Evaluation of Relativistic Plasma Dispersion Functions Using Downward Recursion and Analytical Relations

Abstract

The Dnestrovskii functions provide a powerful framework for understanding wave propagation, attenuation and instabilities in plasmas where relativistic effects dominate, as relativistic plasma dispersion functions. To calculate the Dnestrovskii functions for a wide range of parameter values, effective analytical and downward recurrence formulae are proposed in this study. These formulae allow users to make efficient calculations specific to high-energy or relativistic plasmas. Because the recurrence formulas are simple, calculating time and accuracy are improved, and the formulas are easy to use. The results obtained using the new analytical and downward recurrence formulae agree well with published results and those obtained using numerical cal culation methods for a wide range of parameters.