臺灣博碩士論文加值系統

摘要

眾所皆知，在基本模態操作的高頻磁旋管，需要用較大的磁場來局限電子。若在高次諧波操作，因其所需的磁場與諧波數N0成反比，故可縮小所需裝置的尺寸。然而，在諧波模態操作的傳統磁旋管，能量轉換效率 很快的跌落，改使用一種為cusp-field結構的磁場可使電子束經由其作用而盡量靠近管壁。在諧波迴旋共振交互作用時，將有加大有限Larmour半徑的效用。再者，使用槽狀邊界之導波管，此結構將在電子集中環繞之軌道處，產生週期性的邊緣場，並能強化導波管波場的共振諧波成分，進而改善迴旋電子與高次諧波模態的交互作用。
在本篇論文中將探討迴旋電子在多葉片介質導波管模態中的共振交互作用，論文中亦包含負質量不穩定的物理機制探討。模型的架構為考慮相對論性的電子旋轉，其在一外加均勻磁場且槽狀周圍的圓柱導波管中，其橫向分量也將促使導波管橫向電場模態的激發。非線性波之動力理論則由勞侖茲力方程、波方程及能量守恆式所導出。數值分析則利用導出公式，解出被單一模態激發的波之歸一化電場值的暫態非線性解。
因希望能有較高的輸出頻率，故我們只專注在模擬2 高次諧波模態下的操作。就TE模態，起源於第二個零點之第零個諧波模態 而言，當N0=8及10，其從粒子輸送能量給波場的轉換效率可高達13.2%及9.1%；而起源於第一個零點之第N0個諧波模態 ，當N0=8及10，其效率亦可達10%及3.4%。

目 錄
目 錄 1
圖表目錄 3
中文摘要 5
英文摘要 6
第一章 緒論 8
1-1 前言 8
1-2 文獻回顧 9
1-3 研究的動機與目的 12
1-4 論文架構 13
第二章 理論分析 15
2-1 群聚現象 15
2-2 負質量不穩定 16
2-3 電子與波場的共振交互作用 18
2-4 、 的物理意義 24
第三章 模擬方法 27
3-1 電子運動空間模型的架構分析 27
3-2 基本假設 28
3-3 電腦模擬方法與步驟 29
3-4 值的計算 32
第四章 結果分析與討論 39
4-1 結果分析 39
4-2 討論 39
第五章 結論 51
5-1 結論 51
5-2 建議與展望 52
附錄A 54
附錄B 58
附錄C 65
參考文獻 67
作者簡歷 71

圖表目錄

圖1.1 微波管和固態元件之應用範圍 14
圖2.1 電子群聚現象 26
圖2.2 座標關係圖 26
圖3.1 採用的模型： 立體圖 33
圖3.2 採用的模型： 截面圖 33
圖3.3 採用磁場的模型： reverse cusp-field的示意圖 34
圖3.4 大、小軌道之比較圖 35
圖3.5 起源於 之 對 關係圖 36
圖3.6 起源於 之 對 關係圖 36
圖3.7 起源於 之 對 關係圖 37
圖3.8 數值計算之流程圖 38
表4.1 模擬結果：起源於 之參數數值 42
表4.2 模擬結果：起源於 之參數數值 42
圖4.1 暫態電場-時間關係圖：起源於 、N0=8 43
圖4.2 電子位置之極座標圖：起源於 、N0=8 44
圖4.3 暫態電場-時間關係圖：起源於 、N0=8 45
圖4.4 電子位置之極座標圖：起源於 、N0=8 46
圖4.5 暫態電場-時間關係圖：起源於 、N0=10 47
圖4.6 電子位置之極座標圖：起源於 、N0=10 48
圖4.7 暫態電場-時間關係圖：起源於 、N0=10 49
圖4.8 電子位置之極座標圖：起源於 、N0=10 50

參考文獻

[1] P. Sprangle and W. M. Manheimer, "Coherent nonlinear theory of a cyclotron instability", Phys. Fluids, Vol. 18, No. 2, pp. 224-230, Feb. 1975.
[2] P. Sprangle and A. T. Drobot, "The linear and self-consistent nonlinear theory of the electron cyclotron maser instability", IEEE Trans. MTT, Vol. 1777-25, No. 6, pp. 528-544, June 1977.
[3] K. R. Chu and J. L. Hirschfield, "Comparative study of the axial and azimuthal bunching mechanisms in electromagnetic cyclotron instabilities", Phys. Fluids, Vol. 21, No. 3, pp. 461-466, March 1978.
[4] S. P. Kuo, S. C. Kuo, B. R. Cheo and M. C. Lee, "Analysis of the harmonic gyrotron traveling wave amplifier", Int. J. Infrared and Millimeter Waves, Vol. 7, No. 4, pp. 635-651, 1986.
[5] W. W. Destler, R. L. Weiler and C. D. Striffler, "High-power microwave generation from a rotating e-layer in a magnetron-type waveguide", Appl. Phys. Lett., Vol. 38, No. 7, pp. 570-572, April 1981.
[6] W. Namkung, "Observation of microwave generation from a cusptron device ", Phys. Fluids, Vol. 27, No. 20, pp. 329-330, Feb. 1984.
[7] W. Lawson, W. W. Dester and C. D. Striffler, "High power microwave generation from a large orbit gyrotron in vane and hole-and-slot conducting wall geometries", IEEE Trans. Plasma Science, Vol. PS-13, No. 6, pp. 444-453, Dec. 1985.
[8] W. Lawson and C. D. Striffler, "A linear growth rate fluid formulation for large orbit, annular electron layers with finite thickness", Phys. Fluids, Vol. 29, No. 5, pp. 1682-1694, May 1986.
[9] Y. Y. Lau and L. R. Barnett, "Theory of low magnetic field gyrotron (gyromagnetron)", Int. J. Infrared and Millimeter Waves, Vol. 3, No. 5, pp. 619-642, 1982.
[10] A. S. Gilmour, Jr. Microwave Tubes, Artech House, INC. , p. 2, 1986.
[11] R. Q. Twiss, "Radiation transfer and the possibility of negative absorption in radio astronomy", Australian J. Phys., Vol. 11,pp. 564-579, 1958.
[12] J. L. Hirshfield and V. L. Geanetftein, "The electron cyclotron maser—an historical survey", IEEE Trans. MTT, Vol. MTT-25, No. 6, pp. 522-527, June 1977.
[13] J. Schneider, "Stimulated emission of radiation by relativistic electrons in a magnetic field", Phys. Rev. Lett., Vol. 2, pp. 504-505, 1959.
[14] A. V. Gaponov, "Addendum", Izv. VUZ., Radiofizika, Vol. 2, p. 836, 1959, and "Interaction between electron flux and electromagnetic waves in waveguides", Izv. VUZ., Radiofizika, Vol. 2, pp. 450-462, 1959.
[15] A. V. Gaponov, "Relativistic dispersion equations for waveguide system with helical and trochoidal electron beam", Izv. VUZ., Radiofizika, Vol. 4, No. 3, pp. 547-560, 1961.
[16] V. K. Yulpatov, "Nonlinear theory of the interaction between a periodic beam and an electromagnetic wave", Radiophys. and Quantum Electronics, Vol. 10, pp. 471-476, 1967.
[17] G. S. Nusinovich and H. Li, "Theory of gyro-travelling-wave tubes at cyclotron harmonics", Int. J. Electronics, Vol. 72, No. 5 and 6, pp. 895-907, 1992.
[18] I. B. Bott, "Tunable source of millimeter and submillimeter electromagnetic radiation", Proc IEEE, Vol. 52, pp. 330-331, Mar. 1964.
[19] I. B. Bott, "A powerful source of millimeter wavelength electromagnetic radiation", Phys. Rev. Lett., Vol. 14, pp. 293-294, Feb. 1965.
[20] W. Namkung and J. Y. Choe, "Experimental results of cusptron microwave tube study", IEEE Trans. NS-32, Oct. 1985.
[21] W. Namkung, J. Y. Choe, H. S. Uhm and V. Ayres, "Operation of cusptron oscillator for sixth harmonic frequency generation with six-vane circuit", Proceeding Particle Accelerator Conf., March 1987.
[22] S. P. Kuo, K. K. Tiong and P. E. Miller, "A comparative study for an eighth harmonic cusptron tube operating in the π-mode and 2π-mode", Phys. Fluids, Vol. 31, No. 6, pp. 1821-1823, June 1988.
[23] K. K. Tiong, S. P. Kuo and S. C. Kuo, "Optimization of the design of cusptron microwave oscillator", Int. J. Electronics, Vol. 65, No. 3, pp. 397-408, 1988.
[24] K. K. Tiong, S. P. Kuo and P. E. Miller, "Operational characteristics of a cusptron microwave oscillator", Int. J. Electronics, 1989.
[25] 陳明方，"多葉片直圓柱導波管特性行為的研究"，國立臺灣海洋大學電機工程研究所碩士論文，1994。
[26] Y. Y. Lau, "Simple macroscopic theory of cyclotron maser instabilities", IEEE Trans. Electron Devices, Vol. ED-29, No. 2, pp. 320-335, Feb. 1982.
[27] E. Ott and W. M. Manheimer, "Theory of microwave emission by velocity space instability of an intense relativistic electron beam", IEEE Trans. Plasma Science, Vol. PS-3, No. 1, pp. 1-5, March 1975.
[28] C. Chen and J. S. Wurtele, "Multi-mode interaction in cyclotron autoresonant maser amplifier", Phys. Rev. Lett., Vol. 65, No. 27, pp. 3389-3392, 1990.
[29] G. Schmidt, "Nonadiabatic particle motion in axial-symmetric fields", Phys. Fluids, Vol. 5, No. 8, pp. 994-1002, Aug. 1962.
[30] J. Sinnis and G. Schmidt, "Experiment trajectory analysis of charged particle in a cusped geometry", Phys. Fluids, Vol. 6, No. 6, pp. 841-845, June 1963.
[31] 陳立業，"電子束的不穩定分析及其模型在電離層的應用"，國立中央大學物理與天文研究所碩士論文，1991。
[32] 周澤亨，"多葉片導波管之模態分析"，國立臺灣海洋大學電機工程研究所碩士論文，1998。