Kinetic Theory of the Presheath and the Bohm Criterion

TL;DR

This paper develops a new kinetic theory of the Bohm criterion based on positive-exponent velocity moments, avoiding unphysical divergences of the conventional approach and providing a more accurate description of plasma presheaths.

Contribution

A novel kinetic theory of the Bohm criterion using positive-exponent moments that corrects flaws in the conventional v^{-1} moment approach.

Findings

The new theory avoids divergences caused by low velocity particles.

Comparison shows the new theory aligns better with physical expectations.

Ion-acoustic instabilities can lead to Maxwellian distributions near the sheath.

Abstract

A kinetic theory of the Bohm criterion is developed that is based on positive-exponent velocity moments of the plasma kinetic equation. This result is contrasted with the conventional kinetic Bohm criterion that is based on a v^{-1} moment of the Vlasov equation. The salient difference between the two results is that low velocity particles dominate in the conventional theory, but are essentially unimportant in the new theory. It is shown that the derivation of the conventional kinetic Bohm criterion is flawed. Low velocity particles can cause unphysical divergences in the conventional theory. These divergent contributions are avoided with this new approach. The two theories are compared using example distribution functions from previous presheath models. The importance of ion-ion and electron-electron collisions to determining the particle distribution functions throughout the presheath is also discussed. A kinetic equation that accounts for wave-particle scattering by convective instabilities is used to show that ion-acoustic instabilities in the presheath of low temperature plasmas (where T_e \gg T_i) can cause both ions and electrons to obtain Maxwellian distribution functions near the sheath.