摘要
强流电子束二极管的研究是高功率微波技术领域的重要课题。论文对阴极等离子体膨胀过程进行了深入细致的理论分析、粒子模拟和实验测量研究。同时，理论分析了爆炸电子发射过程中等离子体的形成、阴极等离子体斑的发展以及阳极等离子体的形成等过程；实验观察了不同时刻阴极等离子体光斑的分布和阳极表面在电子束辐照后微观结构的变化；测量了铜尖峰阴极表面附近等离子体的数密度分布。论文得到的结果对研制高性能的用于高功率微波源的阴极具有参考价值。论文研究的主要内容包括以下几个方面：
（1）通过求解阴极等离子体膨胀的流体模型得到了阴极等离子体膨胀速度的解析表达式。在该表达式中，等离子体膨胀速度决定于等离子体在边缘处和中心区域处的离子数密度的比值和声速。中心区域的等离子体数密度越高等离子体膨胀速度越大，等离子体边缘附近的离子数密度越高等离子体膨胀速度越小。该表达式预示了在整个高压脉冲期间，阴极等离子体膨胀速度随时间近似成“U”字型变化；多成分阴极等离子的体膨胀速度取决质量最轻的离子的量；抑制氢离子的形成有利于降低等离子体膨胀速度。
（2）实现了阴极等离子体运动过程的PIC模拟。通过粒子模拟，观察了粒子数密度分布和电势分布演化过程，并在此基础上，讨论了阴极等离子体膨胀的机制。结果表明，阴极等离子体出现后，由于电子速度远大于离子速度，较多的电子离开等离子体区域，部分离子未被等离子体电子中和，这些离子将中和电子束的空间电荷，使二极管中的电流密度得到增大。二极管中的电流密度增大将导致二极管中的电势降低。随着等离子体的不断积累，等离子体边缘附近的电势不断减小，当等离子体边缘附近的电势小于或等于等离子体电势时，离子就可以运动到电势小于或等于等离子体电势的区域，等离子体向阳极的膨胀得到实现。模拟还通过改变等离子体参数验证了流体模型给出的等离子体膨胀速度的解析表达式。
（3）通过高速分幅照相，观察了平面天鹅绒阴极和铜尖峰阴极表面等离子体光斑的分布特点和演化过程。天鹅绒阴极表面的发光是由许多离散分布的阴极等离子体光斑组成的，在整个高压脉冲持续时间内，离散的阴极等离子体光斑并没有合并成为覆盖整个阴极表面的发光层；不同的脉冲之间等离子体光斑出现的位置是随机的。对铜尖峰阴极等离子体光斑随时间的演化过程的分析表明，不同亮度等离子体层的膨胀速度并不相同，亮度越高的等离子体层膨胀速度越慢。
（4）引入了干涉测量法对阴极等离子体数密度分布进行测量。测量系统由干涉仪连续地输出干涉条纹图样，由高速分幅相机记录阴极等离子体形成的干涉条纹图样，在一个高压脉冲过程中输可以出4幅干涉条纹图样。在电压100kV，电流8kA，脉宽150ns的实验条件下，测量得到不同时刻铜尖峰阴极表面的等离子体形成的干涉条纹图样。通过比较不同时刻的干涉条纹得到等离子体膨胀速度约为1.7cm/μs；通过Abel反变换得到电子数密度的径向分布和轴向分布，在阴极表面附近电子数密度大于4×1018cm-3，在等离子体边缘附近电子数密度约为4×1017cm-3，在轴向的边缘上电子数密度约为5×1016cm-3；根据等离子体在径向边缘上的磁流体力学平衡条件，得到阴极等离子体的温度约为3.5eV；在整个测量区域对等离子体数密度积分，得到阴极等离子体中电子数约为二极管转移电子数的3倍。
（5）实验观察了铜板阳极和不锈钢网阳极在强流脉冲电子束作用下微观结构的变化，讨论了阳极等离子体的形成过程以及阳极离子流对二极管束流的影响。电子束轰击后的Cu阳极横截面上出现分层结构，厚度~20μm的表层物质分布较为均匀，内层中有大量的孔穴。不锈钢阳极网在电子束反复轰击下其表面出现了高300~500μm、宽200μm沿不锈钢丝轴向准周期分布的微尖峰。阳极表面汽化形成等离子体所需的时间与二极管阻抗成正比与电子束流的截面积成反比。电子束电离阳极表面解吸附气体将形成离子，离子在电场作用下进入加速空间而形成阳极离子流，在阳极离子流达到空间电荷限制离子流之前，二极管电流与空间电荷限制电子流的差与阳极离子流的大小近似成正比。
High-current electron beam diode is an important topic in high power microwavetechnology. In this dissertation, the expansion process of cathode plasma is investigatedbased on detailed theoretical analysis, particle-in-cell (PIC) simulation and experimentalmeasurements. At the same time, the plasma formation during explosive electronemission, the evaluation of cathode plasma spots and the generation of anode plasma areanalyzed theoretically. The distribution of plasma light emission on cathode surface andthe variation of anode surface after the irrigation of electron beam are observed. Thedistribution of plasma number density near a copper tip cathode is measured. Theseefforts are instructive for the development of high quality cathode used in high powermicrowave sources. The detailed contents and innovative works are as follows.
The analytic expression of plasma expansion velocity has been given based on ahydromechanical model. It is shown that the plasma expansion velocity is determinedby its sound speed together with the ratio of ion density at plasma front to the iondensity in plasma center. The decrease of ion density at plasma front or the increase ofthe ion density in plasma center leads to the increase of plasma expansion. During thehigh-voltage pulse, the variation of plasma expansion velocity has the shape as letter“U”. The expansion velocity of multicomponent plasma depends on the amount oflightest ion. The suppression of H+generation is helpful in reducing the plasmaexpansion velocity.
The PIC simulation on cathode plasma expansion is realized. The dynamics ofexpanding cathode plasma has been obtained by observing the potential and ion densitydistributions along axes. At initial state of the formation of cathode plasma, moreelectrons than ions would escape from the plasma region. The ions are consequently nottotally neutralized. The residual ions would partially neutralize the space charge ofelectron beam, leading to a larger electron beam density than the case without thepresence of cathode plasma. The electric potential in region without plasma is thereforedecreased. With the accumulation of residual ions in the plasma region, the potential inregion without plasma becomes lower and lower. When the potential at plasma front isequal to or lower than the plasma potential, ions move towards the anode and theplasma expansion occurs. The analytic expression of plasma expansion velocity is alsoverified by the simulations over different plasma parameters.
The distribution and the evolution of cathode spots on a velvet plane cathode andon a copper tip cathode are observed by a high-speed frame camera. The camera hasfour optical channel, and four photographs at given time delay can be recorded during ahigh voltage pulse. The light emission on a velvet plane cathode is composed by manyseparated spots. The cathode spots have not merged to be a bright layer covering on the cathode surface. The positions, where cathode spots appear, are quite different amongdifferent pulses. The expansion velocity of plasma layer depends on its brightness.Plasma layer with high brightness has low expansion velocity.
The interferometry is introduced to measuring the distribution of cathode plasmanumber density. In the interferometry, a difference interferometer generatesinterferograms continuously, and interferograms generated by cathode plasma arerecorded by a four-channel fast frame camera. Four interferograms during ahigh-voltage pulse can be recorded. Interferograms generated by the plasma near thecopper cathode tip in a~100kV,~8kA,~150ns tip-plane diode are obtained. Thevariation of fringes between interferograms taken at different given gate delay indicatesthat the velocity of the plasma edge is about1.7cm/μs. Abel inversion of fringe shifthas yielded the densities distributions along radius. The plasma density on the cathodesurface is larger than4×1018electrons/cm3, and it is decreased to be about4×1017electrons/cm3near the radial plasma edge. By calculating the radial distribution ofplasma density at different axial position, the plasma density along axis has beenobtained. The plasma density at the axial plasma edge is about5×1016electrons/cm3.The magneto hydrodynamic pressure balance on the radial edge of plasma implies aplasma temperature of about3.5eV. The integral of plasma density over the plasmaregion shows that the number of plasma electrons is about three times of the number ofelectrons emitted from cathode.
The variations of microstructure on the surface of a copper plane anode and astainless steel mesh anode under the irradiation of electron beam are checked. Stratifiedstructure appears on the copper anode. The depth of the first layer is about20μm.Carbon element from cathode deposits in this layer, and the material distribution iscorrespondingly uniform. Many holes appear in the second layer. The components inthe second layer dose not change. Many tiny tip of300~500μm in height,200μm inwidth appear quasi-periodically on the stainless steel mesh. The time when the anodesurface melts under the heating of electron beam is ratio to the impedance of the diodeand inverse ratio to the beam density. The anode ion flow appears when the gasdisrobed from anode surface ionized by the electron beam. When the ion flow is lowerthan the space-charge limited ion flow, the difference of the diode current and thespace-charge limited electron flow is ratio to the ion flow.
引文
[1] R. B. Miller, An Introduction to the Physics of Intense Charged Particle Beams[M]. New York: Plenum,1982.
[2] R. J. Barker and E. Schamiloglu, Eds., High-Power Microwave Sources andTechnologies [M]. New York: Willey,2001.
[3] J. Benford, et al., High Power Microwaves [M]. New York: Taylor and Francis,2007.
[4] M. K. Matzen, et al., Pulsed-power-driven high energy density physics and inertialconfinement fusion researcha [J], Phys. Plasmas,2005,(12):055503.
[5] R. J. Barker and E. Schamiloglu, High-Power Microwave Sources andTechnologies [M], New York: IEEE/Wiley,2003.
[6] R. B. Miller, Mechanism of explosive electron emission for dielectric fiber (velvet)cathodes [J], J. Appl. Phys.,1998,(84):3880-3889.
[7] D. Shiffler, et al., Review of Cold Cathode Research at the Air Force ResearchLaboratory [J], IEEE Trans. plasma. sci.,2008,(36):718-728.
[8] Y. E. Krasik, et al., Characterization of the plasma on dielectric fiber "velvet"cathodes [J], J. Appl. Phys.,2005,(98):093308.
[9] L. Li, et al., Plasma-induced evolution behavior of space-charge limited current formultiple-needle cathodes [J], Plasma Sources Sci. Technol.,2009,(18):015011.
[10] S. A. Barengolts, et al., Plasma initiation of an explosive emission center-ecton
[C],24th Int. Symp. on Discharges and Electrical Insulation in Vacuum,Brunswick,2010.
[11] R. L. Boxman, Twenty-Five Years of Progress in Vacuum Arc Research andUtilization [J], IEEE Trans. Plasma Sci.,1997,(25):1174-1186.
[12] Q. Liao, et al., Plasma-induced field emission and plasma expansion of carbonnanotube cathodes [J], J. Phys. D: Appl. Phys.,2007,(40):3456–3460.
[13] J. Yang, et al., Time-resolved plasma characteristics in a short-pulse high-powerdiode with a dielectric fiber (velvet) cathode [J], IEEE Trans. Plasma Sci.,2012,(40):1696-1701.
[14] D. Price and J. N. Benford, General Scaling of Pulse Shortening inExplosive-Emission-Driven Microwave Sources [J], IEEE Trans. Plasma Sci.,1998,(26):256-262.
[15] M. D. Haworth, et al., Significant Pulse-Lengthening in a MultigigawattMagnetically Insulated Transmission Line Oscillator [J], IEEE Trans. Plasma Sci.,1998,(26):312-319.
[16]宫彬,等，高功率微波器件中脉冲缩短现象的粒子模拟[J],物理学报,2004,(53):3990-3995.
[17]宋法伦,等,平面二极管爆炸发射阴极特性实验研究[J],强激光与粒子束,2008,(20):1511-1515.
[18]杨杰,等,强流电子束二极管等离子体光学诊断[J],强激光与粒子束,2012,(24):963-968.
[19]廖庆亮,等,碳纳米管阴极的短脉冲爆炸场发射与等离子体膨胀[J]物理学报, vol.57, pp.1779-1784,2008.
[20]夏连胜,等,"强流电子二极管中阴极等离子体的膨胀[J],"物理学报,2004.(53):1779-1784.
[21] V. Vekselman, et al., Plasma characterization in a diode with a carbon-fibercathode [J], Appl. Phys. Lett.,2008,(93):081503.
[22] A. Dunaevsky, et al., Spectroscopy of a ferroelectric plasma cathode [J], J. Appl.Phys.,2001(90):4108-4118.
[23] D. Shiffler, et al., Emission uniformity and emission area of explosive fieldemission cathodes [J], Appl. Phys. Lett,2001,(79):2871-2873.
[24] A. Roy, et al., Plasma expansion and fast gap closure in a high power electronbeam diode [J], Phys. Plasmas,2009,(16):053103.
[25] L. Liu, et al., Pulse-width increase of eflex triode virator using the carbon fibercathode [J], Chin. Phys.Lett,2006,(23):899-903.
[26] Y. Fan, et al., Complex magnetically insulated transmission line oscillator [J], Phys.Plasmas,2008,(15):083108.
[27] D. H. Kim, et al., Dynamics of mode competition in a gigawatt-class magneticallyinsulated line oscillator [J], Appl. Phys. Lett,2007(90):124103.
[28] Y. Chen, et al., Cathode and anode optimization in a virtual cathode oscillator [J],IEEE Trans. Dielectr. Elect. Insul.,2007,(14):1037-1044.
[29] G. A. Mesyats, Ed., Cathode Phenomena in a Vacuum Discharge: The Breakdown,the Spark and the Arc [M]. Moscow: Nauka,2000.
[30] Y. M. Saveliev, et al., Current conduction and plasma distribution on dielectric(velvet) explosive emission cathodes [J], J. Appl. Phys.,2003,(94):7416-7421.
[31] D. A. Shiffler, et al., Emission Uniformity and Shot-to-Shot Variation in ColdField Emission Cathodes [J], IEEE Trans. Plasma Sci.,2004,(32):1262-1266.
[32] Y. E. Krasik, et al., Plasma sources for high-current electron beam generation [J],Phys. Plasmas,2001(8):2466-2472.
[33] A. E. Blaugrund, Measurements of electron emission uniformity from cathodes inhigh-voltage electron beam diodes [J], Appl. Phys. Lett,2003,(83):1264-1265.
[34] Y. M. Saveliev, et al., Perveance of a planar diode with explosive emissionfinite-diameter cathodes [J], Appl. Phys. Lett,2002,(81):2343-2345.
[35] L. Liu, et al., Carbon fiber-based cathodes for magnetically insulated transmissionline oscillator operation [J], Appl. Phys. Lett,2007(91):161504.
[36] H. S. Uhm, et al., A study of diode perveance for high-power relativistic electronbeams [J], Phys. Plasmas,2002,(9):2850-2853.
[37] Y. M. Saveliev, et al., On anode effects in explosive emission diodes [J], J. Appl.Phys.,2003(94,):5776-5781.
[38] D. A. Shiffler, et al., Effects of Anode Materials on the Performance of ExplosiveField Emission Diodes [J], IEEE Trans. Plasma Sci.,2002,(30):1232-1237.
[39] L. Lie, et al., Fabrication of Carbon-Fiber Cathode for High-Power MicrowaveApplications [J], IEEE Trans. Plasma Sci.,2004,(32):1742-1746.
[40] M. S. Litz, Rep-rate Explosive Whisker Emission Cathode Investigations [C], SPlEVol.2154, Intense Microwave Pulses Ⅱ,1994, pp:110-118.
[41] R. J. Umstattd, et al., Gas Evolution During Operation of a CsI-Coated CarbonFiber Cathode in a Closed Vacuum System [J], IEEE Trans. Plasma Sci.,2005,(33):901-910.
[42] T. K. Statom,"Pulsed CsI-coated tufted carbon fiber cathode plasma [J], IEEETrans. electron devices,2006,(53):386-371.
[43] J. D. Ivers, et al., Electron beam diode using ferroelectric cathodes [J], J. Appl.Phys.,1993,(73):2667-2671.
[44] D. A. Shiffler, et al., Comparison of Carbon Fiber and Cesium Iodide-CoatedCarbon Fiber Cathodes [J], IEEE Trans. Plasma Sci.,2000,(28):517-522.
[45] D. Shiffler, et al., Comparison of Velvet-and Cesium Iodide-Coated Carbon FiberCathodes [J], IEEE Trans. Plasma Sci.,2001,(29):445-451.
[46] D. Shiffler, et al., Carbon velvet field-emission cathode [J], Rev. Sci. Instrum.,2002,(73):4358-4362.
[47] D. A. Shiffler, et al., Emission Uniformity and Emittance of ExplosiveField-Emission Cathodes [J], IEEE Trans. Plasma Sci.,2002,(30)1592-1596.
[48] D. Shiffler, et al., A High-Current, Large-Area, Carbon Nanotube Cathode [J],IEEE Trans. Plasma Sci.,2004,(32):2152-2154.
[49] A. Roy, et al., Shot to shot variation in perveance of the explosive emissionelectron beam diode [J], Phys. Plasmas,2009,(16):053103.
[50] A. Roy, et al., Electron beam current in high power cylindrical diode [J], Phys.Plasmas,2010,(17):013103.
[51] A. Dunaevsky, et al., Electron energy and potential distribution in a diode with aferroelectric cathode [J], J. Appl. Phys.,2000,(87):3270-3278.
[52] Y. E. Krasik, et al., Study of Electron Diodes with a Ferroelectric Plasma Cathode[J], IEEE Trans. Plasma Sci.,2000,(28):1642-1647.
[53] K. Chirko, et al.,"Enhanced emission mode of a ferroelectric plasma cathode [J], J.Appl. Phys.,2002,(92):5691-5697.
[54] Y. E. Krasik, et al., Electron beam generation in a diode with different ferroelectriccathodes [J], J. Appl. Phys.,2003,(94):5158-5162.
[55] D. Yarmolich, et al., Micron-scale width multislot plasma cathode [J], Phys.Plasmas,2008,(15):123507.
[56] V. Vekselman, et al., Plasma characterization in a diode with a carbon-fibercathode [J], Appl. Phys. Lett.,2008,(93):081503.
[57] L. Liu, et al., Robust, easily shaped, and epoxy-free carbon-fiber-aluminumcathodes for generating high-current electron beams [J], Rev. Sci. Instrum.,2009,(80):023309.
[58] J. Mankowski, et al., A low-cost metallic cathode for a vircator HPM source [C],presented at the IEEE2005.
[59] E. A. Litvinov,"Theory of explosive electron emission [J], IEEE Trans. Dielectr.Elect. Insul.,1985,(20):683-689.
[60] G. A. Mesyats, Ecton Mechanism of the Vacuum Arc Cathode Spot [J], IEEETrans. Plasma Sci.,1995,(23):879-884.
[61] E. A. Litvinov and A. Z. Nemirovskii, Model of the explosive-emission centerigniyion on a cathode surface [C],20th International Symposium on Dischargesand Electrical Insulation in Vacuum, Tours,2002.
[62] S. A. Barengolts, et al., Initiation of Explosive Electron Emission in MicrowaveFields [J], IEEE Trans. Plasma Sci.,1998,(26):252-255.
[63] G. A. Mesyats, Ecton processes at the cathode in a vacuum discharge [C],17thInternational Symposium on Discharges and Electrical Insulation in Vacuum,Berkeley,1996.
[64] G. A. Mesyats and S. A. Barengolts, The Cathode Spot of a High-Current VacuumArc as a Multiecton Phenomenon [J], IEEE Trans. Plasma Sci.,2001,(29):704-707.
[65] C. D. Child, Discharge from hot CaO [J], Phys. Rev,1911(32):492-511.
[66] I. Langmuir, The effect of space charge and initial velocities on the potentialdistribuation and thermionic current between parallel plane electrodes [J], Phys.Rev,1923,(21):419-435.
[67] R. R. Puri, et al., Generalization of the Child–Langmuir law for nonzero injectionvelocities in a planar diode [J], Phys. Plasmas,2003,(11):1178-1186.
[68] W. S. Koh, et al., Space-charge-limited bipolar flow in a nano-gap [J], Appl. Phys.Lett,2005,(87):193112.
[69] P. Zhang, et al., Short-pulse space-charge-limited electron flows in a drift space [J],Phys. Plasmas,2008,(15):063105.
[70] J. W. Luginsland, et al., Beyond the Child–Langmuir law: A review of recentresults on multidimensional space-charge-limited flow [J], Phys. Plasmas,2002,(9):2371-2375.
[71] R. J. Umstattd and J. W. Luginsland,"Two-Dimensional Space-Charge-LimitedEmission: Beam-Edge Characteristics and Applicationsv, Phys. Rev. Lett.,2001,(87):145002.
[72] J. J. Watrous, et al., An improved space-charge-limited emission algorithm for usein particle-in-cell codes [J], Phys. Plasmas,2001,(8):289-216.
[73] Y. E. Krasik, et al., Ferroelectric Plasma Sources and Their Applications [J], IEEETrans. Plasma Sci.,2003,(31):49-59.
[74] Q. Liao, et al., Explosive field emission and plasma expansion of carbon nanotubecathodes [J], Appl. Phys. Lett,2007,(90):151540.
[75] L. Li, et al., An intense-current electron beam source with low-level plasmaformation [J], J. Phys. D: Appl. Phys,2008,(41):125201.
[76] F. Hegeler, et al., Electron Density Measurements During Microwave Generationin a High Power Backward-Wave Oscillator [J], IEEE Trans. plasma. sci.,1998,(26):257-281.
[77] B. V. Weber and D. D. Hinshelwooda,"He-Ne interferometer for densitymeasurements in plasma opening switch experiments [J], Rev. Sci. Instrum,1992,(63):5199-5202.
[78] Y. Teramoto, et al., Observation of Plasma Motion in a Coaxial Plasma OpeningSwitch With a Chordal Laser Interferometer [J], IEEE Trans. Plasma Sci.,2002,(30):1886-1891.
[79] G. A. Rochau, et al., Applied spectroscopy in pulsed power plasmas [J], Phys.Plasmas,2010,(17):055501.
[80] S. A. Popov, Dense plasma cluster formation around drop in vacuum dischargecathode plasma [C],20th International Symposium on Discharges and ElectricalInsulation in Vacuum, Tours, France,2002.
[81] B. V. Weber and S. F. Fulghum, A high sensitivity two-color interferometer forpulsed power plasmas [J], Rev. Sci. Instrum.,1997,(68):1227-1232.
[82] J. G. Kelly and L. P. Mix, Measurements of high-current relativistic electron diodeplasma properties with holographic interferometry [J], J. Appl. Phys.,1974,(46):1084-1090.
[83] Z. Mao, et al., Evolution of the electrically exploding wire observed with aMach–Zehnder interferometer [J], Appl. Phys. Lett.,2009,(94):181501.
[84] Q. Zhang, et al., Measurement of the electron density in a microwave plasma torchat atmospheric pressure [J], Rev. Sci. Instrum,2009,(95):201502.
[85] X. Cai, et al., Recovery of gas density in a nitrogen gap after breakdown [J], Appl.Phys. Lett,2010,(97):01501.
[86] J. C. Riordan, Radiation Source Research at L-3Pulse Sciences [C], Beams2006,Riodan,2006.
[87] X. X. Wang, et al., A three-frame Mach-Zenhder interferometer for measuringplasma implosion in Z-pinch [c], Beams2006, Riodan,2006.
[88] D. R. Welch, et al., Hybrid simulation of electrode plasmas in high-power diodes[J], Phys. Plasmas,2009,(16):123102.
[89] E. A. Litvinov and A. Z. Nemirovskii, Reycling of centers of explosive emossionin a cathode spot of a vacuum arc [C], IEEE21" Int. Symp. on Discharges andElectrical Insulation in vacuum,2004.
[90] E. A. Litvinov, et al., Inition of explosin centers under operation of naturalmicrowave radiation in a cathode spot of a vacuum arc[C], IEEE19" Int. Symp. onDischarges and Electrical Insulation in vacuum, xi'an,2000.
[91]米夏兹,真空放电物理和高功率脉冲技术.北京:国防工业出版社,2007.
[92] S. D. Korovin, et al., Degradation and Recovery of the Emission From a GraphiteCathode in Relation to the Repetition Frequency of Nanosecond AcceleratingPulses [J] IEEE Trans. Plasma Sci.,2006,(34):1771-1776.
[93] E. A. Litvinov and A. Z. Nemirovskii,"The mechanism of development of acathode spot of a vacuum arc [C], IEEE18th Int. Symp. on Discharges andElectrical Insulation in Vacuum, Eindhoven,1998.
[94] G. A. Mesyats and I. V. Uimanov, On the Limiting Density of Field EmissionCurrent from Metals [J], IEEE Trans. Dielectr. Electr. Insul.,2006,(13):105-120.
[95] S. A. Barengolts, et al., Structure and time behavior of arc cathode spots [C],20thInternational Symposium on Discharges and Electrical Insulation in Vacuum,Tours,2002.
[96] D. I. Proskurovsky,"Explosive electron emission from liquid-metal cathode [C],23rd Int. Symp. on Discharges and Electrical Insulation in Vacuum, Bucharest2008.
[97] F. Hegeler, et al., Reduction of edge emission in electron beam diodes [J], Phys.Plasmas,2002,(9):4309-4315.
[98] W. S. Koh, et al., Three-dimensional Child–Langmuir law for uniform hot electronemission [J], Phys. Plasmas,2005,(12):053107.
[99] E. Nardi, et al., Dynamic screening and charge state of fast ions in plasma andsolids [J], Laser Part. Beams,2009,(27):355-361.
[100] G. A. Mesyats, Ectons and their role in plasma processes [J], Plasma Phys.Control. Fusion,2005,(47): A109-A151.
[101] J. J. Coogan and E. A. Rose, Observation of screening effect in large-area,cold-cathode diodes [J], Appl. Phys. Lett,1992,(60):2062-2064.
[102] I. I. Beilis, Kinetics of Plasma Particles and Electron Transport in theCurrent-Carrying Plasma Adjacent to an Evaporating and Electron Emitting Wall[J], IEEE Trans. Plasma Sci.,2006,(34):855-866.
[103] D. R. Welch, et al., Simulation of charged-particle beam transport in a gas using ahybrid particle-fluid plasma model [J], Phys. Plasmas,1994,(1):764-773.
[104] V. kvortsov, et al., Computer simulation of MHD-processes in cathode spots [C],IEEE17th International Symposium on Discharges and Electrical Insulation inVacuum, Berkeley,1996.
[105] D. L. Shmelev and E. A. Litvinov, The computer simulation of the vacuum arcemission center [J], IEEE Trans. Plasma Sci.,1997,(25):533-537.
[106] D. L. Shmelev and E. A. Litvinov, About the current and ions flow to the anode inthe current vacuum arc [C], IEEE18th Int. Symp. on Discharges and ElectricalInsulation in Vacuum, Eindhove,1998.
[107] J. W. Schumer, et al., MHD-to-PIC Transition for Modeling of Conduction andOpening in a Plasma Opening Switch [J], IEEE Trans. Plasma Sci.,2001,(29):479-486.
[108] D. R. Welch, et al., Simulations of intense heavy ion beams propagating through agaseous fusion target chamber [J], Phys. Plasmas,2002,(9):2344-2353.
[109] D. Kim and D. J. Economou, Simulation of a two-dimensional sheath over a flatinsulator-conductor interface on a radio-frequency biased electrode in ahigh-density plasma [J], J. Appl. Phys.,2004,(95):3311-3318.
[110] D. R. Welch, et al., Optimized transmission-line impedance transformers forpetawatt-class pulsed-power accelerators [J], Phys. Rev. ST Accel. Beams,2008,(11):030401.
[111] A. B. Sefkow, et al., Simulations and experiments of intense ion beam currentdensity compression in space and time [J], Phys. Plasmas,2009,(16):056701.
[112] L. J. Wang, et al., Numerical simulation of high-current vacuum arccharacteristicsunder combined action of axial magnetic field and external magneticfieldfrom bus bar [J], Phys. Plasmas,2009,(16):123102.
[113] J. Zhou, et al., CHIPIC: An Efficient Code for Electromagnetic PIC Modeling andSimulation [J], IEEE Trans. Plasma Sci.,2009,(37):2002-2010.
[114] S. He, et al., Numerical study on rectangular microhollow cathode discharge [J],Phys. Plasmas,2011,(18):032102.
[115] Y. Y. Lau, Simple Theory for the Two-Dimensional Child-Langmuir Law [J],Phys. Rev. Lett.,2001,(87):1-3.
[116] I. I. Beilis, et al., Anode plasma plume development in a vacuum arc with a“Black-Body” anode-cathode assembly [J], IEEE Trans. Plasma Sci.,2008,(36):1030-1031.
[117] R. F. Hoeberling and M. V. Fazio, Advances in virtual cathode microwavesources [J] IEEE TranS. Elec. Comp.,1992,(34):252-260.
[118] W. Jiang and M. Kristiansen, Theory of the virtual cathode oscillator [J], Phys.Plasmas,2001,(8):3781-3788.
[119] M. B. Lara, et al., Reflex-triode geometry of the virtual-cathode oscillator [J],14th IEEE International Pulsed Power Conference,2003.
[120] R. Kumar, et al., On the relation between the frequency of oscillation of a virtualcathode and injected current in one-dimensional grounded drift space [J], Phys.Plasmas,2004(11):324-327.
[121] P. Appelgren, et al., Study of a compact HPM system with a reflex triode and aMarx generator [J], IEEE Trans. Plasma Sci.,2006,(34):1796-1805.
[122] L. Li, et al., Dynamics of virtual cathode oscillation analyzed by impedancechanges in high-power diodes [J], J. Appl. Phys.,2007,(102):123309.
[123] L. Liu, et al., Efficiency Enhancement of Reflex Triode Virtual Cathode OscillatorUsing the Carbon Fiber Cathode [J], IEEE Trans. Plasma Sci.,2007,(35):361-368.
[124] A. Young, et al., A Compact, Self-Contained High Power Microwave SourceBased on a Reflex-Triode Vircator and Explosively Driven Pulsed Power [C],IEEE International Power Modulators and High Voltage Conference,2008.
[125] A. Roy, et al., Oscillation Frequency of a Reflex-Triode Virtual CathodeOscillator [J], IEEE Trans. Plasma Sci.,2011,(58):553-561.
[126] M. Elfsberg, et al., Experimental studies of anode and cathode materials in arepetitive driven axial vircator [J], IEEE Trans. Plasma Sci.,2008,(36):688-675.