ANALYTIC SOLUTIONS AND PARTICLE SIMULATIONS OF CROSS-FIELD PLASMA SHEATHS

Particle simulations have been made of an infinite plasma slab, bounded by absorbing conducting walls, with a magnetic field parallel to the walls. The simulations have been either one dimensional or two dimensional, with the magnetic field normal to the simulation plane. Initially, the plasma has a uniform density between the walls and there is a uniform source of ions and electrons to replace particles lost to the walls. In the one-dimensional (1-D) case, there is no diffusion of the particle guiding centers and the plasma remains uniform in density and potential over most of the slab, with sheaths about a Debye length wide where the potential rises to the wall potential. In the two-dimensional (2-D) case, the density profile becomes parabolic, going almost to zero at the walls, and there is a quasineutral presheath in the bulk of the plasma, in addition to sheaths near the walls. Analytic expressions are found for the density and potential profiles in both cases, including, in the 2-D case, the magnetic presheath resulting from a finite ion Larmor radius, and the effects of the guiding center diffusion rate being either much less than or much greater than the energy diffusion rate. These analytic expressions are shown to agree with the simulations. A 1-D simulation with Monte Carlo guiding center diffusion included gives results that are in good agreement with the much more expensive 2-D simulation. © 1990 American Institute of Physics.