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

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.

13 pages, 13 figures, to be published in Physics of Plasmas

References in corpus (4)

• Kinetic Theory of the Presheath and the Bohm Criterion
• Undamped electrostatic plasma waves
• Particle-in-cell simulations of a current-free double layer
• The incomplete plasma dispersion function: properties and application to waves in bounded plasmas

Cited by in corpus (7)

• Interaction of Biased Electrodes and Plasmas: Sheaths, Double Layers and Fireballs
• Generalized Plasma Dispersion Function: One-Solve-All Treatment, Visualizations, and Application to Landau Damping
• The incomplete plasma dispersion function: properties and application to waves in bounded plasmas
• On the collisional damping of plasma velocity space instabilities
• A dispersion function for the regularized kappa distribution function
• Dispersion and the Speed-Limited Particle-in-Cell Algorithm
• Gaussian integrals depending by a quantum parameter in finite dimension