One-over-polynomial approximation for linear kinetic dispersion and its application to relativistic cyclotron resonance

In this paper we propose a new method to calculate the plasma dispersion relation for a wide variety of distribution functions with a complicated resonance mechanism. An approximation with a one-over-polynomial function enables us to apply the residue theorem for integration, and gives an analytical form of the dispersion equation. The solution is highly accurate with typical error less than 10−4 when applied to the ordinary plasma dispersion function (Z function). Application of this method is not limited to the dispersion functions that can be expressed by the Z function; it can be applied to much wider class of problems with arbitrary velocity distributions. One example is the general solution to the dispersion equation for a weakly relativistic magnetized plasma.