A dispersion function for the regularized kappa distribution function

Abstract

In this work, we define the plasma dispersion function for a suprathermal plasma described with a regularized kappa distribution. As is known from Maxwellian as well as (standard) kappa plasmas, the respective Fried–Conte and the modified plasma dispersion functions are valuable tools for various analytical studies. For the latter it has been proven very useful to know about the mathematical properties, as analytical continuation, series expansions as well as asymptotic expressions. Given the growing popularity of the regularized kappa distribution, as indicated by its increasing number of applications to various problems related to suprathermal plasmas, we extend its theoretical treatment here by providing the corresponding plasma dispersion function along with various properties.