Relativistic dispersion relation of electron cyclotron waves

The dispersion relation for electron cyclotron (EC) waves in a magnetized Maxwellian plasma is investigated for the cases of both the fully relativistic and the weakly relativistic resonance conditions. A compact form for the dielectric tensor is derived that is valid for frequencies close to any harmonic of the cyclotron frequency and at any given order in the Larmor radius expansion. This formulation is particularly suitable for implementation in numerical codes for the computation of EC absorption and emission. In ITER-like plasmas, it is shown that relativistic effects play a relevant role and that the absorption profile may differ appreciably from that obtained in the weakly relativistic approximation.