A two-fluid analysis of waves in a warm ion-electron plasma

TL;DR

This paper provides a comprehensive analysis of wave modes in a warm two-fluid plasma, revealing mode crossings, critical magnetisation effects, and connections to relativistic MHD and kinetic theory, with applications to exotic astrophysical environments.

Contribution

It introduces a general dispersion relation for warm two-fluid plasmas, analyzing wave behaviour, mode crossings, and magnetisation effects in various regimes, including astrophysical conditions.

Findings

Identification of six wave modes and their crossing behaviour.

Discovery of a critical magnetisation affecting mode cutoffs.

Connection of fluid model results with kinetic theory and MHD.

Abstract

Following recent work, we discuss waves in a warm ideal two-fluid plasma consisting of electrons and ions starting from a completely general, ideal two-fluid dispersion relation. The plasma is characterised by five variables: the electron and ion magnetisations, the squared electron and ion sound speeds, and a parameter describing the angle between the propagation vector and the magnetic field. The dispersion relation describes 6 pairs of waves which we label S, A, F, M, O, and X. Varying the angle, it is argued that parallel and perpendicular propagation (with respect to the magnetic field) exhibit unique behaviour. This behaviour is characterised by the crossing of wave modes which is prohibited at oblique angles. We identify up to 6 different parameter regimes where a varying number of exact mode crossings in the special parallel or perpendicular orientations can occur. We point out how any ion-electron plasma has a critical magnetisation (or electron cyclotron frequency) at which the cutoff ordering changes, leading to different crossing behaviour. These are relevant for exotic plasma conditions found in pulsar and magnetar environments. Our discussion is fully consistent with ideal relativistic MHD and contains light waves. Additionally, exploiting the general nature of the dispersion relation, phase and group speed diagrams can be computed at arbitrary wavelengths for any parameter regime. Finally, we recover earlier approximate dispersion relations that focus on low-frequency limits and make direct correspondences with some selected kinetic theory results.