Generalized plasma dispersion function for a plasma with a kappa-Maxwellian velocity distribution

A generalized plasma dispersion function has previously been obtained for waves in plasmas with isotropic kappa distributions for arbitrary real kappa [Mace and Hellberg, Phys. Plasmas 2, 2098 (1995)]. In many instances plasmas are found to have anisotropic power-law distributions, and hence a similar dispersion function for electrostatic waves in plasmas having a one-dimensional kappa distribution along a preferred direction in space, and a Maxwellian distribution perpendicular to it has now been developed. It is used to study the effect of superthermal electrons and ions on ion-acoustic waves propagating at an angle to a magnetic field. This dispersion function should find application to wave studies both in space plasmas, where the magnetic field defines a preferred direction, and in dusty plasma crystal studies, where the ion flow direction is unique.