The similarity laws for the maintenance field and the absorbed power per electron in low-pressure surface wave produced plasmas and their extension to HF plasmas in general

This paper presents a theoretical analysis of high-frequency, diffusion-controlled discharges in which the ionization is provided by direct electron impact with gas atoms within the discharge volume. The theoretical formulation uses the electron Boltzmann equation along with two-moment, hydrodynamic-type equations for the electrons and the ions. The treatment followed covers a wide range of applied field frequencies, ω/2π, from ω ≪ ν c to ω ≫ ν c , where ν c is the electron-neutral collision frequency for momentum transfer; it is, however, limited to situations for which ω ≫ τ −1 , where τ is the characteristic electron energy relaxation time by collisions. It is shown that, under steady-state conditions, the maintenance field and the average absorbed power per electron are practically independent of the field configuration and essentially determined by the gas pressure, the configuration and the dimensions of the discharge vessel, and ω, and not by the applied HF power level. Both the maintenance field and the average absorbed power per electron are shown to obey similarity laws as a function of the discharge operating parameters.