A conservative finite difference method for the numerical solution of plasma fluid equations

This paper describes a numerical method for the solution of a system of pla sma fluid equations. The fluid model is similar to those employed in the si mulation of high-density, low-pressure plasmas used in semiconductor proces sing. The governing equations consist of a drift-diffusion model of the ele ctrons, together with an internal energy equation, coupled via Poisson's eq uation to a system of Euler equations for each ion species augmented with e lectrostatic force, collisional, and source/sink terms. The time integratio n of the full system is performed using an operator splitting that conserve s space charge and avoids dielectric relaxation timestep restrictions. The integration of the individual ion species and electrons within the time-spl it advancement is achieved using a second-order Godunov discretization of t he hyperbolic terms, modified to account for the significant role of the el ectric field in the propagation of acoustic waves, combined with a backward Euler discretization of the parabolic terms. Discrete boundary conditions are employed to accommodate the plasma sheath boundary layer on underresolv ed grids. The algorithm is described for the case of a single Cartesian gri d as the first step toward an implementation on a locally refined grid hier archy in which the method presented here may be applied on each refinement level. (C) 1999 Academic Press.