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Analytical and numerical study of the relativistic dispersion relation of the extraordinary mode for a relativistic loss-cone electron distribution

The fully relativistic dispersion relation of the extraordinary mode around the electron cyclotron frequency is investigated, both analytically and numerically, for perpendicular propagation in a relativistic loss-cone plasma. The effects of the anisotropy of the distribution on both the cold right-hand-cut-off and the upper-hybrid resonance are evaluated and found to weaken the mode dispersion more significantly than predicted is the isotropic case. The dispersion equation is solved numerically for plasma parameters such that strong absorption and pronounced deviations of the mode dispersion from both the cold and tenuous-plasma dispersion occur. Negative absorption is found close to the high frequency edge of the cyclotron resonance and the effect of higher order finite Larmor radius corrections on the absorption are investigated. The absorption of the ordinary modes is also evaluated numerically.