Large-scale resistive instability of a relativistic electron beam in a plasma channel

The kinetic equation method is used to study the stability of a heavy-current electron beam in a dense plasma channel with a relatively low conductivity. Increments and critical currents are obtained. It is shown that even slightly nonlinear transverse motion stabilizes the system. The main conclusions agree with the experimental results.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 84–89, April, 1986.     

Calculation of force exerted by the Ohmic plasma channel on a relativistic electron beam propagating in a dense gas-plasma medium

The problem on the interaction of an Ohmic plasma channel displaced in the transverse direction with a paraxial azimuthally symmetric relativistic electron beam propagating in a dense gas-plasma medium is considered. The formula for determining the force of the beam-plasma interaction is derived using the “hard” model of the beam and the channel in the case of an arbitrary displacement of the symmetry axis of the plasma channel relative to the corresponding axis of the beam. The forces are calculated in the Bennett and Gauss approximations for the radial profiles of the beam and the channel.     

Equation for the envelope of a relativistic electron beam propagating in a resistive plasma channel during the evolution of resistive hose instability

Kinetic methods are used to derive the transport equations, virial equation, dynamic equilibrium condition, and the equation of the envelope of an axially symmetric paraxial relativistic electron beam propagating in an Ohmic plasma channel during the evolution of resistive firehose instability. The equation of the beam envelope is generalized by taking this instability into account.     

Simulation of the dynamics of resistive hose instability of a relativistic electron beam propagating in a resistive plasma channel with arbitrary conductivity

The spatial dynamics of the resistive hose instability of a relativistic electron beam has been studied for the case when the charge neutralization time is much longer, on the order of, or much shorter than the current compensation time. It has been found that the growth of this instability has the highest increment when the charge neutralization time is on the order of skin time.

     

A planar relativistic electron beam in a plasma channel bounded by conducting walls

The force interaction of a relativistic electron beam with a plasma in a channel bounded by planegeometry highly conducting walls is studied. The steady-state interaction regime, ω=ku, is analyzed using the model of a cold collisional electron plasma. The formulas for the transverse component of the force acting on the beam electrons are derived for an arbitrary deviation of the beam from the symmetry plane of the channel.     

Transverse dynamics of a low-density relativistic electron beam propagating in the plasma along an external magnetic field

It is shown that a low-density relativistic electron beam can be transported under conditions of (i) periodic oscillation of the beam radius, (ii) unlimited beam expansion, and (ii) pinching. Analytical expressions for the radial evolution of the beam under these transport condition are obtained.     

Anomalous scattering of a relativistic electron beam in a beam created plasma

Measurements of the velocity angular distribution of a relativistic electron beam (0.8 MV, 6 kA, 150 ns) after propagation through hydrogen gas are presented. At a pressure of 25 Pa scattering of the beam electrons into a preferential angular interval is observed. At 190 Pa anomalously large scattering is observed, up to an angular width of 90°, during about 30 ns.     

Laser-driven relativistic electron dynamics in a cylindrical plasma channel

The energy and trajectory of the electron, which is irradiated by a high-power laser pulse in a cylindrical plasma channel with a uniform positive charge and a uniform negative current, have been analyzed in terms of a single-electron model of direct laser acceleration. We find that the energy and trajectory of the electron strongly depend on the positive charge density, the negative current density, and the intensity of the laser pulse. The electron can be accelerated significantly only when the positive charge density, the negative current density, and the intensity of the laser pulse are in suitable ranges due to the dephasing rate between the wave and electron motion. Particularly, when their values satisfy a critical condition,the electron can stay in phase with the laser and gain the largest energy from the laser. With the enhancement of the electron energy, strong modulations of the relativistic factor cause a considerable enhancement of the electron transverse oscillations across the channel, which makes the electron trajectory become essentially three-dimensional, even if it is flat at the early stage of the acceleration.     

Calculation of the interaction force between a relativistic electron beam and an Ohmic plasma channel

A formula for calculating the interaction force between a relativistic electron beam and a preformed Ohmic plasma channel with an arbitrary offset of the channel axis from the beam axis is obtained in the case of complete charge neutralization. It is shown that this force is repulsive for radial profiles of the conductivity with a peak on the channel axis. Zh. Tekh. Fiz. 67, 69–76 (June 1997)     

Parametric instabilities produced by a relativistic electron beam in a plasma

The parametric instability driven by the primary spectrum of the hydrodynamic two-stream instability produced by a relativistic electron beam in a plasma is investigated. The saturated level of the primary wave electric field is determined by electron trapping in the potential well of the wave or by the quasilinear beam relaxation process. After saturation, the primary wave collapses by way of the oscillating two-stream instability. The cases of the strong and weak primary electric field in comparison with the thermal energy of a plasma are considered. For a strong field the growth rates of the parametric instability and plasma heating due to the latter are found. Ion heating is not significant in comparison with electron heating (approximately as the cube root of the mass ratio). In a weak field the parametric oscillating two-stream spectrum of saturation is found. In the one-dimensional case this spectrum of electric field energy fluctuations varies as k⁻² if the fluctuation field exceeds the threshold pump electric field for the oscillating two-stream instability. For the weak field plasma heating rate is found. Since the energy transfer is via Landau damping, the particle heating is characterized by the formation of high-energy tails on the distribution function.     

Generalization of the Bennett equilibrium condition for a relativistic electron beam propagating in the Ohmic plasma channel and ion focusing regime along an external magnetic field

The problem of formulating the generalization of the Bennett equilibrium condition is considered for a relativistic electron beam propagating in the Ohmic plasma channel, as well as in the ion focusing regime in the presence of an external longitudinal uniform magnetic field. We assume that the electron component of the background plasma is not completely removed from the region occupied by the beam. This equilibrium condition is derived using the mass and momentum transport equations obtained for a paraxial monoenergetic beam from the Fokker–Planck kinetic equation.     

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.     

相对论电子束在动态加载等离子体中的自聚焦传输

为了进一步研究相对论电子束-离子通道辐射实验和理论的需要, 研究了相对论电子束入射中性气体以及通过碰撞电离动态加载等离子体实现对高能束流的自聚焦传输过程PIC(particle in cell) 模拟发现, 电子束电离出的离子背景能够实现对电子束的聚焦传输. 但是离子背景横向和纵向的不均匀性对束流的传输特性有显著影响. 在此基础之上, 提出了电子束在横向不均匀离子背景中传输的理论模型, 给出了束流的自聚焦条件.数值计算结果表明, 横向不均匀性会导致电子束的混合相位传输, 使得焦点附近内层电子可能跑到电子束外而被散焦损失, 这与PIC模拟的结果相符. 此外, PIC模拟还发现, 由于电子束的自聚焦, 在焦点处将电离出更多的离子而引起纵向不均匀性, 纵向不均匀性使得碰撞后的低能电子被俘获, 俘获电子效应会大幅降低电子束的传输效率. 但是俘获电子在纵向呈准周期分布, 对传输电子起到静电Wiggler场的作用, 可能实现静电Wiggler场的动态加载. 研究结果对于进一步研究电子束-等离子体系统的实验以及理论模型提出有一定的参考价值.     

Intense laser beam propagating in a plasma channel with flat-bottom leaky density profile

The propagation characteristics of an intense laser beam in a preformed plasma channel with the flat-bottom leaky density profile are investigated in detail. The evolution equation of the laser spot size is derived by employing variational technique. Seven propagation modes of the laser spot size are identified and some numerical results are presented. By comparison, we find that the results in this Letter may be more realistic since the flat-bottom leaky plasma channel comes closer to the practical plasma channel.     

Ion-focused propagation of a relativistic electron beam in the self-generated plasma in atmosphere

It is known that ion-focused regime (IFR) can effectively suppress expansion of a relativistic electron beam (REB). Using the particle-in-cell Monte Carlo collision (PIC-MCC) method, we numerically investigate the propagation of an REB in neutral gas. The results demonstrate that the beam body is charge neutralization and a stable IFR can be established. As a result, the beam transverse dimensions and longitudinal velocities keep close to the initial parameters. We also calculate the charge and current neutralization factors of the REB. Combined with envelope equations, we obtain the variations of beam envelopes, which agree well with the PIC simulations. However, both the energy loss and instabilities of the REB may lead to a low transport efficiency during long-range propagation. It is proved that decreasing the initial pulse length of the REB can avoid the influence of electron avalanche. Using parts of REB pulses to build a long-distance IFR in advance can improve the beam quality of subsequent pulses. Further, a long-distance IFR may contribute to the implementation of long-range propagation of the REB in space environment.     

Inhomogeneous relativistic electron beam interaction with inhomogeneous warm plasma

The interaction of inhomogeneous relativistic electron beam with inhomogeneous bounded warm plasma, which leads to amplification of waves, is analyzed. It is shown that due to the resonant increase in wave’s field with a decrease in the plasma permittivity to zero, the power absorbed by plasma is finite and depends on the plasma thermal velocity. The relativistic electron beam not only amplifies waves in plasma but also provides efficient absorption of these waves by plasma.