Absorption of waves in the second harmonic resonance layer

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Abstract
Absorption caused by relativistic broadening of quasiperpendicular incident waves within the second cyclotron harmonic layer is investigated in an inhomogeneous electron plasma. The resonance region is treated by a boundary layer analysis, and field equations valid in this region are derived by solving the rescaled (with respect to the parameter η which is the ratio of the thermal speed and the speed of light) linearized relativistic Vlasov equation. The geometrical optics solutions valid in the nonresonant region are evaluated near the resonance, and they are connected to the asymptotic forms of the inner solutions. The energy conservation theorems appropriate for this problem allow the evaluation of fractional transmitted and reflected energy, and thus distinguish between the energy mode converted to the quasielectrostatic (relativistic Bernstein) mode and that absorbed by the plasma (which does not exist for the purely perpendicular propagation and nonrelativistic case). Numerical methods are developed which enable one to handle the computation of the excessively stiff differential equations in the high‐field side. The three fundamental scattering problems are then evaluated numerically for various values of electron density and the product of electron temperature and scale length for the variation of the magnetic field for the case of perpendicular propagation. It is found that, unlike the mode coupling, the transmission of the X mode is not affected by the relativistic corrections. In the case of high‐field side incidence, the reflection is still zero as predicted in the nonrelativistic approach. However, in contrast to the zero absorption in the nonrelativistic case, there is significant absorption caused by relativistic broadening, particularly in the case of low‐field side incidence.