Theory of linear propagation and absorption of ion Bernstein waves in toroidal geometry

Ion Bernstein Waves (IBW) injection experiments at high power level (1 MW) carried out on DIII-D tokamak machine have shown a very peripherical wave absorption and no significant central ion heating. In this paper we attempt to find an explanation of this unsuccessful result within the framework of the linear theory of IBW propagation and absorption without invoking non-linear theories as the onset of parametric decay instability. The ray tracing equations for IBW propagation in toroidal geometry can be solved by choosing an appropriate ordering scheme for the relevant parameters kρi and ω. To be specific we assume kρi∼0(ε-1) and (ω -NΩci)/ω∼0(ε), where is the perpendicular wavenumber ρi is the ion Larmor radius, N is the harmonic number of the ion cyclotron resonance and ε is the inverse aspect ratio. Details of the calculation are given elsewhere. The solution of the ray tracing equations shows an oscillating behaviour of the parallel refractive index and a strong dependence of its amplitude on the poloidal angle at the antenna or alternatively on the value of θ0 at the lower hybrid conversion layer. The calculation of the absorption along the trajectory has been also obtained, showing that rays launched at angles θ0 > 5o are absorbed at the plasma periphery because of the strong increase of n||. (author) 5 refs., 2 figs