Gyromagnetic Emission and Absorption: Approximate Formulas of Wide Validity

Abstract

Approximate formulas of wide validity are derived for gyro magnetic emission and absorption of gyromagnetic waves by mildly relativistic electrons. An averaged emissivity is defined by replacing the sum over harmonic number by an integral and averaging over the pitch angle distribution of the radiating particles. A method for performing the average over pitch angle without approximation to the Bessel functions is developed and the resulting expressions are then approximated using Wild-Hill formulas which interpolate between the non-relativistic and ultra-relativistic limits.