具有中心导体轴的螺旋槽慢波系统及注—波互作用的研究
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摘要
慢波系统作为行波管注波互相作用以激励微波能量的核心部件，它的优劣直接决定了行波管的性能。本论文从理论研究和数值计算两方面对一类新型的具有中心导体轴的矩形螺旋槽慢波系统以及我们提出具有中心导体轴的任意槽形螺旋槽慢波系统进行了深入的研究。主要工作成果和创新点在于：
1．对具有中心导体轴的矩形螺旋槽慢波系统的高频特性进行了理论研究：
(1)在冷系统中的研究结果表明：频率较低时，槽深的改变对相速的影响不是很大，随着频率的增大相速略有减小，同时带宽也有所减小，色散变得稍强，耦合阻抗增大。槽口宽增大相速减小较多，频宽几乎没有什么变化，耦合阻抗增大。轴半径增大，相速明显减小，频宽有一定程度的增加，色散减弱，耦合阻抗值降低。
(2)我们用线性理论模型研究了具有中心导体轴的矩形螺旋槽行波管内的注-波互作用特性，对电子注参量对小信号增益和带宽的影响进行了分析。得出的主要结论为：电流和电子注半径的增大使得该结构的行波管的增益有较大增加，电压的降低可使增益加大但带宽减小。因此，合理选择慢波结构几何尺寸和电子注参数，具有中心导体轴螺旋槽行波管的相对工作带宽可以达到30—40％。槽深不能太浅，槽口宽应该适当取大些，中心互作用空间不宜太窄。
2．首次对具有中心导体轴的任意槽形螺旋槽结构的普遍理论进行了研究，通过以多层矩形阶梯来近似代替任意形状槽的边界的方法，同时对导纳的递推关系进行了详细的推导。它可以适用于边界光滑或有突变的任何形状槽的分析。
3．采用近似场论的方法，获得了一种分析任意槽形螺旋槽结构的普遍理论。首次提出了具有中心导体轴的任意形状螺旋槽慢波结构的色散方程和耦合阻抗表达式；并在这些理论的基础上通过数值计算详细研究了槽形状对螺旋槽慢波系统高频特性的影响。结论为：
中文摘要
（1）适当槽深情况下，槽形状对高截止频率影响较大；槽形状从三角形
变化到余弦形直到燕尾形，高截止频率依次降低。
门）当槽的深度较浅时，三角形螺旋槽的频带宽度最大，且色散最弱，
波的相速最大。
（3）具有相同槽日宽度的燕尾形螺旋槽结构在槽深度较深情况下用作大
功率行波管的互作用系统具有最大的耦合阻抗和最低的相速。
4．采用近似自洽场论的方法，首次得到了适用于分析不同螺旋槽结构的
统一的“热”色散方程。进而进行的数值计算表明，各种不同形状的槽
结构其最大增益和带宽差异较大。通过改变各种槽的结构参数，可以找
到具有最好的符合设计需求的慢波结构。
As the key component of the beam-wave interaction of a Traveling Wave Tube (TWT) for exciting microwave energy, the slow-wave structure (SWS) basically determines the performance of the TWT. In this dissertation, we have made detailed theoretical study and numerical computing on some new types of helical groove SWS including the conductor-centered rectangle-shaped helical groove and the conductor-centered arbitrarily-shaped helical groove; Several important new conclusions and valuable results are achieved and listed as the followings:
1. The research on the RF characteristics of the conductor-centered helical groove SWS.
(a) In the 'cold ' system, we found that the changing of depth of the groove has no distinct effects on the phase velocity at the lower frequency region; but with the increasing of the frequency, the phase velocity and bandwidth are reduced slightly, the structure is more dispersive and the coupling impedance is enhanced. The increasing of the width of the groove makes the phase velocity decreased largely but almost no effects on the bandwidth, and the coupling impedance enhanced. With the radius of the center conductor increasing, the phase velocity is also decreased a lot, the bandwidth is relatively widened, and the dispersion of the structure is weakened but the coupling impedance is lowered.
(b) The linear fluid model is used to study the conductor-centered helical groove TWT. We have analyzed the effects of the beam parameters on the gain and the bandwidth of the TWT. The results show that by increasing the beam current or beam radius, the gain of the structure can be increased. The decreasing of the beam voltage increases the gain of the TWT but reduces the bandwidth. The bandwidth of this kind of TWT can reach 30-40% if choosing the optimal parameters of the structure and the beam. And we also know the depth of the groove should not be too shallow; The width of the groove should be widened relatively, and the space of the interaction area should not be too narrow.
2. For the first time we investigate detailedly on the theory of the conductor-centered arbitrarily-shaped helical groove structure. We divide the arbitrarily-shaped helical groove into many consecutive small rectangle area to approximate the original groove. The recurrence relation of the admittance is obtained. It can be used in the situations of both smooth boundary and discontinuous boundary.
3. A theory for the analysis of the arbitrarily-shaped helical groove structure is obtained by means of an approximate field-theory. The dispersion equation and the coupling impedance expressions of the conductor-centered arbitrarily-shaped helical groove structure are presented for the first time; Based on these theories, the effects of the groove shape on RF characteristics of the structure are investigated by numerical calculation. The results show that:
(a) The influence of the groove shape on the high cut-off frequency is great at certain groove depth; the high cut-off frequency is gradually lowered from triangle profile, cosine profile to swallow-tailed profile.
(b) When the depth of the groove is relatively shallow, the helical triangle-shaped helical groove has the widest bandwidth, the least dispersion, and the fastest phase velocity.
(c) For the helical swallow-tailed structures with same groove width, the deep groove depth one which is suitable for the use in a interaction system of high power TWTs, has the largest coupling impedance and the lowest phase velocity in comparison with the other different groove profiles.
4. For the first time, the unified 'hot' dispersion equation which can be used to analyze structures with different groove profiles is obtained by means of an approximate self-consistent field-theory. The results of the following calculations show that we can get a structure with the best performance through choosing the optimal parameters.
1．对具有中心导体轴的矩形螺旋槽慢波系统的高频特性进行了理论研究：
(1)在冷系统中的研究结果表明：频率较低时，槽深的改变对相速的影响不是很大，随着频率的增大相速略有减小，同时带宽也有所减小，色散变得稍强，耦合阻抗增大。槽口宽增大相速减小较多，频宽几乎没有什么变化，耦合阻抗增大。轴半径增大，相速明显减小，频宽有一定程度的增加，色散减弱，耦合阻抗值降低。
(2)我们用线性理论模型研究了具有中心导体轴的矩形螺旋槽行波管内的注-波互作用特性，对电子注参量对小信号增益和带宽的影响进行了分析。得出的主要结论为：电流和电子注半径的增大使得该结构的行波管的增益有较大增加，电压的降低可使增益加大但带宽减小。因此，合理选择慢波结构几何尺寸和电子注参数，具有中心导体轴螺旋槽行波管的相对工作带宽可以达到30—40％。槽深不能太浅，槽口宽应该适当取大些，中心互作用空间不宜太窄。
2．首次对具有中心导体轴的任意槽形螺旋槽结构的普遍理论进行了研究，通过以多层矩形阶梯来近似代替任意形状槽的边界的方法，同时对导纳的递推关系进行了详细的推导。它可以适用于边界光滑或有突变的任何形状槽的分析。
3．采用近似场论的方法，获得了一种分析任意槽形螺旋槽结构的普遍理论。首次提出了具有中心导体轴的任意形状螺旋槽慢波结构的色散方程和耦合阻抗表达式；并在这些理论的基础上通过数值计算详细研究了槽形状对螺旋槽慢波系统高频特性的影响。结论为：
中文摘要
（1）适当槽深情况下，槽形状对高截止频率影响较大；槽形状从三角形
变化到余弦形直到燕尾形，高截止频率依次降低。
门）当槽的深度较浅时，三角形螺旋槽的频带宽度最大，且色散最弱，
波的相速最大。
（3）具有相同槽日宽度的燕尾形螺旋槽结构在槽深度较深情况下用作大
功率行波管的互作用系统具有最大的耦合阻抗和最低的相速。
4．采用近似自洽场论的方法，首次得到了适用于分析不同螺旋槽结构的
统一的“热”色散方程。进而进行的数值计算表明，各种不同形状的槽
结构其最大增益和带宽差异较大。通过改变各种槽的结构参数，可以找
到具有最好的符合设计需求的慢波结构。
As the key component of the beam-wave interaction of a Traveling Wave Tube (TWT) for exciting microwave energy, the slow-wave structure (SWS) basically determines the performance of the TWT. In this dissertation, we have made detailed theoretical study and numerical computing on some new types of helical groove SWS including the conductor-centered rectangle-shaped helical groove and the conductor-centered arbitrarily-shaped helical groove; Several important new conclusions and valuable results are achieved and listed as the followings:
1. The research on the RF characteristics of the conductor-centered helical groove SWS.
(a) In the 'cold ' system, we found that the changing of depth of the groove has no distinct effects on the phase velocity at the lower frequency region; but with the increasing of the frequency, the phase velocity and bandwidth are reduced slightly, the structure is more dispersive and the coupling impedance is enhanced. The increasing of the width of the groove makes the phase velocity decreased largely but almost no effects on the bandwidth, and the coupling impedance enhanced. With the radius of the center conductor increasing, the phase velocity is also decreased a lot, the bandwidth is relatively widened, and the dispersion of the structure is weakened but the coupling impedance is lowered.
(b) The linear fluid model is used to study the conductor-centered helical groove TWT. We have analyzed the effects of the beam parameters on the gain and the bandwidth of the TWT. The results show that by increasing the beam current or beam radius, the gain of the structure can be increased. The decreasing of the beam voltage increases the gain of the TWT but reduces the bandwidth. The bandwidth of this kind of TWT can reach 30-40% if choosing the optimal parameters of the structure and the beam. And we also know the depth of the groove should not be too shallow; The width of the groove should be widened relatively, and the space of the interaction area should not be too narrow.
2. For the first time we investigate detailedly on the theory of the conductor-centered arbitrarily-shaped helical groove structure. We divide the arbitrarily-shaped helical groove into many consecutive small rectangle area to approximate the original groove. The recurrence relation of the admittance is obtained. It can be used in the situations of both smooth boundary and discontinuous boundary.
3. A theory for the analysis of the arbitrarily-shaped helical groove structure is obtained by means of an approximate field-theory. The dispersion equation and the coupling impedance expressions of the conductor-centered arbitrarily-shaped helical groove structure are presented for the first time; Based on these theories, the effects of the groove shape on RF characteristics of the structure are investigated by numerical calculation. The results show that:
(a) The influence of the groove shape on the high cut-off frequency is great at certain groove depth; the high cut-off frequency is gradually lowered from triangle profile, cosine profile to swallow-tailed profile.
(b) When the depth of the groove is relatively shallow, the helical triangle-shaped helical groove has the widest bandwidth, the least dispersion, and the fastest phase velocity.
(c) For the helical swallow-tailed structures with same groove width, the deep groove depth one which is suitable for the use in a interaction system of high power TWTs, has the largest coupling impedance and the lowest phase velocity in comparison with the other different groove profiles.
4. For the first time, the unified 'hot' dispersion equation which can be used to analyze structures with different groove profiles is obtained by means of an approximate self-consistent field-theory. The results of the following calculations show that we can get a structure with the best performance through choosing the optimal parameters.
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2. N.L. Lindenblad, U.S. Patent 2,300,052, filed May 4,1940, issued October 27,1942.
3. R. Kompfner, The Traveling Wave Value, Wireless World, Vol. 53, No. 11, 1946, P369-372.
4. R .Kompfner, The Traveling Wave Tubes as an Amplifier at Microwaves, Proc. IRE, Vol. 35, No. 2,1947, P124-127.
5. R. Kompfner, The Traveling Wave Tube, Wireless Engineer World, Vol. 53, No. 9, 1947, P255-266.
6. R. Kompfner, The Invention of the Traveling Wave Tube, from a lecture series at University of California at Berkeley, published by Sanfrancisco Press, 1963.
7. J. R. Pierce,L.M. Field, Traveling Wave Tubes, Proc. IRE, Vol. 35, No. 2, 1947, P108-111.
8. J.R. Pierce, U.S. Patent 2,602,148, field October 22,1946, issued July 1,1952.
9. L.M. Field, U.S. Patent 2,575,383, field October 22,1946, issued Nov. 20, 1951.
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，第十二章，北京：国防工业出版社，1985。
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