  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.
