Self consistent radio-frequency wave propagation and peripheral direct current plasma biasing: Simplified three dimensional non-linear treatment in the “wide sheath” asymptotic regime

Abstract

A minimal two-field fluid approach is followed to describe the radio-frequency (RF) wave propagation in the bounded scrape-off layer plasma of magnetic fusion devices self-consistently with direct current (DC) biasing of this plasma. The RF and DC parts are coupled by non-linear RF and DC sheath boundary conditions at both ends of open magnetic field lines. The physical model is studied within a simplified framework featuring slow wave (SW) only and lateral walls normal to the straight confinement magnetic field. The possibility is however kept to excite the system by any realistic 2D RF field map imposed at the outer boundary of the simulation domain. The self-consistent RF + DC system is solved explicitly in the asymptotic limit when the width of the sheaths gets very large, for several configurations of the RF excitation and of the target plasma. In the case of 3D parallelepipedic geometry, semi-analytical results are proposed in terms of asymptotic waveguide eigenmodes that can easily be implemented numerically. The validity of the asymptotic treatment is discussed and is illustrated by numerical tests against a quantitative criterion expressed from the simulation parameters. Iterative improvement of the solution from the asymptotic result is also outlined. Throughout the resolution, key physical properties of the solution are presented. The radial penetration of the RF sheath voltages along lateral walls at both ends of the open magnetic field lines can be far deeper than the skin depth characteristic of the SW evanescence. This is interpreted in terms of sheath-plasma wave excitation. Therefore, the proper choice of the inner boundary location is discussed as well as the appropriate boundary conditions to apply there. The asymptotic scaling of various quantities with the amplitude of the input RF excitation is established.

3-Dimensional density profiles in edge plasma simulations for ICRF heating

“…perpendicular terms in the laplacian, and ω 0 is the antenna frequency. In SSWICH-SW's asymptotic mode [8], which we use in this paper, the boundary condition at the limiter surfaces is E = 0.…”

“…The SSWICH-SW code [7][8][9] self-consistently determines the nonlinear plasma sheath potential. Unlike RAPLICA-SOL, it is essentially 2D: it operates on consecutive 2D radial-parallel slices, as shown in figure 1, and neglects derivatives in the vertical direction.…”

“…• SSWICH-SW (Self-consistent Sheaths and Waves for Ion Cyclotron Heating (Slow Wave) [7][8][9]) to selfconsistently determine the nonlinear plasma sheath potential and related quantities.…”

SOL RF physics modelling in Europe, in support of ICRF experiments

“…In Europe, these are implemented in the Self-consistent Sheaths and Waves for Ion Cyclotron Heating (SSWICH) code [1], [2], [3], using the Newton-Raphson scheme in the multiphysics solver COMSOL. As an intermediate step the code also computes the complex oscillating voltages V RF at sheath boundaries.…”

Sequential modelling of ICRF wave near RF fields and asymptotic RF sheaths description for AUG ICRF antennas

“…The SSWICH [13][14][15] code follows a three-field approach to self-consistently model the interplay between RF waves and edge plasma DC biasing. In the SSWICH-SW version which is used in this study, the RF waves are reduced to the slow magnetosonic wave (SW) only.…”