Comprehensive test electron simulations supported by theory are carried out to determine the diffusion and distribution function of tokamak edge electrons interacting with the lower hybrid (LH) grill electric field. Edge electrons respond to the antenna field by diffusing in velocity space within a region of overlapping LH grill spectrum Fourier modes, and streaming along magnetic field lines in both directions away from the LH grill. The intrinsic electron stochasticity induced by the grill field depends here not only on field strength but also on electron velocity. Electron velocity phases between successive scattering events on wave-guides are thereby strongly correlated with the result that after an initial quasi-linear rise the electron mean velocity and variance show a tendency to saturate and the diffusion coefficient decreases along the grill. The diffusive electron response in velocity space permits the representation of the LH field effect by a Langevin stochastic process, based upon a diffusion coefficient derived herein. Results from corresponding Monte Carlo calculations agree with simulation results which use the full radio-frequency-induced electron trajectories. The rapid radio-frequency timescale ≈1/ωLH in the problem can be thus replaced by the much slower electron transit time across a wave-guide. This gives here a reduction of about ten in CPU time. We also analytically find one-sided solutions of the diffusion electron kinetic equation under thermal Maxwellian boundary conditions imposed at either grill end, describing the two counter-propagating electron populations resonant with the grill spectrum.
Structure-preserving electromagnetic–kinetic simulations of lower hybrid-wave injection and current drive