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

The magnetization |Ω_e|/ω_e is an important parameter in plasma astrophysics, where Ω_e and ω_e are the electron gyro-frequency and electron plasma frequency, respectively. It depends only on the mass ratio m_i/m_e and the light-to-Alfvén speed ratio c/v_Ai, where m_i (m_e) is the ion (electron) mass, c is the speed of light, and v_Ai is the ion Alfvén speed. Non-linear numerical plasma models such as particle-in-cell simulations must often assume unrealistic values for m_i/m_e and for c/v_Ai. 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 m_i/m_e and c/v_Ai. We analyse their dependence on m_i/m_e and c/v_Ai in quasi-parallel and quasi-perpendicular directions of propagation with respect to the background magnetic field for a plasma with β_j ∼ 1, where β_j is the ratio of the thermal to magnetic pressure for species j. Although their dispersion relations are largely independent of c/v_Ai for c/v_Ai ≳ 10, the mass ratio m_i/m_e 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 m_i/m_e than for a more realistic value of c/v_Ai 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/v_Ai.