Analytic calculation of the nonzero fast wave reflection coefficient from the tunneling equation with absorption

Abstract

An analytic series expression of the nonzero fast wave reflection coefficient has been found from the tunneling equation which models the wave propagation in weakly inhomogeneous media near a back-to-back resonance-cutoff pair. Explicit calculations are done for both second ion cyclotron and second electron cyclotron harmonic cases. Numerical values of. this expression are compared to those calculated by solving an integral 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.

FLR mode conversion effects in the coupling analysis of the ICRF strap antenna in the IGNITOR machine

“…Therefore, we will express G yy in terms of the impedances at wall and plasma edge and further relate these to the reflection coefficients for the electric field at these boundaries. For the plasma, the reflection coefficient is then derived by considering a fast wave propagating through the plasma and then undergoing a scattering process in the mode conversion layer, where it is partly reflected and partly transmitted; this will allow a physical representation of the antenna-plasma coupling which is different from the approaches already employed [1][2][3][4][5][6].…”

“…The wave interactions in the F-IB confluence region, or mode conversion (MC) region, will be described by employing accurate ad hoc results [3,4]; the same applies to reflection and transmission at cut-off points. In the other regions, henceforth called regular regions, the wave interactions are dominated by propagation; we will be interested in solving a propagation problem as such, i.e.…”

“…The first papers dealing with antenna-plasma coupling in the ICRF range [1,2] solved Maxwell's equations in a cold plasma, disregarding the phenomenon of mode conversion between the fast and the ion Bernstein wave. Later on, more insight was gained into the physics of this mode conversion [3], including the effects of collisionless absorption on the scattering coefficients [4]. In the last few years, efforts were made to include some of the finite Larmor radius effects [5,6] in the computation of plasmaantenna coupling, i.e.…”

“…In this paper, the problem of the coupling between a strap antenna and a collisionless fusion plasma is studied with due regard to the theory developed in Refs [3,4] for the reflection at the mode conversion layer. A substantial portion of the present work is devoted to the derivation of the expression, in Fourier space, for Green's function connecting the electric field on the antenna to the (electric) current in the same antenna; this result is then applied to the (numerical) evaluation of the radiation resistance for the ICRH strap antennas proposed for the IGNITOR machine.…”

“…This yields equations representing coupled transmission lines that are solved explicitly via a structured perturbation approach, which recovers the WKB approximation and the subsequent Born-like corrections and also allows stronger variations of the plasma parameters to be treated with predetermined accuracy. This approach, together with the theory set forth in Refs [3,4] and with an analytical description of the propagation through evanescence regions, permits a comprehensive treatment of distributed reflections, mode conversion and tunnelling, with expressions in closed form. Geometry of wall-antenna-plasma system; the plasma extends from x = 0 to x = Ls, the antenna is located at a distance b from the plasma edge and at a distance a from the perfectly conducting wall.…”