A new tool for analyzing microinstabilities in space plasmas modeled by a generalized Lorentzian (Kappa) distribution

In space plasmas, e.g., planetary magnetospheres and the solar wind, it has been observed that particle velocity distributions typically possess a non‐Maxwellian high‐energy tail that can be well modeled by a generalized Lorentzian (kappa) distribution. The generalized Lorentzian distribution is characterized by a spectral index κ, varies as {energy} −(κ+1) at high velocities, and approaches a Maxwellian distribution as κ → ∞. As a natural analogue to the widely used plasma dispersion function Z (ξ), which is based on the Maxwellian distribution, we have recently introduced a new special function Z κ * (ξ) based on the generalized Lorentzian distribution; we call Z κ * (ξ) the modified plasma dispersion function. Because Z κ * (ξ) can be expressed in simple closed form, Z κ * (ξ) is easier to use than Z (ξ) both from analytical and computational points of view. Z κ * (ξ) is, moreover, a natural tool for analyzing microinstabilities in a variety of space plasmas. In this paper we use Z κ * (ξ) to analyze three classical problems of plasma physics: Landau damping of Langmuir waves; ion acoustic instability in a current‐carrying plasma; and cyclotron resonant instability of electromagnetic R mode waves propagating parallel to an ambient magnetic field. In each case we find that results for a generalized Lorentzian plasma can differ significantly from those in a Maxwellian plasma. Previous calculations based on a Maxwellian distribution, that purport to apply to waves in space, may therefore be subject to reexamination.