A helium discharge with neutral gas flow: Theoretical calculations

Abstract

This study carries out numerical calculations using the ‘‘theory for rf ionization of noble gases with turbulent flow based on a two-electron group model,’’ which was developed in order to investigate the problem of ionizing a high speed neutral gas by the application of an external rf electric field. The plasma model is described by the electron energy and the particle balance equations and accounts for the high-speed neutral gas flow through the turbulent diffusion coefficient and the convection loss term. The calculated results based on the two-electron group model demonstrate that the I-V curves are affected by the magnitude of the turbulent diffusion coefficient, the high-speed flow affects the discharge parameters through the turbulent diffusion coefficient and through the convection loss term, and as the electron density is increased the electron-electron interactions became more intense and the distribution function approaches a Maxwellian at a single electron temperature. The numerical evaluation of the energy exchange terms between the two groups of electrons show that the bulk electrons attain their temperature primarily by the balance between the energy gain due to the electric field and the energy loss due to the elastic collisions with the neutrals and ions, and the tail electrons gain energy primarily by the electron-electron collisions and by the bulk to tail conversion due to the applied electric field, and loose energy primarily by the excitation from the ground level and by the tail to bulk electron conversion due to elastic collisions. The results of calculations for two particular cases indicate that for pressure in the range of 400–510 Torr, temperature in the range 480–511 K, velocity in the range 449–485 m/s, ionizer tube diameter of 0.022 m, one can attain electron densities in the range 1017–1018 m−3 with the application of moderate rf electric fields in the range of 200–400 V/cm.