Abstract

In this chapter we focus on the recent progress made on numerical analysis and tools facilitating the investigation of dispersion and stability of anisotropic Kappa distributed plasmas. Plasma waves and fluctuations are directly dependent on the non-thermal features of the particle velocity distributions, and understanding their properties is a primary goal, especially for collision-poor plasmas where physical processes are conditioned by the wave-particle interactions. Numerical dispersion solvers are developed to resolve complex (integral) dispersion relations and decode the full spectra of stable or unstable modes, but, traditionally, limited to idealized (bi-)Maxwellian representation of plasma populations. Here we discuss the advanced dispersion solvers recently developed for magnetized plasmas with anisotropic Kappa populations (e.g., bi-Kappa, combined or not with drifts), and compare their capabilities. The implication of these numerical solvers was extended to quasi-linear (QL) studies of kinetic instabilities, providing a complete description of their saturation as well as the relaxation of anisotropic populations. We will also emphasize the progress made in numerical simulations using different techniques, e.g., Vlasov or Particle-In-Cell (PIC) codes, to capture suprathermal effects in the initial Kappa distributions. Some illustrative cases of kinetic instabilities are considered to describe capabilities of these new codes, and compare the simulations with the results provided by the linear and QL numerical solvers.