Kinetic transverse dispersion relation for relativistic magnetized electron-positron plasmas with Maxwell-Jüttner velocity distribution functions

Abstract

We use a kinetic treatment to study the linear transverse dispersion relation for a magnetized isotropic relativistic electron-positron plasma with finite relativistic temperature. The explicit linear dispersion relation for electromagnetic waves propagating along a constant background magnetic field is presented, including an analytical continuation to the whole complex frequency plane for the case of Maxwell-Jüttner velocity distribution functions. This dispersion relation is studied numerically for various temperatures. For left-handed solutions, the system presents two branches, the electromagnetic ordinary mode and the Alfvén mode. In the low frequency regime, the Alfvén branch has two dispersive zones, the normal zone (where ∂ω/∂k > 0) and an anomalous zone (where ∂ω/∂k < 0). We find that in the anomalous zone of the Alfvén branch, the electromagnetic waves are damped, and there is a maximum wave number for which the Alfvén branch is suppressed. We also study the dependence of the Alfvén velocity and effective plasma frequency with the temperature. We complemented the analytical and numerical approaches with relativistic full particle simulations, which consistently agree with the analytical results.

ALPS: the Arbitrary Linear Plasma Solver

“…We apply the technique proposed by Lerche (1967) to transform Equation (2.9) from the (p ⊥ , p ) coordinate system to the (Γ,p ) coordinate system (see also Swanson 2002;Lazar & Schlickeiser 2006;López et al 2014López et al , 2016. This transformation yields the code automatically transforms from (p ⊥ , p ) to (Γ,p ) coordinates and applies the polyharmonic spline algorithm described in Appendix C to create an equally spaced and homogeneous grid in (Γ,p ) coordinates.…”

“…The left panel shows the real part of the frequency, and the right panel shows the imaginary part of the frequency. The lines show ALPS solutions, and the crosses show the results fromFigure 1ofLópez et al (2014). The three colours correspond to βp = βe = 0.2 (red), βp = βe = 0.4 (green), and βp = βe = 1.0 (blue) in both panels and for both modes.…”

Dispersion relations in hot magnetized plasmas

“…They give access to a preliminary treatment of wave propagation. There are more recent works dealing with the relativistic features [16,25] or with the numerical aspects [34,39]. Most of these contributions [2,11,22,35] are restricted to the case of a constant external magnetic field and also to the case of a homogeneous velocity distribution function.…”

“…It is because they are involved in a wide range of astrophysical contexts and laboratory experiments through wave-particle interaction [21,36], transfer of power between waves and particles, heating of plasmas, reflectometry techniques [19], and so on. The preparatory works from the 1960s, 1970s and 1980s [2,11,12,22,31,32,35] are the template for recent numerical studies [34,39], for contemporary investigations in more complex situations [17,25,28,30] or, like in the present text which is about tokamaks, for developments up to the case of non-uniform magnetized plasmas.…”

Dispersion relation of low-frequency electrostatic waves in plasmas with relativistic electrons

“…For high-frequency electrostatic (plasma waves) and electromagnetic modes recent work has been developed in Refs. (Fichtner & Schlickeiser, 1995;Schlickeiser & Kneller, 1997;Melrose, 1999;Bergman & Eliasson, 2001;Podesta, 2008;Bers et al, 2009;Schlickeiser, 2010;Zhang et al, 2013;López et al;2014) in the context of laser thermonuclear fusion. Our work is therefore an extension of these works to low-frequency spectrum.…”