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)     

Effect of the return plasma current radial profile on the dynamics of resistive hose instability of a relativistic electron beam propagating in a dense gas-plasma medium

The effect of the return plasma current with a characteristic radius differing from the relevant radius of the current density in a relativistic electron beam on the dynamics of the resistive hose instability of the beam is analyzed. The equations are derived for the linear stage of instability evolution. It is shown that when the return plasma current is broader in the radial direction (as compared to the beam), the resistive hose instability becomes noticeably weaker.     

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.     

Envelope equation for a relativistic electron beam with a self-similar current density profile propagating in a dense or rarefied gas-plasma medium along an applied magnetic field

An equation for the envelope of an azimuthally symmetric relativistic electron beam with an arbitrary self-similar profile is derived. It includes the nonlaminarity of the beam and its scattering by the residual gas, as well as the presence of a longitudinal magnetic field and a focusing radial electric field produced by the ionic background.     

Equation for the RMS radius of a relativistic electron beam propagating in dense and rarefied gas-plasma media along an external magnetic field

Transport and virial equations, as well as the equation for the mean total transverse energy of a particle from a transverse segment of an electron beam, are used for deriving an expression for the rms radius of a beam propagating in dense and rarefied gas-plasma media along an external magnetic field.     

Moment equations and the dynamic equilibrium condition for a relativistic electron beam propagating along an external magnetic field in dense and rarefied gas-plasma media

Equations of transfer of mass, momentum, and energy for a transverse segment of a paraxial relativistic electron beam propagating in dense and rarefied gas-plasma media along an external magnetic field are derived from the kinetic equation. A virial equation is obtained, and the dynamic equilibrium condition that generalizes the wellknown Bennet equation for the cases under study is found.     

Kinetic approach to the envelope equation for a relativistic electron beam propagating through a scattering gas-plasma medium in the presence of the reverse plasma current with an arbitrary radial profile

A kinetic approach is applied to derive the transport equations, the virial equation, the dynamic-equilibrium equation, and the envelope equation for an axially symmetric paraxial relativistic electron beam propagating through a scattering gas-plasma medium in the presence of a reverse plasma current with a radial density profile that is generally different from the beam density profile. The equations obtained include additional terms that account for this difference.     

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.     

Effect of the parameters of the plasma channel produced by a high-current relativistic electron beam in dense gaseous media on the beam transportation stability

Results are presented from experimental studies of the time evolution of the plasma channel produced by a high-current electron beam (with an electron energy of E _e = 1.1 MeV, a beam current of I _b = 24 kA, and a pulse duration of t = 60 ns) in helium, nitrogen, neon, air, argon, krypton, xenon, and humid air (air: H₂O) at pressures from 1 to 760 Torr. It is shown that, in gases characterized by a small ratio of the collision frequency to the gas ionization rate u _i , the electron beam produces a broad high-conductivity plasma channel, such that R _b/R _p < 1, where R _b and R _p are the beam and channel radii, respectively. As a result, large-scale resistive hose instability is suppressed.     

Effect of the ionization process on the focusing of a relativistic electron beam by a gas-plasma lens

A numerical simulation is made of the processes occurring in a plasma lens under conditions when the focusing of a relativistic electron beam is strongly affected by the ionization of the residual gas in the lens region by the beam itself. The paraxial, azimuthally symmetric, 1.5-dimensional, electrostatic kinetic model, taking account of plasma production, expansion of the plasma electrons away from the beam region, and contraction of the ions toward the axis of the beam, was used for the calculation. The dynamics of the formation of a focal spot is studied, and the size and position of the spot are determined as functions of time for different values of the gas pressure, initial plasma density, and energy of the beam electrons. Zh. Tekh. Fiz. 67, 90–94 (October 1997)     

Asymptotic form of the radial profile of a relativistic electron beam propagating in a gas-plasma medium in the presence of an external magnetic field and a neutralizing ion background

Boltzmann’s H theorem and variational methods are used to find the temporally asymptotic form of the radial current density profile of a paraxial relativistic electron beam propagating in a scattering gas-plasma medium along a static external magnetic field and a neutralizing ion background. It is shown that in this case the radial profile is Gaussian. Zh. Tekh. Fiz. 67, 62–65 (November 1997)     

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.     

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.     

Calculation of the electrostatic tracking force in the transport of relativistic electron beams in Ohmic plasma channels of low conductivity

The interaction force between a paraxial relativistic electron beam and a preformed Ohmic plasma channel of low conductivity is calculated in the electrostatic limit. The dependence of this force on the channel conductivity and the distance from the beam front is found for concrete parameters of the relativistic electron beam and various values of the beam current rise rate. Zh. Tekh. Fiz. 67, 78–80 (December 1997)     

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.

     

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.     

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.     

Computation of the tracking force acting on a relativistic electron beam propagating in a conducting waveguide under the ohmic and ion-focused regimes

The force of interaction between a relativistic electron beam deflected by resistive hose instability and the eddy current induced in a tubular plasma channel of finite conductivity is computed. Dependences of the force on channel ohmic conductivity and current rise time in a beam pulse are studied. For a beam propagating through a perfectly conducting waveguide under the ion-focused regime, the interaction of the beam with the ion-channel electrostatic image on the waveguide wall is studied for the case when the beam and the channel are deflected from the waveguide axis as a result of ion hose instability. The dependence of the force on both deflection amplitudes is ascertained for the nonlinear phase of instability. It is demonstrated that the force under study may become comparable to the beam-channel interaction force if the deflections are large.