The combined theory of ion cyclotron wave coupling, mode conversion and absorption is developed for bounded inhomogeneous plasmas in slab geometry. The plasma response to the RF waves is described by the linearized Vlasov equation, with an equilibrium distribution function and a poloidal magnetic field profile which are selfconsistent solutions of the equilibrium Vlasov and Maxwell's equations. A general form of the wave equation, valid to arbitrary order in Larmor radius and including first order gradient terms, is derived. Expressions are also derived for the plasma intrinsic impedance. The wave equation, keeping second order terms in Larmor radius, is solved numerically for a plasma bounded by two conducting walls using the INTOR tokamak design parameters. It was found that the effect of the one-dimensional poloidal field is small. Also, a rough estimate of the error due to truncation to second order in Larmor radius was made and was found to be very small except in the high temperature regions. The effects of plasma boundedness and reflections from the mode conversion region on the coupling of waves from the RF source as a function of the plasma parameters and antenna spectra are studied. It is found that, at certain values of the plasma and antenna parameters, eigenmodes are formed, resulting in an increase in the loading impedance. It is verified that the impedance is not symmetric with respect to the spectrum in the poloidal direction, with highly peaked resonances. As the plasma temperature is increased, the resonances broaden and eventually disappear at very high temperatures. This is attributed to increased single pass absorption and decreasing reflection from the mode conversion region.
Numerical simulation of ion cyclotron waves in tokamak plasmas