Passage of a high-current relativistic electron beam through matter

A solution is presented for the problem of passage of a high-current relativistic electron beam through matter in the stationary case with one-dimensional geometry. The system of equations describing the passage of the beam consists of the kinetic equation for fast electrons, which considers the effect of the electric field on the magnitude and direction of particle momentum, the equations for the field produced by the space charge generated by thermalized electrons, and relations connecting the conductivity of the medium to the radiation field. Higher-order perturbation theory is used for the solution. The solutions reveal that the distribution of expended energy, thermalized electrons, and other properties of the flow are highly dependent on the density of the incident flux and the conductivity of the medium. It will be shown that linear transfer theory may be applied to calculation of the passage of high-current beams through matter over a wide range of currents and conductivities, if the barrier thickness does not exceed one-half the path length, but cannot be used for calculation of passage through large-thickness barriers, i.e., with thickness comparable to the electron free path length.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 67–74, September, 1979.The author thanks A. N. Didenko and A. M. Kol'chuzhkin for their evaluation of the study.     

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。     

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。     

Magnetically guided fast electrons in cylindrically compressed matter

Fast electrons produced by a 10 ps, 160 J laser pulse through laser-compressed plastic cylinders are studied experimentally and numerically in the context of fast ignition. K(α)-emission images reveal a collimated or scattered electron beam depending on the initial density and the compression timing. A numerical transport model shows that implosion-driven electrical resistivity gradients induce strong magnetic fields able to guide the electrons. The good agreement with measured beam sizes provides the first experimental evidence for fast-electron magnetic collimation in laser-compressed matter.     

Nonlinear Theory of the Plasma Wave Excitation in a Bounded Beam-Plasma System

The excitation of symmetric and antisymmetric plasma waves by a beam layer that moves within a homogeneous plasma enclosed by a metallic wall was dealt with theoretically. Investigations were carried out for the magnetic field free case and for a magnetized electron beam. In the latter case, the beam electrons are assumed to be unable to move in the perpendicular direction. The theoretical model bases upon an extension of the well known single wave theory to a two-dimensional beam-plasma system. Special emphasis should be paid to the fact that the perpendicular wave profile of the excited waves was determined self-consistently. Energy and momentum balance equations are derived for this system. The theoretical method outlined in this paper which is based on a Green's-function technique can be extended easily to three-dimensional systems or to beam-plasma systems with other boundary conditions. The main features of the saturation process of the basic unstable wave types are discussed. Several interesting effects were found in the magnetic field free case: (i) numerical solutions describe an increasing steepening of the wave amplitudes in perpendicular direction near the center of the system for the symmetric potential wave; (ii) for the antisymmetric wave, a smoothing tendency was found in the development of the perpendicular wave potential profile; (iii) spatial separation of the slow and fast beam electrons was observed; (iv) it is shown for the antisymmetric potential wave type that, under certain conditions, a very efficient beam particle retardation mechanism occurs which is connected with a strong reduction of the formation of a fast particle group; (v) generally it was shown that the conversion of the kinetic energy of the beam electrons into the plasma wave energy may be more effective as compared with the case of the magnetized beam.     

Certain general questions of fast-electron transport II. Kinetic equations and conditions governing the accelerated motion of fast electrons in dielectrics in an electric field

A general kinetic equation for the differential density of fast particles moving in a medium in an external field is derived on the basis of the continuity equation in phase space. An equation is written for the differential flux in the case of fixed target particles. This equation is used to derive equations for fast electrons; account is taken of the coupling of energy-loss and scattering events in an electric field for various particular problems analogous to those studied in the theory of electron transport in the absence of a field. The kinetic equations are used to analyze the conditions governing accelerated motion of electrons in a dielectric in an external electric field in the continuous-deceleration approximation. Account is taken of fluctuations in the energy loss and of multiple scattering. There are two energy ranges of particles moving in a dielectric in which accelerated motion can occur; in the case of an electron beam with a continuous energy spectrum, this acceleration would be accompanied by monochromatization of the beam.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 7–12, February, 1972.     

220 GHz回旋管脉冲磁场系统和电子枪的设计与实验研究

 根据220 GHz回旋管的工作要求,设计了其所需的脉冲磁场系统与电子枪。脉冲磁场系统采用哑铃状结构,具有均匀区长、电阻小与电感小等优点,可以在较低电容与电压下获得更高的脉冲峰值磁场,并分析了其脉冲放电特性。电子枪采用双阳极磁控注入枪,用EGUN对其进行了设计优化,电子注纵横速度比为1.53,速度零散为3.1%。实验研究表明,脉冲磁场峰值强度达到8 T,电子注电流达到2 A,电子电流基本传输到靶片,控制极与阳极没有截获到电子,脉冲磁场系统与电子枪工作正常,达到设计要求。     

220 GHz回旋管脉冲磁场系统和电子枪的设计与实验研究

根据220 GHz回旋管的工作要求,设计了其所需的脉冲磁场系统与电子枪。脉冲磁场系统采用哑铃状结构,具有均匀区长、电阻小与电感小等优点,可以在较低电容与电压下获得更高的脉冲峰值磁场,并分析了其脉冲放电特性。电子枪采用双阳极磁控注入枪,用EGUN对其进行了设计优化,电子注纵横速度比为1.53,速度零散为3.1%。实验研究表明,脉冲磁场峰值强度达到8 T,电子注电流达到2 A,电子电流基本传输到靶片,控制极与阳极没有截获到电子,脉冲磁场系统与电子枪工作正常,达到设计要求。     

Electron Motion in the Three-Dimensional Field of Undulator

In this paper we consider the motion of relativistic electrons in an ideal three-dimensional magnetic field of an undulator. The ideality of the magnetic field means that, on the undulator axis, the field is directed strictly vertically upward and has a strictly sinusoidal shape. In the overwhelming majority of cases, only this leading component of the field is taken into account in calculating the electron trajectory. In this paper, in the equations of motion of an electron in the magnetic field of an undulator, all three components of the field are taken into account, so that the undulator field under consideration satisfies the stationary Maxwell equations. In this case, the differential equations of motion of the electron are solved analytically with the help of perturbation theory, and not by the method of averaging over fast oscillations of the electron, as was done in a number of previous papers. These analytic expressions for trajectories describe the behavior of particles in the focusing magnetic field of an undulator much more completely. An analysis of these expressions shows that the behavior of electrons in such a three-dimensional field of the undulator is much more complicated than what follows from the equations obtained by the averaging method. In particular, there is a cross effect when changes in the initial vertical parameters of the electron trajectory cause changes in the horizontal component of its trajectory and vice versa. A comparison of the solutions obtained analytically with the results of numerical calculations of electron trajectories using the Runge–Kutta method demonstrates their high accuracy.     

Kinetic equation for a relativistic electron beam propagating along an external magnetic field in dense and rare gas-plasma media

A kinetic equation that describes the transverse dynamics of an axisymmetric paraxial relativistic electron beam propagating along an external magnetic field in a gas-plasma medium is derived with allowance for the influence of the self-consistent electromagnetic field on the beam, the effects related to the nonlaminar motion and rotation of the beam electrons at the exit from the injector, and the scattering and energy loss of the beam electrons in their collisions with the neutral particles of the background gas.     

大回旋半径电子枪渐变线圈磁场的设计及优化

对大回旋半径电子枪的渐变线圈磁场进行了设计,采用3个线圈实现所需要的渐变磁场分布,增加了线圈磁场系统的调节能力,理论和计算机仿真的磁场分布结果符合得很好。将实现的渐变磁场分布同给定的静电场分布相结合,通过求解带电粒子的运动方程得到了粒子轨迹,在此基础上建立大回旋半径电子枪的3维粒子仿真模型,在给定静电场分布条件下分析了3个线圈安匝数对电子束参数的影响,完成了工作电压为40 kV、工作电流为1 A的大回旋半径电子枪的参数优化,得到了横纵速度比为1.4～2.5,纵向速度离散小于8%(横纵速度比为1.9时)的大回旋半径电子束。     

Coupling Instability of a Warm Relativistic Electron Beam with Ion-Channel Guiding

In this paper, the coupling instability of warm relativistic electron beam (WREB) propagating through the ion channel guiding is investigated in detail. Obtaining the equilibrium state of the system by considering the self-electric and azimuthal magnetic field, the fluid-Maxwell equations as well as linear perturbation theory are employed to derive the dispersion relation of the excited modes in the system. Numerical analysis of the obtained dispersion relation shows that the electromagnetic (EM) instability can be induced nearly the center of the beam through coupling between the fast electron plasma wave (FEPW), originated from the longitudinal oscillation of WREB, and fast forward electromagnetic wave (FFEW). In this sense, growing the perturbation amplitude occurs due to transport the kinetic energy of WREB to the EM wave at the specific frequency range, where the phase velocity of FEPW and FFEW is coincided. The results of the present investigation will greatly contribute to the understanding of the stability of the warm relativistic electron beam in laboratory experiments, such as in free electron laser experiments, where the ion-channel guiding is used to confine the electrons against the self-repulsive forces generated by the beam itself.     

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.     

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.     

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.     

Analytical Description of Electron Motion in a Three-Dimensional Undulator Field

The motion of relativistic electrons in an ideal three-dimensional magnetic undulator field satisfying the stationary Maxwell equation is considered. The system of nonlinear differential equations of the electron motion is solved analytically using perturbation theory rather than the method for averaging fast oscillations of the electron trajectory (the focusing approximation), as was done in a series of previous studies. The obtained analytical expressions for the trajectories describe the behavior of particles in a three-dimensional magnetic undulator field much more accurately than the formulas obtained within the framework of the focusing approximation. The analysis of these expressions shows that the behavior of electrons in a three-dimensional undulator field is much more complicated than that described by equations obtained using the averaging method. In particular, it turns out that the electron trajectories in the undulator have a cross dependence; in this case, variations in the initial trajectory parameters in the vertical plane cause changes in the horizontal trajectory components, and vice versa. The results of calculations of the trajectories carried out using analytical expressions are close to those of numerical calculations using the Runge-Kutta 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.     

On possibility of measurement of the electron beam energy using absorption of radiation by electrons in magnetic field

A possibility of precise measurement of the electron beam energy using absorption of radiation by electrons in a homogeneous magnetic field for electrons of high energy in the range up to a few hundred GeV, was considered earlier. In this paper, with the purpose of experimental checking of this method in the range of several tens MeV of electrons energies, a possibility of measurement of absolute energy of the electron beam with a relative accuracy up to 10^?4, is considered. We take into account influence of the laser beam diffraction, of the spread of electrons over energies, and of the length of formation of radiation absorption in the process of electron beam energy measurement. The laser wavelength and the length of the magnet are chosen depending on the length of photon absorption formation. It is found that the kinematical restrictions on the photon absorption process lead to the selection in angles of propagation of photons, which can be absorbed by the beam electrons. It is shown that parameters of the electron beam will noticeably not vary during the measurement of the energy.     

Current drive generation based on autoresonance and intermittent trapping mechanisms

Two mechanisms for generating streams of high-velocity electrons are presented. One has its origin in auto resonance (AR) interaction, which takes place in the system after a trapping conditioning stage, the second being dominated by the trapping process itself. These mechanisms are revealed from the study of the relativistic motion of an electron in a configuration consisting of two counterpropagating electromagnetic waves along a constant magnetic field in a dispersive medium. Using a Hamiltonian formalism, we have numerically solved the equations of motion and presented the results in a set of figures showing the generation of streams of electrons having high parallel velocities. Insight into these numerical results is gained from a theoretical analysis, which consists of a reformulation of the equations of motion. The operation of these mechanisms was found to circumvent the deterioration of the electron acceleration process that is characteristic for a dispersive medium, thus allowing for an effective generation of a current drive. Discussion of the results follows.     

大回旋半径电子枪渐变线圈磁场的设计及优化

对大回旋半径电子枪的渐变线圈磁场进行了设计,采用3个线圈实现所需要的渐变磁场分布,增加了线圈磁场系统的调节能力,理论和计算机仿真的磁场分布结果符合得很好。将实现的渐变磁场分布同给定的静电场分布相结合,通过求解带电粒子的运动方程得到了粒子轨迹,在此基础上建立大回旋半径电子枪的3维粒子仿真模型,在给定静电场分布条件下分析了3个线圈安匝数对电子束参数的影响,完成了工作电压为40 kV、工作电流为1 A的大回旋半径电子枪的参数优化,得到了横纵速度比为1.4～2.5,纵向速度离散小于8%(横纵速度比为1.9时)的大回旋半径电子束。