BO: A unified tool for plasma waves and instabilities analysis

A unified numerically solvable framework for dispersion relations with an arbitrary number of species drifting at arbitrary directions and with Krook collision is derived in linear uniform/homogenous kinetic plasma model, which greatly extends the standard one given by Stix (1992). The purpose of this work is to provide a kinetic plasma dispersion relation tool not only in the physical model but also the numerical approach as general/powerful as possible. As a general application, we give the dispersion relations which assume the equilibrium distribution function to be bi-Maxwellian including parallel drift, two directions of perpendicular drift (i.e., drift across magnetic field), ring beam and loss-cone. Both electromagnetic and electrostatic versions are provided, with also the Darwin (a.k.a., magnetoinductive or magnetostatic) version. The species can be treated either magnetized or unmagnetized. Later, the equations are transformed to the matrix form that can be solved by using the powerful matrix algorithm (Xie and Xiao, 2016), which is the first approach can give all the important solutions of a linear kinetic plasma system without requiring initial guess for root finding. To the best of our knowledge, the present model is the most comprehensive model in literature for the distribution function constructed from Maxwellian distributions, which thus can be applied widely for studying waves and instabilities in space, astrophysics, fusion and laser plasmas. We limit the present work to non-relativistic case.