A comparative study of the nonrelativistic and ultrarelativistic linear dispersion relations of electromagnetic waves in anisotropic classical plasmas: an alternative approach

An alternative form of the dielectric tensor, for evaluating unmagnetized response functions in thermally anisotropic collisionless plasma, is considered. The approach incorporates anisotropy in the momentum space, characterized by the modified momentum magnitude. Previously applied to Fermi distributed systems, this momentum space anisotropy concept is extended to classical systems. The method involves adjusting an isotropic distribution function along one direction in the momentum space. The equilibrium bi-Maxwellian distribution function is presented, parameterized by the anisotropy parameter xi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\xi $$\end{document} and the pitch angle theta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta $$\end{document}. Our results align with standard nonrelativistic outcomes. For ultrarelativistic classical systems, our findings, except for Landau damping and the hydrodynamic growth rate, coincide with the standard nonrelativistic case. The formulation offers a fresh perspective on the unmagnetized response functions in collisionless plasma by considering thermal anisotropy in classical systems. The extension of momentum space anisotropy to such systems provides a valuable framework for understanding plasma behavior, with potential applications in diverse physical scenarios.