Analytic solutions and particle simulations of cross-field plasma sheaths

Abstract

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.

The plasma-wall transition with collisions and an oblique magnetic field: Reversal of potential drops at grazing incidences

“…that can be injected in Eq. (21). After integration between the Chodura sheath entrance and the plasma center, it comes that φ c − φ(0) = −0.5T e , which is independent of the magnetic field incidence.…”

“…Note that in the limit of θ → 0, in a 1d/3V description of the plasma, the particle flux at the wall is expected to cancel in the collisionless limit because particles can not drift perpendicular to the field line. Some authors have addressed this quasi-static issue theoretically and by using particle-in-cell (PIC) simulations [17][18][19][20][21][22][23][24] . They showed that the potential drop at the vicinity of the surface is opposite, ie.…”

The plasma-wall transition layers in the presence of collisions with a magnetic field parallel to the wall

“…Theilhaber and Birdsall showed in the context of bi-dimensional PIC simulations that Kelvin-Helmholtz instability due to the velocity shear within the sheath allows a particles drift across the magnetic field lines. They evidenced that the potential drop within the sheath keeps a positive value and that the sheath extent reaches 5R l [17][18][19] . When collisions are taken into account, both ions and electrons diffuse through the field line at a different rate.…”

Plasma sheath properties in a magnetic field parallel to the wall

“…In further studies, authors faced the impossibility of solving the Poisson equation from a kinetic theory and used numerical calculations to derive scaling laws. They found that s scales with R L /λ d and a ∆φ of the order of the ion temperature 12,[15][16][17] , but no simple expression connecting s, or ∆φ, with the plasma parameters such as the ion and electron temperature and mass (T i , T e , m i and m e resp. ), or with B, has ever been derived.…”