Dynamics of self-consistent planar axisymmetric motions of an electron beam in a magnetic field

The dynamics of self-consistent planar axisymmetric motions of a cylindrical electron beam is investigated analytically. The beam electrons move under the action of an unneutralized space-charge field against an immobile ion background or in a vacuum in the presence of a magnetic field. The electric field strength and the electron density and velocity are determined as functions of the distance traveled by the beam electrons.     

Contraction of the space of electron drift in low-frequency bunchers

In the paper we theoretically investigate the mechanism by which the space of drift electrons is contracted in klystron-type bunchers which modulate the electron beam in ion accelerators, in particular to excite an rf field. The contraction of the drift length is effected through a decrease in the mean beam velocity in the field of an electrostatic lens or a metal tube and is based on the fact that the relative motion of velocity-modulated electrons are independent of the mean velocity of the electron beam in a weak modulation regime.     

Numerical investigation of the methods for reducing the runaway electron beam divergence

We have performed a comparative numerical analysis of two methods for reducing the runaway electron beam divergence using an external magnetic field or a dielectric tube. The generation of runaway electrons takes place in an inhomogeneous medium that consists of a hot channel (spark channel, laser torch, etc.) surrounded by air under normal conditions. The model makes it possible to consistently calculate the formation of a subnanosecond gas discharge and the generation of accelerated electrons under these conditions. The possibility of effectively decreasing the runaway electron beam divergence using an external magnetic field, as well as a dielectric tube, has been demonstrated. However, the number of runaway electrons in the case with the tube is considerably smaller than in the case with the magnetic field due to the fact that some runaway electrons settle on the tube walls. The energy spectra of the runaway electrons significantly differ in these cases, which can be explained by the differences in the dynamics of the discharge formation.     

Effect of the self-field of an intense relativistic electron beam on its interaction with matter

The effect of the self-field of an intense relativistic electron beam on its interaction with a dense medium was studied by solving a system of equations consisting of the kinetic equation for the fast electrons, the hydrodynamic equations for the plasma electrons, and Maxwell's equations for the electromagnetic field. It was assumed that the macroscopic parameters of the medium (its density, conductivity, and electron collision frequency) were independent of time. The system of equations was solved using high-order perturbation theory. The results show that a magnetic field is formed by the beam of fast electrons and to an equal degree by a current of thermalized electrons, which has not been taken into account before. It is shown also that the magnetic field of the beam affects its transmission through matter. In particular, the penetration depth of the electrons in matter and the transverse dimensions of the beam are both smaller than in a weak-current beam.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 10, pp. 19–24, October, 1987.The author deeply thanks K. A. Dergobuzov for support of the work, and A. V. Arzhannikov, V. A. Klimenko, and A. V. Lapp for useful discussions.     

Die Elektronenbewegung im Neutralgas bei hohen elektrischen Feldern

In strong electric fields the acceleration of the electrons by the field exceeds the deceleration by collisions with neutral molecules. Thus run-away or beam electrons are produced. This paper investigates the motion of the beam electrons in a neutral gas considering ionization processes by electron-molecule-impacts. We start with a time independent current of primary electrons (case a) and a space independant density of primary electrons (case b). The further development of the velocity distribution is calculated. For a molecular hydrogen gas the amplification of the initial electrons, the average ionization, and the velocity distribution of the electrons as a function of space or time respectively is given. The average ionization has an asymptotic solution, which becomes valid, when one primary electron has produced by ionization an avalanche of approximately 100 electrons. The Townsend coefficient α for high values of the field strength is independant of space only in the region of this asymptotic solution.     

分子束穿透托卡马克等离子体的机理

由于分子束分子密度远高于周围等离子体密度,沿托卡马克内的磁力线进入分子束区域的电子因非弹性碰撞而失去部分能量和动量,引起分子束区的电子堆积,形成静电双层,其屏蔽效应是分子束可以较深透入托卡马克等离子体的主要机制。     

Distribution function of an electron beam in a focusing magnetic field

The distribution function of electrons moving in an axially symmetric focusing magnetic field is constructed. The macromotion and self-field of the beam are taken into account. The nonrelativistic and relativistic limits are discussed. Upon switching off the magnetic field the distribution functions obtained change into the Maxwell-Boltzmann distribution. The motion of charged particles in a focusing magnetic field is the simplest model for investigation of a beam of particles, for example, electrons, in storage or accelerator rings. In accordance with the well-known theorem of N. Bohr, a magnetic field has no effect on the distribution function for a one-dimensional distribution of electrons with respect to the momenta. However, the situation is altered if macromotion occurs in a static system, for example, the revolution of electrons in storage or accelerator rings. Maintaining the focusing of the beam in an equilibrium orbit, the magnetic field thereby affects the electron distribution function. For an actual electron beam the distribution function is determined by the initial conditions of formation of the beam; however, as a result of scattering processes it will approach some steady-state equilibrium distribution function. We will discuss the problem of finding such a distribution function in the nonrelativistic and relativistic cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 35–40, July, 1978.The author thanks Professor I. M. Ternov of Moscow University for his constant interest in this research and Professor V. G. Bagrov of Tomsk University for help in the research.     

On the influence of the voltage pulse rise time and cathode geometry on the generation of a supershort avalanche electron beam

The influence of the voltage pulse rise time on the amplitude of a runaway electron beam and X-ray generation in air and nitrogen under atmospheric pressure is studied experimentally and theoretically. Generalization of the whistle criterion for the case of a nonuniform field is suggested. It is shown that the maximal energy of beam electrons and the beam current amplitude grow when the voltage pulse rise time decreases. It is found that the amplitude of the runaway electron current reaches a maximum at a certain curvature of the cathode. The maximal energy of electrons increases when the radius of curvature of the cathode exceeds the value at which the beam current amplitude is the highest. If the field is nonuniform, its critical value at which many electrons run away is more than an order of magnitude lower than in the uniform field.     

激光驱动强流电子束产生和控制

在惯性约束聚变(ICF)电子束快点火物理方案中,需要超强拍瓦激光脉冲驱动MeV能量的强流电子束,并沉积数十kJ能量到压缩氘氚芯区。强流电子束的束流品质是影响点火成功的关键因素之一,为深入了解强流电子束产生物理过程,研制成了三维高性能、适应上万CPU核规模的并行粒子模拟程序,并开展了大规模数值模拟研究,探索了强流电子束的产生机制和输运规律。回顾了近几年来快点火研究团队围绕强流电子束产生和控制开展的研究,介绍了导致束流品质差的两大物理原因:预等离子体效应和束流不稳定性磁场的随机散射。针对这两个物理原因,提出了四种提高强流电子束品质的方法:(1)双层金锥靶减弱预等离子体的负面效应;(2)输运丝产生环向磁场准直强流电子束;(3)外加磁场导引强流电子束提高耦合效率;(4)抑制束流不稳定性以降低随机磁场对电子束流的散射。     

Effect of the anode-current magnetic field on the motion of electrons in a triode with a virtual cathode

The effect of the anode-current magnetic field on the electron motion in a triode with a virtual cathode is considered. It is shown that the anode-current magnetic field influences the oscillation period and trajectories of electrons. The condition of self-isolation of the electron beam is investigated as a function of the diode parameter. It is shown that the displacement of the beam electrons under the action of the anode-current magnetic field leads to a decrease in the electron phase modulation and an increase in the spread in the electron oscillation amplitude; as a result, the generation efficiency of microwave radiation decreases.     

电子在激光驻波场中运动产生的太赫兹及X射线辐射研究

采用单电子模型和经典辐射理论分别对低能和高能电子在线偏振激光驻波场中的运动和辐射过程进行了研究. 结果表明: 垂直于激光电场方向入射的低速电子在激光驻波场中随着光强的增大, 逐渐从一维近周期运动演变为二维折叠运动, 并产生强的微米量级波长的太赫兹辐射; 高能电子垂直或者平行于激光电场方向入射到激光驻波场中, 都会产生波长在几个纳米的高频辐射; 低能电子与激光驻波场作用中, 激光强度影响着电子的运动形式、辐射频率以及辐射强度; 高能电子入射时, 激光强度影响了电子高频辐射的强度, 电子初始能量影响着辐射的频率; 电子能量越高, 产生的辐射频率越大. 研究表明可以由激光加速电子的方式得到不同能量的电子束, 并利用电子束在激光驻波场的辐射使之成为太赫兹和X射线波段的小型辐射源. 研究结果可以为实验研究和利用激光驻波场中的电子辐射提供依据.     

Microscopic analysis of merging processes of relativistic electron beams propagating in a high-density plasma

The dynamical processes of an energetic electron beam propagating through a high-density plasma have been analyzed using an electromagnetic two-dimensional hybrid simulation code. After an initially solid cylindrical electron beam breaks up into a number of small beamlets, they start to merge with each other by means of their mutual current attractive force. The results show that detailed processes which take place when a pair of beamlets merge into a single one are different for different sizes of beamlets. When the size of the beamlet is small, the merging process is accompanied by magnetic field generation and the energy of the beam electrons then decreases in time. On the other hand, when the beamlet becomes sufficiently large, the merging no longer generates an excess magnetic field, and the energy of beam electrons is kept constant. The difference comes from the magnitude of the return current induced in the surrounding background plasma.     

A New Scheme for High‐Intensity Laser‐Driven Electron Acceleration in a Plasma

We propose a new approach to high‐intensity relativistic laser‐driven electron acceleration in a plasma. Here, we demonstrate that a plasma wave generated by a stimulated forward‐scattering of an incident laser pulse can be in the longest acceleration phase with injected relativistic beam electrons. This is why the plasma wave has the maximum amplification coefficient which is determined by the acceleration time and the breakdown (overturn) electric field in which the acceleration of the injected beam electrons occurs. We must note that for the longest acceleration phase the relativity of the injected beam electrons plays a crucial role in our scheme. We estimate qualitatively the acceleration parameters of relativistic electrons in the field of a plasma wave generated at the stimulated forward‐scattering of a high‐intensity laser pulse in a plasma. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Field properties and vacuum electron acceleration in a laser beam of high-order Laguerre–Gaussian mode

The electric field intensity distribution and the phase velocity distribution of high-order Laguerre–Gaussian (LGρ?) mode laser beams are analyzed. Using three-dimensional test particle simulation, the numerical results of electrons accelerated by LG00, LG40 and LG41 mode laser beams are presented. Compared with the LG00 mode (the fundamental mode) laser beam, low-energy injection electrons can be more favorably accelerated in a high-order LG mode laser beam. Contrary to anticipation, a high-order LG mode laser beam with intense axial electric field distribution is inferior to the LG00 mode in capture acceleration for electrons with high injection energy.     

Separator of primary and signal electrons for very low energy SEM

High resolution can be obtained in the scanning electron microscope (SEM) for a very low landing energy of electrons, even for that below 50 eV, when a cathode lens is used with the specimen as a cathode held at a high negative potential but the detection of signal electrons is totally different compared with classical SEM. Primary electrons with an energy of the order of tens of keV are decelerated in the field of the cathode lens to a very low landing energy and signal electrons originating in the specimen are accelerated and collimated by the same field to a narrow beam with an electron energy nearly the same as that of the primary beam. To detect these signal electrons we must deflect them from the optical axis without deteriorating the properties of the primary beam. The design of a novel type of separator of the primary and signal electrons consisting of two stages, each of them formed by the electric and magnetic crossed fields, is presented, together with calculated trajectories for both primary and signal electrons.Presented at the Seminar on Secondary Electrons in Electron Spectroscopy, Microscopy, and Microanalysis, Chlum (The Czech Republic), 21–24 September 1993.For computations of fields and trajectories, the software package of the Delft Particle Optics Foundation developed by Dr. B. Lencová and Dr. G. Wisselink [10] was used. The design was consulted with Dr. M. Lenc.     

Spectra of electrons and X-ray photons in a diffusive nanosecond discharge in air under atmospheric pressure

The spectra of electrons and X-ray photons generated in nanosecond discharges in air under atmospheric pressure are investigated theoretically and experimentally. Data for the discharge formation dynamics in a nonuniform electric field are gathered. It is confirmed that voltage pulses with an amplitude of more than 100 kV and a rise time of 1 ns or less causing breakdown of an electrode gap with a small-radius cathode generate runaway electrons, which can be divided into three groups in energy (their energy varies from several kiloelectronvolts to several hundreds of kiloelectronvolts). It is also borne out that the formation of the space charge is due to electrons appearing in the gap at the cathode and a major contribution to the electron beam behind the foil comes from electrons of the second group, the maximal energy of which roughly corresponds to the voltage across the gap during electron beam generation. X-ray radiation from the gas-filled diode results from beam electron slowdown both in the anode and in the gap. It is shown that the amount of group-3 electrons with an energy above the energy gained by runaway electrons (in the absence of losses) at a maximal voltage across the gap is much smaller than the amount of group-2 electrons.     

The Electrostatic Trapping of an Intense Relativistic Electron Beam in a Magnetic Mirror

Observations of rapid axial oscillations of an intense relativistic electron beam in a magnetic mirror are reported. The mirror field primarily provides radial confinement of the relativistic electrons. The axial confinement was achieved by placing thin aluminized mylar foils at the conjugate mirror field maxima. The region between these foils was filled with a few Torr air to provide a beam induced plasma for charge and current neutralization. The regions outside these foils were maintained at ~10-4 Torr. One foil formed the anode of a space-charge limited relativistic electron diode which launched the beam into the mirror. When the beam passed through the second foil it was no longer charge neutralized. In a manner quite similar to the anode foil oscillations observed by others, a space-charge limited electrostatic well was established which stopped the electrons and re-accelerated them through the foil-thereby reflecting the beam. When the reflected electrons re-entered the diode, they were once again "electrostatically" reflected. This process continued until the oscillating beam was either lost through the "virtual cathodes" outside the foils, dissipated in the drift region or quenched in the diode plasma after gap closure.     

Momentum spread in a relativistic electron beam in an undulator

The motion of the relativistic electron beam in the spatially periodic magnetic field of an undulator has been considered taking into account the effect of the incoherent field of the spontaneous undulator radiation on the motion of the electrons. An expression for the rms momentum of the electrons has been obtained. It has been shown that the momentum spread in the ultrarelativistic electron beam increases in the spontaneous incoherent emission mode. Conditions for the self-amplification of the spontaneous undulator radiation in ultrashort-wavelength free-electron lasers have been discussed.     

Production of low-emittance MeV protons by localized electrons

Energetic proton beam generation and the suppression of transverse proton beam divergence are investigated in this paper. In laser-foil interactions, foil ions are accelerated by an ambipolar field created by accelerated high-energy electrons. The high-energy electrons are generated by the ponderomotive force of an intense laser. When an intense laser illuminates a hydrogen foil target, the electrons are strongly accelerated longitudinally, and a localized negative electrostatic potential is generated at the opposite side of the laser illumination. Foil protons are accelerated longitudinally and at the same time extracted to the central axis of the laser by the localized potential in the transverse direction. Consequently, transverse proton divergence is suppressed and a low-emittance MeV proton beam is produced.     

串列加速器电离性束流截面探测器设计

基于GIC4117串列加速器束流引出线束流测量需求,开展了电离型束流截面探测器设计工作,主要包括系统收集信号强度的计算,采用有限元软件进行电场系统、磁场系统优化设计,给出了电场系统与磁场系统设计参数。通过引入辅助磁场,测量系统能够实现束流轨道的自动校正,系统对束流的影响可以忽略。对影响测量精度的电离电子横向位置偏移进行了分析,并对电离电子进行轨迹跟踪。跟踪结果表明:电离电子在横向位置的运动偏移可以控制在0.3 mm以内,与理论分析一致。