Modeling of microwave discharges in the presence of plasma resonances

This study presents a kinetic model of microwave generated discharges sustained, under the conditions of a diffusion controlled regime, by the propagation of azimuthally symmetric surface waves. The effect of the plasma resonances, which can appear over the radial density profile in the vicinity of the walls and lead to sharp peaks in the radial component of the high-frequency wave electric field in the plasma, is introduced. This effect modifies the surface wave damping and results in a collisional as well as collisionless (quasilinear) transfer of energy from the radial field component to the plasma. In the Boltzmann equation the latter appears as a third channel of energy transfer, which is added to the Joule heating by the axial and radial wave field components. The spatially inhomogeneous Boltzmann equation for the electron-energy distribution function, which accoutns for the radial ambipolar field, is solved in the nonlocal approximation. A complete set of relations is formed by simultaneous consideration of the fluid equations for the ion motion and the field equations for the surface wave electric field. The problem is solved numerically. It yields self-consistent radial electron density profiles and radial electric field distributions. The obtained solutions evidence indeed the occurrence of plasma resonances. The study is extended also to obtaining results for the axial variation of the (radially averaged) electron density. It turns out that the widely used concept of approximate constancy of wave power absorbed by one electron in a diffusion controlled regime keeps its validity also in the presence of plasma resonances and of the corresponding collisional, as well as collisionless, power transfer to the plasma in the resonance regions.