Theory of the collisional presheath in an oblique magnetic field

Abstract

In the limit of a small Debye length (11,0->0), the plasma boundary layer in front of a negative absorbing wall is split up into a collision-free planar space charge sheath and a quasineutral presheath, where the ions are accelerated to ion sound speed (Bohm criterion). Usually the presheath mechanism depends decisively on collisional friction of the ions, on ionization, or on geometric ion current concentration. If the ion dynamics in the presheath is dominated by a magnetic field (nearly) parallel to the wall, an additional effect must be considered to provide an ion transport to the wall. The special cases (a) of an ion transport by field lines intersecting the wall at a finite angle and (b) of an ion transport by collisions result in somewhat contradictory conclusions. To get a coherent picture, a hydrodynamic model of the presheath is investigated accounting for an oblique magnetic field and for collisions. The limiting cases (a) and (b) are discussed, and it is shown that (in plane geometry) the presheath ion acceleration depends always on elementary processes. The main effect of a strong magnetic field is to "compress" the collisional presheath into a thin layer with a characteristic extension of the ion gyroradius Pi'

Two-region model for positive and negative plasma sheaths and its application to Hall thruster metallic anodes

“…15 The suitability of a macroscopic formulation of the TL presheath, even in the collisionless limit, has been discussed repeatedly; [16][17][18] in particular, the comparison of the solution of the TL kinetic model with four fluid models found disagreements in particle and heat fluxes within the range of 10%. 17 Presheath solutions for large sheaths and wall-parallel magnetic fields have been formulated macroscopically by Behnel 19 and Ahedo 20 and kinetically by Schmitz et al 21 Most models for large sheaths consider a Maxwell-Boltzmann equilibrium law for the repelled species, which comes from either a macroscopic force equilibrium or the assumption of a Maxwellian distribution function.…”

The magnetic presheath boundary condition with E×B drifts

“…The solution in the external plasma region cannot in general be collisionless, because that would prevent acceleration from occuring 4 . The most typical presumption is that collisions in the form of ionization are present in the external region; although sources such as momentum drag are also effective in providing a well-posed problem 2 . In either case, the equations of the external plasma are not invariant under the Galilean transformation discussed, and the matching must therefore be considered in the lab frame.…”

Electron current to a probe in a magnetized, collisional plasma

“…Multilayer structures in magnetized plasmas next to walls have been discussed in other respects as fully one dimensional. [26][27][28] Throughout the inner layers, which are thin compared to the outer region, z-gradients are steep, and the electron continuity equation …”