Self-consistent modeling of surface wave produced discharges at low pressures

Abstract

A self-consistent theory of a low-pressure gas discharge sustained by a surface wave (SW) is presented which provides a complete description of the plasma density (ne) and SW-field distribution both in the radial (r) and the axial (z) directions. The theory is based on a complete set of equations including Maxwell’s equations and the boundary conditions for the SW-field, the electron Boltzmann equation which yields local collisional and transport data versus the SW-electric field E, and the continuity and momentum transfer equations for the electrons and the ions. For given operating frequency, gas density, setup dimensions and total incident power Pi(0), the theory enables the determination of: (i) the SW-dispersion relation; (ii) ne(r,z) and E(r,z); (iii) Pi(z); and (iv) θ(z), the radially averaged mean absorbed power per electron. It is shown that Ē(z), the radially averaged field in the plasma, and θ(z) are practically constant along z, in spite of the fact that Pi(z) steadily decreases. Comparison with experiment is made for SW discharges in Ar operated at the frequencies of 433 MHz and 2.45 GHz.