Modeling of nonlocal electron kinetics in a low-pressure inductively coupled plasma.

Abstract

Two different kinetic calculations have been employed to model electron behavior in a low-pressure inductively coupled plasma (ICP) in order to investigate the processes governing the formation of the electron distribution function (EDF). One approach involves a numerical ``propagator'' treatment of time-resolved electron motion in five-dimensional phase space (two spatial and three velocity coordinates) based on the ``convected scheme'' (CS). The other one, referred to as the ``nonlocal'' approach, uses the difference between momentum and energy relaxation rates of electrons to simplify the Boltzmann equation. For the majority of electrons, the nonlocal approach reduces the kinetic equation for the isotropic part of the EDF to a form that exhibits a resemblance to that for homogeneous plasmas. Both calculations incorporate the principal physical effects in a collisional ICP: electron heating by an inductive electric field and nonlocal electron kinetics in which the electrons rapidly lose momentum but travel long distances before suffering a substantial energy loss in collisions. The collision processes that are important in the discharge include quasielastic and inelastic collisions with heavy particles and electron-electron interactions. A comparison of the results of the two methods validates the assumptions employed in the nonlocal approach for the considered range of discharge conditions. To good accuracy the EDF of the majority of the electrons in the ICP is found to be solely a function of the total (kinetic plus potential) electron energy and to be largely independent of the spatial coordinates. The extent to which this is true, and the circumstances under which it is true, are a major focus of this paper. In a rare gas ICP, as a result of Coulomb collisions between electrons, a Maxwell-Boltzmann distribution is typically found in the elastic energy range. The CS calculations demonstrate that trapped electrons can carry a substantial circulating current within the plasma that exceeds the current of free electrons to the walls. \textcopyright{} 1996 The American Physical Society.