Experimental evidence on the nonlocality of the electron distribution function

Abstract

In view of the increasing interest in the modeling of complete plasma devices the influence of the spatial inhomogeneity on the formation of the electron distribution function (EDF) is attracting growing attention. In this paper the radial dependence of the EDF has been investigated experimentally in a cylindrical high frequency (hf) sustained plasma by means of Langmuir probe diagnostics. As a conclusion of the experimental results the electron distribution function can be considered as a spatially homogeneous function of the total energy (i.e., kinetic plus potential energy) of the electrons. The correspondence between the experimental result and the basic ideas of the so-called ‘‘nonlocal approach’’ for solving the spatially inhomogeneous electron Boltzmann equation is pointed out. The main simplification achieved by the nonlocal approach is that the EDF is obtained from a spatially averaged kinetic equation. Nevertheless no information about the spatial variation of the distribution of the kinetic energies of the electrons is lost. A quantitative comparison between a self-consistent plasma model for the considered hf surface wave sustained plasma, based on the nonlocal approach, and measured EDF’s is performed. For sufficiently small pressures good quantitative agreement is found. The deviations at higher pressures are attributed to the influence of stepwise ionization, which is only considered in a rough manner in the present investigation.