A new formulation for the synchrotron absorption–emission coefficient in plasmas

Starting from single particle radiation theory for a relativistic Maxwell distribution of electrons, a new exact representation of the absorption coefficient for synchrotron radiation in a plasma which offers considerable numerical advantages is derived. For the propagation perpendicular to the magnetic field, the same results were obtained as with formulas derived from plasma kinetic theory, however, with considerably reduced effort in numerical evaluation. Performing the integration analytically, a representation is arrived at, without any restricting assumptions, by an infinite sum which is shown to converge very fast at all temperatures below several tens of keV and to reproduce the strong resonant behavior at low temperatures. For higher temperatures the discrete sum was replaced by an integral which is solved analytically, again without any restricting assumptions such as the usual kT/m0c2≪1. The superiority of these analytical representations even to the alternatives that have been previously published is shown.