A COLLISIONAL-RADIATIVE MODEL FOR MICROWAVE DISCHARGES IN HELIUM AT LOW AND INTERMEDIATE PRESSURES

A stationary collisional-radiative model for helium microwave discharges in cylindrical geometry is developed by coupling the rate balance equations for the n less-than-or-equal-to 6 excited states of helium to the continuity and transport equations for the electrons, He+ atomic ions and He-2+ molecular ions, and to the homogeneous Boltzmann equation. The latter is solved using the Dc effective field approximation but taking into account stepwise inelastic and superelastic processes from the 2(3)S, 2(1)S and 2(3)P states, as well as electron-electron collisions. A coherent set of electron cross sections is deduced in order to solve the Boltzmann equation. Special attention is paid to the atomic collisions considered (by taking into account I-change reactions and associative ionization reactions), and to the effects of radiation imprisonment. This, together with the inclusion of the kinetics of the molecular ions, allows the range of validity of the model to extend up to atmospheric pressure. The theoretical populations for the excited states, characteristics for the steady-state reduced maintenance electric field and mean absorbed power per electron at unit gas density agree very well with experimental data from surface wave discharges for 0. 1 Torr less than or similar to P less than or similar to 30 Torr, 300 MHz less than or similar to omega/2 pi less than or similar to 2500 MHz, 5 X 10(11) cm-3 less than or similar to n(e) less than or similar to 5 X 10(12) cm-3, 500 K less than or similar to T(g) less than or similar to 2000 K and 0.3 cm less than or similar to R less than or similar to 1.0 cm, where P is the gas pressure, omega is the angular frequency of the applied HF field, n(e) is the electron density, T(g) is the gas temperature, and R is the tube radius. Relatively small dependence of the discharge characteristics on omega, n(e), T(g) and R is observed. The model also predicts that the molecular ions will be mainly produced by associative ionization and lost by diffusion to the wall.