The dielectric tensor for a fully anisotropic regularized Kappa plasma

Abstract

It has been known for some decades that the plasma in the Solar System is invariably in a state away from thermal equilibrium. In several plasma environments, be it in the Solar Wind or within planetary magnetospheres, the plasma has been found in a quasi-stationary nonthermal state, with a substantial fraction of its high-energy particles fitting along power-law distributions, instead of the exponential decay of thermal systems. Translating the observations in energy to velocity distribution functions (VDFs), the Kappa plasma model has been employed by the space plasma community, with the (standard) Kappa VDF (SKD) being the preferred choice. However, recent works have called attention to the limitations of the SKD model, proposing as a viable alternative the regularized Kappa VDF (RKD) model, which corrects the deficiencies of the SKD. The RKD model introduces a Gaussian-like dependency on the very high-energy part of the VDF that effectively cut-offs, via a regularization parameter, the Lorentzian profile of the intermediate-energy range. In this work, we employ a generalized RKD that supports anisotropies both in the thermal speed parameters and in the regularization parameters, including as well the possibility of drifts parallel to the magnetic field. This generalized RKD (called the bi-regularized Kappa with drift distribution, bRKd), is employed to derive for the first time the components of the susceptibility tensor for a suprathermal plasma species/population modelled by the bRKd. The tensor components are valid for waves with any propagation angle, frequency range and polarization. During the derivation, new special functions are defined and analyzed, which generalize previous expressions restricted to the parallel propagation limit.