Calculation of the dielectric tensor for a generalized Lorentzian (kappa) distribution function

Expressions are derived for the elements of the dielectric tensor for linear waves propagating at an arbitrary angle to a uniform magnetic field in a fully hot plasma whose constituent particle species σ are modeled by generalized Lorentzian distribution functions. The expressions involve readily computable single integrals whose integrands involve only elementary functions, Bessel functions, and modified plasma dispersion functions, the latter being available in the form of finite algebraic series. Analytical forms for the integrals are derived in the limits λ→0 and λ→∞, where λ=(k⊥ρLσ)2/2, with k⊥ the component of wave vector perpendicular to the ambient magnetic field, and ρLσ the Larmor radius for the particle species σ. Consideration is given to the important limits of wave propagation parallel and perpendicular to the ambient magnetic field, and also to the cold plasma limit. Since most space plasmas are well modeled by generalized Lorentzian particle distribution functions, the results obtained in this paper provide a powerful tool for analyzing kinetic (micro-) instabilities in space plasmas in a very general context, limited only by the assumptions of linear plasma theory.