Propagation characteristics of parallel propagating waves in a relativistic magnetized electron plasma

Waseem Khan,M Ali,Huzaifa Bilal,Yousaf Habib,Ayesha Kanwal,Tajammal H Khokhar

doi:10.1017/s0022377821001227

Abstract

Propagation characteristics (propagation regions and cutoffs) of parallel propagating modes (Langmuir, right- and left-handed circularly polarized waves) are studied for relativistic, weakly relativistic and non-relativistic magnetized electron plasma using the kinetic model. The dispersion relation for parallel propagating modes in relativistic electron plasma is investigated by employing the Maxwell–Boltzmann–J üttner distribution function and the final dispersion relation obtained is more general since no approximation is used. As the integrals in the relativistic dispersion relation cannot be done analytically so these integrals have been solved with the numerical quadrature approach. For $\eta \leq 1$ (ratio of rest mass energy to thermal energy), the increase in the effective mass of electrons will result in a change in the mass-dependent quantities (plasma frequency, electron cyclotron frequency, electron sound velocity, etc.) which in turn significantly affect the propagation characteristics of parallel propagating modes. It is observed that the propagation region for these parallel propagating modes decreases and cutoff points are shifted to lower values when we consider a relativistic plasma environment. Moreover, a low-density and high-temperature plasma is more transparent as compared with a high-density and low-temperature plasma for these modes.

Highlights

Plasma parameters like density, magnetic field and temperature vary over a wide range in various space and laboratory plasma environments
+ log ω − kzv ω + kzv Classical non-interacting particles at thermal equilibrium can be described by the Maxwell–Boltzmann distribution whereas to include the relativistic effects we need to use the Maxwell–Jüttner equilibrium distribution function (MJDF) (Buti 1963; Montgomery & Tidman 1964; Georgiou 1996; Ali et al 2019; Khan et al 2020b,c), given as f0(p)
As we know that the Langmuir mode remains unaffected by the magnetic field, so it is expected to get the same curves as presented in Khan et al (2020a) for the case of the weak

Summary

Introduction

Magnetic field and temperature vary over a wide range in various space and laboratory plasma environments. Lazar & Schlickeiser (2006) derived a relativistically correct dispersion relation of parallel propagating waves in magnetized thermal plasma of non-relativistic temperature. Sazhin (1987) presented an approximate analysis of different types of electromagnetic wave propagation in a weakly relativistic electron plasma He deduced that in the vicinity of certain frequencies, relativistic effects on the refractive index of these waves cannot be disregarded even when the electron energy is quite small. There has been extensive work done by Kepppens et al to present a relativistically complete two-fluid analysis for a pair plasma They discuss the advantages of using the governing 12th-degree polynomial in the wave frequency ω which represents 12 non-trivial waves and that can be separated into six pairs of forward- and backward-propagating waves, as the polynomial is sixth order in ω2 (Keppens & Goedbloed 2019; Keppens et al 2019; De Jonghe & Keppens 2020).

Parallel propagating waves in magnetized relativistic plasma

Dispersion relation

Discussion and graphical representation

Conclusion