Kinetic theory of the presheath and the Bohm criterion

Abstract

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