Dispersion Relations for Bernstein Waves in a Relativistic Pair Plasma

TL;DR

This paper provides a numerical analysis of Bernstein wave dispersion relations in a relativistic electron-positron plasma, revealing new wave modes relevant for astrophysical phenomena involving hot magnetized pair plasmas.

Contribution

It introduces a numerical method to compute dispersion curves for relativistic pair plasmas, identifying new wave modes at large wavelengths and frequencies near the cyclotron frequency.

Findings

Identification of two wave modes existing only at large wavelengths

Wave modes occur at frequencies near the cyclotron frequency

Results have implications for astrophysical plasma radiation mechanisms

Abstract

A fully relativistic treatment of Bernstein waves in an electron-positron pair plasma has remained too formidable a task owing to the very complex nature of the problem. In this article, we perform contour integration of the dielectric response function and numerically compute the dispersion curves for a uniform, magnetized, relativistic electron-positron pair plasma. The behavior of the dispersion solution for several cases with different plasma temperatures is highlighted. In particular, we find two wave modes that exist only for large wavelengths and frequencies similar to the cyclotron frequency in a moderately relativistic pair plasma. The results presented here have important implications for the study of those objects where a hot magnetized electron-positron plasma plays a fundamental role in generating the observed radiation.