环板行波管注波互作用及热力学特性研究
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摘要
行波管是雷达、通信、电子对抗、遥控遥测和精密制导等设备的“心脏”，在当代国防装备和国民经济各部门发挥着举足轻重的作用，而慢波系统作为行波管进行注-波互作用激励微波能量的主要部件，是行波管的核心，其性能优劣直接决定着行波管的技术水平。本学位论文采用理论分析和计算机数值模拟相结合的方法就环板这种全金属慢波结构进行了一系列的深入研究，得到了许多有价值的结论，为大功率行波管的研制提供了理论支持和技术保障。
主要工作和创新成果如下：
一、对环板行波管的导波特性进行了详细的数值模拟分析。采用场匹配和变分相结合的方法，推导出了环板行波管中的对称模的色散方程，并对选用不同个数的基函数数值求解该方程的结果精度进行了比较，结果证明只要选用较少几项的基函数就可以得到比较满意的精度。然后在此基础上就慢波结构的结构尺寸进行数值模拟，得到结构的几何尺寸与导波特性之间的关系，结果表明：环板是一种尺寸大，功率容量大的慢波结构，我们可以通过改变其结构参数，以改善导波特性，使环板行波管有一个相对宽的带宽。
二、对环板行波管注-波互作用的线性理论进行了研究。首先考虑了电子注的厚度，分区求出各区对称模式慢电磁波的场方程，然后利用严格的场匹配方法和变分法在环板间隙进行场匹配，得到了考虑空间电荷效应的“热”色散方程。然后再针对电子注电压很高的实际情况，考虑电子注的相对论效应，数值求解“热”色散方程，得到环板慢波系统几何尺寸和电子注参量与小信号增益的关系。研究表明：对应最大增益，有一饱和注电压存在；小信号增益随电子注电流增加而增加；电子注半径对小信号增益影响强烈，随电子注外半径的增大，小信号增益也增大；环板行波管具有高增益、窄频带的特点，适合用作大功率毫米波行波管；合理的选择电子注参量和慢波系统的几何尺寸，可以使环板行波管既获得大的功率输出，又获得相对较宽的带宽。
三、对环板行波管的互作用区进行了热分析。首先由热传导方程导出了求
解热传导率随温度改变的部件的温升方程。然后为了求解该方程，详细分析了．
各部件的几何因子，在此基础上，给定单位轴向长度的耗散功率和几何参量，
对各部件的温升和环上的最高点温度进行了详细的数值模拟，分析了热的和几
何的参量对环板行波管的热状态的影响。最后由分析结果得到这样的结论，为
了尽可能提高环板行波管的功率水平，进行互作用系统的设计时，在保证工作
带宽的同时，我们还应遵循如下的原则：在保证电子注聚焦的前提下，应尽量
减小极靴的厚度，增大极靴的纵向宽度；在保证色散较弱的前提下，要兼顾板
的径向长度及其厚度，尽量使板的径向长度短一点，厚度大一点；环的尺寸对
功率容量和色散都有重要影响，在进行环的结构设计时，要同时考虑这两方面
的因素，减小环半径，增加环厚和纵向宽度，以提高功率容量。该结论可以推
广到环板慢波系统的变态结构。
Travelling wave tubes (TWT) are the heart parts of radar systems, communication systems, electronic counter-measures, remote-control &test devices, accurate guidance equipment, etc., and play important roles in the modern nation defensive equipment and economic areas. Moreover, as the key component of the beam-wave interaction of a travelling wave tube for exiting microwave energy, the slow-wave structure (SWS) basically determines the performance of the TWT. In this dissertation, a series of detailed studies have been made by theoretical method combining with numerical analysis, and a great deal of valuable conclusions have been obtained. All the works in this dissertation provide theoretical basis and technical ensurance for designing the high power TWTs.
Our main and creative works are as following:
1. A detailed numerical calculation for the propagating wave's dispersion characteristics has been made. The dispersion equation of the symmetrical mode propagating in the high power ring-plane slow wave circuit is developed, by means of the special variational method, combining with the field matching method. The numerical results of the dispersion equation are also compared with the experimental values when the different number of basic functions is chosen. Finally, the numerical results are given in terms of dispersion relation curve and the influence of several geometrical dimensions on the dispersion characteristics is discussed. It shows that the ring-plane TWT, which is of large diameter, and allows for high average power capability, can improve the propagating wave's characteristics and gain a relative broad bandwidth by means of modifying the geometrical dimensions of the circuits.
2. Linear theory of the beam-wave interaction in the ring-plane TWT has been studied. Firstly, in considering the thickness and the relativistic effect of the hollow electron beam, the hot dispersion relation including the electron beam space charge
in
effect for the ring-plane traveling wave tube is obtained in this paper, by making use of the variational method and combining with the field matching method. Secondly, the numerical results are given in terms of the small signal gain curve. Finally, the influence of the radius of the electron beam, current of the electron beam, the acceleration voltage and the geometrical dimension of the slow-wave structure on the small signal gain are discussed. Studies present that: there exists an optimum beam voltage for the maximum gain; the gain increases with the beam current; the beam radius effects the gain intensively; the ring-plane TWT is appropriate to work in the millimeter wave band for it's character of high gain and narrow band, and can gain both high power output and relative broad bandwidth by choosing appropriate beam parameters and geometry dimensions.
3. The thermal behavior of the ring-plane TWT in the interaction area is analyzed by means of the thermodynamic method. The geometric factor is defined by solving the heat conductive equation, which describes the temperature characteristics in the case of the constant heat transferring coefficient. Starting from the definition of the geometric factor, the actual temperature rising of all the assembly of the TWT is calculated, under the case of that the heat conducting coefficient varies with the temperature. Making use of the numerical results, the maximum temperature is also given in diagrams. The influences of the thermal and geometrical parameters on the heat behavior are discussed. By the discussion we can get the designing principles as following: the thickness of the pole pieces should been decreased and the axial width should been increased as possible as on the condition of ensuring the focus of beam; the radial length and thickness of plane should been considered carefully, and make radial length more shorter, thickness more bigger but not cause strong dispersion; the dimension of the ring have dramatically affect on both the power capability and the dispersion, so the
主要工作和创新成果如下：
一、对环板行波管的导波特性进行了详细的数值模拟分析。采用场匹配和变分相结合的方法，推导出了环板行波管中的对称模的色散方程，并对选用不同个数的基函数数值求解该方程的结果精度进行了比较，结果证明只要选用较少几项的基函数就可以得到比较满意的精度。然后在此基础上就慢波结构的结构尺寸进行数值模拟，得到结构的几何尺寸与导波特性之间的关系，结果表明：环板是一种尺寸大，功率容量大的慢波结构，我们可以通过改变其结构参数，以改善导波特性，使环板行波管有一个相对宽的带宽。
二、对环板行波管注-波互作用的线性理论进行了研究。首先考虑了电子注的厚度，分区求出各区对称模式慢电磁波的场方程，然后利用严格的场匹配方法和变分法在环板间隙进行场匹配，得到了考虑空间电荷效应的“热”色散方程。然后再针对电子注电压很高的实际情况，考虑电子注的相对论效应，数值求解“热”色散方程，得到环板慢波系统几何尺寸和电子注参量与小信号增益的关系。研究表明：对应最大增益，有一饱和注电压存在；小信号增益随电子注电流增加而增加；电子注半径对小信号增益影响强烈，随电子注外半径的增大，小信号增益也增大；环板行波管具有高增益、窄频带的特点，适合用作大功率毫米波行波管；合理的选择电子注参量和慢波系统的几何尺寸，可以使环板行波管既获得大的功率输出，又获得相对较宽的带宽。
三、对环板行波管的互作用区进行了热分析。首先由热传导方程导出了求
解热传导率随温度改变的部件的温升方程。然后为了求解该方程，详细分析了．
各部件的几何因子，在此基础上，给定单位轴向长度的耗散功率和几何参量，
对各部件的温升和环上的最高点温度进行了详细的数值模拟，分析了热的和几
何的参量对环板行波管的热状态的影响。最后由分析结果得到这样的结论，为
了尽可能提高环板行波管的功率水平，进行互作用系统的设计时，在保证工作
带宽的同时，我们还应遵循如下的原则：在保证电子注聚焦的前提下，应尽量
减小极靴的厚度，增大极靴的纵向宽度；在保证色散较弱的前提下，要兼顾板
的径向长度及其厚度，尽量使板的径向长度短一点，厚度大一点；环的尺寸对
功率容量和色散都有重要影响，在进行环的结构设计时，要同时考虑这两方面
的因素，减小环半径，增加环厚和纵向宽度，以提高功率容量。该结论可以推
广到环板慢波系统的变态结构。
Travelling wave tubes (TWT) are the heart parts of radar systems, communication systems, electronic counter-measures, remote-control &test devices, accurate guidance equipment, etc., and play important roles in the modern nation defensive equipment and economic areas. Moreover, as the key component of the beam-wave interaction of a travelling wave tube for exiting microwave energy, the slow-wave structure (SWS) basically determines the performance of the TWT. In this dissertation, a series of detailed studies have been made by theoretical method combining with numerical analysis, and a great deal of valuable conclusions have been obtained. All the works in this dissertation provide theoretical basis and technical ensurance for designing the high power TWTs.
Our main and creative works are as following:
1. A detailed numerical calculation for the propagating wave's dispersion characteristics has been made. The dispersion equation of the symmetrical mode propagating in the high power ring-plane slow wave circuit is developed, by means of the special variational method, combining with the field matching method. The numerical results of the dispersion equation are also compared with the experimental values when the different number of basic functions is chosen. Finally, the numerical results are given in terms of dispersion relation curve and the influence of several geometrical dimensions on the dispersion characteristics is discussed. It shows that the ring-plane TWT, which is of large diameter, and allows for high average power capability, can improve the propagating wave's characteristics and gain a relative broad bandwidth by means of modifying the geometrical dimensions of the circuits.
2. Linear theory of the beam-wave interaction in the ring-plane TWT has been studied. Firstly, in considering the thickness and the relativistic effect of the hollow electron beam, the hot dispersion relation including the electron beam space charge
in
effect for the ring-plane traveling wave tube is obtained in this paper, by making use of the variational method and combining with the field matching method. Secondly, the numerical results are given in terms of the small signal gain curve. Finally, the influence of the radius of the electron beam, current of the electron beam, the acceleration voltage and the geometrical dimension of the slow-wave structure on the small signal gain are discussed. Studies present that: there exists an optimum beam voltage for the maximum gain; the gain increases with the beam current; the beam radius effects the gain intensively; the ring-plane TWT is appropriate to work in the millimeter wave band for it's character of high gain and narrow band, and can gain both high power output and relative broad bandwidth by choosing appropriate beam parameters and geometry dimensions.
3. The thermal behavior of the ring-plane TWT in the interaction area is analyzed by means of the thermodynamic method. The geometric factor is defined by solving the heat conductive equation, which describes the temperature characteristics in the case of the constant heat transferring coefficient. Starting from the definition of the geometric factor, the actual temperature rising of all the assembly of the TWT is calculated, under the case of that the heat conducting coefficient varies with the temperature. Making use of the numerical results, the maximum temperature is also given in diagrams. The influences of the thermal and geometrical parameters on the heat behavior are discussed. By the discussion we can get the designing principles as following: the thickness of the pole pieces should been decreased and the axial width should been increased as possible as on the condition of ensuring the focus of beam; the radial length and thickness of plane should been considered carefully, and make radial length more shorter, thickness more bigger but not cause strong dispersion; the dimension of the ring have dramatically affect on both the power capability and the dispersion, so the
引文
1. R. Kompfner, The Traveling Wave Value, Wireless World, 1946, Vol. 53, No. 11, P369-372.
2. R. Kompfner, The Traveling Wave Tubes as an Amplifier at Microwaves, Proc. IRE, 1947, Vol. 35, No. 2, P124-127.
3. R. Kompfner, The Traveling Wave Tube, Wireless Engineer World, 1947, Vol. 53, No. 9, P255-266.
4. R. Kompfner, The Invention of the Traveling Wave Tube, from a lecture series at University of California at Berkeley, published by Sanfrancisco Press, 1963.
5. J.R. Pierce, L.M.Field, Traveling Wave Tubes, Proc. IRE, 1947, Vol. 35, No. 2, P108-111.
6. J.R. Pierce, U.S. Patent 2,602,148, field October 22,1946, issued July 1,1952.
7. L.M. Field, U.S. Patent 2,575,383, field October 22,1946, issued July 1, 1952.
8. D.C. Roger, Proc. IEE 9．廖复疆，大功率微波管——21世纪军事电子装备的关键器件，中国电子学会真空电子学分会第十届年会论文集(上册)，P1-7．
10. J.R. Pierce, Travelling Wave Tubes, Princeton, N.J.:Van Norstrand, 1950.
11．刘盛纲，李宏福，王文祥，莫元龙，微波电子学导论，北京：国防工业出版社，1985，第十二章。
12. J.E. Rowe, Nonlinear Electron-Wave Interaction Phenomena, New York: Academic Press, 1965.
13．刘盛纲，李宏福，王文祥，莫元龙，微波电子学导论，北京：国防工业出版社，1985，第十八章。
14．廖复疆，真空电子技术——信息装备的心脏，北京：国防工业出版社，1999，P52-53．
15．J.R.Pierce，行波管，吴鸿适译，北京，科学出版社，1961。
16. J.F. Gittins, Power Travelling-wave Tube, London, English Univ. Press, 1965.
17．陆钟祚，行波管，上海，上海科技出版社，1962。
18. A.E. Acker, Interest in mm Waves Spurs Tube Growth, Microwaves,, July, 1982, 21, P55-74.
19. D. Deml, Mikrowellenrohren: Derzeitigen stand and Trend, NTZ-Fachberichte'85:Elektrinentonhren, Berlin, VDE-VERLAG GmbH, 1983, P61-67.
20． H. Hashimoto, T. Ide, T. Konishi, etc. , A 30Ghz 40 watt helix TWT, IEDM 83, 1983, P133-136．
21． A. Jacquez, 44Ghz helix TWTs for Satellite Communication Systems, IEDM 84, 1984, P506-508．
22． E. Glass, Mikrowellen Magazin, March, 1981, P273．
23． C. W. Linn, Microwave Journal, 25, July,1982, P16．
24． 王文祥，余国芬，宫玉彬，行波管慢波系统的新进展--全金属慢波结构，真空电子 技术，1995，第五期，P30-37
25． C.K. Birdsall, T. E. Everhart, Modified Contra-wound Helix Circuits of High-power TWTs, IRE Trans. On ED, Oct. 1956, P190-204．
26． R. M. White, C. E. Enderby and C. K. Birdsall, Properties of ring-plane slow wave circuits, IEEE Trans on Electron Devices, June, 1964, Vol. ED-11, P247-261．
27． C. E. Enderby, Ring-plane travelling-wave amplifier: 40KW at 9mm, IEEE trans, on Electron Devices, June, 1964, Vol. ED-11, P262-266．
28． Y. Gong, W. Weng, Y. Wei, S. Liu, Theoritical analysis of ridge-loaded ring-plane slow wave structure by variational methods, IEE Proc.-Microw. Antennas Propag. , Oct,1998, Vol.145, No. 5, P397-405．
29． Yubin Gong, Wengxiang Wang, Shengang Liu, Small signal theory of a ridge-loaded travelling wave tube, Int. J. of Electronics, 1998, Vol.85, P681-696．
30． Jack A. Lucken, Some Aspects of Circuit Power Dissipation in High Power CW Helix Traveling Wave Tubes, Part I: General Theory, IEEE Trans. On ED, 1969, Vol. 16, No. 9, P813-820．
31． Jack A. Lucken, Some Aspects of Circuit Power Dissipation in High Power CW Helix Traveling Wave Tubes, Part II: Scaling Laws, IEEE Trans. On ED, 1969, Vol.16, No. 9, P821-826．
32． Alexander S.Gilmour, Martin R. Gillette, and JENN-TSUNG Chen, Theoretical and Experimental TWT Helix Losses Determination, IEEE Trans. On ED, 1979, Vol. 26, No. 10, P1581-1588．
33． Roberto Crivello, Richard W. Grow, Thermal Analysis of PPM-focused Rod-supported TWT Helix Structures, IEEETrans. On ED, 1988, Vol. 35, No. 10, P1701-1720．
34． 王基奎，螺旋线慢波系统的散热能力分析，电子学报，1982年第6期，P25-51．
35． 开敞型慢波线热传导的一维分析，电子学通讯，1981年第3期，P160-166．
36． Crepeau P J, McIssac P R, Consequenences of symmetry in periodic structures, PIEEE, Jan, 1964:33-43．
37． Chodorow M, Chu E L, Cross wound twin helices for TWTs, JAP, 26,1955:33
38． F. B. Hildebrand, Methods of applied mathematics, 2nd ed. , Englewood cliffs, New Jersey: Prentice-Hall, 1965
39． R.F.Harrington, Field computation by moment method, New York: Macmillan, 1968
40． H. P. Freund, M. A. Kodis, N. R.Vanderplaats, Self-consistent field theory of a helix travelling wave tube amplifier, IEEE Trans on ED, 1992,Vol.20, No. 5, P543-553．
2. R. Kompfner, The Traveling Wave Tubes as an Amplifier at Microwaves, Proc. IRE, 1947, Vol. 35, No. 2, P124-127.
3. R. Kompfner, The Traveling Wave Tube, Wireless Engineer World, 1947, Vol. 53, No. 9, P255-266.
4. R. Kompfner, The Invention of the Traveling Wave Tube, from a lecture series at University of California at Berkeley, published by Sanfrancisco Press, 1963.
5. J.R. Pierce, L.M.Field, Traveling Wave Tubes, Proc. IRE, 1947, Vol. 35, No. 2, P108-111.
6. J.R. Pierce, U.S. Patent 2,602,148, field October 22,1946, issued July 1,1952.
7. L.M. Field, U.S. Patent 2,575,383, field October 22,1946, issued July 1, 1952.
8. D.C. Roger, Proc. IEE
10. J.R. Pierce, Travelling Wave Tubes, Princeton, N.J.:Van Norstrand, 1950.
11．刘盛纲，李宏福，王文祥，莫元龙，微波电子学导论，北京：国防工业出版社，1985，第十二章。
12. J.E. Rowe, Nonlinear Electron-Wave Interaction Phenomena, New York: Academic Press, 1965.
13．刘盛纲，李宏福，王文祥，莫元龙，微波电子学导论，北京：国防工业出版社，1985，第十八章。
14．廖复疆，真空电子技术——信息装备的心脏，北京：国防工业出版社，1999，P52-53．
15．J.R.Pierce，行波管，吴鸿适译，北京，科学出版社，1961。
16. J.F. Gittins, Power Travelling-wave Tube, London, English Univ. Press, 1965.
17．陆钟祚，行波管，上海，上海科技出版社，1962。
18. A.E. Acker, Interest in mm Waves Spurs Tube Growth, Microwaves,, July, 1982, 21, P55-74.
19. D. Deml, Mikrowellenrohren: Derzeitigen stand and Trend, NTZ-Fachberichte'85:Elektrinentonhren, Berlin, VDE-VERLAG GmbH, 1983, P61-67.
20． H. Hashimoto, T. Ide, T. Konishi, etc. , A 30Ghz 40 watt helix TWT, IEDM 83, 1983, P133-136．
21． A. Jacquez, 44Ghz helix TWTs for Satellite Communication Systems, IEDM 84, 1984, P506-508．
22． E. Glass, Mikrowellen Magazin, March, 1981, P273．
23． C. W. Linn, Microwave Journal, 25, July,1982, P16．
24． 王文祥，余国芬，宫玉彬，行波管慢波系统的新进展--全金属慢波结构，真空电子 技术，1995，第五期，P30-37
25． C.K. Birdsall, T. E. Everhart, Modified Contra-wound Helix Circuits of High-power TWTs, IRE Trans. On ED, Oct. 1956, P190-204．
26． R. M. White, C. E. Enderby and C. K. Birdsall, Properties of ring-plane slow wave circuits, IEEE Trans on Electron Devices, June, 1964, Vol. ED-11, P247-261．
27． C. E. Enderby, Ring-plane travelling-wave amplifier: 40KW at 9mm, IEEE trans, on Electron Devices, June, 1964, Vol. ED-11, P262-266．
28． Y. Gong, W. Weng, Y. Wei, S. Liu, Theoritical analysis of ridge-loaded ring-plane slow wave structure by variational methods, IEE Proc.-Microw. Antennas Propag. , Oct,1998, Vol.145, No. 5, P397-405．
29． Yubin Gong, Wengxiang Wang, Shengang Liu, Small signal theory of a ridge-loaded travelling wave tube, Int. J. of Electronics, 1998, Vol.85, P681-696．
30． Jack A. Lucken, Some Aspects of Circuit Power Dissipation in High Power CW Helix Traveling Wave Tubes, Part I: General Theory, IEEE Trans. On ED, 1969, Vol. 16, No. 9, P813-820．
31． Jack A. Lucken, Some Aspects of Circuit Power Dissipation in High Power CW Helix Traveling Wave Tubes, Part II: Scaling Laws, IEEE Trans. On ED, 1969, Vol.16, No. 9, P821-826．
32． Alexander S.Gilmour, Martin R. Gillette, and JENN-TSUNG Chen, Theoretical and Experimental TWT Helix Losses Determination, IEEE Trans. On ED, 1979, Vol. 26, No. 10, P1581-1588．
33． Roberto Crivello, Richard W. Grow, Thermal Analysis of PPM-focused Rod-supported TWT Helix Structures, IEEETrans. On ED, 1988, Vol. 35, No. 10, P1701-1720．
34． 王基奎，螺旋线慢波系统的散热能力分析，电子学报，1982年第6期，P25-51．
35． 开敞型慢波线热传导的一维分析，电子学通讯，1981年第3期，P160-166．
36． Crepeau P J, McIssac P R, Consequenences of symmetry in periodic structures, PIEEE, Jan, 1964:33-43．
37． Chodorow M, Chu E L, Cross wound twin helices for TWTs, JAP, 26,1955:33
38． F. B. Hildebrand, Methods of applied mathematics, 2nd ed. , Englewood cliffs, New Jersey: Prentice-Hall, 1965
39． R.F.Harrington, Field computation by moment method, New York: Macmillan, 1968
40． H. P. Freund, M. A. Kodis, N. R.Vanderplaats, Self-consistent field theory of a helix travelling wave tube amplifier, IEEE Trans on ED, 1992,Vol.20, No. 5, P543-553．