Kinetic formulation of wave-particle interaction with coherent radio frequency waves

Coherent radio-frequency (RF) waves are routinely used for heating the plasma and for controlling the current profile in fusion plasmas. In ITER-like settings and beyond (DEMO) RF waves can significantly alter the particle distribution function away from an equilibrium Maxwell-Boltzmann distribution through wave-particle interactions in a global (non-resonant) as well local (resonant) manner. Meanwhile, collisions try to restore the distribution function to its equilibrium state. In high temperature plasmas, the modification due to RF waves occurs over time scales much shorter than collisional times. In this long mean-free path limit, particles interacting with RF waves do not undergo Brownian or Markovian diffusion. There persist long time correlations which invalidate the Markovian assumption inherent in the quasilinear models. We have recently developed a kinetic theory in action-angle phase space (J,θ) for particles interacting with coherent RF waves taking into account collisions in velocity space, u, via the collisional flux S_c in the long mean-free path limit which characterizes high temperature fusion plasmas. The angle- averaged distribution function F_e(J,t) is evolved concurrently with the particle motion and takes into account the complexity of the dynamical phase space in the presence of RF waves through an action and time dependent diffusion tensor D_t which is also depends on a characteristic angle de-correlation time τ_θ: ∂F_e(J,t)/∂t =∇_Jθ[D_tJ(J,t;τ).∇_θF_e(J,t_u-τ )]-〈∇.S_c〉_θ In stark contrast to the usual quasilinear theories, the waveparticle interaction operator in the evolution equation is time dependent resulting in markedly different results. This will be illustrated by comparing averaged quantities lik- current and temperature in ITER relevant fusion plasma settings.