Plasma Instabilities in Arbitrary Distributions: Comparison between ALPS and BO

Abstract

Determining accurate wave dispersion relations is a central problem in plasma physics. Recent advances have enabled the numerical computation of linear dispersion relation in plasmas with arbitrary particle velocity distribution functions (VDFs), using two distinct solvers, BO and ALPS. Their reliability and mutual consistency, however, have not been systematically tested for a broad range of VDFs. Here we compare the dispersion relations obtained from BO and ALPS for several representative distributions. We find that the two solvers give consistent unstable modes for kappa distributions with large values of $κ$, as well as for ring-beam, shell, and proton core-beam distributions. BO, however, becomes unreliable for kappa distributions with $κ< 4$. For an observationally derived VDF, the two solvers give similar real frequencies for the unstable waves but substantially different growth rates. This difference is mainly caused by the imperfect fitting of the input distribution required by BO. Despite this limitation, BO has a clear computational advantage because it can obtain all roots in a single run. Considering the complementary strengths of the two solvers, their combined use can provide a more reliable and effective framework for investigating instabilities in non-Maxwellian plasma environments.