The Bohm criterion and sheath formation

Abstract

In the limit of a small Debye length (,ID+ 0) the analysis of the plasma boundary layer leads to a two-scale problem of a collision free sheath and of a quasi-neutral presheath. Bohm's criterion expresses a necessary condition for the formation of a stationary sheath in front of a negative absorbing wall. The basic features of the plasma-sheath transition and their relation to the Bohm criterion are discussed and illustrated from a simple cold-ion fluid model. A rigorous kinetic analysis of the vicinity of the sheath edge allows one to generalize Bohm's criterion accounting not only for arbitrary ion and electron distributions, but also for general boundary conditions at the wall. It is shown that the generalized sheath condition is (apart from special exceptions) marginally fulfilled and related to a sheath edge field singularity. Due to this singularity smooth matching of the presheath and sheath solutions requires an additional transition layer. Previous investigations concerning particular problems of the plasma-sheath transition are reviewed in the light of the general relations.

pdFOAM: A PIC-DSMC code for near-Earth plasma-body interactions

“…The interaction of a plasma with an immersed object can be complex; ranging from surface absorption, deep penetration, and neutralization, to the emission of other charged particles through secondary electron emission or sputtering [27,45,56]. Before considering such phenomena, it is essential to demonstrate that the plasma-body interaction is modeled correctly; this applies to both FK and HK simulations.…”

“…The following discussion outlines the theory describing the general structure of a 1D plasma sheath for a fixed wall potential. For a detailed analysis, we refer the reader to [45]. Consider a freestream plasma at x = 0 such that it is sufficiently far from a large flat plate with a fixed potential φ p at x = L that the freestream may be considered quasi-neutral i.e.…”

Current collection by a positively charged spacecraft: Effects of its magnetic presheath

“…Cooke (private communication, 1995) has pointed out that the quasineutral potentials shown in Figures 7-9 are "Bohm-unstable". This means that at potentials larger than these quasineutral values, the attractedparticle (electron) density is larger than the repelledparticle (ion) density, and this situation is characteristic of a sheath rather than a presheath [Bohm, 1949;Riemann, 1991] Instability effects may also occur in the ion-enhancement region. As we saw in section 2, the ion trajectories are relatively "stiff", so quasineutrality in this region is achieved mostly by redistribution of the electrons, whose density we assumed to be an increasing function of potential given by (5).…”

Space charge formation and Bohm’s criterion in the edge of thermal electronegative plasma

“…Indeed, the positive space charge is responsible to maintain the plasma potential. Understanding the space charge formation and its mechanism is necessary for plasma surface interaction as well as plasma diagnostics such as of Langmuir probe [1][2][3][4][5][6][7].…”

“…In other word, for the asymptotic case k D L ! 0, the ionizing collisions can be ignored where L is the plasma dimension which is usually in the order of ionizing length ( [2] and references therein). However, the presence of elastic collisions between the accelerated ions and the neutral atom in the background sheath region can significantly influence the plasma-sheath characteristics.…”