A Fresh Look at Waves in Ion-Electron Plasmas

Abstract

Exploiting the general dispersion relation describing all waves in an ideal ion-electron fluid, we revisit established treatments on wave families in a cold ion-electron plasma. These contain the magnetohydrodynamic Alfv\'en and fast waves at low frequencies, long wavelengths, but are enriched by short wavelength resonance behaviours, electrostatic and electromagnetic mode types, and cut-off frequencies distinguishing propagating from evanescent waves. Our theoretical treatment exploits purely polynomial expressions, which for the cold ion-electron case only depend on 2 parameters: the ratio of masses over charges $\mu$ and the ratio $E$ of the electron gyro frequency to the combined ion-electron plasma frequency. We provide a complete description of all waves, which stresses the intricate variation of all five branches of eigenfrequencies $\omega(k,\vartheta)$ depending on wavenumber $k$ and angle $\vartheta$ between wavevector and magnetic field $\bfB$. Corresponding 5-mode phase and group diagrams provide insight on wave transformations and energy transport. Special cases, like the high frequency modes in magneto-ionic theory following from Appleton-Hartree dispersion relations, are naturally recovered and critically discussed. Faraday rotation for electromagnetic waves is extended to all propagation angles $\vartheta$. {\bf The discussion covers all cold ion-electron plasma waves, up into the relativistic regime.}