Жданов С.К Цветков И.В - Основы физических процессов в плазме и в плазменных установках (2000)
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§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 |
- ɭɩɪɭɝɨɟ ɪɚɫɫɟɹɧɢɟ; |
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2) |
Ⱥȼ + CD → Ⱥȼ* + ɋD |
- ɧɟɭɩɪɭɝɨɟ ɪɚɫɫɟɹɧɢɟ. Ɇɨɥɟɤɭɥɚ Ⱥȼ* ɨɤɚɡɚɥɚɫɶ |
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ɜ ɜɨɡɛɭɠɞɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ (ɡɧɚɱɨɤ * ). Ɇɨɠɟɬ ɨɤɚɡɚɬɶɫɹ |
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ɜɨɡɛɭɠɞɟɧɧɨɣ CD* ɢɥɢ Ⱥȼ* ɢ ɋD* ɨɞɧɨɜɪɟɦɟɧɧɨ. ɉɨɥɧɚɹ |
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ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɭɦɟɧɶɲɢɥɚɫɶ ɧɚ ɷɧɟɪɝɢɸ |
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ɜɨɡɛɭɠɞɟɧɢɹ. ȼɨɡɦɨɠɧɵ ɪɚɡɥɢɱɧɵɟ ɜɢɞɵ ɜɨɡɛɭɠɞɟɧɢɣ; |
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3) |
Ⱥȼ + ɋD → Ⱥ + ȼ + ɋD |
-ɞɢɫɫɨɰɢɚɰɢɹ. Ɉɞɧɚ ɢɡ ɦɨɥɟɤɭɥ |
ɢɥɢ |
ɨɛɟ |
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Ⱥȼ + CD → Ⱥȼ +ɋ+D |
ɦɨɥɟɤɭɥɵ ɪɚɫɩɚɥɢɫɶ ɧɚ ɚɬɨɦɵ; |
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Ⱥȼ + ɋD → Ⱥ + ȼ + ɋ + D |
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4) |
Ⱥȼ + ɋD → Ⱥȼ+ + ɋD + ɟ |
-ɢɨɧɢɡɚɰɢɹ. |
Ɉɞɧɚ |
ɢɡ |
ɦɨɥɟɤɭɥ |
(ɢɥɢ |
ɨɛɟ) |
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Ⱥȼ + ɋD → Ⱥȼ + CD+ + ɟ |
“ɩɨɬɟɪɹɥɚ” ɷɥɟɤɬɪɨɧ ɢ ɫɬɚɥɚ ɢɨɧɨɦ. |
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Ⱥȼ + ɋD → Aȼ+ + ȼɋ+ + 2ɟ |
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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:
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ɝɞɟ ɷɧɟɪɝɢɹ R=(Ɋɢɞɛɟɪɝ) 13.6 ɷȼ – ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɚ ɧɚ ɩɟɪɜɨɦ |
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ɛɨɪɨɜɫɤɨɦ ɪɚɞɢɭɫɟ ɚɬɨɦɚ ɜɨɞɨɪɨɞɚ, I- ɷɧɟɪɝɢɹ ɢɨɧɢɡɚɰɢɢ, nl - |
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ɱɢɫɥɨ ɷɤɜɢɜɚɥɟɧɬɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɜ ɨɛɨɥɨɱɤɟ ɚɬɨɦɚ, l - |
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ɨɪɛɢɬɚɥɶɧɨɟ ɤɜɚɧɬɨɜɨɟ ɱɢɫɥɨ, E -ɷɧɟɪɝɢɹ ɢɨɧɢɡɢɪɭɸɳɟɝɨ |
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ɷɥɟɤɬɪɨɧɚ, ɚ u=(E-I)/I. Ɏɭɧɤɰɢɹ Ɏ(u) ɜ ɛɨɪɧɨɜɫɤɨɦ ɩɪɢɛɥɢɠɟɧɢɢ, |
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ɫɩɪɚɜɟɞɥɢɜɨɦ, ɤɨɝɞɚ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɚ ɜɟɥɢɤɚ |
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(u>1), ɪɚɜɧɚ |
u + 1 |
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u + 1 |
0.012 |
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ɋɟɱɟɧɢɹ ɢɨɧɢɡɚɰɢɢ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ ɞɥɹ ɭɩɨɬɪɟɛɢɬɟɥɶɧɵɯ ɧɚ |
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Ɋɢɫ. 1.1. ɋɟɱɟɧɢɹ ɢɨɧɢɡɚɰɢɢ |
ɩɪɚɤɬɢɤɟ ɝɚɡɨɜ ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 1.1. |
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ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ ɢɡ |
ɋɟɱɟɧɢɹ ɮɨɬɨɢɨɧɢɡɚɰɢɢ ɨɛɵɱɧɨ ɧɚ ɞɜɚ - ɬɪɢ |
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ɨɫɧɨɜɧɨɝɨ ɫɨɫɬɨɹɧɢɹ |
ɩɨɪɹɞɤɚ ɧɢɠɟ ɫɟɱɟɧɢɣ ɢɨɧɢɡɚɰɢɢ ɷɥɟɤɬɪɨɧɧɵɦ |
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ɭɞɚɪɨɦ. |
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ȼ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɩɪɢɜɟɞɟɦ ɮɨɪɦɭɥɭ ɞɥɹ ɪɚɫɱɟɬɚ ɫɟɱɟɧɢɹ ɮɨɬɨɢɨɧɢɡɚɰɢɢ ɜɨɞɨɪɨɞɚ ɢɥɢ
ɜɨɞɨɪɨɞɨɩɨɞɨɛɧɨɝɨ ɢɨɧɚ[5]: |
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π 2 |
α a |
2 § |
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exp( −4κ arctgκ ) |
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29 |
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Z2 |
B ¨ |
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th |
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1 − exp( −2πκ ) |
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ph |
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ω ¹ |
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ω − ωth |
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ɝɞɟ α = 1 |
137 |
- ɩɨɫɬɨɹɧɧɚɹ ɬɨɧɤɨɣ ɫɬɪɭɤɬɭɪɵ, ω - ɤɪɭɝɨɜɚɹ ɱɚɫɬɨɬɚ ɮɨɬɨɧɚ, ɢɨɧɢɡɢɪɭɸɳɟɝɨ ɚɬɨɦ, |
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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]:
σ ph [ ɫɦ2 ] = 23.8 λ7[ ɫɦ/ 2 ] .
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.
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ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɜ ɧɟɤɨɬɨɪɨɦ ɨɛɴɟɦɟ ɮɥɭɤɬɭɚɬɢɜɧɨ |
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ɪɚɡɨɲɥɢɫɶ ɡɚɪɹɞɵ (ɪɢɫ.1.2, ɫɱɢɬɚɟɦ, ɱɬɨ ɢɨɧɵ ɩɨɤɨɹɬɫɹ, ɚ |
Ɋɢɫ. 1.2. ɋɯɟɦɚ |
ɷɥɟɤɬɪɨɧɵ ɭɯɨɞɹɬ), ɢ ɨɰɟɧɢɦ ɦɚɤɫɢɦɚɥɶɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɬɚɤɨɝɨ |
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 |
4π e2 n |
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A = ³eEdx = |
d 2 |
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(1.4) |
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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 |
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4πne2 . |
(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
m |
x = −eE = −4πne2 x, |
(1.6) |
e |
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ɢ ɫɨɜɩɚɞɚɟɬ ɩɨ ɜɢɞɭ ɫ ɭɪɚɜɧɟɧɢɟɦ ɞɜɢɠɟɧɢɹ ɞɥɹ ɨɞɧɨɦɟɪɧɨɝɨ ɨɫɰɢɥɥɹɬɨɪɚ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɷɥɟɤɬɪɨɧ ɛɭɞɟɬ ɫɨɜɟɪɲɚɬɶ ɤɨɥɟɛɚɧɢɹ ɫ ɱɚɫɬɨɬɨɣ
ω p = |
4πne2 |
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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
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(1.8) |
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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
r ∂r 2 ( rϕ ) = −4πe( Zni − ne ) ,
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|<<Te,i, ɪɚɡɥɨɠɢɦ ɜɯɨɞɹɳɢɟ ɜ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ȼɨɥɶɰɦɚɧɚ ɷɤɫɩɨɧɟɧɬɵ ɜ ɪɹɞ. ɍɱɢɬɵɜɚɹ ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɫɬɶ ɩɥɚɡɦɵ, ɬ.ɟ. ɜɵɩɨɥɧɟɧɧɵɦ ɭɫɥɨɜɢɟ Znoi=noe, ɩɨɥɭɱɢɦ ɭɩɪɨɳɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɭɪɚɜɧɟɧɢɹ ɉɭɚɫɫɨɧɚ:
∂ 2 |
4πZe( n T |
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ɝɞɟ ɨɛɨɡɧɚɱɟɧɨ
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- ɪɚɞɢɭɫ Ⱦɟɛɚɹ - ɏɸɤɤɟɥɹ.
Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (1.9) (ɩɨɬɟɧɰɢɚɥ Ⱦɟɛɚɹ – ɏɸɤɤɟɥɹ) ɢɦɟɟɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ:
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ɝɞɟ q - ɡɚɪɹɞ ɜɵɞɟɥɟɧɧɨɣ ɧɚɦɢ “ɩɪɨɛɧɨɣ” ɱɚɫɬɢɰɵ. ȿɫɥɢ ɷɬɨ ɩɨɥɨɠɢɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɵɣ ɢɨɧ ɫ ɤɪɚɬɧɨɫɬɶɸ ɢɨɧɢɡɚɰɢɢ Z, ɬɨ q=Z|e|.
ȼɛɥɢɡɢ ɱɚɫɬɢɰɵ, ɧɚ ɪɚɫɫɬɨɹɧɢɹɯ r<<d, ɩɨɬɟɧɰɢɚɥ ɩɨɥɹ ɫɨɜɩɚɞɚɟɬ ɫ ɩɨɬɟɧɰɢɚɥɨɦ ɩɨɥɹ, ɫɨɡɞɚɜɚɟɦɨɝɨ ɱɚɫɬɢɰɟɣ ɜ ɜɚɤɭɭɦɟ (ϕ≈q/r), ɚ ɧɚ ɪɚɫɫɬɨɹɧɢɹɯ r>>d ɩɨɥɟ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ ɛɵɫɬɪɨ ɡɚɬɭɯɚɟɬ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɝɨɜɨɪɹɬ, ɱɬɨ ɧɚ ɬɚɤɢɯ ɪɚɫɫɬɨɹɧɢɹɯ ɨɬ ɱɚɫɬɢɰɵ ɩɥɚɡɦɚ ɷɤɪɚɧɢɪɭɟɬ ɫɨɡɞɚɜɚɟɦɨɟ ɱɚɫɬɢɰɟɣ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ. ɉɨɷɬɨɦɭ ɭɪɚɜɧɟɧɢɟ (1.9) ɢɧɨɝɞɚ ɧɚɡɵɜɚɸɬ ɭɪɚɜɧɟɧɢɟɦ ɷɤɪɚɧɢɪɨɜɤɢ.
ɉɨɦɟɫɬɢɦ ɜ ɩɥɚɡɦɭ ɩɥɨɫɤɢɣ ɷɥɟɤɬɪɨɞ, ɢɦɟɸɳɢɣ ɩɨɬɟɧɰɢɚɥ ϕ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɞɪɭɝɨɦɭ ɩɥɨɫɤɨɦɭ ɷɥɟɤɬɪɨɞɭ, ɭɞɚɥɟɧɧɨɦɭ ɨɬ ɩɟɪɜɨɝɨ ɧɚ ɪɚɫɫɬɨɹɧɢɟ x>>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:
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ɉɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɨɫɶ ɯ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚ ɤ ɷɥɟɤɬɪɨɞɭ. |
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ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ |
ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ, ɱɬɨ |
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eϕ/T<<1, ɢɦɟɟɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ: |
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ɝɞɟ Eo - ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɩɨɥɹ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɩɥɚɫɬɢɧɵ, ɪɚɫɩɨɥɨɠɟɧɧɨɣ ɩɪɢ ɯ=0 [7]. Ɇɵ ɜɢɞɢɦ, ɱɬɨ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɩɪɨɧɢɤɚɸɳɟɝɨ ɜ ɩɥɚɡɦɭ, ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ ɛɵɫɬɪɨ ɡɚɬɭɯɚɟɬ. ɏɚɪɚɤɬɟɪɧɨɣ ɜɟɥɢɱɢɧɨɣ
Ɋɢɫ.1.3. ɋɯɟɦɚ ɪɚɫɩɨɥɨɠɟɧɢɹ ɞɥɢɧɵ ɡɚɬɭɯɚɧɢɹ ɹɜɥɹɟɬɫɹ ɪɚɞɢɭɫ Ⱦɟɛɚɹ:
ɷɥɟɤɬɪɨɞɨɜ
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Ȼɨɥɟɟ ɫɥɨɠɧɚɹ ɤɚɪɬɢɧɚ ɜɨɡɧɢɤɚɟɬ, ɟɫɥɢ ɜ ɩɥɚɡɦɭ ɩɨɦɟɳɟɧɨ ɢɡɨɥɢɪɨɜɚɧɧɨɟ ɧɟɡɚɪɹɠɟɧɧɨɟ ɬɟɥɨ (ɧɚɩɪɢɦɟɪ, ɩɥɚɫɬɢɧɚ, ɫɦ. ɪɢɫ. 1.4).
Ɍɚɤɨɟ ɬɟɥɨ ɜ ɩɥɚɡɦɟ ɞɨɥɠɧɨ ɡɚɪɹɠɚɬɶɫɹ, ɩɪɢɱɟɦ, ɜɜɢɞɭ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟɣ ɩɨɞɜɢɠɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ, ɨɛɵɱɧɨ ɨɧɨ ɩɪɢɨɛɪɟɬɚɟɬ ɨɬɪɢɰɚɬɟɥɶɧɵɣ - ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ ɩɥɚɜɚɸɳɢɣ – ɩɨɬɟɧɰɢɚɥ. ȼɛɥɢɡɢ ɩɥɚɫɬɢɧɵ, ɤɚɤ ɩɨɤɚɡɵɜɚɸɬ ɱɢɫɥɟɧɧɵɟ ɪɚɫɱɟɬɵ [8], ɜɨɡɧɢɤɚɟɬ ɫɥɨɠɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ, ɤɚɱɟɫɬɜɟɧɧɨ ɩɨɤɚɡɚɧɧɨɟ ɧɚ ɪɢɫ. 1.4. ȼɛɥɢɡɢ ɩɥɚɫɬɢɧɵ, ɤɚɤ ɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɪɢɦɟɪɟ, ɜɨɡɧɢɤɚɟɬ ɞɟɛɚɟɜɫɤɢɣ ɫɥɨɣ ɫ ɫɭɳɟɫɬɜɟɧɧɵɦ ɪɚɡɞɟɥɟɧɢɟɦ ɡɚɪɹɞɚ. Ɋɚɡɦɟɪ ɷɬɨɝɨ ɫɥɨɹ ɩɪɢɦɟɪɧɨ ɪɚɜɟɧ ɞɟɛɚɟɜɫɤɨɦɭ ɪɚɞɢɭɫɭ (1.10).
Ɋɢɫ. 1.4. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜɛɥɢɡɢ Ɉɞɧɚɤɨ ɩɨɥɟ, ɫɨɝɥɚɫɧɨ ɪɟɡɭɥɶɬɚɬɚɦ ɪɚɫɱɟɬɨɜ, ɩɨɦɟɳɟɧɧɨɣ ɜ ɩɥɚɡɦɭ ɩɥɚɫɬɢɧɵ. ɩɪɨɧɢɤɚɟɬ ɜ ɩɥɚɡɦɭ ɝɨɪɚɡɞɨ ɞɚɥɶɲɟ, ɨɛɪɚɡɭɹ ɜɛɥɢɡɢ ɩɥɚɫɬɢɧɵ “ɩɪɟɞɫɥɨɣ” ɤɜɚɡɢɧɟɣɬɪɚɥɶɧɨɣ ɩɥɚɡɦɵ.
Ɍɟɨɪɢɹ ɷɬɨɣ ɫɬɪɭɤɬɭɪɵ ɫɥɨɠɧɚ ɢ ɡɞɟɫɶ ɟɟ ɨɛɫɭɠɞɚɬɶ ɧɟ ɛɭɞɟɦ.
ɉɥɚɜɚɸɳɢɣ ɩɨɬɟɧɰɢɚɥ, ɤɨɬɨɪɵɣ ɩɪɢɨɛɪɟɬɚɟɬ ɬɟɥɨ, ɯɨɪɨɲɨ ɨɩɢɫɵɜɚɟɬɫɹ ɮɨɪɦɭɥɨɣ
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Ɍɚɤɨɣ ɪɟɡɭɥɶɬɚɬ ɧɟɫɥɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢɡ ɫɥɟɞɭɸɳɢɯ ɩɪɨɫɬɵɯ ɫɨɨɛɪɚɠɟɧɢɣ. ȿɫɥɢ ɫ ɬɟɱɟɧɢɟɦ ɜɪɟɦɟɧɢ ɩɨɬɟɧɰɢɚɥ ɢɡɨɥɢɪɨɜɚɧɧɨɣ ɩɥɚɫɬɢɧɵ ɩɟɪɟɫɬɚɟɬ ɦɟɧɹɬɶɫɹ, ɬɨ ɷɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɬɨɤɢ ɩɪɢɯɨɞɹɳɢɯ ɧɚ ɧɟɟ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɡɚɪɹɞɨɜ ɤɨɦɩɟɧɫɢɪɭɸɬɫɹ. Ɉɰɟɧɢɜɚɹ ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɢɨɧɨɜ ɜɞɚɥɢ ɨɬ ɬɟɥɚ ɤɚɤ
1
ji = 4 n0 vTi ,
ɚ ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɷɥɟɤɬɪɨɧɨɜ ɫ ɭɱɟɬɨɦ ɢɯ ɬɨɪɦɨɠɟɧɢɹ “ɧɚ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɝɨɪɤɟ” ɤɚɤ
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ɢ ɩɪɢɪɚɜɧɢɜɚɹ ɢɯ, ɩɪɢɯɨɞɢɦ ɤ ɮɨɪɦɭɥɟ (1.14).
ȼɟɪɧɟɦɫɹ ɤ ɮɨɪɦɭɥɟ (1.10). ȿɫɥɢ ɜ ɧɟɣ ɩɨɥɨɠɢɬɶ, ɱɬɨ ne=ni ɢ Te=Ti, ɬɨ ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ (1.13). ȿɫɥɢ ɠɟ ɫɱɢɬɚɬɶ, ɱɬɨ ɩɥɚɡɦɚ ɹɜɥɹɟɬɫɹ ɫɢɥɶɧɨ ɧɟɢɡɨɬɟɪɦɢɱɟɫɤɨɣ, ɬɚɤ ɱɬɨ Ti>>Ɍe, 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.
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 = ωLe2 + ωLi2 ,ωLe = |
4πe2 n |
e ,ωLi = |
4πZ2e2 n |
i , |
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me |
mi |
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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 |
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1 |
1 |
, rDe = |
Te |
, rDi = |
Ti |
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d |
= |
r2 |
+ r2 |
4πe2 n |
4πZ2e2 n |
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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:
e2 n1/ 3 |
<< T , |
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ɢɥɢ |
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γ = |
e6 n |
<< 1 , |
(1.15) |
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T |
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ɝɞɟ γ - ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ ɩɚɪɚɦɟɬɪ ɧɟɢɞɟɚɥɶɧɨɫɬɢ.
ɗɬɨɦɭ ɭɫɥɨɜɢɸ ɦɨɠɧɨ ɩɪɢɞɚɬɶ ɢ ɧɟɫɤɨɥɶɤɨ ɢɧɨɣ ɫɦɵɫɥ. ɋɟɱɟɧɢɟ ɤɭɥɨɧɨɜɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɱɚɫɬɢɰ ɨɩɪɟɞɟɥɹɟɬɫɹ ɚɦɩɥɢɬɭɞɨɣ ɪɚɫɫɟɹɧɢɹ, ɩɨ ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧɵ ɪɚɜɧɨɣ
f ~ e2 . T
Ɉɱɟɜɢɞɧɨ, ɩɥɚɡɦɚ ɹɜɥɹɟɬɫɹ ɢɞɟɚɥɶɧɨɣ, ɟɫɥɢ ɚɦɩɥɢɬɭɞɚ ɪɚɫɫɟɹɧɢɹ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ ɫɪɟɞɧɟɝɨ ɦɟɠɱɚɫɬɢɱɧɨɝɨ ɪɚɫɫɬɨɹɧɢɹ (ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɫɭɳɟɫɬɜɟɧɧɵ ɤɨɪɪɟɥɹɰɢɢ ɜɡɚɢɦɧɨɝɨ ɪɚɫɩɨɥɨɠɟɧɢɹ ɱɚɫɬɢɰ)
f<< R ~ n−1/3 ,
ɢɜɧɨɜɶ ɩɪɢɯɨɞɢɦ ɤ ɤɪɢɬɟɪɢɸ (1.15).
ɉɨɥɟɡɧɨ ɭɫɥɨɜɢɸ ɢɞɟɚɥɶɧɨɫɬɢ ɩɥɚɡɦɵ ɩɪɢɞɚɬɶ ɛɨɥɟɟ ɧɚɝɥɹɞɧɵɣ ɫɦɵɫɥ, ɞɥɹ ɷɬɨɝɨ ɩɨɫɬɭɩɢɦ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. ȼɵɞɟɥɢɦ ɜ ɨɛɴɟɦɟ ɩɥɚɡɦɵ ɲɚɪ ɫ ɪɚɞɢɭɫɨɦ, ɪɚɜɧɵɦ ɪɚɞɢɭɫɭ Ⱦɟɛɚɹ, ɢ ɩɨɞɫɱɢɬɚɟɦ ɱɢɫɥɨ ɱɚɫɬɢɰ ND, ɫɨɞɟɪɠɚɳɢɯɫɹ ɜ ɷɬɨɦ ɲɚɪɟ:
N |
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πnr 3 |
~ γ −3/ 2 . |
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ɋɪɚɜɧɢɜ ɫ ɤɪɢɬɟɪɢɟɦ (1.15), ɩɪɢɯɨɞɢɦ ɤ ɡɚɤɥɸɱɟɧɢɸ, ɱɬɨ ɩɥɚɡɦɚ ɹɜɥɹɟɬɫɹ ɢɞɟɚɥɶɧɨɣ, ɟɫɥɢ ɱɢɫɥɨ ɱɚɫɬɢɰ ɜ ɲɚɪɟ ɫ ɞɟɛɚɟɜɫɤɢɦ ɪɚɞɢɭɫɨɦ ɜɟɥɢɤɨ. ɑɚɫɬɨ ɢɦɟɧɧɨ ɱɢɫɥɨ ND ɢɫɩɨɥɶɡɭɟɬɫɹ ɜ ɤɚɱɟɫɬɜɟ ɦɟɪɵ ɢɞɟɚɥɶɧɨɫɬɢ ɢɥɢ ɧɟɢɞɟɚɥɶɧɨɫɬɢ ɩɥɚɡɦɵ.
ɉɪɨɢɥɥɸɫɬɪɢɪɭɟɦ ɩɨɥɭɱɟɧɧɵɣ ɪɟɡɭɥɶɬɚɬ ɱɢɫɥɟɧɧɵɦ ɩɪɢɦɟɪɨɦ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɡɧɚɱɟɧɢɣ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɩɥɨɬɧɨɫɬɢ, ɬɢɩɢɱɧɵɯ ɞɥɹ ɬɟɪɦɨɹɞɟɪɧɨɣ ɩɥɚɡɦɵ (ɫɦ. §2), ɩɨɥɭɱɚɟɦ ND~108 >>1, ɢ ɬɚɤɚɹ ɩɥɚɡɦɚ ɹɜɥɹɟɬɫɹ ɜ ɜɵɫɨɤɨɣ ɫɬɟɩɟɧɢ ɢɞɟɚɥɶɧɨɣ. Ɍɨɝɞɚ ɤɚɤ ɞɥɹ ɩɥɚɡɦɵ ɥɢɧɟɣɧɨɣ ɦɨɥɧɢɢ, ɬɢɩɢɱɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɤɨɬɨɪɨɣ ɫɨɫɬɚɜɥɹɟɬ ~104Ʉ, ɚ ɤɨɧɰɟɧɬɪɚɰɢɹ ɩɪɢɦɟɪɧɨ ɪɚɜɧɚ ɤɨɧɰɟɧɬɪɚɰɢɢ ɜɨɡɞɭɯɚ, ~1019ɫɦ-3, ɩɨɥɭɱɚɟɦ ND~0.1. Ɍɚɤɚɹ ɩɥɚɡɦɚ ɹɜɥɹɟɬɫɹ ɫɥɚɛɨɧɟɢɞɟɚɥɶɧɨɣ, ɫɩɨɫɨɛɧɨɣ ɤ ɪɨɠɞɟɧɢɸ ɫɚɦɨɩɨɞɞɟɪɠɢɜɚɸɳɢɯɫɹ ɧɟɥɢɧɟɣɧɵɯ ɫɬɪɭɤɬɭɪ. ȼɨɡɦɨɠɧɨ, ɤɚɤ ɩɨɥɚɝɚɸɬ, ɢɦɟɧɧɨ ɬɚɤɨɜɚ ɩɪɢɪɨɞɚ ɲɚɪɨɜɨɣ ɦɨɥɧɢɢ, ɜɨɡɧɢɤɚɸɳɟɣ ɱɚɫɬɨ ɩɪɢ ɨɛɵɱɧɨɦ ɝɪɨɡɨɜɨɦ ɪɚɡɪɹɞɟ. ȼɩɪɨɱɟɦ, ɞɟɬɚɥɶɧɵɣ ɦɟɯɚɧɢɡɦ ɷɬɨɝɨ ɩɪɢɪɨɞɧɨɝɨ ɹɜɥɟɧɢɹ ɩɨɤɚ ɨɤɨɧɱɚɬɟɥɶɧɨ ɧɟ ɜɵɹɫɧɟɧ.
§ 5. ɉɪɹɦɵɟ ɢ ɨɛɪɚɬɧɵɟ ɩɪɨɰɟɫɫɵ ɜ ɩɥɚɡɦɟ
Ɋɚɧɟɟ ɦɵ ɭɫɬɚɧɨɜɢɥɢ, ɱɬɨ ɜ ɝɚɡɟ-ɩɥɚɡɦɟ ɦɨɝɭɬ ɩɪɨɢɫɯɨɞɢɬɶ ɧɟɭɩɪɭɝɢɟ ɩɪɨɰɟɫɫɵ: ɜɨɡɛɭɠɞɟɧɢɟ ɱɚɫɬɢɰ, ɞɢɫɫɨɰɢɚɰɢɹ ɦɨɥɟɤɭɥ, ɢɨɧɢɡɚɰɢɹ ɱɚɫɬɢɰ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɞɨɥɠɧɵ ɛɵɬɶ ɢ ɨɛɪɚɬɧɵɟ ɩɪɨɰɟɫɫɵ - ɫɧɹɬɢɟ ɜɨɡɛɭɠɞɟɧɢɹ ɬɟɦ ɢɥɢ ɢɧɵɦ ɩɭɬɟɦ (ɬɚɤɢɟ ɩɪɨɰɟɫɫɵ ɱɚɫɬɨ ɧɚɡɵɜɚɸɬ ɬɭɲɟɧɢɟɦ), ɨɛɴɟɞɢɧɟɧɢɟ ɚɬɨɦɨɜ ɜ ɦɨɥɟɤɭɥɵ (ɨɛɵɱɧɨ ɬɚɤɨɣ ɩɪɨɰɟɫɫ ɧɚɡɵɜɚɸɬ ɚɫɫɨɰɢɚɰɢɟɣ), ɨɛɴɟɞɢɧɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ (ɪɟɤɨɦɛɢɧɚɰɢɹ). ɉɪɹɦɵɟ ɢ ɨɛɪɚɬɧɵɟ ɩɪɨɰɟɫɫɵ ɦɨɝɭɬ ɨɫɭɳɟɫɬɜɥɹɬɶɫɹ ɪɚɡɥɢɱɧɵɦɢ ɩɭɬɹɦɢ: ɞɥɹ ɩɪɹɦɵɯ ɩɪɨɰɟɫɫɨɜ ɧɟɨɛɯɨɞɢɦɨ ɫɨɨɛɳɢɬɶ ɱɚɫɬɢɰɚɦ ɞɨɫɬɚɬɨɱɧɭɸ ɷɧɟɪɝɢɸ, ɱɬɨɛɵ ɪɚɡɨɪɜɚɬɶ ɭɞɟɪɠɢɜɚɸɳɢɟ ɢɯ ɫɜɹɡɢ, ɩɪɢ ɨɛɪɚɬɧɵɯ ɩɪɨɰɟɫɫɚɯ ɞɨɥɠɟɧ ɜɵɞɟɥɢɬɶɫɹ ɢɡɛɵɬɨɤ ɷɧɟɪɝɢɢ ɩɨɪɹɞɤɚ ɷɧɟɪɝɢɢ ɫɜɹɡɢ. ɉɪɢ ɷɬɨɦ ɧɟɨɛɯɨɞɢɦɨ ɜɵɩɨɥɧɟɧɢɟ ɡɚɤɨɧɨɜ ɫɨɯɪɚɧɟɧɢɹ ɷɧɟɪɝɢɢ ɢ ɢɦɩɭɥɶɫɚ. Ɋɚɫɫɦɨɬɪɢɦ ɷɬɢ ɩɪɨɰɟɫɫɵ ɩɨɞɪɨɛɧɟɟ.
ȼɨɡɛɭɠɞɟɧɢɟ ɢ ɬɭɲɟɧɢɟ
ȼɨɡɛɭɠɞɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɜɨɡɦɨɠɧɵ ɞɥɹ ɜɫɟɯ ɫɥɨɠɧɵɯ ɱɚɫɬɢɰ - ɦɨɥɟɤɭɥ, ɚɬɨɦɨɜ, ɦɨɥɟɤɭɥɹɪɧɵɯ ɢ ɚɬɨɦɚɪɧɵɯ ɢɨɧɨɜ (ɤɪɨɦɟ ɢɨɧɚ ɚɬɨɦɚ ɜɨɞɨɪɨɞɚ). ȼ ɦɨɥɟɤɭɥɚɯ ɢ ɦɨɥɟɤɭɥɹɪɧɵɯ ɢɨɧɚɯ ɦɨɝɭɬ ɛɵɬɶ ɜɨɡɛɭɠɞɟɧɵ ɜɪɚɳɚɬɟɥɶɧɵɟ, ɤɨɥɟɛɚɬɟɥɶɧɵɟ ɢ ɷɥɟɤɬɪɨɧɧɵɟ ɫɨɫɬɨɹɧɢɹ, ɚ ɜ ɚɬɨɦɚɯ ɢ ɚɬɨɦɚɪɧɵɯ ɢɨɧɚɯ - ɬɨɥɶɤɨ ɷɥɟɤɬɪɨɧɧɵɟ. ɋ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ, ɧɚɢɛɨɥɟɟ ɥɟɝɤɨ ɜɨɡɛɭɠɞɚɸɬɫɹ ɜɪɚɳɚɬɟɥɶɧɵɟ ɭɪɨɜɧɢ, ɬɪɭɞɧɟɟ ɤɨɥɟɛɚɬɟɥɶɧɵɟ, ɟɳɟ ɬɪɭɞɧɟɟ ɷɥɟɤɬɪɨɧɧɵɟ. ȿɫɥɢ ɩɪɢɧɹɬɶ ɡɚ ɟɞɢɧɢɰɭ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɷɥɟɤɬɪɨɧɧɵɦɢ ɭɪɨɜɧɹɦɢ δȿɷ, ɬɨ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɤɨɥɟɛɚɬɟɥɶɧɵɦɢ ɭɪɨɜɧɹɦɢ δȿν
ɛɭɞɟɬ ɦɟɧɶɲɟ ɜ |
m |
ɪɚɡ, ɚ ɦɟɠɞɭ ɜɪɚɳɚɬɟɥɶɧɵɦɢ ɭɪɨɜɧɹɦɢ δȿj ɟɳɟ ɦɟɧɶɲɟ: ɜ |
m |
ɪɚɡ, |
M |
M |
ɝɞɟ M - ɦɚɫɫɚ ɦɨɥɟɤɭɥɵ, ɚ m - ɦɚɫɫɚ ɷɥɟɤɬɪɨɧɚ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɦɨɥɟɤɭɥɵ ɇ2 ɪɚɫɱɟɬɧɵɟ ɡɧɚɱɟɧɢɹ ɷɧɟɪɝɢɣ ɜɨɡɛɭɠɞɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɫɨɫɬɨɹɧɢɣ ȿɷ= 4,7 ɷȼ, ȿν= 0,54 ɷȼ,
ȿj= 7,6 10-3 ɷȼ.
Ⱦɥɹ ɜɨɡɛɭɠɞɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɫɨɨɛɳɢɬɶ ɦɨɥɟɤɭɥɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɷɧɟɪɝɢɸ, ɧɚɩɪɢɦɟɪ ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ ɫ ɞɪɭɝɨɣ ɱɚɫɬɢɰɟɣ.
ɋɯɟɦɚɬɢɱɧɨ ɜɨɡɛɭɠɞɟɧɢɟ ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ ɫ ɷɥɟɤɬɪɨɧɨɦ ɫɢɦɦɟɬɪɢɱɧɨɣ ɞɜɭɯɚɬɨɦɧɨɣ ɦɨɥɟɤɭɥɵ (ɇ2, N2, O2 ɢ ɬ.ɞ.) ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ.1.5. ȼ ɬɚɤɢɯ ɦɨɥɟɤɭɥɚɯ ɦɨɝɭɬ ɜɨɡɛɭɠɞɚɬɶɫɹ ɷɥɟɤɬɪɨɧɧɵɟ, ɨɞɧɚ ɜɪɚɳɚɬɟɥɶɧɚɹ ɢ ɨɞɧɚ ɤɨɥɟɛɚɬɟɥɶɧɚɹ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ.
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɜ ɛɨɥɟɟ ɫɥɨɠɧɵɯ ɦɨɥɟɤɭɥɚɯ ɛɨɥɶɲɟɟ ɱɢɫɥɨ ɜɨɡɦɨɠɧɵɯ ɤ ɜɨɡɛɭɠɞɟɧɢɸ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ.
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ɋɭɳɟɫɬɜɨɜɚɧɢɟ |
ɜɪɚɳɚɬɟɥɶɧɵɯ |
ɢ |
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ɤɨɥɟɛɚɬɟɥɶɧɵɯ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɜ ɦɨɥɟɤɭɥɹɪɧɵɯ |
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ɝɚɡɚɯ |
ɨɩɪɟɞɟɥɹɟɬ |
ɨɫɧɨɜɧɵɟ |
ɫɜɨɣɫɬɜɚ |
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ɫɥɚɛɨɢɨɧɢɡɨɜɚɧɧɨɣ ɩɥɚɡɦɵ ɷɬɢɯ ɝɚɡɨɜ ɢ ɞɚɟɬ |
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Ɋɢɫ.1.5. |
ɋɯɟɦɚ ɜɨɡɛɭɠɞɟɧɢɹ ɭɞɚɪɨɦ |
ɜɨɡɦɨɠɧɨɫɬɶ ɢɫɩɨɥɶɡɨɜɚɬɶ ɢɯ ɜ ɩɥɚɡɦɨɯɢɦɢɱɟɫɤɢɯ |
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ɢ ɥɚɡɟɪɧɵɯ ɫɢɫɬɟɦɚɯ. |
Ⱦɟɥɨ ɜ ɬɨɦ, ɱɬɨ |
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ɫɟɱɟɧɢɹ |
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ɭɩɪɭɝɨɝɨ ɢ ɧɟɭɩɪɭɝɨɝɨ ɩɪɨɰɟɫɫɨɜ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɦɨɥɟɤɭɥ ɫ ɜɨɡɛɭɠɞɟɧɢɟɦ ɤɨɥɟɛɚɬɟɥɶɧɵɯ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɩɨɱɬɢ ɨɞɢɧɚɤɨɜɵ (ɨɬɥɢɱɚɸɬɫɹ ɥɢɲɶ ɜ ɧɟɫɤɨɥɶɤɨ ɪɚɡ), ɚ ɩɟɪɟɞɚɜɚɟɦɚɹ ɨɬ ɷɥɟɤɬɪɨɧɚ ɷɧɟɪɝɢɹ ɨɬɥɢɱɚɟɬɫɹ ɜ ɫɨɬɧɢ ɢ ɬɵɫɹɱɢ ɪɚɡ. ɉɪɢ ɭɩɪɭɝɨɦ ɫɨɭɞɚɪɟɧɢɢ ɦɨɥɟɤɭɥɟ ɩɟɪɟɞɚɟɬɫɹ ɦɚɥɚɹ (~m/Ɇ) ɞɨɥɹ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ, ɚ ɩɪɢ ɜɨɡɛɭɠɞɟɧɢɢ ɤɨɥɟɛɚɧɢɣ ɩɟɪɟɞɚɟɬɫɹ ɷɧɟɪɝɢɹ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɷɧɟɪɝɢɢ ɩɟɪɟɯɨɞɚ, ɬɨ ɟɫɬɶ ɦɚɫɲɬɚɛɚ ɞɟɫɹɬɵɯ ɞɨɥɟɣ ɷɥɟɤɬɪɨɧ-ɜɨɥɶɬɚ. Ʉɨɥɟɛɚɬɟɥɶɧɚɹ ɪɟɥɚɤɫɚɰɢɹ - ɩɟɪɟɯɨɞ ɤɨɥɟɛɚɬɟɥɶɧɨɣ ɷɧɟɪɝɢɢ ɜ ɬɟɩɥɨɜɭɸ - ɜɟɫɶɦɚ ɡɚɬɪɭɞɧɟɧɚ (ɩɪɢ ɤɨɦɧɚɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ - ɜɟɪɨɹɬɧɨɫɬɶ ɦɚɫɲɬɚɛɚ 10-5-10-9). ɉɨɷɬɨɦɭ ɫɭɳɟɫɬɜɭɸɬ ɫɢɫɬɟɦɵ ɫ ɜɵɫɨɤɨɣ ɤɨɥɟɛɚɬɟɥɶɧɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ ɩɪɢ ɦɚɥɨɣ ɩɨɫɬɭɩɚɬɟɥɶɧɨɣ (ɬɟɩɥɨɜɨɣ). Ɍɚɤ ɦɨɠɧɨ ɨɛɟɫɩɟɱɢɬɶ ɜɵɫɨɤɭɸ ɢɧɜɟɪɫɧɭɸ ɡɚɫɟɥɟɧɧɨɫɬɶ ɤɨɥɟɛɚɬɟɥɶɧɨ-ɜɪɚɳɚɬɟɥɶɧɵɯ ɩɟɪɟɯɨɞɨɜ, ɬ.ɟ. ɫɨɡɞɚɬɶ ɚɤɬɢɜɧɭɸ ɫɪɟɞɭ ɞɥɹ ɥɚɡɟɪɨɜ.