Propagation of electron cyclotron waves in a weakly relativistic plasma with steep density and temperature profiles

A detailed analysis is made of the deduction of systems of differential equations describing the propagation of both ordinary and extraordinary waves in the electron cyclotron frequency range in a stratified plasma, perpendicularly to the magnetic field and across the electroncyclotron fundamental resonance layer. The equations are derived under conditions of not too large electron temperature (the so-called weakly relativistic condition) and of very weak nonuniformities of the confining magnetic field. The effects of the nonhomogeneities of the equilibrium plasma density and temperature are carefully examined. It is shown that the propagation equations derived previously in the literature can be extended with only a moderately larger effort in computations to take account also of very strong density and temperature gradients.