A theory of fast-wave absorption, transmission, and reflection in the ion cyclotron range of frequencies

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Abstract
A second-order differential equation for the fast wave propagating in a hot, two-ion species plasma is obtained. This second-order approximation is obtained unambiguously and allows the wave amplitude to be identified with one of the electric field components. The approximation is based on replacing the coupling to the ion-Bernstein wave by a localized perturbation of the fast wave. For the case of perpendicular propagation, the second-order equation reduces to Budden’s equation giving the well-known transmission coefficient for both two-ion hybrid and second-harmonic resonance. The equation includes the effect of simultaneous minority fundamental and majority second-harmonic cyclotron damping. The solutions of the second-order equation as a function of n∥ give absorption transmission and reflection coefficients that agree well with the results based on models giving higher-order differential equations and solved by means of much more complex numerical codes.