Dependence of kinetic plasma waves on ion-to-electron mass ratio and light-to-Alfvén speed ratio

The magnetization |Ωe|/ωe is an important parameter in plasma astrophysics, where Ωe and ωe are the electron gyro-frequency and electron plasma frequency, respectively. It depends only on the mass ratio mi/me and the light-to-Alfvén speed ratio c/vAi, where mi (me) is the ion (electron) mass, c is the speed of light, and vAi is the ion Alfvén speed. Non-linear numerical plasma models such as particle-in-cell simulations must often assume unrealistic values for mi/me and for c/vAi. Because linear theory yields exact results for parametric scalings of wave properties at small amplitudes, we use linear theory to investigate the dispersion relations of Alfvén/ion-cyclotron and fast-magnetosonic/whistler waves as prime examples for collective plasma behaviour depending on mi/me and c/vAi. We analyse their dependence on mi/me and c/vAi in quasi-parallel and quasi-perpendicular directions of propagation with respect to the background magnetic field for a plasma with βj ~ 1, where βj is the ratio of the thermal to magnetic pressure for species j. Although their dispersion relations are largely independent of c/vAi for c/vAi ≥ 10, the mass ratio mi/me has a strong effect at scales smaller than the ion inertial length. Moreover, we study the impact of relativistic electron effects on the dispersion relations. Based on our results, we recommend aiming for a more realistic value of mi/me than for a more realistic value of c/vAi in non-relativistic plasma simulations if such a choice is necessary, although relativistic and sub-Debye-length effects may require an additional adjustment of c/vAi.