35GHz三次谐波复合腔回旋管理论及模拟研究
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摘要
从线性理论和非线性理论的角度，对三次谐波复合腔回旋管的高频
场分布、注—波互作用、起振、模式竞争以及电子注偏心对注—波互作
用的影响进行了深入细致的研究。
首先用模式耦合理论研究了渐变复合腔中高频场纵向分布所满足
的普遍方程，并进行了数值求解。然后，从一般有源传输线方程出发，
推导出了渐变复合腔回旋管的自洽理论模型，该理论模型考虑了复合腔
过渡段中模式的耦合。在冷腔研究的基础之上，用自洽场理论模拟了三
次谐波35 GHz复合腔回旋管，工作模式为TE_(61)/TE_(62)。分析了多种尺寸
因素对复合腔回旋管性能的影响，优选出的腔体尺寸用于加工8mm三次
谐波回旋管并进行了热测实验；探索了多种工作参数对复合腔回旋管工
作性能的影响，为回旋管的热测试验提供了理论依据。
其次，在第三章中用动力学理论分析了三次谐波突变结构复合腔回
旋管中的注-波互作用，选取了工作点；建立了突变复合腔回旋管的自洽
非线性理论模型，该模型既考虑了电子和高频场的自洽相互作用又考虑
了复合腔过渡部分模式的耦合；基于该理论模型，编写了高次回旋谐波
注-波互作用计算程序，并利用该程序对三次谐波35GHz突变结构复合
腔回旋管进行了数值模拟，非线性计算的结果证实和补充了动力学理论
得出的结论，当电流20A，磁场为0.442T时，互作用效率为24％，输出
功率为210kW。本章还用用考虑了电子注偏心的ECRM动力学理论和考
虑了偏心的突变复合腔回旋管的自洽非线性理论分析了三次谐波复合腔
回旋管中的注-波互作用。计算表明偏心的存在会使单一模式的起振电流
增大，有可能使工作模式对H_(61)~(3)-H_(62)~(3)的起振电流大于寄生模式H_(14)~(3)的
起振电流，从而增大了激励起寄生模式的危险性，高次谐波模式的起振
电流随偏心值起伏变化的规律比基波回旋管的情形复杂。
在第四章，首先建立了描述回旋管中多模注-互作用过程的多模非线
性电子运动方程和耦合场方程，并在波导轴坐标系中将这一方程组拓展
为偏心形式。文中讨论了方程组的简化和求解，并对方程中多模平均的
物理意义、模式竞争和起振过程的研究方法进行了详细的讨论。然后，
本文研究了偏心造成的单一模式互作用效率下降，并用起振电流的计算
结果进行了解释。
电子科技大学博士论文
一
在电子科技大学高stw三次谐波复合腔回旋管的实际工作条件下，
采用冷腔场模型，计算了开放复合腔中工作模式和竞争模式的谐振频率。
品质因素和纵向场分布：研究了在不同互作用条件和不同初始场幅值下
的模式竞争清况：根据高gMt三次谐波复合腔回旋管实际工作条件下的
电压、电流和a的上升过程，进行了起振过程的模拟，得到了回旋管达
到的稳定工作状态。本文对通常采用的抑制模式竞争的方法进行了计算
和分析，证实了采用适当电压上升方式可有效的控制模式竟争，在此基
础上，研究了偏心条件下的模式竟争和起振过程，阐明了偏心对回旋管
互作用的影响，不仅仅表现在偏心引起的工作模式的效率下降，也不仅：
仅在于加剧回旋管中的模式竟争，而且还表赃偏心可能使使控制模式
竟争的有效方法失去作用。最后，对本文中有关方法和结果进行了讨论，
分析了在进一步互作用研究中采用时间相关、空间相关的完全自洽理论
研究模式竞争和偏心问题的必要性。
在第五章中，分别建立了渐变结构复合腔回旋管和突变结构复合腔
回旋管的多模式、多频率、时间相关的自洽非线新理论，编制了计算机
模拟程序，对一只三次iw 35GHz突变结构复合腔回旋管进行了数值模
拟计算中引入了一个最有可she振的竟争模式，计算结果表明，工作模
式对能建立稳定的工作状态，竞争模式最终保持在噪声水平，这在一次
验证了动力学理论分析的结果。
This paper was mainly concerned with the nonlinear analysis and simulation of mode competitions and staitup processed in third harmonic complex cavity gyrotron. The nonlinear results were compared with those from linear theory.
First, Starting from general transmission line equations with an electron beam source, a self-consistent nonlinear theoretical model for a complex cavity gyrotron with gradual transitions is presented in this paper. The model accounts for mode coupling in the transition region of the complex cavity. The interaction between the electron beam and H61-H62 RE field in the complex cavity for a third harmonic gyrotron is simulated; many calculations are carried out under different cavity dimensions and electron beam parameters.
A self-consistent nonlinear theoretical model for the complex cavity gyrotron with abrupt transition is presented in this paper. The model accounts for beam loading effects self-consistently as well as mode coupling in the transition step of the complex cavity gyrotron. A field matching technique is used to treat mode conversion at the cavity step. First based on the general theory of modal expansion techniques, we got the general equations for the modal field expansion coefficients then a large waveguide step is illuminated by two sets of traveling wave from both sides. Then we directly combined out the standing wave amplitudes and their derivatives. The interaction between the electron beam and TE61,TE62 RE field in the complex cavity for a third harmonic gyrotron is simulated; nrany calculations are carried out under different electron beam parameters
In the first place, the multimode nonlinear electron motion equations and the coupling field equations were established to depict the beam-wave circumstances. We discussed in detail the simplifying and evaluation of the
interaction equations, the physical meanings of process of multimode averaging and the methods to study the mode competition and startup process. The effect of monomode efficiency decline caused by eccentricity was studied, and averaging and the methods to study the mode competition and startup process, ~vith starting current of these modes computed from linear theory to explain it.
On the wrking condition of UESTC third harmonic complex cavity gyrotron , we caculated the longitudinal field profiles, resonant frequencies and Q values of the working mode and the parasitic one, using a cold cavity model.
Then, we studied the mode competition statues and found possible steady states m TE611FE62 and TE14 multimode. After that, we simulated the start-up process and reached the actual steady state in UESTC gyrotmn, taking into account the actual voltage, current and a rising processes.
In this paper, some mode competition controlling methods were analyzed, and the suggestion that mode selection could be realized by adopting appropriate voltage rising process was demonstrated. On the basis of the above, mode competition and startup process in eccenttic gyrotmns were studied, and the view that the eccentricity of electron beam would not only declining the interaction efficiency, not only even aggravate mode competition in gyrotrons, but also would possibly vitiate the mode competition controlling measures was clarified. The last part of the paper was devoted to the discussing of the
methods used and the results obtained in this paper, and the necessity of using fully consistent, spatially and chronologically, nonlinear theory in future work was pointed out.
场分布、注—波互作用、起振、模式竞争以及电子注偏心对注—波互作
用的影响进行了深入细致的研究。
首先用模式耦合理论研究了渐变复合腔中高频场纵向分布所满足
的普遍方程，并进行了数值求解。然后，从一般有源传输线方程出发，
推导出了渐变复合腔回旋管的自洽理论模型，该理论模型考虑了复合腔
过渡段中模式的耦合。在冷腔研究的基础之上，用自洽场理论模拟了三
次谐波35 GHz复合腔回旋管，工作模式为TE_(61)/TE_(62)。分析了多种尺寸
因素对复合腔回旋管性能的影响，优选出的腔体尺寸用于加工8mm三次
谐波回旋管并进行了热测实验；探索了多种工作参数对复合腔回旋管工
作性能的影响，为回旋管的热测试验提供了理论依据。
其次，在第三章中用动力学理论分析了三次谐波突变结构复合腔回
旋管中的注-波互作用，选取了工作点；建立了突变复合腔回旋管的自洽
非线性理论模型，该模型既考虑了电子和高频场的自洽相互作用又考虑
了复合腔过渡部分模式的耦合；基于该理论模型，编写了高次回旋谐波
注-波互作用计算程序，并利用该程序对三次谐波35GHz突变结构复合
腔回旋管进行了数值模拟，非线性计算的结果证实和补充了动力学理论
得出的结论，当电流20A，磁场为0.442T时，互作用效率为24％，输出
功率为210kW。本章还用用考虑了电子注偏心的ECRM动力学理论和考
虑了偏心的突变复合腔回旋管的自洽非线性理论分析了三次谐波复合腔
回旋管中的注-波互作用。计算表明偏心的存在会使单一模式的起振电流
增大，有可能使工作模式对H_(61)~(3)-H_(62)~(3)的起振电流大于寄生模式H_(14)~(3)的
起振电流，从而增大了激励起寄生模式的危险性，高次谐波模式的起振
电流随偏心值起伏变化的规律比基波回旋管的情形复杂。
在第四章，首先建立了描述回旋管中多模注-互作用过程的多模非线
性电子运动方程和耦合场方程，并在波导轴坐标系中将这一方程组拓展
为偏心形式。文中讨论了方程组的简化和求解，并对方程中多模平均的
物理意义、模式竞争和起振过程的研究方法进行了详细的讨论。然后，
本文研究了偏心造成的单一模式互作用效率下降，并用起振电流的计算
结果进行了解释。
电子科技大学博士论文
一
在电子科技大学高stw三次谐波复合腔回旋管的实际工作条件下，
采用冷腔场模型，计算了开放复合腔中工作模式和竞争模式的谐振频率。
品质因素和纵向场分布：研究了在不同互作用条件和不同初始场幅值下
的模式竞争清况：根据高gMt三次谐波复合腔回旋管实际工作条件下的
电压、电流和a的上升过程，进行了起振过程的模拟，得到了回旋管达
到的稳定工作状态。本文对通常采用的抑制模式竞争的方法进行了计算
和分析，证实了采用适当电压上升方式可有效的控制模式竟争，在此基
础上，研究了偏心条件下的模式竟争和起振过程，阐明了偏心对回旋管
互作用的影响，不仅仅表现在偏心引起的工作模式的效率下降，也不仅：
仅在于加剧回旋管中的模式竟争，而且还表赃偏心可能使使控制模式
竟争的有效方法失去作用。最后，对本文中有关方法和结果进行了讨论，
分析了在进一步互作用研究中采用时间相关、空间相关的完全自洽理论
研究模式竞争和偏心问题的必要性。
在第五章中，分别建立了渐变结构复合腔回旋管和突变结构复合腔
回旋管的多模式、多频率、时间相关的自洽非线新理论，编制了计算机
模拟程序，对一只三次iw 35GHz突变结构复合腔回旋管进行了数值模
拟计算中引入了一个最有可she振的竟争模式，计算结果表明，工作模
式对能建立稳定的工作状态，竞争模式最终保持在噪声水平，这在一次
验证了动力学理论分析的结果。
This paper was mainly concerned with the nonlinear analysis and simulation of mode competitions and staitup processed in third harmonic complex cavity gyrotron. The nonlinear results were compared with those from linear theory.
First, Starting from general transmission line equations with an electron beam source, a self-consistent nonlinear theoretical model for a complex cavity gyrotron with gradual transitions is presented in this paper. The model accounts for mode coupling in the transition region of the complex cavity. The interaction between the electron beam and H61-H62 RE field in the complex cavity for a third harmonic gyrotron is simulated; many calculations are carried out under different cavity dimensions and electron beam parameters.
A self-consistent nonlinear theoretical model for the complex cavity gyrotron with abrupt transition is presented in this paper. The model accounts for beam loading effects self-consistently as well as mode coupling in the transition step of the complex cavity gyrotron. A field matching technique is used to treat mode conversion at the cavity step. First based on the general theory of modal expansion techniques, we got the general equations for the modal field expansion coefficients then a large waveguide step is illuminated by two sets of traveling wave from both sides. Then we directly combined out the standing wave amplitudes and their derivatives. The interaction between the electron beam and TE61,TE62 RE field in the complex cavity for a third harmonic gyrotron is simulated; nrany calculations are carried out under different electron beam parameters
In the first place, the multimode nonlinear electron motion equations and the coupling field equations were established to depict the beam-wave circumstances. We discussed in detail the simplifying and evaluation of the
interaction equations, the physical meanings of process of multimode averaging and the methods to study the mode competition and startup process. The effect of monomode efficiency decline caused by eccentricity was studied, and averaging and the methods to study the mode competition and startup process, ~vith starting current of these modes computed from linear theory to explain it.
On the wrking condition of UESTC third harmonic complex cavity gyrotron , we caculated the longitudinal field profiles, resonant frequencies and Q values of the working mode and the parasitic one, using a cold cavity model.
Then, we studied the mode competition statues and found possible steady states m TE611FE62 and TE14 multimode. After that, we simulated the start-up process and reached the actual steady state in UESTC gyrotmn, taking into account the actual voltage, current and a rising processes.
In this paper, some mode competition controlling methods were analyzed, and the suggestion that mode selection could be realized by adopting appropriate voltage rising process was demonstrated. On the basis of the above, mode competition and startup process in eccenttic gyrotmns were studied, and the view that the eccentricity of electron beam would not only declining the interaction efficiency, not only even aggravate mode competition in gyrotrons, but also would possibly vitiate the mode competition controlling measures was clarified. The last part of the paper was devoted to the discussing of the
methods used and the results obtained in this paper, and the necessity of using fully consistent, spatially and chronologically, nonlinear theory in future work was pointed out.
引文
[1]G. Saraph, T. M. Antonsen, Jr., B. Levush, and G. I. Lin, "Regions of stability of high power gyrotron oscillators," IEEE Trans. Plasma Sci., vol.20, pp. 115-125, 1994.
[2]S.Y. Cai, T. M. Antonsen, Jr., G. Saraph, and b. Levush, "Mulifrequency theory of high power gyrotron oscillators," Int. J. Electron., vol. 72, pp.759-777, 1992.
[3]T.M. Antonsen, Jr., W. M. Manheimer, and B. Levush, "Effect of ac and dc transverse self-fields in gyrotrons," Int. J. Electron., vol. 61, pp.823-854, 1984.
[4]R. G. Kleva, T. M. Antonsen, Jr., and B. Levush," The effect of the time-dependent self-consistent electostafic field on gyrotron operation,"Phys. Fluids, vol. 31, pp. 375-386, 1988.
[5]P. Latham, "Ac space-charge effects in gyro-klystron amplifiers," IEEE Trans. Plasma Sci., vol. 18, pp. 273-285, 1990.
[6]A. P. Keyer, L. A. Aksenova, M. V. Agapova, V. E. Myasnikov, V. S.Musatov, L. G. Popov, E. V. Sokolov, and E. V. Zasypkin, "Theoretical and experimental investigation of ac space-charge effect on gain and bandwidth of two and three cavity gyro-klystrons with TE_(011)operating mode," in SPIE Proc. Intense Microwave Pulses Ⅲ, H. E. Brandt Ed., 1995, vol. 2557, pp. 393-402.
[7]G. S. Nusinovich, "Mode interaction in gyrotrons," Int J. Electron., vol. 51, pp. 457-474, 1981.
[8]G. S. Nusinovich and V. Ye. Zapevalov, "Serf-modulation instability of gyrotron radiation," Radio. Electron, vol. 3, pp. 563-570, 1985.
[9]I. G. Zamitsyna and G. S. Nusinovich, "Stability of single-mode self excited oscillations in a gyromonotron" Radiophys. Quantum Electron.,vol.17, pp. 1418-1424, 1974.
[10]D. Dialetis and K. Chu "Mode competition and stability analysis of gyrotron oscillator," in Infrared and Millimeter Waves, Vol. &, K J.Button, Ed. New York: Academic, 1983, ch. 10, pp. 537-581.
[11]D. R. Whaley, M. Q. Tran S. Alberti, T. M. Tran, T. M. Antonsen Jr., and C. Tran, "Startup methods for single-mode gyrotron operation," Phys. Rev.Lett., vol. 75, p. 1304, 1995.
[12]D. R. Whaley, M. Q. Tran, T M. Tran, and T M. Antonsen Jr., "Mode competition and start-up in cylindrical cavity gryotrons using high-order operating modes," IEEE Trans. Plasma Sci., vol. 22, p. 850, 1994.
[13]V. Bratman, M. Moseev, M. Petelin, and R Erm, "Theory of gyrotrons with a nonfixed structure of the high-frequency field," Radiophys.Quantum Electron., vol. 16, pp. 474-480, 1973.
[14]W. Fliflet, M. E. Read, K. R. Chu and R.Seely, "A self_consistent field theory for gyrotron oscillators: application to a low Q gyromonotron," Int J. Electronics, Vol. 52, No. 6, pp. 505-521 1982.
[15]A. K. Cranguly and S. Ahn, "Self-consistent large signal theory of the gyrotron traveling wave amplifier," Int. J. Electron., vol. 53, pp. 641-658,1982.
[16]S. Ginzburg, g. S. Nusinovich, and N. A. Zavolsky, "Theory of nonstationary processed in gyrotrons with low Q resonator," Int. J.Electron., vol. 61, pp. 881-894, 1986.
[17]K. e. Kreischer, T. L. Grimm, W. C. Guss, A. W. Mobius, And R Temkin, "Experimental study of high frequency megawatt gyrotron oscillator,"Phys. Fluids, vol. B2, p. 640, 1990.
[18]W. C. Guss, M. A. Basten, K. E. Kreischer, R Temkin, T. Antonsen, Jr., S.Y. Cai, G. Saraph, and B. Levush, "Sideband mode competition in a gyrotron oscillator," Phys, Rev. Lett., vol. 69, pp. 3727-3730, 1992.
[19]A. Bondeson, W. M. Manheimer, and E. ott, "Multimode analysis of quasi-optical gyrotrons and gyroklystrons," in Infrared Millim. Waves, K.J. Button, Ed. New York: Academic, 1983, vol. 9, pp. 309-340.
[20]P. E. Latham, W. Lawson, and V. Irwin, "The design of a 100 MW, Ku band second harmonic gyro-klystron experiment," IEEE Trans. Plasma Sci., vol. 22. pp. 804-817, 1994.
[21]J. M. Neilson, P. E. Latham, M. Caplan, and W. Lawson, "Determination of the resonant frequencies in a complex cavity using the scattering matrix formulation," IEEE Trans. Microwave Theory Tech., vol. 37, pp.1165-1170, 1989.
[22]M. Blank, B. G. Danly, P. E. Latham, and B. Levush, "Experimental study of a high power w-band gyro-klystron amplifier," presented at the 22~(nd) Int. Conf. Infrared and Millimeter Waves, Wintergreen, VA, July20-25.
[23]M. Botton, T. M. Antonsen, Jr., and B. Levush, "MAGY: Time dependent, multifrequency , self-consistent code for modeling electron beam devices," in Computational Accelerator Physics, AIP Conf. Proc., J. J.Bisognano and A. Mondelli, Eds., 1997, vol. 391, pp. 59-64.
[24]S. H. Gold and A. w. Fliflet, Int. J. Electronics, Vol. 72, No. 5, p. 779,1992.
[2]S.Y. Cai, T. M. Antonsen, Jr., G. Saraph, and b. Levush, "Mulifrequency theory of high power gyrotron oscillators," Int. J. Electron., vol. 72, pp.759-777, 1992.
[3]T.M. Antonsen, Jr., W. M. Manheimer, and B. Levush, "Effect of ac and dc transverse self-fields in gyrotrons," Int. J. Electron., vol. 61, pp.823-854, 1984.
[4]R. G. Kleva, T. M. Antonsen, Jr., and B. Levush," The effect of the time-dependent self-consistent electostafic field on gyrotron operation,"Phys. Fluids, vol. 31, pp. 375-386, 1988.
[5]P. Latham, "Ac space-charge effects in gyro-klystron amplifiers," IEEE Trans. Plasma Sci., vol. 18, pp. 273-285, 1990.
[6]A. P. Keyer, L. A. Aksenova, M. V. Agapova, V. E. Myasnikov, V. S.Musatov, L. G. Popov, E. V. Sokolov, and E. V. Zasypkin, "Theoretical and experimental investigation of ac space-charge effect on gain and bandwidth of two and three cavity gyro-klystrons with TE_(011)operating mode," in SPIE Proc. Intense Microwave Pulses Ⅲ, H. E. Brandt Ed., 1995, vol. 2557, pp. 393-402.
[7]G. S. Nusinovich, "Mode interaction in gyrotrons," Int J. Electron., vol. 51, pp. 457-474, 1981.
[8]G. S. Nusinovich and V. Ye. Zapevalov, "Serf-modulation instability of gyrotron radiation," Radio. Electron, vol. 3, pp. 563-570, 1985.
[9]I. G. Zamitsyna and G. S. Nusinovich, "Stability of single-mode self excited oscillations in a gyromonotron" Radiophys. Quantum Electron.,vol.17, pp. 1418-1424, 1974.
[10]D. Dialetis and K. Chu "Mode competition and stability analysis of gyrotron oscillator," in Infrared and Millimeter Waves, Vol. &, K J.Button, Ed. New York: Academic, 1983, ch. 10, pp. 537-581.
[11]D. R. Whaley, M. Q. Tran S. Alberti, T. M. Tran, T. M. Antonsen Jr., and C. Tran, "Startup methods for single-mode gyrotron operation," Phys. Rev.Lett., vol. 75, p. 1304, 1995.
[12]D. R. Whaley, M. Q. Tran, T M. Tran, and T M. Antonsen Jr., "Mode competition and start-up in cylindrical cavity gryotrons using high-order operating modes," IEEE Trans. Plasma Sci., vol. 22, p. 850, 1994.
[13]V. Bratman, M. Moseev, M. Petelin, and R Erm, "Theory of gyrotrons with a nonfixed structure of the high-frequency field," Radiophys.Quantum Electron., vol. 16, pp. 474-480, 1973.
[14]W. Fliflet, M. E. Read, K. R. Chu and R.Seely, "A self_consistent field theory for gyrotron oscillators: application to a low Q gyromonotron," Int J. Electronics, Vol. 52, No. 6, pp. 505-521 1982.
[15]A. K. Cranguly and S. Ahn, "Self-consistent large signal theory of the gyrotron traveling wave amplifier," Int. J. Electron., vol. 53, pp. 641-658,1982.
[16]S. Ginzburg, g. S. Nusinovich, and N. A. Zavolsky, "Theory of nonstationary processed in gyrotrons with low Q resonator," Int. J.Electron., vol. 61, pp. 881-894, 1986.
[17]K. e. Kreischer, T. L. Grimm, W. C. Guss, A. W. Mobius, And R Temkin, "Experimental study of high frequency megawatt gyrotron oscillator,"Phys. Fluids, vol. B2, p. 640, 1990.
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