Kinetic evolution of electron distribution function in presence of RF waves

Radio frequency (RF) waves are routinely used to modify the current profile in tokamaks. In ITER, electron cyclotron waves will be used for such a purpose. We have formulated a kinetic description for the evolution of the electron distribution function $f_e$ in the presence of RF waves in a tokamak magnetic geometry [1]. The evolution of $f_e$ and the electron orbits is treated simultaneously, so that the evolution equation for $f_e$ is a functional mapping. This is useful as the electron phase space is inhomogeneous and bounded. All possible electron orbits, correlated and uncorrelated, are properly included. We use action-angle variables of an axisymmetric toroidal plasma. If we assume that $f_e$ is randomly distributed in one or all of the angles, a diffusion-like equation for the evolution of $f_e$ is obtained. The diffusion coefficient is time dependent and non-singular. In the limit of infinite time, we obtain the usual, singular, quasilinear diffusion coefficient. However, this description is incorrect as the time scale for the evolution of $f_e$ is inconsistent with the infinite time scale for determining the diffusion coefficient. The consequences of our description on the evolution of $f_e$ will be discussed.\newline [1] Y. Kominis et al., Phys. Plasmas {\bf 15}, 122501 (2008).