Fitting the dielectric response of collisionless plasmas by continued fractions

TL;DR

This paper introduces a new approximation method using continued fractions to accurately model the dielectric response of collisionless plasmas across various degeneracy levels, facilitating easier implementation and error assessment.

Contribution

The authors develop a continued fraction approximation scheme for the dielectric function of collisionless plasmas, providing tables and algorithms for practical use across different degeneracy parameters.

Findings

Accurate fitting of dielectric response across degeneracy levels

Provision of tables and algorithms for implementation

Error analysis of the approximation method

Abstract

We present an approximation scheme for the dielectric response of thermal collisionless plasmas at arbitrary degeneracy. A T-fraction representation is obtained from the known expansions of the real part of the dielectric function for small and large arguments. The partial numerators and denominators of the continued fraction are generated by a modified Q-D algorithm. For several typical values of the degeneracy parameter $\theta$, extensive tables for the expansion coefficients and the partial numerators and denominations are given allowing for an easy implementation of the fitting function. Also, an error analysis is performed.