Numerical solution of the spatially inhomogeneous Boltzmann equation and verification of the nonlocal approach for an argon plasma

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Abstract
The spatially dependent description of the electron kinetics is of vital interest for the modeling of complete plasma devices. A possible method of dealing with this problem is by the solution of the Boltzmann equation accounting for the spatial inhomogeneity. This approach can be a complicated task. On the other hand, this method may be much more efficient than the treatment of the electron kinetics by simulation techniques. In this paper, the numerical solution of the spatially dependent Boltzmann equation for an argon plasma in cylindrical geometry is reported. A detailed discussion on the boundary conditions is presented. The numerical results are compared to results of the ‘‘nonlocal approach,’’ which is a very efficient method for the solution of the spatially dependent Boltzmann equation for the limiting case that the energy relaxation length of electrons exceeds the discharge dimensions. The range of applicability of the nonlocal approach is discussed in terms of the neutral gas density and the inhomogeneity of the electric field.