Plasma Channel Formation in Inert Gases He and Ar by Low-energy Electron Beam

Abstract

To effective use of low-energy electron beams for technological purposes it is necessary to transport them to the target. For this a previously created plasma channel is used or the beam is injected in a neutral gas and creates independently the plasma channel. A longitudinal external magnetic field is often used for more stable beam movement. In this work, we consider the question of plasma channel formation by the lowenergy electron beam when a drift tube filled with argon or helium. A mathematical model of plasma channel formation is developed with the passage of the high-current electron beam in low-pressure inert gases in the presence or absence of the external magnetic field. This model is a system of nonlinear partial differential equations. Based on the proposed model are given preliminary numerical calculations of plasma channel parameters. The current neutralization of the low-energy electron beam in the low-pressure gas can be obtained. Keywords—electron beam; argon; helium; plasma channel formation I. PRIMARY EQUATIONS The gas ionization in the drift space is due to the ionization of the gas atoms by fast beam electrons and by fields on the front edge of the beam. Plasma channel parameters changes due to gas pressure, geometry of the drift tube and beam parameters. This is an electron density, a plasma temperature and a plasma conductivity. Plasma current appears, current neutralization of the beam and conditions of the beam transportation are change. Plasma current emergence changes beam magnetic field. This current must be taken into account in the calculation of the vector potential. Below we consider a model describing the beam transport in the gas at pressures p < 0.1 Torr in full charge neutralization of the beam. To obtain the results until full charge neutralization an additional model of initial conditions used. Let the electron beam with radius rb is injected in a plane z = 0 along the axis z of the drift tube with radius Rc. The basic heterogeneity associated with the beam and plasma density distribution along the radius because passing time of the beam through the pipe drift is much smaller than the beam rise time. Fields of beam and plasma in the cylindrical coordinate system described by a nonlinear equation:  1 4π ( ) z bz pz A r j j r r r c                where Az is the vector potential, which satisfies the boundary conditions Az(r=Rc) = ∂Az/∂r|r = 0 = 0 and defines the electric field Ez = −(1/c)(∂Az/∂t) and the magnetic field Bθ = −∂Az/∂r; jbz = evbnb – the beam current density; jpz – the plasma current density; c – the speed of light; e is the elementary charge; vb is the speed of beam electrons; nb is the beam density. Let us suppose the drift tube has an ideal wall. The drift tube has ground potentials on its ends. The plasma current is accepted equal to zero in initial time. The initial condition for the vector potential is derived from (1). An interaction between the plasma current density, the electric field and the plasma conductivity is defined by the equation:  1 σ ν pz z pz ef j E j t       where σ = ene / (meνef) is the plasma conductivity; me is electron mass; ne is the plasma electron density; νef = νea + νei + νei is the effective collision frequency between plasma electrons and heavy particles; νea is the frequency of collisions between plasma electrons and gas atoms; νei = 1.45∙10niTeln(2.4∙10Te/ni) is the frequency of collisions between plasma electrons and ions; ni – the atomic (l=1) and molecular (l=2) ion density; Te is the electron plasma temperature, eV [1]; νea = 3.7∙10ngTe for argon, νea = 4.4∙10ngTe for helium [2]; ng is the gas density. The balance of particles is described by the following equations: