɦɚɥɶɧɭɸ ɞɥɢɧɭ ɩɪɨɥɟɬɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ:
(6.12)
Ɋɢɫ. 6.2. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɥɟɬɧɨɦ ɩɪɨɦɟɠɭɬɤɟ
d < (4 2 /3)rd = dm |
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ɗɤɫɬɪɟɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ dm ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɤɪɢɬɢɱɟɫɤɨɦɭ ɡɧɚɱɟɧɢɸ ɦɚɤɫɢɦɭɦɚ ɩɨɬɟɧɰɢɚɥɚ:
Um = (3/4)U0. |
(6.15) |
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:
jȻ |
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2e U 03 / |
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(6.16) |
9π |
M d 2 |
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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 |
= |
π |
2e U 03 / 2 |
≈ |
9π |
2 |
(6.17) |
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+ (m / M )1/ 3 ) |
m |
d 2 |
4 |
j3 / 2 . |
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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) |
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dx2 |
dy 2 |
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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 ),
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
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= eEx , ɩɨɥɭɱɢɦ ɩɪɨɮɢɥɶ |
ɞɜɢɠɟɧɢɹ mx |
ɝɪɚɧɢɰɵ ɩɭɱɤɚ, ɤɨɬɨɪɚɹ ɨɩɢɫɵɜɚɟɬɫɹ ɡɚɜɢɫɢɦɨɫɬɶɸ x(z):
x = x0 + tgγ z + pz2/2 , |
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(6.20) |
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ɝɞɟ p = |
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J |
, |
ɝɞɟ |
γ |
- |
ɭɝɨɥ |
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2e |
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4ε |
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U 3 / 2 |
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ɫɯɨɞɢɦɨɫɬɢ |
0 m |
0 |
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ɩɭɱɤɚ |
ɧɚ |
ɜɯɨɞɟ, |
ɬ. |
ɟ. |
ɭɝɨɥ |
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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: |
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dx/dz = 0, ɬ.ɟ. zɤɪ= tgγ/p. |
(6.21) |
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(6.19)
Ɋɢɫ. 6.3. ɉɥɨɫɤɢɣ ɷɥɟɤɬɪɨɧɧɵɣ ɥɟɧɬɨɱɧɵɣ ɩɭɱɨɤ
Ⱦɥɹ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɩɭɱɤɚ, ɜɥɟɬɚɸɳɟɝɨ ɜ ɩɪɨɥɟɬɧɵɣ ɭɱɚɫɬɨɤ ɩɚɪɚɥɥɟɥɶɧɨ ɨɫɢ z ɫ ɧɚɱɚɥɶɧɵɦ ɪɚɞɢɭɫɨɦ r0, ɡɚɜɢɫɢɦɨɫɬɶ ɪɚɞɢɭɫɚ ɩɭɱɤɚ r(z) ɡɚɞɚɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ:
Ɋɢɫ. 6.4. Ɋɚɫɯɨɞɢɦɨɫɬɶ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɷɥɟɤɬɪɨɧɧɨɝɨ ɩɭɱɤɚ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɨɛɫɬɜɟɧɧɨɝɨ ɨɛɴɟɦɧɨɝɨ ɡɚɪɹɞɚ
z |
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e U 03 / 4 R |
dς |
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U 03 / 4 [ɤȼ] R |
dς |
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r |
= 4 |
2m I 1 / 2 ³ |
ln ς |
= 32.3 |
I 1 / 2 [ɦȺ] |
³ |
ln ς |
, |
(6.22) |
0 |
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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):
z |
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2e |
R |
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dς |
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= |
³ |
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(6.23) |
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r |
m U 0 |
8e |
I ln ς + 2e U 0 tg 2γ |
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mU 0 |
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m |
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Ɋɚɞɢɭɫ ɩɭɱɤɚ |
ɜ |
ɧɚɢɛɨɥɟɟ |
ɭɡɤɨɦ |
ɦɟɫɬɟ (ɜ |
ɤɪɨɫɫɨɜɟɪɟ) |
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ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ |
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ɫɨɨɬɧɨɲɟɧɢɹ: ln |
r |
= |
U 3 / 2 |
e |
tg 2γ |
≈1.04 103 |
U 3 / 2 |
[ɤȼ] |
tg 2γ |
, |
(6.24) |
0 |
0 |
2m |
0 |
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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 |
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ɭɪɚɜɧɟɧɢɸ |
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Ʌɚɩɥɚɫɚ: |
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d 2U |
+ |
d |
2U |
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=0 , |
ɧɚ |
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dx2 |
dy 2 |
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Ɋɢɫ. 6.5. Ƚɟɨɦɟɬɪɢɹ ɷɤɜɢɩɨɬɟɧɰɢɚɥɟɣ ɜ ɩɭɲɤɟ ɉɢɪɫɚ, ɮɨɪɦɢɪɭɸɳɟɣ ɩɚɪɚɥɥɟɥɶɧɵɣ ɩɭɱɨɤ
ɝɪɚɧɢɰɟ ɩɭɱɤɚ ɜɵɩɨɥɧɹɥɨɫɶ ɭɫɥɨɜɢɟ dU/dy = 0. Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɟ Ʌɚɩɥɚɫɚ ɫ ɭɱɟɬɨɦ ɷɬɨɝɨ ɭɫɥɨɜɢɹ ɢ ɡɚɜɢɫɢɦɨɫɬɢ ɩɨɬɟɧɰɢɚɥɚ ɧɚ ɨɫɢ U (x) =U (a)(dx )4 / 3
ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ ɬɪɟɛɭɟɦɭɸ ɝɟɨɦɟɬɪɢɸ ɷɥɟɤɬɪɨɞɨɜ, ɤɨɬɨɪɚɹ ɞɥɹ ɩɥɨɫɤɨɝɨ ɫɥɭɱɚɹ ɡɚɞɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ:
(x2 + y 2 )2 / 3 cos( |
4 |
arctg( y / x)) =U . |
(6.25) |
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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:
& |
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&& |
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ψk( r |
) = |
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exp(ikr ) , |
(7.1) |
3 / 2 |
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L |
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ɝɞɟ L3 = V – ɨɛɴɟɦ ɦɟɬɚɥɥɚ, ɜɨɥɧɨɜɨɣ ɜɟɤɬɨɪ k = 2π/L, ɩɨɞɱɢɧɹɸɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɸ Ɏɟɪɦɢ-Ⱦɢɪɚɤɚ, ɬ. ɟ. ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɱɚɫɬɢɰ ɜ ɨɞɧɨɦ ɫɨɫɬɨɹɧɢɢ
f(E) = |
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E − EF |
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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 . |
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Ʉɨɥɢɱɟɫɬɜɨ ɱɚɫɬɢɰ ɫ ɷɧɟɪɝɢɟɣ ɦɟɧɶɲɟ E:
n(E) = |
1 |
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2mE |
)3 / 2 |
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(7.4) |
3π 2 |
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ɬɨɝɞɚ ɩɥɨɬɧɨɫɬɶ ɱɚɫɬɢɰ (ɱɢɫɥɨ ɱɚɫɬɢɰ, ɢɦɟɸɳɢɯ ɷɧɟɪɝɢɸ ɨɬ E ɞɨ E + dE)
ρ(E) = dn = |
1 |
( |
2m |
)3 / 2 |
E1/ 2 dE . |
2π 2 |
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(7.3)
Ɋɢɫ. 7.1. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɜɦɟɬɚɥɥɟ ɩɨ ɷɧɟɪɝɢɹɦ
ɋɭɱɟɬɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ɏɟɪɦɢ-Ⱦɢɪɚɤɚ:
ρ(E) = |
1 |
( |
2m |
)3 / 2 |
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E1 / |
2 dE |
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(7.5) |
2π 2 |
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E − EF |
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+ exp( |
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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:
jt |
= AT 2 exp(− |
eϕ a |
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ɝɞɟ ϕa = |
Wa - EF – ɪɚɛɨɬɚ ɜɵɯɨɞɚ ɷɥɟɤɬɪɨɧɚ ɢɡ ɦɚɬɟɪɢɚɥɚ ɤɚɬɨɞɚ, ɪɚɜɧɚɹ |
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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
A0 [ |
Ⱥ |
] = |
4πmek B |
2 |
= 120 .4 |
(7.7) |
ɫɦ2 Ʉ 2 |
h 3 |
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- ɭɧɢɜɟɪɫɚɥɶɧɚɹ ɩɨɫɬɨɹɧɧɚɹ. ɋɥɟɞɭɟɬ ɭɱɟɫɬɶ, ɱɬɨ ɪɚɛɨɬɚ ɜɵɯɨɞɚ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ (ɜɫɥɟɞɫɬɜɢɟ ɬɟɩɥɨɜɨɝɨ ɪɚɫɲɢɪɟɧɢɹ), ɨɛɵɱɧɨ ɷɬɚ ɡɚɜɢɫɢɦɨɫɬɶ ɥɢɧɟɣɧɚɹ:
ϕa = ϕ0 + α(T-T0), |
(7.8) |
= 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:
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jɌ = enevɫɪ/4, |
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(7.9) |
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ɝɞɟ |
ne = 2( |
me kBT |
)3 / 2 exp(− |
eϕ a |
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(7.10) |
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- ɩɥɨɬɧɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ, vɫɪ = |
8kTe |
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- ɫɪɟɞɧɹɹ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɚɹ ɫɤɨɪɨɫɬɶ. |
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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, ɡɚɜɢɫɢɦɨɫɬɶ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ jɌ ɨɬ ɧɚɩɪɹɠɟɧɢɹ jɌ Ua3/2. 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)
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 / 4E , |
(7.13) |
ɚ ɩɨɬɟɧɰɢɚɥ ɜ ɦɚɤɫɢɦɭɦɟ |
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Um = EF + ϕa - e3/2E1/2. |
(7.14) |
ɋɧɢɠɟɧɢɟ ɪɚɛɨɬɵ ɜɵɯɨɞɚ: |
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e∆ϕɲ[ɷȼ] = e3/2E1/2 = 3.79 E1/2 [ȼ/ɫɦ]. |
(7.15) |
ɉɥɨɬɧɨɫɬɶ ɬɟɪɦɨɷɦɢɫɫɢɨɧɧɨɝɨ ɬɨɤɚ ɫ ɭɱɟɬɨɦ ɷɮɮɟɤɬɚ ɒɨɬɬɤɢ: |
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