Modelling RF heating in toroidal geometry: on the discrete bounce spectrumand the continuous bounce average

Starting from a more general formalism due to Lamalle [Plasma Phys. Contr. Fusion 32. 1409 (1997)], the dielectric response of a tokamak plasma to a r adiofrequency (RF) perturbation is evaluated using a simple decorrelation m odel, assuming the poloidal cross-section of the magnetic surfaces to be ci rcular and retaining leading-order terms in the drift parameter. Toroidicit y, poloidal magnetic field and particle trapping are included in the model. Constants of the motion are used as independent variables. A semi-analytic al method is adopted to evaluate the bounce spectrum of the dielectric resp onse (needed to solve the wave equation) and the associated RP diffusion op erator (required for solving the Fokker-Planck equation). The accent is on a study of this bounce spectrum. In particular, the link between the discre te bounce spectrum and the continuous bounce integral is highlighted. The c ritical parameter for the global justification of the replacement of the su m on the bounce spectrum by a bounce average is the relative magnitude of t he decorrelation and bounce times. That for the local justification is the second derivative of the periodic part of the relative wave-particle phase. Numerical examples are provided to give a qualitative feeling for the just ification of this substitution. The relation between the results presented here and those based on Hamiltonian models or on a simplified geometry is d iscussed.