Finite Larmor radius wave equations in Tokamak plasmas in the ion cyclotron frequency range

The constitutive relation of a non-homogeneous plasma for h.f. waves in the ion cyclotron frequency domain is derived by integrating the Vlasov equation along the unperturbed particle orbits in the drift approximation. The integro-differential wave equations and the corresponding power balance equation in Tokamak geometry are obtained by expanding the h.f. current to second order in the ratio of the ion Larmor radius to the typical perpendicular wavelength; terms proportional to the much smaller ratio of Larmor radius to the length characterizing equilibrium gradients are neglected. This allows the author to cast the FLR wave equations into an explicitly vector form, and to identify clearly the physical meaning of each term. By specializing to a plane stratified model of the Tokamak, the author compared the complete set of FLR wave equations with a considerably simpler set previously derived by Swanson (1981) and by Colestock and Kashuba (1983), which has been extensively used for analytic and numerical studies of ICR heating. The author concludes that at least in the important scenario of a hydrogen minority in a deuterium plasma (and of pure first harmonic heating as a particular case), the use of the reduced set of equations is well justified, provided that finite Larmor radius contributions to electron absorption are taken into account.