Perpendicular electron cyclotron emission and absorption for relativistic loss-cone type distributions

The electron cyclotron emissivity and the absorption coefficient of the extraordinary and ordinary mode propagating perpendicularly to the magnetic field are calculated, both analytically and numerically, for relativistic loss-cone particle distributions with either Maxwellian or non-monotone distribution in energy, with full account of both finite Larmor radius and finite-density effects. The analytic expressions, comprising the limiting cases of extremely anisotropic pitch angle distributions, are discussed with respect to the scaling with the various physical parameters and conditions for negative absorption (amplification) are derived for moderate temperatures. A detailed numerical analysis of the frequency dependence of both the emission and absorption is performed over a wide range of loss-cone strength and temperature and discussed with respect to the case of a relativistic Maxwellian distribution. A comparative analysis of the emissivities for the two classes of loss-cone distributions considered indicates no significant difference provided that the energy distribution and the degree of anisotropy are the same.