Boundary conditions for drift-diffusion equations in gas-discharge plasmas

TL;DR

This paper presents a comprehensive method for deriving boundary conditions in hydrodynamic plasma models, clarifying existing ambiguities and analyzing their effects on plasma component behavior at boundaries.

Contribution

It introduces a unified approach to boundary conditions for plasma drift-diffusion equations, including effects of partial reflection and emission at boundaries.

Findings

Clarified ambiguous boundary terms in plasma models

Derived boundary conditions for electrons and ions with emission effects

Analyzed boundary behavior through practical examples

Abstract

This paper develops a general approach to the derivation of the boundary conditions for hydrodynamic equations for charged and neutral plasma components. It includes both a well-known classical case for pure diffusion, and considers the expressions for diffusion and drift together - for an absorbing (neutralizing) wall with partial reflection and the possible emission of plasma components. Some unclear and controversial terms found in the existing literature are clarified. Several examples of applications of the results, which illustrate the properties of boundary conditions for electrons and ions, are calculated and analyzed.