The incomplete plasma dispersion function: properties and application to waves in bounded plasmas

TL;DR

This paper introduces the incomplete plasma dispersion function, a mathematical tool for analyzing wave behavior in bounded plasmas with non-Maxwellian electron distributions, especially near boundaries.

Contribution

It defines and explores the properties of the incomplete plasma dispersion function and demonstrates its application to wave dispersion in non-Maxwellian, bounded plasma environments.

Findings

The incomplete plasma dispersion function effectively models wave dispersion in bounded plasmas.

Application to depleted Maxwellian distributions shows modified wave dispersion relations.

The function provides a useful framework for boundary plasma wave analysis.

Abstract

The incomplete plasma dispersion function is a generalization of the plasma dispersion function in which the defining integral spans a semi-infinite, rather than infinite, domain. It is useful for describing the linear dielectric response and wave dispersion in non-Maxwellian plasmas when the distribution functions can be approximated as Maxwellian over finite, or semi-infinite, intervals in velocity phase-space. A ubiquitous example is the depleted Maxwellian electron distribution found near boundary sheaths or double layers, where the passing interval can be modeled as Maxwellian with a lower temperature than the trapped interval. The depleted Maxwellian is used as an example to demonstrate the utility of using the incomplete plasma dispersion function for calculating modifications to wave dispersion relations.