Wave instabilities in anisotropic regularized Kappa plasmas: New plasma dispersion functions and numerical validation

Plasmas in space and astrophysical environments are frequently found in (quasi-)stationary states not in thermal equilibrium, indicated by velocity distribution functions (VDFs) featuring nonthermal characteristics, such as Lorentzian high-energy tails and kinetic (temperature and strahl/beam) anisotropies. For decades, in-situ observations of electrons and ions in the solar corona, solar wind or planetary magnetospheres have been modelled using so-called Kappa VDFs, whose standard form, however - depending on the considered VDF moment - imposes stringent constraints on the minimum value of the Kappa power-law parameter. Such limitations have posed difficulties on the derivation of a fully-consistent hydrodynamic formulation of suprathermal plasmas. To improve this situation, the recently proposed regularized Kappa VDF avoids strict constraints on the Kappa parameter by introducing an exponential, regularizing cut-off. In this work we assume that the plasma particles are described by regularized-Kappa VDFs that feature anisotropies not only in their thermal velocity spread parameters but also in their exponential cut-offs. The dielectric tensor components for waves propagating along a magnetic field are derived, in terms of new plasma dispersion functions. The resulting dispersion equations are solved with two complementary techniques, namely by using the analytical expressions derived here and by employing the ALPS code. This is done for physical parameters that give rise to electromagnetic and electrostatic instabilities. Both approaches show excellent agreement and the results demonstrate how an anisotropy in the regularizing cut-off of VDFs can serve, depending on an instability's nature, either as a stabilization factor or as an additional free energy source.