Bohm criterion of plasma sheaths away from asymptotic limit

TL;DR

This paper extends the Bohm criterion analysis to intermediate plasma regimes, deriving a more general Bohm speed that accounts for local heat flux, temperature isotropization, and thermal forces, validated by kinetic simulations.

Contribution

It introduces a generalized Bohm criterion applicable away from asymptotic limits, incorporating additional plasma parameters for more accurate sheath modeling.

Findings

Derived explicit dependence of Bohm speed on heat flux and temperature isotropization.

Validated the generalized Bohm criterion against kinetic simulations.

Showed improved accuracy in plasma-sheath transition regions.

Abstract

The plasma exit flow speed at the sheath entrance is constrained by the Bohm criterion. The so-called Bohm speed regulates the plasma particle and power exhaust fluxes to the wall, and it is commonly deployed as a boundary condition to exclude the sheath region in quasi-neutral plasma modeling. Here the Bohm criterion analysis is performed in the intermediate plasma regime away from the previously known limiting cases of adiabatic laws and the asymptotic limit of infinitesimal Debye length in a finite-size system, using the transport equations of an anisotropic plasma. The resulting Bohm speed has explicit dependence on local plasma heat flux, temperature isotropization, and thermal force. Comparison with kinetic simulations demonstrates its accuracy over the plasma-sheath transition region in which quasineutrality is weakly perturbed and Bohm criterion applies.