Collisional damping of wave modes in ion-electron plasmas

TL;DR

This paper extends the analysis of ion-electron plasmas by including collisional effects, deriving damping rates for wave modes, and exploring how collisions influence wave mode crossings and damping in various regimes.

Contribution

It introduces collisional terms into the two-fluid plasma equations, providing analytical expressions for wave frequencies and damping rates across different wavelength limits.

Findings

Collisional damping causes negative imaginary parts in wave frequencies.

Collision frequency influences wave mode crossings and avoided crossings.

Analytical expressions match kinetic damping in relevant regimes.

Abstract

To expand on recent work, we introduce collisional terms in the analysis of the warm ion-electron, two-fluid equations for a homogeneous plasma at rest. Consequently, the plasma is now described by six variables: the magnetisation, the ratio of masses over charges, the electron and ion sound speeds, the angle between the wave vector and the magnetic field, and a new parameter describing the electron-ion collision frequency. This additional parameter does not introduce new wave modes compared to the collisionless case, but does result in complex mode frequencies. Both for the backward and forward propagating modes the imaginary components are negative and thus quantify collisional damping. We provide convenient (polynomial) expressions to quantify frequencies and damping rates in all short and long wavelength limits, including the cut-off and resonance limits, whilst the one-fluid magnetohydrodynamic limit is retained with the familiar undamped slow, Alfv\'en and fast (SAF) waves. As collisions only introduce a damping, the previously introduced labelling of the wave modes S, A, F, M, O and X can be kept and assigned based on their long and short wavelength behaviour. The obtained damping at cut-off and resonance limits is parametrised with the collision frequency, and can be tailored to match known kinetic damping expressions. It is demonstrated that varying the angle can introduce crossings between the wave modes, as was already present in the ideal ion-electron case, but also a collision frequency exceeding a critical collision frequency can lead to crossings at angles where previously only avoided crossings were found.