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

摘要

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