Waveguide coupling of ion Bernstein waves to tokamak plasmas

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Abstract
The paper proposes a theoretical model of coupling of ion Bernstein (IB) waves to tokamak plasmas using phased waveguides. To describe the propagation of these waves near higher harmonics of the ion cyclotron frequency, a set of differential wave equations is used, constructed by analogy to the familiar finite Larmor radius wave equations, but in such a way that its three independent WKB solutions correspond to the two cold plasma waves and the Bernstein wave to all orders in the ion Larmor radius. This system has a meaningful energy theorem and unambiguous boundary conditions at the plasma edge. It is integrated numerically to obtain the surface admittance matrix of the plasma. The efficiency of waveguide launching is evaluated by extending the theory developed for lower hybrid (LH) wave grills to take into account the finite height of the waveguides as well as the coupling between TE and TM modes at the waveguide mouths due to the fact that at these frequencies the admittance matrix is not diagonal. If the density at the plasma edge is sufficiently low, in particular well below the LH resonance density, results similar to those predicted by the cold plasma approximation are obtained. In this situation, low reflection coefficients in the waveguides can be achieved with antisymmetric excitation. Excitation of IB waves, however, occurs via mode transformation near the LH resonance layer, typically a few centimetres away from the antenna. Whether this is possible without energy losses cannot be investigated with the present model. As the density increases, the plasma surface becomes very reflective for waves with the ordinary polarization. As a consequence, direct linear coupling to IB waves by raising the edge density above the LH resonance density appears to be impossible according to this model.