Theory of Low-Pressure Plasma Columns Produced by Electromagnetic Waves in the Presence of a Constant Axial Magnetic Field

Abstract

The axial structure of an isotropic plasma column, sustained by an electromagnetic surface wave, as well as the wave characteristics (wave power, wave number and wave field components) for the simplest configuration — plasma surrounded by vacuum — is specified by three numerical parameters: σ = ω R/c (ω being the wave angular frequency, R the plasma column radius, c the speed of light), β (β = 0 for freefall/diffusion gas-discharge regime and 0 < β ≤ 2 for recombination one) and the mode number m (m = 0 for azimuthally-symmetric waves and m = ±1 for dipolar waves). In particular, when the plasma is created by a wave in the dipolar mode the parameter σ should be greater than a critical value σ cr = 0.3726, specified by the wave dispersion characteristics.1 Our approach in this matter is to extend the theoretical knowledge to the case, where the discharges are submitted to an axial static magnetic field B 0. The influence of the magnetic field is twofold: First, in a magnetic field the plasma becomes anisotropic, which reflects in a change of the propagation characteristics and the field structure of the electromagnetic wave. Second, a relatively strong magnetic field must reduce the radial electron diffusion, which leads to a decrease of the electron temperature. Moreover, the magnetic field modifies the density radial distribution of the exited atoms in radiative and metastable states.2 The presence of a constant axial magnetic field introduces an additional parameter Ω = ω c/ω (ω c is the electron cyclotron frequency). For given gas-discharge conditions (a and s fixed) the magnetic field action is completely different for the symmetric and dipolar waves respectively. The change of wave dispersion characteristics, due to the magnetic field, turns out to be crucial. When the plasma is created by a symmetric wave, the stronger the magnetic field, the longer the column length.3 In the case of dipolar wave the status is just the opposite: for a fixed wave power the stronger the magnetic field, the shorter the column length. Moreover then the wave polarization becomes decisive and only the right-handed (m = +1) circularly polarized electromagnetic waves can produce plasma.4,5 An important feature is that the magnetic field makes it possible to sustain a plasma column for value of σ smaller than σ cr and the magnitude of Ω can be optimized to yield an almost constant axial profile of the plasma density.5