A dielectric tensor for magnetoplasmas comprising components with generalized Lorentzian distributions

We report on a new form for the dielectric tensor for a plasma-containing superthermal particles. The individual particle components are modelled by 3-dimensional isotropic kappa, or generalized Lorentzian, distributions with arbitrary real-valued index re. The new dielectric tensor is valid for arbitrary wavevectors. The dielectric tensor, which resembles Trubnikov's dielectric tensor for a relativistic plasma, is compared with the familiar Maxwellian form. When the dielectric tensor is used in the plasma dispersion relation for waves propagating parallel to the magnetic field it reproduces previously derived dispersion relations for various electromagnetic and electrostatic waves in plasmas modelled by Lorentzian particle distributions. Within the constraints of propagation parallel to the ambient magnetic field, we extend the above results to incorporate loss-cone Lorentzian particle distributions, which have important applications in laboratory mirror devices, as well as in space and astrophysical environments.