Axial structure of low-pressure high-frequency discharges sustained by travelling electromagnetic surface waves

Abstract

For the last two decades, the discharges sustained by RF and microwave surface waves (SW) have been a subject of both experimental and theoretical studies. These plasmas are created by the electric field of an electromagnetic wave travelling along the discharge vessel. The RF or microwave power flow is supplied by a high-frequency generator coupled to the discharge through various matched wave launching structures (surfatron, surfaguide, waveguide surfatron, or Ro-box) the individual operating frequency band of which overlaps to cover the domain from less than one MHz up to 10 GHz. As a rule, these discharges are sustained in a cylindrical dielectric tube. The plasma column surrounded by its dielectric discharge tube is a self supporting waveguide or an integral part of the waveguiding structure when the tube is within a metallic enclosure. The length of the plasma column is generally much larger than its diameter. The whole system extends axially and, under travelling wave conditions, it is axially nonuniform since plasma density decreases away from the launcher. Our concern is the theoretical description of these discharges. The electric field maintaining the discharge is assumed small enough for the wave propagation across the plasma medium to be described by relations for the linear regime. The local electromagnetic properties of the plasma are univocally determined by the local value of its relative permittivity ε p = 1 − ω p 2 ω(ω + iv) , where ω and ω p are the wave and plasma angular frequencies, respectively, and v is the effective electron-neutral collision frequency for momentum transfer. A steady state discharge exists when the production of charged particles is balanced by their recombination loss. With reduced pressure plasmas depending on specific conditions, one can observe either the diffusion or the recombination gas-discharge regime. In a diffusion controlled discharge, the charged particles generated in the discharge volume are all lost at the walls, while in a recombination controlled discharge, the particle loss occurs through recombination in the bulk of the plasma. The balance between the power input from the electromagnetic field to the plasma and the power loss due to collisions of electrons with the gas atoms governs the steady state of any RF or microwave discharge. The model of a plasma column sustained by a travelling electromagnetic wave consists of at least three basic equations: (i) a local wave dispersion relation; (ii) a wave to electron power balance equation, and (iii) a relation between the absorbed power per unit length and the electron density, which depends on the gas-discharge regime. Such a model generally yields the conditions for a steady-state discharge to exist and also allows one to calculate the axial distribution of the electron density n( z), wave power S( z), wave number k( z) and the wave field components. Only the quantities which can be externally controlled when running the discharge are given a priori in the calculations. These are the quantities describing the discharge vessel dimensions and configuration, the waveguiding structure if any, the nature and pressure of the gas, the operating angular frequency ω and the input microwave power S exc. Note that the plasma densities n exc and n end at the origin (near the wave exciter) and at the end of the column are not set externally and have to be determined from calculations. Our theoretical review of SW plasmas includes models of plasmas sustained by surface waves in various electromagnetic modes (azimuthally symmetric and dipolar) and considers the influence of an axially directed static magnetic field. The basic results of these theoretical studies are in a good agreement with the available experimental data.