Numerical Calculations for Relativistic Electron Cyclotron Damping with an Arbitrary Distribution Function at Arbitrary Harmonics

The relativistic expressions for the anti-hermitian (damping) parts of the dielectric tensor elements can be expressed as a single integral over the parallel momentum variable (see Eq.(1) below). A computer program has been written for the calculation of this single integral [1]. The numerical results are tested for a relativistic Maxwellian distribution and agree with analytical expressions derived for this case [1,2]. The computer code is therefore an essential element for the validation of powerful analytical results. The computer code is then applied to calculate electron cyclotron damping at arbitrary harmonics for any electron distribution function, distorted for example by an electric field or by both electron cyclotron and lower hybrid waves. For generality, we also include the case of relativistic Landau damping.