Simulation of relaxation processes in electron beams at high magnetic fields

Molecular-dynamics simulations of relaxation processes in electron beams at high magnetic fields are presented. The result of the longitudinal–longitudinal relaxation and the rate of the transverse–longitudinal relaxation are calculated for magnetic fields between 0.006 and 0.1 T for electron beam parameters typical of those in low-energy electron coolers. Comparisons with theoretical and experimental values are made. This revised version was published online in July 2006 with corrections to the Cover Date.     

Numerical simulation and experimental study of an electron-optical system of a megawatt gyrotron with step frequency tuning in the range 100–170 GHz

We present the results of numerical simulation and experimental studies of the systems of forming helical electron beams with different topologies for a 1-MW gyrotron with step frequency tuning in the range 100–170 GHz. We analyze variations in the beam parameters including the distribution of electrons over the oscillatory velocities, as functions of the beam current for various accelerating voltages and magnetic fields. The results of experimental studies of a prototype of the multifrequency gyrotron in the oscillation regime such that the designed optimized electron-optical system forms an intense helical electron beam with specified parameters in a wide interval of magnetic fields are shown. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 9, pp. 773–784, September 2007.     

周期会切磁场聚焦强流相对论带状电子束的理论分析和粒子模拟

对低幅值、短周期、有偏置磁极的周期会切磁场中300 keV,3 kA带状电子束的传输进行了理论分析和粒子模拟。给出了将波导宽度考虑在内的轴向均匀带状电子束的空间电荷场和作用在有限厚度的带状电子束的短边和宽边上的聚焦力的表达式,并利用束匹配的方法得到了磁场的幅值和周期,以及电子束通道的宽度和高度等参数。最后根据理论计算的结果进行了3维粒子模拟验证,结果表明:束宽边上聚焦良好,而在短边上带状电子束的轴向有限长效应使得聚焦力与散焦力沿轴向不能完全匹配,在束包络上产生了Betatron振荡,但在300 mm的距离上传输效率仍能达到98%以上,说明有偏置磁极的周期会切磁场聚焦强流带状电子束在理论上是可行的。     

Nonlinear transverse-wave interactions in divergent axially symmetric magnetic fields

The dynamics of transverse-wave interactions in intense electron beams in divergent axially symmetric magnetic fields has been investigated by computer simulation. The case of a short magnetic field was analyzed. The conversion of electron-beam transverse waves in the presence of a decelerating electric field was considered.     

Vibration and instability of a single-walled carbon nanotube in a three-dimensional magnetic field

The vibration and instability of a single-walled carbon nanotube (SWCNT) under a general magnetic field are of particular interest to researchers. Using nonlocal Rayleigh beam theory and Maxwell’s equations, the dimensionless governing equations pertinent to the free vibration of a SWCNT due to a general magnetic field were derived. The effects of the longitudinal and transverse magnetic fields on the longitudinal and flexural frequencies as well as their corresponding phase velocities were addressed and are discussed below. The critical transverse magnetic field (CTMF) associated with the lateral buckling of the SWCNT was obtained. The obtained results reveal that the CTMF increases with the longitudinally induced magnetic field. Further, its value decreases as the effect of the small-scale parameter increases.     

Stability of high-current beams of relativistic electrons in cyclic systems

Stability conditions of high-current thin beams of relativistic electrons against excitation of long-wave oscillations in a stellatron and modified betatron have been investigated theoretically. The influence of self electric and magnetic fields obtained from electron beam delayed potentials has been taken into consideration. The correspondent dispersion relation has been found. The electron beam of the modified betatron has been shown to be always unstable against excitation of the oscillations considered. Necessary and sufficient conditions for the elec-tron beam confinement in a stellatron have been found.     

Formation and transportation of low-energy high-current electron beams in the plasma-filled diode under the effect of the external magnetic field

The mechanisms behind limitation of current of nonrelativistic high-current electron beams in the plasma-filled diode immersed in the external guiding magnetic field whose intensity is comparable with that of the beam self magnetic field are studied. It is shown that the beam current is limited by transmission capacity of the double layer between the cathode and anode plasma on the one hand and, on the other hand, by charge neutralization of the beam and by the decrease of the longitudinal velocity of the beam electrons under the action of the induced electric field and of the beam self magnetic field. The effect of the beam self fields on its cross-sectional current density and energy distributions is studied. Results of the numerical simulations are in good agreement with the experimental data.     

Structure formation and tearing of an MeV cylindrical electron beam in a laser-produced plasma

The stability of a cylindrical, solid hot electron beam propagating in a high density plasma has been studied using a two-dimensional, hybrid Darwin code. The initially solid beam evolves into a hollow, annular beam due to the Weibel instability and generates strong magnetic fields on both sides of the annular ring. The annular structure subsequently breaks up into several beamlets via a mechanism similar to a tearing instability. It is found that the magnetic fields parallel to the direction of beam propagation also grow due to the tearing process.     

准矩形截面强流相对论带状电子束的传输

提出利用准矩形截面带状电子束传输强电流.相对于目前广泛采用的椭圆形截面带状电子束,在大横纵比,即电子束的宽度(横向)远大于厚度(纵向)的情况下,其厚度沿横向更加均匀,利用冷阴极爆炸发射容易产生.该电子束利于高功率微波发生器中腔体模式的控制和束波作用效率的提高,如果利用模块化的结构还可使阴极及聚焦磁铁在宽度上的扩展更加容易.首先给出了准矩形截面带状电子束空间电荷场的典型分布,然后根据该分布和束匹配的方法对相互独立的周期会切磁铁和边聚焦磁铁分别进行了设计.其中边聚焦磁铁的磁化方向与以往的纵向不同,为横向磁化,其激励的边聚焦磁场在电子束宽边的边缘附近的梯度更大,有利于横向的束匹配.最后根据理论分析的结果进行了粒子模拟.结果表明,300keV,3kA的准矩形截面强流相对论带状电子束可以在0.163T的周期会切磁场和0.064T的横向磁化边聚焦磁场中稳定传输,电流传输效率大于98%.     

Interaction of space-charge waves in an electron beam with electromagnetic waves in a longitudinal magnetic field

The effect of space charge on the interaction between an electron beam and an electromagnetic wave in a longitudinal magnetic field has been considered. The equations describing the interaction processes have been formulated within the two-dimensional linear theory and solved using the dispersion-equation approach and the successive approximation method.     

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.     

Nonlinear interactions between electrons and RF waves in crossedelectric and magnetic fields

A laboratory experiment has been initiated to study nonlinear electron-wave interactions. In this experiment, the interaction between a guided RF wave and an electron beam is investigated using a large crossed field amplifier. The electron beam is injected through externally imposed crossed electric and magnetic fields. The large-amplitude RF wave is guided by a serpentine slow wave structure and travels at a phase velocity approximately equal to the average velocity of the electron beam. The formation of long-wavelength density structures has been proposed to affect the emission characteristics of the RF wave itself. Possible applications of the experiment in space plasmas are discussed     

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.     

Angular velocity spread of relativistic electron beam generated by high current diode

Theoretical analysis and numerical simulations of the Relativistic Electron Beam (REB) generation in a high current diode immersed in an external magnetic field has been done. The calculations have confirmed that the generated beam is homogeneous and monoenergetic in a broad central region. In the case of cylindrical diode the mixing of electron trajectories has been observed only in a narrow periphery beam region. The angle between particle trajectories and external longitudinal magnetic field varies chaotically from 0° to –25°. This phenomenon suppresses the excitation of two stream instability excited by the REB in the plasma column.     

Advanced Numerical and Experimental Investigation for Gyrotrons Helical Electron Beams

The paper presents a modern approach to studies of characteristics of intense helical electron beams (HEBs) for gyrotrons. The essence of the method consists in finding functions of electron distribution with respect to oscillatory velocities in the beam both by numerical simulation and experimentally. Experimental and calculated data for beams with different topologies were compared in different frequency ranges. Evolution of the electron oscillatory velocities distribution function as the beam current grows has been traced. Influence of the reflected electrons on beam parameters has been simulated numerically.     

Measurements of harmonic wake fields excited by rough surfaces

An experiment has been carried out at the TESLA Test Facility linac to investigate the wake fields generated by picosecond electron bunches in narrow beam pipes with an artificially roughened inner surface. The energy structure imposed on the bunches by the wake fields has been analyzed with a magnetic spectrometer. Strong harmonic-wake-field effects are observed as expected from simulations in which the rough surface is modeled by a dielectric layer.     

Elementary pinning forces measured using low temperature scanning electron microscopy

Magnetic flux penetrating Josephson tunnel junctions parallel and transverse to the tunnel barrier has been imaged using low temperature scanning electron microscopy. Employing this technique we have studied the behavior of magnetic flux quanta under the influence of external forces. The strength of pinning centers acting on vortices existing within the barrier has been determined by measuring the turning angle of these flux quanta in rotating magnetic fields. Trapped transverse flux quanta could be depinned by applying a sufficient Lorentz force or electron beam irradiation. The strength of the pinning centers has been determined.     

周期场聚焦电子束

引言 自从发现“强聚焦效应”可以应用在粒子加速器内以后,人们知道利用周期磁场能把离子束控制得更细,于是可以减少磁铁的需要量。因此近年来为了改建或新设计各种类型粒子加速器,对周期场聚焦离子束或电子束方面曾进行了很多研究工作。另一方面人们也开始研究用周期电场和磁场聚焦各种电子管内的电子束,例如行波管内电子束的聚焦等。聚焦电子束的主要特点在於必要考虑空间电荷。     

Experimental investigation of stochastic pulsation and formation of light bullets with megagauss magnetic fields by an intense laser pulse propagating in a preionized plasma

The generation of extremely stable light bullets in a preformed plasma near critical density has been observed experimentally during the interaction of intense picosecond laser beam with a metallic target in air. Optical probing measurements indicate the formation of pulsating channels, typically of about 5 microm in diameter, directed towards a heating laser beam, as well as of disconnected massive plasma blocks moving also towards the laser beam. The velocities of the dense plasma blocks reach the values of 4.5x10(8) cm/s. The blocks are stable during their acceleration and propagation in air. Self-generated magnetic fields up to 4-7 MG were observed by means of the Faraday rotation of a probe laser beam.     

宽束和细束电磁复合聚焦球面阴极透镜的象差理论

本文研究了对宽束和细束阴极透镜普遍适用的电磁复合聚焦球面阴极透镜的象差理论。在考虑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象差在内的全部三级横向象差矩阵公式。所得的结果较为完整、普遍。本文详细讨论了宽束和细束阴极透镜的关系,并用轨迹法和变分法严格证明了:当考虑阴极面逸出电子具有一定的初能量和初角度分布,并采用准规范化电位表示的近轴轨迹方程来讨论系统的理想成象时,宽束和细束两类阴极透镜从象差理论以至导出的三级横向象差、象差系数表示式都可以统一起来。本文采用矢量描写轨迹,运用矩阵表示象差,形式简洁,象差系数积分收敛,适合于计算机计算。 关键词：