Theory of Bernstein waves coupling with loop antennas

We present a fully three-dimensional theory of antenna coupling to Ion Bernstein Waves near the first harmonic of the ion cyclotron resonance in tokamak plasmas. The boundary conditions in vacuum are solved analytically for arbitrary orientation of the antenna and Faraday screen conductors. The wave equations in the plasma, which include Finite Larmor Radius and finite electron inertia effects, cyclotron and harmonic damping by the ions, and Landau and collisional damping by the electrons, are solved numerically using a Finite Elements discretisation with cubic Hermite interpolating functions. Applications to Alcator C give reasonably good agreement between the calculated and measured radiation resistance in the range in which efficient heating is observed; outside this range the calculated resistance is lower than the experimental one. In general, the coupling efficiency is found to be very sensitive to the edge plasma density, good coupling requiring a low density plasma layer in the vicinity of the Faraday screen. Coupling also improves with increasing scrape-off ion temperature, and is appreciably better for antisymmetric than for symmetric toroidal current distributions in the antenna. (orig.)