Dispersion of electron Bernstein waves including weakly relativistic and electromagnetic effects. Part 1. Ordinary modes

Ordinary solutions of the weakly relativistic, electromagnetic dispersion relation are investigated for waves propagating perpendicular to a uniform magnetic field in a Maxwellian plasma. Weakly relativistic resonance broadening, frequency downshift and damping are found to alter dramatically the dispersion predicted by the corresponding strictly non-relativistic (‘classical’) theory in the neighbourhood of harmonics of the cyclotron frequency Ω_e. All classical resonances and cut-offs are removed except the cut-off at the plasma frequency ω_p. At frequencies above ω_p the infinite family of classically predicted modes is replaced by a single weakly damped mode whose dispersion differs only slightly from that predicted by cold plasma theory. No weakly damped modes exist in the range of harmonics s satisfying (ω_p/Ω_e)⅔/8 S < Ω_p/Ω_e, however, one such mode is located immediately below each harmonic for s (ω_p/Ω_e)⅔/8. A companion paper investigates extraordinary solutions of the dispersion relation.