BO 2.0: Plasma Wave and Instability Analysis with Enhanced Polarization Calculations

Besides the relation between the wave vector $\bm k$ and the complex frequency $\omega$, wave polarization is useful for characterizing the properties of a plasma wave. The polarization of the electromagnetic fields, $\delta \bm E$ and $\delta \bm B$, have been widely used in plasma physics research. Here, we derive equations for the density and velocity perturbations, $\delta n_s$ and $\delta{\bm v}_s$, respectively, of each species in the electromagnetic kinetic plasma dispersion relation by using their relation to the species current density perturbation $\delta {\bm J}_s$. Then we compare results with those of another commonly used plasma dispersion code (WHAMP) and with those of a multi-fluid plasma dispersion relation. We also summarize a number of useful polarization quantities, such as magnetic ellipticity, orientation of the major axis of the magnetic ellipse, various ratios of field energies and kinetic energies, species compressibility, parallel phase ratio, Alfv\'en-ratio, etc., which are useful for plasma physics research, especially for space plasma studies. This work represents an extension of the BO electromagnetic dispersion code [H.S. Xie, Comput. Phys. Comm. 244 (2019) 343-371] to enhance its calculation of polarization and to include the capability of solving the electromagnetic magnetized multi-fluid plasma dispersion relation.