Approximation of the dielectric properties of Maxwellian plasmas: dispersion functions and physical constraints

The dielectric properties of Maxwellian plasmas are approximated using both Padé approximants to the dispersion function and direct approximation of the distribution. Physical constraints on permissible approximations are discussed, and it is found that some previously published results can lead to predictions of qualitatively incorrect wave properties, including unphysical negative damping. Approximate dispersion functions for Maxwellian distributions are given explicitly, and some of the effects of these approximations on the resulting dispersion are discussed. The approximations discussed here are of use both in analytic work and in accelerating large-scale numerical computations.