Statistical theory of wave propagation and multipass absorption for current drive in tokamaks

Abstract

In this work the effect of ray stochasticity on the multipass absorption of lower‐hybrid waves, used to drive current in tokamaks, is considered. In toroidal geometry, stochasticity arises as an intrinsic property of the Hamiltonian ray trajectories for lower‐hybrid waves. Based on the wave kinetic equation, a diffusion equation is derived, with damping and sources, for the wave energy density in the stochastic layer. This equation is solved simultaneously with the electron Fokker–Planck equation to describe the quasilinear flattening of the electron distribution function and the subsequent modification of the wave damping. Steady‐state solutions of this system (obtained numerically) indicate that the spectral gap is filled in a self‐regulating manner, so that the boundaries of the diffused wave spectrum are independent of the level of ray stochastic diffusion. This allows the development of a simple (semianalytic) model for the self‐consistent wave spectrum and the radial profile of absorbed power.