Tokamak edge electron diffusion and distribution function in the lower hybrid antenna electric field

Abstract

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.

Lower hybrid current drive experiments in support of high confinement long pulse operation in EAST

“…Electron acceleration at the plasma edge due to Landau damping on high n // -components does not seem to be the cause, since infrared measurements of the divertor do not indicate higher heat load with the 2.45 GHz launcher. In addition, calculations of the electron acceleration using the electric field from ALOHA [10] and a model for the electron dynamics in the LH electric field [14], show that the heat flux produced by edge electron acceleration is comparable for the two LH launchers [15].…”

Numerical stability of 2nd order Runge-Kutta integration algorithms for use in particle-in-cell codes

“…which can represent particle velocity-space diffusion due to collisions [2] or radiofrequen-cy heating [3]. In (5) D and F are, respectively, the diffusion and friction coefficients and σ is a normally distributed random variable with zero mean and unity variance.…”

“…Next, we present 1-D (toroidal) PIC simulations along a 16 wave-guide lower hybrid (LH) grill [3] surrounded by field-free plasma regions. The boundary conditions are a Maxwellian particle influx to compensate for the outflow.…”

“…3. In the second case we represent the electron response by a Langevin process (5), where the diffusion and friction coefficients are given in [3], and we integrate Eqs (1) using the Runge-Kutta method. The results are shown in Fig.…”

“…However, this scheme can only be used for forces independent of velocity unless a simple enough implicit implementation is possible. The LF scheme is therefore inapplicable in Monte-Carlo treatments of particle collisions [2] and/or interactions with radio-frequency fields [3]. We examine here the suitability of the 2 nd order Runge-Kutta (RK) method.…”