螺旋线慢波结构特性研究与应用设计
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摘要
螺旋线慢波结构是最重要的宽频带高增益行波管慢波系统,良好的色散特性、低的相速度、高的耦合阻抗、简单的制造工艺,使其广泛应用于通信系统、现代雷达和电子对抗等军事领域。螺旋线慢波结构的慢波特性研究对提升行波管的工作带宽与增益有重要意义；而它的选频及贮能特性研究是铷原子频标星载小型化所需考虑的重要方面。
本博士学位论文围绕螺旋线慢波结构的理论分析与应用设计展开研究工作,详细分析了螺旋线慢波结构以及它的变型：加载介质夹持杆和金属翼的螺旋线慢波结构。从分析电磁慢波系统开始,以螺旋导电面理论为基础,采用场匹配方法,建立了单螺旋绕线慢波结构理论模型、加载圆柱形和矩形夹持杆螺旋线慢波结构理论模型、加载扇形金属翼与T型金属翼螺旋线慢波结构理论模型。利用VBA自编程序处理计算数据。根据CST MWS软件建模结果,在实验结果验证的基础上,对色散特性和耦合阻抗特性进行了比对分析,总结出各项结构参量对慢波特性的具体影响,为行波管的慢波结构设计提供参考。同时,在此基础上,详细分析了螺旋线慢波结构在铷原子频标中的电磁波传播特性,研究螺距和介质材料对特性的影响程度,从而对现有结构进行改进性设计,实现了铷原子频标星载小型化之目的。主要工作和结论如下：
(1)以电磁慢波系统为基础,建立单螺旋绕线慢波结构的螺旋线导电面模型。同时以有限积分理论为基础,利用数值模拟方法,对单螺旋绕线慢波结构进行建模设计。结合理论模型和建模结果,首次呈现该结构的电磁场分布状态,为将螺旋线慢波结构应用到铷原子频标中提供理论基础。
(2)针对加载介质夹持杆螺旋线慢波结构,建立了考虑螺旋带厚度、螺旋带宽度、以及夹持杆形状的螺旋带模型。利用等效介质圆环计算等效介电常数。通过场匹配法得到加载圆柱形和矩形块夹持杆慢波系统的色散关系和耦合阻抗。比对不同管壳半径、夹持杆材料、几何形状、螺旋带厚度和宽度对系统慢波特性的具体影响,提出了优化结构参量之方法,为含有夹持杆的螺旋线慢波结构设计提供指导。
(3)针对加载金属翼螺旋线慢波结构,提出采用傅里叶空间转换方法,将金属翼片所在区域转换为傅氏空间,建立电磁场方程,求解系统色散关系和耦合阻抗。利用此种方法使分析加载金属翼片螺旋线慢波结构的理论模型计算精度得到提高,相比有限厚度翼片螺旋导电面模型,其精度提高了一倍。在此基础上分析了加载扇形翼片与T型翼片系统的慢波特性,得出对于相同结构参数的两种翼片慢波系统,加载T型金属翼的螺旋线慢波结构特性优于加载扇形金属翼；同时首次提出通过调节翼片参数可以使得系统呈现出正性或负性的色散关系,为应用在超高频带宽的螺旋线慢波结构设计提供指导。
(4)在利用CST MWS模拟圆柱型谐振腔体的基础上,研究了应用在铷原子频标中TE111腔体的电磁场分布状态,得到了腔体品质因数和设计参数,设计了加载介质的TE111模谐振腔体,使腔体体积得以压缩,为铷原子频标星载小型化提供设计思路。
(5)以螺旋线导电面模型为基础,首次分析了应用在铷原子频标中的螺旋线慢波结构腔体的电磁场方程,求解了色散关系和耦合阻抗,比对了不同螺距和介电常数对慢波特性的影响。同时沿着在腔体中添加介质层用以压缩体积的思路,设计出改进型螺旋线慢波结构腔体。利用更小的螺距及恰当的介质使得腔体体积进一步压缩。利用温控电路用以减小改进型螺旋线慢波腔体的腔牵引效应。通过将该腔体应用于铷原子频标中,获得其腔体谐振吸收线、铷原子频标的频率稳定度,信噪比,及温度稳定度,这些关键参量能够达到星载铷原子频标小型化设计要求。
Helix slow wave structure (helix SWS)is the most important slow wave system of the traveling wave tube (TWT). The good dispersion relationship, low phase velocity, high interaction impedance, and easy manufacture make the helix SWS widely used in modern military, including communication system, modern radar, electronic warfares and, etc. The investigations of the slow wave characteristics, frequency selective and storing energy characteristic are very useful for improving the performance of TWT and miniaturizing Rubidium Atomic Frequency Standards (RAFS).
In this doctoral dissertation, the theoretical analysis and application design of the helix SWS have been investigated. We research on the performance of the helix SWS and its modified structures such as with loaded on the dielectric cylindrical or rectangular sup-port rods and sector shaped or T-shaped metallic vanes. Studying on the electromagnetic slow-wave system and field-match theory, we build up some theoretical models based on the spiral conducting surface. Using VBA program to process data and CST MWS mod-eling, the simulated results, including phase velocity, on-axis interaction impedance, and distribution of the electromagnetic field, are implemented and compared with the experi-mented results. The effect of the structure's parameters on the slow-wave characteristics are analyzed in detail and it can be referenced to the design of the helix SWS in TWT. At the same time, an improved helix SWS based on good propagation characteristics as a resonator for RAFS is designed. The effects of the different helical pitch and dielectric material in the insulator cylinder on the slow-wave characteristics are analyzed in detail. The main tasks and several valuable results are listed as following:
(1) Based on the electromagnetic slow-wave system, a spiral conducting surface modeling of the single helix SWS is designed. The theoretical analysis is performed together with the simulations of the propagation characteristics. The distributions of elec-tromagnetic field are presented at the first time. Those conclusions can be the theoretical basis of the applying the helix SWS for RAFS.
(2) For analysis of the dielectric support rods-loaded helix SWS, a helical tape model is built up by considering the width or thickness of the helix and the rods'shapes. The dielectric constant is calculated by the equivalent dielectric annulus. The dispersion re-lationship and interaction impedance of loading the cylindrical or rectangular dielectric support rods are gained by field-matched method. Considering the detailed effects of the helix width and thickness, several ways of optimizing structural parameters are proposed for improving the performance of the helix SWS.
(3) The effects of different metallic vane-loaded helix SWS of TWT are proposed based on the analysis of Fourier expansions in the exterior region with metallic vanes. The influences of the metallic vanes dimensions on the phase velocity and interaction impedance are considered in detail. The computed data is compared with the reference data in the practical frequency range with a good consistency. The analytical results reveal that the method of using Fourier expansions can contribute effectively to the reducing of the error between the theoretical and experimented data. By analyzing the computed re-sults, the performances of the helix SWS, with T-shaped metallic vanes are superior to the sector-shaped with the same designed parameters. Adjustments can be made to the outer radius of T-shaped metallic vanes which then control the dispersion relationship showing either negative or positive, and it is similar to sector-shaped vanes by adjusting its inner radius. It is useful to design the helix SWS worked in the ultra high broadband.
(4) Based on the simulation of the cylindrical resonator in RAFS using CST MWS models, the distribution of the electromagnetic field and the quality factor Q of TE111 mode are proposed. From analyzing the parameters, we design a miniaturized cavity with loaded the dielectric materials to compact the volume of RAFS. It is helpful to design a more smaller RAFS.
(5) Based on the helix conducting surface model, the electromagnetic field equations of the helix SWS as the resonator cavity for RAFS is solved at the first time. An im-proved helix SWS based on good propagation characteristics as a helical resonator for RAFS is designed. The theoretical analysis is performed together with the simulations of the propagation characteristics. The simulated results, including phase velocity, on-axis interaction impedance, and distribution of the magnetic field, are implemented and compared with the experimented results. The effects of the different helical pitch and di-electric material in the insulator cylinder on the propagation characteristics are analyzing in detail. The analyzed results show that smaller helical pitch and proper usage of dielec-tric material in the insulator cylinder can make the propagation characteristics of the helix SWS superior. Then a heating circuit of temperature stability is designed to weaken the cavity-pulling effect. The improved helix SWS have been applied in RAFS and the rela-tion parameters, including the resonant cavity's resonance line, frequency stability, SNR, and temperature stability are all achieved.
本博士学位论文围绕螺旋线慢波结构的理论分析与应用设计展开研究工作,详细分析了螺旋线慢波结构以及它的变型：加载介质夹持杆和金属翼的螺旋线慢波结构。从分析电磁慢波系统开始,以螺旋导电面理论为基础,采用场匹配方法,建立了单螺旋绕线慢波结构理论模型、加载圆柱形和矩形夹持杆螺旋线慢波结构理论模型、加载扇形金属翼与T型金属翼螺旋线慢波结构理论模型。利用VBA自编程序处理计算数据。根据CST MWS软件建模结果,在实验结果验证的基础上,对色散特性和耦合阻抗特性进行了比对分析,总结出各项结构参量对慢波特性的具体影响,为行波管的慢波结构设计提供参考。同时,在此基础上,详细分析了螺旋线慢波结构在铷原子频标中的电磁波传播特性,研究螺距和介质材料对特性的影响程度,从而对现有结构进行改进性设计,实现了铷原子频标星载小型化之目的。主要工作和结论如下：
(1)以电磁慢波系统为基础,建立单螺旋绕线慢波结构的螺旋线导电面模型。同时以有限积分理论为基础,利用数值模拟方法,对单螺旋绕线慢波结构进行建模设计。结合理论模型和建模结果,首次呈现该结构的电磁场分布状态,为将螺旋线慢波结构应用到铷原子频标中提供理论基础。
(2)针对加载介质夹持杆螺旋线慢波结构,建立了考虑螺旋带厚度、螺旋带宽度、以及夹持杆形状的螺旋带模型。利用等效介质圆环计算等效介电常数。通过场匹配法得到加载圆柱形和矩形块夹持杆慢波系统的色散关系和耦合阻抗。比对不同管壳半径、夹持杆材料、几何形状、螺旋带厚度和宽度对系统慢波特性的具体影响,提出了优化结构参量之方法,为含有夹持杆的螺旋线慢波结构设计提供指导。
(3)针对加载金属翼螺旋线慢波结构,提出采用傅里叶空间转换方法,将金属翼片所在区域转换为傅氏空间,建立电磁场方程,求解系统色散关系和耦合阻抗。利用此种方法使分析加载金属翼片螺旋线慢波结构的理论模型计算精度得到提高,相比有限厚度翼片螺旋导电面模型,其精度提高了一倍。在此基础上分析了加载扇形翼片与T型翼片系统的慢波特性,得出对于相同结构参数的两种翼片慢波系统,加载T型金属翼的螺旋线慢波结构特性优于加载扇形金属翼；同时首次提出通过调节翼片参数可以使得系统呈现出正性或负性的色散关系,为应用在超高频带宽的螺旋线慢波结构设计提供指导。
(4)在利用CST MWS模拟圆柱型谐振腔体的基础上,研究了应用在铷原子频标中TE111腔体的电磁场分布状态,得到了腔体品质因数和设计参数,设计了加载介质的TE111模谐振腔体,使腔体体积得以压缩,为铷原子频标星载小型化提供设计思路。
(5)以螺旋线导电面模型为基础,首次分析了应用在铷原子频标中的螺旋线慢波结构腔体的电磁场方程,求解了色散关系和耦合阻抗,比对了不同螺距和介电常数对慢波特性的影响。同时沿着在腔体中添加介质层用以压缩体积的思路,设计出改进型螺旋线慢波结构腔体。利用更小的螺距及恰当的介质使得腔体体积进一步压缩。利用温控电路用以减小改进型螺旋线慢波腔体的腔牵引效应。通过将该腔体应用于铷原子频标中,获得其腔体谐振吸收线、铷原子频标的频率稳定度,信噪比,及温度稳定度,这些关键参量能够达到星载铷原子频标小型化设计要求。
Helix slow wave structure (helix SWS)is the most important slow wave system of the traveling wave tube (TWT). The good dispersion relationship, low phase velocity, high interaction impedance, and easy manufacture make the helix SWS widely used in modern military, including communication system, modern radar, electronic warfares and, etc. The investigations of the slow wave characteristics, frequency selective and storing energy characteristic are very useful for improving the performance of TWT and miniaturizing Rubidium Atomic Frequency Standards (RAFS).
In this doctoral dissertation, the theoretical analysis and application design of the helix SWS have been investigated. We research on the performance of the helix SWS and its modified structures such as with loaded on the dielectric cylindrical or rectangular sup-port rods and sector shaped or T-shaped metallic vanes. Studying on the electromagnetic slow-wave system and field-match theory, we build up some theoretical models based on the spiral conducting surface. Using VBA program to process data and CST MWS mod-eling, the simulated results, including phase velocity, on-axis interaction impedance, and distribution of the electromagnetic field, are implemented and compared with the experi-mented results. The effect of the structure's parameters on the slow-wave characteristics are analyzed in detail and it can be referenced to the design of the helix SWS in TWT. At the same time, an improved helix SWS based on good propagation characteristics as a resonator for RAFS is designed. The effects of the different helical pitch and dielectric material in the insulator cylinder on the slow-wave characteristics are analyzed in detail. The main tasks and several valuable results are listed as following:
(1) Based on the electromagnetic slow-wave system, a spiral conducting surface modeling of the single helix SWS is designed. The theoretical analysis is performed together with the simulations of the propagation characteristics. The distributions of elec-tromagnetic field are presented at the first time. Those conclusions can be the theoretical basis of the applying the helix SWS for RAFS.
(2) For analysis of the dielectric support rods-loaded helix SWS, a helical tape model is built up by considering the width or thickness of the helix and the rods'shapes. The dielectric constant is calculated by the equivalent dielectric annulus. The dispersion re-lationship and interaction impedance of loading the cylindrical or rectangular dielectric support rods are gained by field-matched method. Considering the detailed effects of the helix width and thickness, several ways of optimizing structural parameters are proposed for improving the performance of the helix SWS.
(3) The effects of different metallic vane-loaded helix SWS of TWT are proposed based on the analysis of Fourier expansions in the exterior region with metallic vanes. The influences of the metallic vanes dimensions on the phase velocity and interaction impedance are considered in detail. The computed data is compared with the reference data in the practical frequency range with a good consistency. The analytical results reveal that the method of using Fourier expansions can contribute effectively to the reducing of the error between the theoretical and experimented data. By analyzing the computed re-sults, the performances of the helix SWS, with T-shaped metallic vanes are superior to the sector-shaped with the same designed parameters. Adjustments can be made to the outer radius of T-shaped metallic vanes which then control the dispersion relationship showing either negative or positive, and it is similar to sector-shaped vanes by adjusting its inner radius. It is useful to design the helix SWS worked in the ultra high broadband.
(4) Based on the simulation of the cylindrical resonator in RAFS using CST MWS models, the distribution of the electromagnetic field and the quality factor Q of TE111 mode are proposed. From analyzing the parameters, we design a miniaturized cavity with loaded the dielectric materials to compact the volume of RAFS. It is helpful to design a more smaller RAFS.
(5) Based on the helix conducting surface model, the electromagnetic field equations of the helix SWS as the resonator cavity for RAFS is solved at the first time. An im-proved helix SWS based on good propagation characteristics as a helical resonator for RAFS is designed. The theoretical analysis is performed together with the simulations of the propagation characteristics. The simulated results, including phase velocity, on-axis interaction impedance, and distribution of the magnetic field, are implemented and compared with the experimented results. The effects of the different helical pitch and di-electric material in the insulator cylinder on the propagation characteristics are analyzing in detail. The analyzed results show that smaller helical pitch and proper usage of dielec-tric material in the insulator cylinder can make the propagation characteristics of the helix SWS superior. Then a heating circuit of temperature stability is designed to weaken the cavity-pulling effect. The improved helix SWS have been applied in RAFS and the rela-tion parameters, including the resonant cavity's resonance line, frequency stability, SNR, and temperature stability are all achieved.
引文
[1]廖复疆.真空电子技术-信息化武器装备的心脏(第二版).国防工业出版社,2008.
[2]R.S. Symons. Tubes:Still vital after all these years. IEEE Spectrum,35(4):52-63,1998.
[3]廖复疆.大功率微波电子注器件及其发展.真空电子技术,1：1-14,1999.
[4]邬显平.世纪之交的微波真空器件.真空电子技术,1：1-11,2003.
[5]杨中海等.微波管CAD技术进展.真空电子技术,4：1-9,2002.
[6]R.H. Abrams et al. Vacuum electronics for the 21st century. IEEE Microwave Maganize, 2(3):61-72,2001.
[7]V.L. Granatstein et al. Vacuum electronics at the dawn of the twenty-first century. Proceedings of the IEEE,87(5):702-716,1999.
[8]刘盛刚.微波电子学导论.国防工业出版社,1985.
[9]黄秉英.新一代原子钟.武汉大学,2006.
[10]王义遒.量子频标原理.科学出版社,1986.
[11]L.L. Lewis. An introduction to frequency standards. Proc. IEEE,79(7):927-935,1991.
[12]P. Rochat et al. Developments of rubidium frequency standards at neuchatel observatory. Proc. IEEE Int. Frequency Control Symp., pages 716-723,1994.
[13]J. Vanier et al. The Quantum Physics of Atomic Frequency Standards. Bristol, PA:Adam Hilger, 1989.
[14]E. Eltsufin et al. Compact rectangular-cylindrical cavity for rubidium frequency standard. Proc. 45th Annu. Symp. Frequency Control, pages 567-571,1991.
[15]J. Deng. Subminiature microwave cavity for atomic frequency standards. Proc. IEEE Int. Fre-quency Control Symp. PDA Exhib., pages 85-88,2001.
[16]Y. Koyama et al. An ultra-miniature rubidium frequency standard. Proc. IEEE/EIA Int. Fre-quency Control Symp. Exhib., pages 694-699,2000.
[17]K. Chiba et al. An ultra-miniature rubidium frequency standard. Proc.39th Annu. Frequency Control Symp., pages 54-58,1985.
[18]H. Schweda et al. Atomic frequency standard. U.S. Patent 5 387 881, Feb.1995.
[19]T. Sphicopoulous et al. Slotted tube cavity:A compact resonator with empty core. Proc. Inst. Elect. Eng.,134(5):405-410,1987.
[20]B. Xia et al. Characteristics of a novel kind of miniaturized cavity-cell assembly for rubidium frequency standards. IEEE Trans. Instrum. Meas.,55(3):1000-1005,2006.
[21]J. Sheen. Microwave measurements of dielectric properties using a closed cylindrical cavity dielectric resonator. IEEE Trans. Dielectr. Elect. Insul.,14(5):1139-1144,2007.
[22]R. G. Carter et al. Calculation of the properties of reentrant cylindrical cavity resonators. IEEE Trans. Microw. Theory Tech.,55(12):2531-2538,2007.
[23]A. E. Serebryannikov. Beyond the narrow-slot approximation in the analysis of periodic magnetron-type cavities. IEEE Trans. Plasma Sci.,33(3):1019-1023,2005.
[24]A. E. Serebryannikov. Mode selection and slow-wave characteristics of groove modes of a magnetron-type cavity. Microw. Opt. Technol. Lett.,21(5):368-372,1999.
[25]G. Busca et al. Passive frequency standard. U.S. Patent 4 947137, Aug.1990.
[26]David M. Pozar. Microwave Engineering, Third Edition. John Wiley and Sons,Inc.,2005.
[27]L.Brillouin. Wave Propagation in Periodic Structures, Second Edition. Dover Publications,1953.
[28]D.A.Watkins. Topics in Electromaganetic Theory. John Wiley and Sons,Inc.,1958.
[29]R.G.E.Hutter. Beam and Wave Electronics in Microwave Tubes. D.Van Nostrand Company Inc., 1960.
[30]吴鸿适.微波电子学原理.科学出版社,1987.
[31]T. Weiland. A discretization method for the solution of maxwell's equations for six-component fields. Electronics and Communications AEU,31(3):116-220,1977.
[32]A. Bossavit et al. Some realizations of a discrete hodge operator:A reinterpretation of the finite element technique. IEEE Transactions on Magnetics,35:1494-1497,1999.
[33]S. Gutschling et al. Fit-formulation for nonlinear dispersive media. International Journal on Numerical Modelling,12(81-92),1999.
[34]Kruger et al. Fit-formulation for gyrotropic media. Proceedings of the ICCEA 1999,1999.
[35]M. Clemens et al. Time integration of slowly-varying electromagnetic field problems using the finite integration technique. Proceedings of the ENUMATH 97, pages 246-253.
[36]T. Weiland. On the unique numerical solution of maxwellian eigenvalue problems in three di-mensions. Particle Accelerators,17:227-242,1985.
[37]M. Clemens and T. Weiland. Discrete electromagnetism with the finite integration technique. Progress In Electromagnetics Research, PIER 32, pages 65-87,2001.
[38]L.G. Robert and N.O. Eric. Calculation of dispersion curves in periodic structures. IEEE Trans. On Magnetics,21 (6):2344-2346,1985.
[39]C.L. Kory and J.A. Dayton. Accurate cold-test model of helical TWT slow-wave circuits. IEEE Trans. On Electron Devices,45(4):966-971,1998.
[40]C.L. Kory and J.A. Dayton. Effect of helical slow-wave circuit variations on TWT cold-test characteristics. IEEE Trans. On Electron Devices,45(4):972-976,1998.
[41]C.T. Chevalier et al. Traveling-wave tube cold-test circuit optimization using CST Microwave Studio. IEEE Trans. On Electron Devices,50(10):2179-2180,2003.
[42]L. Kumar et al. Modeling of a vane-loaded helical slow-wave structure for broad-band traveling-wave tubes. IEEE Transactions on Electron Devices,36(9):1991-1999,1989.
[43]S. Ghosh et al. Rigorous tape analysis of inhomogeneously-loaded helical slowwave structures. IEEE Transactions on Electron Devices,44(7):1158-1168,1997.
[44]S. DAgostino et al. Accurate analysis of helix slow-wave structures. IEEE Transactions on Electron Devices,45(7):1605-1613,1998.
[45]D. Chernin et al. Exact treatment of the dispersion and beam interaction impedance of a thin tape helix surrounded by a radially stratified dielectric. IEEE Transactions on Electron Devices, 46(7):1472-1483,1999.
[46]M. V. Kartikeyan et al. Effective simulation of the radial thickness of helix for broad band, practical twt's. IEEE Transaction Plasma Science,27(4):1115-1123,1999.
[47]S. K. Datta et al. Broadbanding of a helical slow-wave structure using chiral dielectric loading. Proceedings of the IEEE Intl. Conference on Infrared and Millimeter Waves, pages 22-26,2002.
[48]J. A. Dayton Jr. et al. Diamond-studded helical traveling wave tube. IEEE Transactions on Electron Devices,52(5):695-701,2005.
[49]S. D'Agostino et al. Effect of tape width and thickness on helix slow-wave structure performance. Microwave and optical technology letters,23(3):147-149,1999.
[50]Z. Y. Duan et al. Investigation into the effect of dielectric loss on rf characteristics of helical sws. Int. J. Infrared Milll.,29(1):23-24,2008.
[51]S. K. Datta et al. Analysis of a chiral dielectric supported broadband helix slow-wave structure for millimeter-wave twts. Int. J. Infrared Milli,28(9):779-787,2007.
[52]C. L. Cory. Investigation of fully three-dimensional helical rf filed effects on twt beam/circuit interaction. IEEE Transactions on Electron Devices,48(8):1718-1726,2001.
[53]M. Aloisio and P. Waller. Analysis of helical slow-wave structures for space twts using 3-d electromagnetic simulators. IEEE Transactions on Electron Devices,52(5):749-754,2005.
[54]朱小芳.螺旋线慢波系统高频特性理论分析与数值模拟.PhD thesis,电子科技大学,2007.
[55]雷文强.宽带大功率行波管高频慢波系统CAD研究.PhD thesis,电子科技大学,2003.
[56]T. Wessel-Berg. Cad of tape helix circuits for traveling wave tubes by convolution methods. IEEE Transactions on Electron Devices,51 (11):1918-1927,2004.
[57]X. F. Zhu et al. Modeling of t-shaped vane loaded helical slow-wave structures. IEEE Trans. Plasma Sci.,34(3):563-571,2006.
[58]Jianhong Yang and Yong Zhang et al. Study on effects of different metallic vane-loaded helix slow-wave structure in traveling-wave tubes. J. Infrared Milli. Terahz Waves,30:611-621,2009.
[59]L. Dalessandro and D. Rosato. Finite-element analysis of the frequency response of a metallic cantilever coupled with a piezoelectric transducer. IEEE Trans. Instrum. Meas.,54(5):1881-1890, Oct 2005.
[60]T. Chiu. Dielectric constant measurement technique for a dielectric strip using a rectangular waveguide. IEEE Trans.Instrum. Meas.,52(5):1501-1508, Oct 2003.
[61]P. K. Jain and B. N. Basu. The effect of conductivity losses on propagation through the helical slow-wave structure of a traveling-wave tube. IEEE Trans. Electron Devices,35(4):549-557, Apr 1988.
[62]J. R. Pierce. Traveling-Wave Tubes. New York:D.Van Nostrand,1950.
[63]S.J. Cooke and B. Levush. Eigenmode solution of 2-d and 3-d electromagnetic cavities contain-ing absorbing magterials using the jacobi-davidson algorithm. J. Comput. Phys.,157(1):350-370,2000.
[64]G.L.G. Sleijpen and H.A. VanderVorst. A jacobi-davidson iteration method for liner eigenvalue problems. SIAM J. Matrix Anal. Appl.,17(2):401-425,1996.
[65]Jianhong Yang and Yong Zhang et al. An improved helical resonator design for rubid-ium atomic frequency standards. IEEE Transactions on instrumentation and measurement, DOI:10.1109/TIM.2009.2023149,2009.
[66]P. J. Chantry et al. Miniaturized atomic frequency standard. U.S. Patent 5 192 921, Mar.
[67]I.Liberman et al. A miniature atomic frequency standard. WO/1997/012298, Apr 1997.
[2]R.S. Symons. Tubes:Still vital after all these years. IEEE Spectrum,35(4):52-63,1998.
[3]廖复疆.大功率微波电子注器件及其发展.真空电子技术,1：1-14,1999.
[4]邬显平.世纪之交的微波真空器件.真空电子技术,1：1-11,2003.
[5]杨中海等.微波管CAD技术进展.真空电子技术,4：1-9,2002.
[6]R.H. Abrams et al. Vacuum electronics for the 21st century. IEEE Microwave Maganize, 2(3):61-72,2001.
[7]V.L. Granatstein et al. Vacuum electronics at the dawn of the twenty-first century. Proceedings of the IEEE,87(5):702-716,1999.
[8]刘盛刚.微波电子学导论.国防工业出版社,1985.
[9]黄秉英.新一代原子钟.武汉大学,2006.
[10]王义遒.量子频标原理.科学出版社,1986.
[11]L.L. Lewis. An introduction to frequency standards. Proc. IEEE,79(7):927-935,1991.
[12]P. Rochat et al. Developments of rubidium frequency standards at neuchatel observatory. Proc. IEEE Int. Frequency Control Symp., pages 716-723,1994.
[13]J. Vanier et al. The Quantum Physics of Atomic Frequency Standards. Bristol, PA:Adam Hilger, 1989.
[14]E. Eltsufin et al. Compact rectangular-cylindrical cavity for rubidium frequency standard. Proc. 45th Annu. Symp. Frequency Control, pages 567-571,1991.
[15]J. Deng. Subminiature microwave cavity for atomic frequency standards. Proc. IEEE Int. Fre-quency Control Symp. PDA Exhib., pages 85-88,2001.
[16]Y. Koyama et al. An ultra-miniature rubidium frequency standard. Proc. IEEE/EIA Int. Fre-quency Control Symp. Exhib., pages 694-699,2000.
[17]K. Chiba et al. An ultra-miniature rubidium frequency standard. Proc.39th Annu. Frequency Control Symp., pages 54-58,1985.
[18]H. Schweda et al. Atomic frequency standard. U.S. Patent 5 387 881, Feb.1995.
[19]T. Sphicopoulous et al. Slotted tube cavity:A compact resonator with empty core. Proc. Inst. Elect. Eng.,134(5):405-410,1987.
[20]B. Xia et al. Characteristics of a novel kind of miniaturized cavity-cell assembly for rubidium frequency standards. IEEE Trans. Instrum. Meas.,55(3):1000-1005,2006.
[21]J. Sheen. Microwave measurements of dielectric properties using a closed cylindrical cavity dielectric resonator. IEEE Trans. Dielectr. Elect. Insul.,14(5):1139-1144,2007.
[22]R. G. Carter et al. Calculation of the properties of reentrant cylindrical cavity resonators. IEEE Trans. Microw. Theory Tech.,55(12):2531-2538,2007.
[23]A. E. Serebryannikov. Beyond the narrow-slot approximation in the analysis of periodic magnetron-type cavities. IEEE Trans. Plasma Sci.,33(3):1019-1023,2005.
[24]A. E. Serebryannikov. Mode selection and slow-wave characteristics of groove modes of a magnetron-type cavity. Microw. Opt. Technol. Lett.,21(5):368-372,1999.
[25]G. Busca et al. Passive frequency standard. U.S. Patent 4 947137, Aug.1990.
[26]David M. Pozar. Microwave Engineering, Third Edition. John Wiley and Sons,Inc.,2005.
[27]L.Brillouin. Wave Propagation in Periodic Structures, Second Edition. Dover Publications,1953.
[28]D.A.Watkins. Topics in Electromaganetic Theory. John Wiley and Sons,Inc.,1958.
[29]R.G.E.Hutter. Beam and Wave Electronics in Microwave Tubes. D.Van Nostrand Company Inc., 1960.
[30]吴鸿适.微波电子学原理.科学出版社,1987.
[31]T. Weiland. A discretization method for the solution of maxwell's equations for six-component fields. Electronics and Communications AEU,31(3):116-220,1977.
[32]A. Bossavit et al. Some realizations of a discrete hodge operator:A reinterpretation of the finite element technique. IEEE Transactions on Magnetics,35:1494-1497,1999.
[33]S. Gutschling et al. Fit-formulation for nonlinear dispersive media. International Journal on Numerical Modelling,12(81-92),1999.
[34]Kruger et al. Fit-formulation for gyrotropic media. Proceedings of the ICCEA 1999,1999.
[35]M. Clemens et al. Time integration of slowly-varying electromagnetic field problems using the finite integration technique. Proceedings of the ENUMATH 97, pages 246-253.
[36]T. Weiland. On the unique numerical solution of maxwellian eigenvalue problems in three di-mensions. Particle Accelerators,17:227-242,1985.
[37]M. Clemens and T. Weiland. Discrete electromagnetism with the finite integration technique. Progress In Electromagnetics Research, PIER 32, pages 65-87,2001.
[38]L.G. Robert and N.O. Eric. Calculation of dispersion curves in periodic structures. IEEE Trans. On Magnetics,21 (6):2344-2346,1985.
[39]C.L. Kory and J.A. Dayton. Accurate cold-test model of helical TWT slow-wave circuits. IEEE Trans. On Electron Devices,45(4):966-971,1998.
[40]C.L. Kory and J.A. Dayton. Effect of helical slow-wave circuit variations on TWT cold-test characteristics. IEEE Trans. On Electron Devices,45(4):972-976,1998.
[41]C.T. Chevalier et al. Traveling-wave tube cold-test circuit optimization using CST Microwave Studio. IEEE Trans. On Electron Devices,50(10):2179-2180,2003.
[42]L. Kumar et al. Modeling of a vane-loaded helical slow-wave structure for broad-band traveling-wave tubes. IEEE Transactions on Electron Devices,36(9):1991-1999,1989.
[43]S. Ghosh et al. Rigorous tape analysis of inhomogeneously-loaded helical slowwave structures. IEEE Transactions on Electron Devices,44(7):1158-1168,1997.
[44]S. DAgostino et al. Accurate analysis of helix slow-wave structures. IEEE Transactions on Electron Devices,45(7):1605-1613,1998.
[45]D. Chernin et al. Exact treatment of the dispersion and beam interaction impedance of a thin tape helix surrounded by a radially stratified dielectric. IEEE Transactions on Electron Devices, 46(7):1472-1483,1999.
[46]M. V. Kartikeyan et al. Effective simulation of the radial thickness of helix for broad band, practical twt's. IEEE Transaction Plasma Science,27(4):1115-1123,1999.
[47]S. K. Datta et al. Broadbanding of a helical slow-wave structure using chiral dielectric loading. Proceedings of the IEEE Intl. Conference on Infrared and Millimeter Waves, pages 22-26,2002.
[48]J. A. Dayton Jr. et al. Diamond-studded helical traveling wave tube. IEEE Transactions on Electron Devices,52(5):695-701,2005.
[49]S. D'Agostino et al. Effect of tape width and thickness on helix slow-wave structure performance. Microwave and optical technology letters,23(3):147-149,1999.
[50]Z. Y. Duan et al. Investigation into the effect of dielectric loss on rf characteristics of helical sws. Int. J. Infrared Milll.,29(1):23-24,2008.
[51]S. K. Datta et al. Analysis of a chiral dielectric supported broadband helix slow-wave structure for millimeter-wave twts. Int. J. Infrared Milli,28(9):779-787,2007.
[52]C. L. Cory. Investigation of fully three-dimensional helical rf filed effects on twt beam/circuit interaction. IEEE Transactions on Electron Devices,48(8):1718-1726,2001.
[53]M. Aloisio and P. Waller. Analysis of helical slow-wave structures for space twts using 3-d electromagnetic simulators. IEEE Transactions on Electron Devices,52(5):749-754,2005.
[54]朱小芳.螺旋线慢波系统高频特性理论分析与数值模拟.PhD thesis,电子科技大学,2007.
[55]雷文强.宽带大功率行波管高频慢波系统CAD研究.PhD thesis,电子科技大学,2003.
[56]T. Wessel-Berg. Cad of tape helix circuits for traveling wave tubes by convolution methods. IEEE Transactions on Electron Devices,51 (11):1918-1927,2004.
[57]X. F. Zhu et al. Modeling of t-shaped vane loaded helical slow-wave structures. IEEE Trans. Plasma Sci.,34(3):563-571,2006.
[58]Jianhong Yang and Yong Zhang et al. Study on effects of different metallic vane-loaded helix slow-wave structure in traveling-wave tubes. J. Infrared Milli. Terahz Waves,30:611-621,2009.
[59]L. Dalessandro and D. Rosato. Finite-element analysis of the frequency response of a metallic cantilever coupled with a piezoelectric transducer. IEEE Trans. Instrum. Meas.,54(5):1881-1890, Oct 2005.
[60]T. Chiu. Dielectric constant measurement technique for a dielectric strip using a rectangular waveguide. IEEE Trans.Instrum. Meas.,52(5):1501-1508, Oct 2003.
[61]P. K. Jain and B. N. Basu. The effect of conductivity losses on propagation through the helical slow-wave structure of a traveling-wave tube. IEEE Trans. Electron Devices,35(4):549-557, Apr 1988.
[62]J. R. Pierce. Traveling-Wave Tubes. New York:D.Van Nostrand,1950.
[63]S.J. Cooke and B. Levush. Eigenmode solution of 2-d and 3-d electromagnetic cavities contain-ing absorbing magterials using the jacobi-davidson algorithm. J. Comput. Phys.,157(1):350-370,2000.
[64]G.L.G. Sleijpen and H.A. VanderVorst. A jacobi-davidson iteration method for liner eigenvalue problems. SIAM J. Matrix Anal. Appl.,17(2):401-425,1996.
[65]Jianhong Yang and Yong Zhang et al. An improved helical resonator design for rubid-ium atomic frequency standards. IEEE Transactions on instrumentation and measurement, DOI:10.1109/TIM.2009.2023149,2009.
[66]P. J. Chantry et al. Miniaturized atomic frequency standard. U.S. Patent 5 192 921, Mar.
[67]I.Liberman et al. A miniature atomic frequency standard. WO/1997/012298, Apr 1997.