Effect of external magnetic field on critical current for the onset of virtual cathode oscillations in relativistic electron beams

In this Letter we research the space charge limiting current value at which the oscillating virtual cathode is formed in the relativistic electron beam as a function of the external magnetic field guiding the beam electrons. It is shown that the space charge limiting (critical) current decreases with growth of the external magnetic field, and that there is an optimal induction value of the magnetic field at which the critical current for the onset of virtual cathode oscillations in the electron beam is minimum. For the strong external magnetic field the space charge limiting current corresponds to the analytical relation derived under the assumption that the motion of the electron beam is one-dimensional [D.J. Sullivan, J.E. Walsh, E. Coutsias, in: V.L. Granatstein, I. Alexeff (Eds.), Virtual Cathode Oscillator (Vircator) Theory, in: High Power Microwave Sources, vol. 13, Artech House Microwave Library, 1987, Chapter 13]. Such behavior is explained by the characteristic features of the dynamics of electron space charge in the longitudinal and radial directions in the drift space at the different external magnetic fields.     

Influence of nonuniformities of a magnetic-mirror field on the space-time characteristics of a long-pulse relativistic electron beam

An experimental investigation is made of the influence of local nonuniformities of a mirror-configuration magnetic field on oscillations of the space charge and the structure of a long-pulse relativistic electron beam. It is found that the outcome depends on the axial configuration of the nonuniformity. A nonuniformity near the cathode can substantially reduce the amplitude of the oscillations and improve the beam transport. The creation of a nonuniformity far from the cathode leads to an accelerated increase in the oscillations and causes spreading of the transverse structure of the beam. A possible explanation is given for the mechanism responsible for the influence of these local magnetic field nonuniformities assuming reflection of the cathode plasma and electron flux from the magnetic mirror, and also allowing for a jump in the drift velocity. Zh. Tekh. Fiz. 67, 83–88 (August 1997)     

Dynamic processes in helical electron beams in gyrotrons

The results of theoretical and experimental studies of collective processes in helical electron beams in gyrotron-type devices are generalized. Main attention is paid to low-frequency oscillations associated with the development of instability in the space charge trapped between the cathode and the magnetic mirror. The mechanism of evolution of instability is substantiated and the effect of oscillations on the main parameters of the electron flow determining its quality is analyzed. Data on the suppression of low-frequency oscillations and resulting enhancement of the gyrotron efficiency are considered.     

TWO-DIMENSIONAL NUMERICAL SIMULATION OF LOW FREQUENCY OSCILLATIONS OF SPACE CHARGE AND POTENTIAL IN THE GYROTRON ADIABATIC TRAP

The development of oscillations of the space charge and potential in the adiabatic trap of a gyrotron between the cathode and the cavity is studied numerically. The PIC method is applied, with the real two-dimensional distributions of the electric and magnetic fields taken into account. Secondary emission is included into the numerical model, as well as such factors as the electron beam space charge, thermal velocities of electrons, and emitter roughness. The value of the trapped space charge as a function of time is calculated. Time dependences of the potential in various cross-sections of the formation system are traced. The amplitudes of its variable component have been found and then the corresponding frequency spectra have been calculated. The process of cathode bombardment is investigated. The energy distribution and time dependence of the current in the electron beam coming to the operating space are found. Some ways to reduce the oscillations of the potential and the space charge are discussed.     

“神龙—Ⅰ”直线感应加速器束流输运系统设计

系统分析了强流相对论电子束在输运过程中影响束流品质的几种因素,针对束流不同能区凸现的主要矛盾,采取对应性措施以抑制空间电荷效应,束包络振荡和束心横向运动,所有措施归结到束流输运系统设计上表现为合适的束输运半径和匹配磁场的选取,提出了束流输运磁场配置的一般策略,初步设计了“神龙－Ⅰ”直线感应加速器束流输运系统的总体布局。     

“神龙-I”直线感应加速器束流输运系统设计

 系统分析了强流相对论电子束在输运过程中影响束流品质的几种因素,针对束流不同能区凸现的主要矛盾,采取对应性措施以抑制空间电荷效应、束包络振荡和束心横向运动。所有措施归结到束流输运系统设计上表现为合适的束输运半径和匹配磁场的选取,提出了束流输运磁场配置的一般策略,初步设计了“神龙 I”直线感应加速器束流输运系统的总体布局。     

Improvement of the helical electron beam quality and the gyrotron efficiency by controlling the electric field distribution near a magnetron injection gun

A technique for controlling the electric field distribution near the cathode of a magnetron injection gun is developed. The feasibility of improving the quality of a helical electron beam by optimizing the electric field distribution in a pulsed 4-mm-wave gyrotron is studied theoretically and experimentally. Field distributions are obtained that minimize the electron velocity spread in the beam, coefficient of electron reflection from a magnetic mirror, and intensity of parasitic low-frequency oscillations. It is demonstrated that the gyrotron efficiency can be increased through a rise in the beam quality at the optimized electric field distribution.     

磁场对球头阴极二极管特性的影响

 采用全电磁PIC粒子模拟方法研究了磁场对球头阴极二极管物理特性的影响。结果表明外加磁场主要是通过对二极管束流轨迹的改变来影响二极管的物理特性。由于外加磁场将约束其产生电子束的发散，结果使其空间电荷限制电流减小，其值在无外加磁场并且自磁场可以忽略时的空间电荷限制电流值的0.5~1倍范围内。当外加磁场足够强时，束流轨迹主要受外加磁场控制，二极管产生的电子束既不箍缩也不发散。强外加磁场条件下的空间电荷限制电流近似为无外加磁场时的一半；在无外加磁场条件下，在阳极处的束流半径随二极管电压电流的增大而减小，空间电荷限制电流增强因子随束流半径的减小而减小，随二极管电压电流增大而减小。这一系列结果是在二极管电流小于其自箍缩临界电流条件下得到的。     

Feasibility Study of Axially- Extracted Virtual Cathode Oscillator

In this paper, we have analyzed the design parameters of the axially - extracted virtual cathode oscillator, which is high-power microwave source based on the concept of the virtual cathode associated with the intense relativistic electrons beam oscillations in the electrostatic potential well. The microwave emission by the virtual cathode oscillator results from both the space and time oscillations of virtual cathode and reflexing electrons trapped in the potential well between the virtual and real cathodes. In the X-band frequency spectrum 700 MW microwave peak power has been obtained analytically by the solid electron beam of 300 kV and 20 kA for feasible design parameters. The analysis has been performed by 2-dimensional, relativistic, electromagnetic particle-in-cell simulation code XOOPIC.     

Study of transients in the formation of heavy-current nanosecond electron beams

Results are presented from experimental and numerical studies of the spatial and temporal microstructure of a relativistic heavy-current electron beam of nanosecond duration. The beam is formed in a magnetically insulated coaxial diode with an edge-emitting cathode. Microcurrent oscillations and azimuthal nonuniformity of the beam are seen, the scale of the latter depending on the maximum cyclotron radius of the electrons. Two- and three-dimensional numerical calculations performed by the macroparticle method show that space-charge oscillations near the cathode produce these phenomena even in the case of a uniform emission surface. It is shown that the increase in the full current of the beam that occurs during the pulse in a weak magnetic field is connected with the gradual propagation of emission to the cylindrical outside surface of the cathode. A study is made of the effect of the discreteness of the emission surface on the impedance and current of the vacuum diode. The linear increase seen in current during the pulse with a small number of emission centers is attributed to an increase in their size as a result of expansion of the cathode plasma. Institute of Heavy-Current Electronics, Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 12, pp. 31–48, December, 1996.     

Weakly relativistic and space charge effects in interaction of high-power microwave with plasma

In the present work, numerical studies on the effects of weakly relativistic ponderomotive force and space charge in the nonlinear interaction of a high-power microwave beam with a plasma are carried out. It is shown that, the profiles of the electron density and dielectric permittivity contain high peaks, and modulation of wavelength occurs in electron density distribution by increasing the microwave energy flux. In addition, it is indicated that the profiles of the electric and magnetic fields in relativistic regime are lengthened more than non-relativistic regime by increasing the initial electron density and the relativistic effects cause the increase in oscillation wavelength of electron density, dielectric permittivity and space charge field, in comparison with the non-relativistic regime. Finally, the results of the research show that the steepening in electron density distributions and their oscillation wavelength are enhanced, when the relativistic effects appear.     

Experimental and theoretical investigation into the effect of the electron velocity distribution on chaotic oscillations in an electron beam under virtual cathode formation conditions

The effect of the electron transverse and longitudinal velocity spread at the entrance to the interaction space on wide-band chaotic oscillations in intense multiple-velocity beams is studied theoretically and numerically under the conditions of formation of a virtual cathode. It is found that an increase in the electron velocity spread causes chaotization of virtual cathode oscillations. An insight into physical processes taking place in a virtual-cathode multiple-velocity beam is gained by numerical simulation. The chaotization of the oscillations is shown to be associated with additional electron structures, which were separated out by constructing charged particle distribution functions.     

电子初始能量对双向流二极管空间电荷限制流密度的影响

 从理论上研究了阴极发射电子初始能量对一维平面非相对论性双向流二极管内空间电荷限制电子、离子流密度的影响,并与阴极发射电子初始能量为0情况下的空间电荷限制电子、离子流密度进行了比较。     

射频腔光阴极注入器发射度研究

 在激光驱动的光阴极注入器产生的高亮度电子束中，空间电荷引起发射度的增长。分析了射频腔中引起发射度增长的因素以及解决这个问题的办法——在射频腔的阴极附近加一个螺旋聚焦磁场进行补偿，也给出了补偿后电子束的发射度并和数值模拟结果进行比较，实验测试表明，所得结果比较符合。     

相对论电子束虚阴极静电振荡的粒子模拟

本文运用有限大小粒子模型,用等离子体粒子模拟方法,对相对论电子束的虚阴极振荡作了一维静电粒子模拟。结果表明,在注入电流小于空间电荷极限电流时,电子束能稳定传输并能全部通过。当注入电流超过空间电荷极限电流时,传输是不稳定的,将有部分电子反射,部分通过。空间电荷形成的虚阴极的位置和电势周期性地振荡。电流越大,虚阴极位置越靠近注入面且变化范围越小,虚阴极电势越低且振幅越大,振荡频率越高且大于电子束等离子体频率。     

Formation and dynamics of a virtual cathode in a tubular electron beam placed in a magnetic field

Mechanisms underlying the formation and dynamics of a virtual cathode (VC) in a tubular electron beam subjected to a magnetic field are studied using a numerical 2D model. Two qualitatively different competing types of space charge dynamics near the VC are discovered. Which of them predominates depends on the magnetic field strength. The beam current critical density at which a nonstationary VC forms in the system is also strongly dependent on the magnetic field. It is shown that the optimal strength of the magnetic field that minimizes the beam current critical density depends on the Brillouin magnetic field.     

电磁复合聚焦—偏转球面阴极透镜的相对论象差理论

本文应用变分原理研究了电磁复合聚焦-偏转球面阴极透镜的相对论象差理论。在考虑阴极面逸出电子具有一定的初能量和初角度分布,物场和象场弯曲以及阴极面上磁场和横向电场不为零的情况下,导出了任意理想象面上的一级近轴横向象差和包括色球差在内的全部三级几何横向象差,以及各种特殊类型象差系数的明显表达式。本文导出的象差公式不仅普遍适用于宽束和细束阴极透镜,而且普遍适用于相对论或非相对论,阴极和屏为球面或平面时的各种情况。本文以复数描写轨迹,用矩阵表示象差,形式简洁,适合于计算机计算。 关键词：     

Impedance Control in Relativistic Electron Diodes with Externally Applied Prepulse

Low impedance relativistic electron accelerators currently produce nominal 50 ns pulses that are capable of power levels near 1 Terawatt at impedances near 1 Ohm. The time-dependent diode impedance characteristic plays a major role In efficiently coupling the pulse line power to an electron beam. In an effort to establish the desired accelerator impedance match early in the pulse, experimentalists have investigated cold cathode vacuum breakdown and subsequent space charge limited emission during the ~ 100 kV machine prepulse. This machine prepulse is due to capacitive coupling across the accelerator switches, and consequently cannot be independently studied and optimized. In this paper, a technique for externally introducing a typically 100 kV, low power conditioning pulse prior to the main pulse of a low impedance relativistic electron diode is described, along with techniques for reducing the machine prepulse to less than 5 kV. For various cathode geometries, the breakdown field, closure velocity, and time-dependent impedance established by this external prepulse is measured and compared with an empirical model of space charge limited emission from a hydro-dynamically expanding plasma. 3 Experimental evidence is presented that the high current accelerator impedance is effectively controlled by the relative time delay between the start of the prepulse and the main pulse.     

空间电荷效应对热场致发射中诺廷汉效应的影响

热场致发射阴极所产生的强流电子束具有很强的空间电荷效应,为研究该效应对热场致发射过程中诺廷汉（Nottingham）效应的影响机理,在理论分析的基础上,用数值方法研究了不同逸出功和多个外加电场条件下考虑空间电荷效应对诺廷汉效应结果的影响,并与不考虑空间电荷效应时的情形进行了对比. 结果表明：空间电荷效应的强弱会显著影响到阴极表面的稳态电场,进而对诺廷汉效应产生不可忽略的影响;当逸出功在3.0–4.52 eV、外加电场在3×10⁹–9×10⁹ V/m范围内时,考虑空间电荷效应的影响后,热场致发射电子所带走的平均能量较不考虑空间电荷效应时增加0–2.5 eV,且温度越高或外加电场越大时,该增加值越大;考虑空间电荷效应对诺廷汉效应的影响后,热场致发射电子从阴极带走的平均能量随外加电场的增加呈非线性下降规律;当阴极表面温度较高时,诺廷汉效应中的冷却效应随二极管间隙距离的变大而增强. 关键词： 热场致发射 诺廷汉效应 空间电荷效应 阴极表面电场     

Excitation of low-frequency oscillations via interaction of a high-current relativistic electron beam with a radial ion flux

The nonlinear excitation of low-frequency oscillations in the case when an ion flux is radially injected into the drift chamber where a tubular relativistic electron beam propagates is studied. A mechanism behind low-frequency ion oscillations is discussed.