Accurate Gaunt factors for non-relativistic quadrupole bremsstrahlung

Abstract

The exact result for non-relativistic quadrupole bremsstrahlung in a Coulomb field was established only recently in Pradler & Semmelrock (2020). It requires the evaluation and integration of hypergeometric functions across a wide range of parameters and arguments, which, in practice, is unfeasible. Here we provide a highly accurate tabulation of the Gaunt factor for quadrupole radiation, its thermal average in a Maxwellian plasma, and the associated cooling function over the entire kinematically relevant range. In addition, we provide a simple approximate formula for the emission cross section which works to within a few percent accuracy for all practical purposes. The results can be applied to the scattering of electrons with themselves, for which quadrupole radiation is the dominant process.