Vlasov-Poisson simulation of wave-induced velocity diffusion of electrons in a collisional plasma

The theory of current drive by plasma waves in tokamak plasmas relies on the quasilinear velocity diffusion of the resonant electrons against collisions. Usually, the driven current is estimated from the Fokker-Planck equation by assuming that the wave-induced diffusion can be described by the quasilinear diffusion term. In a previous paper, we investigated the validity of the quasilinear theory by one-dimensional Vlasov-Poisson simulations. For a fairly small number of large-amplitude waves, the diffusion was found to be slightly different from quasilinear. We have now included a simplified Balescu-Lenard collision term in the Vlasov-Poisson code. In the following, we investigate the formation of a steady-state current with Vlasov simulations. We compare the distribution function and the current obtained from simulations with the more conventional Fokker-Planck approach. The present simulations deal with the electron plasma waves. In the high-frequency limit, the lower hybrid waves can be approximated by magnetized electrostatic electron plasma waves. In this limit, the dispersion relation of the lower hybrid waves is approximately ω² = ω_p²k_||²/k², where k_||²<< k², and k_|| and k refer to the wave numbers parallel and perpendicular to the magnetic field, respectively. Our one-dimensional Vlasov-Poisson simulation is therefore analogous to solving the velocity distribution of the electrons in the direction parallel to the magnetic field for lower hybrid waves.