Cs. Ng et Dg. Swanson, ANALYTIC CALCULATION OF THE NONZERO FAST-WAVE REFLECTION COEFFICIENT FROM THE TUNNELING EQUATION WITH ABSORPTION, Physics of plasmas, 1(4), 1994, pp. 815-821
An analytic series expression of the nonzero fast wave reflection coef
ficient has been found from the tunneling equation which models the wa
ve propagation in weakly inhomogeneous media near a back-to-back reson
ance-cutoff pair. Explicit calculations are done for both second ion c
yclotron and second electron cyclotron harmonic cases. Numerical value
s of this expression are compared to those calculated by solving an in
tegral equation iteratively. They agree well with each other whenever
both the series and the iteration converge. This result is based on a
new method of evaluating integrals derived from the integral equation
without having to solve the equation itself. This new method may have
more applications and deserves further research and development.