Simulation of cold magnetized plasmas with the 3D electromagnetic software CST Microwave Studio ®

Detailed designs of ICRF antennas were made possible by the development of sophisticated commercial 3D codes like CST Microwave Studio® (MWS). This program allows for very detailed geometries of the radiating structures, but was only considering simple materials like equivalent isotropic dielectrics to simulate the reflection and the refraction of RF waves at the vacuum/plasma interface. The code was nevertheless used intensively, notably for computing the coupling properties of the ITER ICRF antenna. Until recently it was not possible to simulate gyrotropic medias like magnetized plasmas, but recent improvements have allowed programming any material described by a general dielectric or/and diamagnetic tensor. A Visual Basic macro was developed to exploit this feature and was tested for the specific case of a monochromatic plane wave propagating longitudinally with respect to the magnetic field direction. For specific cases the exact solution can be expressed in 1D as the sum of two circularly polarized waves connected by a reflection coefficient that can be analytically computed. Solutions for stratified media can also be derived. This allows for a direct comparison with MWS results. The agreement is excellent but accurate simulations for realistic geometries require large memory resources that could significantly restrict the possibility of simulating cold plasmas to small-scale machines

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

A European project was undertaken to improve the available SOL ICRF physics simulation tools and confront them with measurements. This paper first reviews code upgrades within the project. Using the multi-physics finite element solver COMSOL, the SSWICH code couples RF full-wave propagation with DC plasma biasing over “antenna-scale” 2D (toroidal/radial) domains, via non-linear RF and DC sheath boundary conditions (SBCs) applied at shaped plasma-facing boundaries. For the different modules and associated SBCs, more elaborate basic research in RF-sheath physics, SOL turbulent transport and applied mathematics, generally over smaller spatial scales, guides code improvement. The available simulation tools were applied to interpret experimental observations on various tokamaks. We focus on robust qualitative results common to several devices: the spatial distribution of RF-induced DC bias; left-right asymmetries over strap power unbalance; parametric dependence and antenna electrical tuning; DC SOL biasing far from the antennas, and RF-induced density modifications. From these results we try to identify the relevant physical ingredients necessary to reproduce the measurements, e.g. accurate radiated field maps from 3D antenna codes, spatial proximity effects from wave evanescence in the near RF field, or DC current transport. Pending issues towards quantitative predictions are also outlined

Simulation of cold magnetized plasmas with the 3D electromagnetic software CST Microwave Studio®

Detailed designs of ICRF antennas were made possible by the development of sophisticated commercial 3D codes like CST Microwave Studio® (MWS). This program allows for very detailed geometries of the radiating structures, but was only considering simple materials like equivalent isotropic dielectrics to simulate the reflection and the refraction of RF waves at the vacuum/plasma interface. The code was nevertheless used intensively, notably for computing the coupling properties of the ITER ICRF antenna. Until recently it was not possible to simulate gyrotropic medias like magnetized plasmas, but recent improvements have allowed programming any material described by a general dielectric or/and diamagnetic tensor. A Visual Basic macro was developed to exploit this feature and was tested for the specific case of a monochromatic plane wave propagating longitudinally with respect to the magnetic field direction. For specific cases the exact solution can be expressed in 1D as the sum of two circularly polarized waves connected by a reflection coefficient that can be analytically computed. Solutions for stratified media can also be derived. This allows for a direct comparison with MWS results. The agreement is excellent but accurate simulations for realistic geometries require large memory resources that could significantly restrict the possibility of simulating cold plasmas to small-scale machines

Simulation of cold magnetized plasmas with the 3D electromagnetic software CST Microwave Studio

Detailed designs of ICRF antennas were made possible by the development of sophisticated commercial 3D codes like CST Microwave Studio® (MWS). This program allows for very detailed geometries of the radiating structures, but was only considering simple materials like equivalent isotropic dielectrics to simulate the reflection and the refraction of RF waves at the vacuum/plasma interface. The code was nevertheless used intensively, notably for computing the coupling properties of the ITER ICRF antenna. Until recently it was not possible to simulate gyrotropic medias like magnetized plasmas, but recent improvements have allowed programming any material described by a general dielectric or/and diamagnetic tensor. A Visual Basic macro was developed to exploit this feature and was tested for the specific case of a monochromatic plane wave propagating longitudinally with respect to the magnetic field direction. For specific cases the exact solution can be expressed in 1D as the sum of two circularly polarized waves connected by a reflection coefficient that can be analytically computed. Solutions for stratified media can also be derived. This allows for a direct comparison with MWS results. The agreement is excellent but accurate simulations for realistic geometries require large memory resources that could significantly restrict the possibility of simulating cold plasmas to small-scale machines

Spatial proximity effects on the excitation of Sheath RF Voltages by evanescent Slow Waves in the Ion Cyclotron Range of Frequencies

International audienceWe investigate theoretically how sheath radio-frequency (RF) oscillations relate to the spatial structure of the near RF parallel electric field E// emitted by Ion Cyclotron (IC) wave launchers. We use a simple model of Slow Wave (SW) evanescence coupled with Direct Current (DC) plasma biasing via sheath boundary conditions in a 3D parallelepiped filled with homogeneous cold magnetized plasma. Within a “wide sheaths” asymptotic regime, valid for large-amplitude near RF fields, the RF part of this simple RF+DC model becomes linear: the sheath oscillating voltage VRF at open field line boundaries can be re-expressed as a linear combination of individual contributions by every emitting point in the input field map. SW evanescence makes individual contributions all the larger as the wave emission point is located closer to the sheath walls. The decay of |VRF| with the emission point/sheath poloidal distance involves the transverse SW evanescence length and the radial protrusion depth of lateral boundaries. The decay of |VRF| with the emitter/sheath parallel distance is quantified as a function of the parallel SW evanescence length and the parallel connection length of open magnetic field lines. For realistic geometries and target SOL plasmas, poloidal decay occurs over a few centimeters. Typical parallel decay lengths for |VRF| are found smaller than IC antenna parallel extension. Oscillating sheath voltages at IC antenna side limiters are therefore mainly sensitive to E// emission by active or passive conducting elements near these limiters, as suggested by recent experimental observations. Parallel proximity effects could also explain why sheath oscillations persist with antisymmetric strap toroidal phasing, despite the parallel anti-symmetry of the radiated field map. They could finally justify current attempts at reducing the RF fields induced near antenna boxes to attenuate sheath oscillations in their vicinity

Spatial proximity effects on the excitation of Sheath RF Voltages by evanescent Slow Waves in the Ion Cyclotron Range of Frequencies

International audienceWe investigate theoretically how sheath radio-frequency (RF) oscillations relate to the spatial structure of the near RF parallel electric field E∥ emitted by ion cyclotron (IC) wave launchers. We use a simple model of slow wave (SW) evanescence coupled with direct current (DC) plasma biasing via sheath boundary conditions in a 3D parallelepiped filled with homogeneous cold magnetized plasma. Within a ‘wide-sheath’ asymptotic regime, valid for large-amplitude near RF fields, the RF part of this simple RF + DC model becomes linear: the sheath oscillating voltage VRF at open field line boundaries can be re-expressed as a linear combination of individual contributions by every emitting point in the input field map. SW evanescence makes individual contributions all the larger as the wave emission point is located closer to the sheath walls. The decay of |VRF| with the emission point/sheath poloidal distance involves the transverse SW evanescence length and the radial protrusion depth of lateral boundaries. The decay of |VRF| with the emitter/sheath parallel distance is quantified as a function of the parallel SW evanescence length and the parallel connection length of open magnetic field lines. For realistic geometries and target SOL plasmas, poloidal decay occursover a few centimeters. Typical parallel decay lengths for |VRF| are found to be smaller than ICantenna parallel extension. Oscillating sheath voltages at IC antenna side limiters are thereforemainly sensitive to E∥ emission by active or passive conducting elements near these limiters,as suggested by recent experimental observations. Parallel proximity effects could also explainwhy sheath oscillations persist with antisymmetric strap toroidal phasing, despite the parallelantisymmetry of the radiated field map. They could finally justify current attempts at reducingthe RF fields induced near antenna boxes to attenuate sheath oscillations in their vicinit

Electromagnetic simulations of JET ICRF ITER-like antenna with TOPICA and SSWICH asymptotic codes

Multi-megawatt Ion Cyclotron Range of Frequencies (ICRF) heating is routinely used in the JET tokamak. To increase the ICRF heating power available from the A2 antennas, the ICRF ITER-Like Antenna (ILA) was reinstalled for the 2015 JET ITER-like wall experimental campaign. The application of high levels of ICRF power typically results in increased plasma wall interaction which leads to the observation of enhanced influx of metallic impurities in the plasma edge. It is assumed that the impurity production is mainly driven by the parallel component of the Radio-Frequency (RF) antenna electric near-field, E// (parallel to the confinement magnetic field of the tokamak), that is rectified in a thin boundary layer (RF sheath). Torino Polytechnic Ion Cyclotron Antenna (TOPICA) code was used to compute E// field maps in front of the ILA and between its poloidal limiters in the presence of plasma using measured density profiles and various antenna feedings. E// field maps calculated between the poloidal limiters were used to estimate the poloidal distribution of RF-sheath Direct Current (DC) potential in this private region of the ILA and make relative comparison of various antenna electrical settings. For this purpose we used the asymptotic version of the Self-consistent Sheaths and Waves for Ion Cyclotron Heating Slow-Wave (SSWICH-SW) code. These estimations can help to study the formation of RF sheaths around the antenna and even at distant locations (∼3m away)

RF Sheath-Enhanced Plasma Surface Interaction Studies using Beryllium Optical Emission Spectroscopy in JET ITER-Like Wall

A dedicated study on JET-ILW, deploying two types of ICRH antennas and spectroscopic observation spots at two outboard, beryllium limiters, has provided insight on long-range (up to 6m) RFenhanced plasma-surface interactions (RF-PSI) due to near-antenna electric fields. To aid in the interpretation of optical emission measurements of these effects, the antenna near-fields are computed using the TOPICA code, specifically run for the ITER-like antenna (ILA); similar modelling already existed for the standard JET antennas (A2). In the experiment, both antennas were operated in current drive mode, as RF-PSI tends to be higher in this phasing and at similar power (∼0.5 MW). When sweeping the edge magnetic field pitch angle, peaked RF-PSI effects, in the form of 2-4 fold increase in the local Be source,are consistently measured with the observation spots magnetically connect to regions of TOPICAL-calculated high near-fields, particularly at the near-antenna limiters. It is also found that similar RF-PSI effects are produced by the two types of antenna on similarly distant limiters. Although this mapping of calculated near-fields to enhanced RF-PSI gives only qualitative interpretion of the data, the present dataset is expected to provide a sound experimental basis for emerging RF sheath simulation model validation

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

A European project was undertaken to improve the available SOL ICRF physics simulation tools and confront them with measurements. This paper first reviews code upgrades within the project. Using the multi-physics finite element solver COMSOL, the SSWICH code couples RF full-wave propagation with DC plasma biasing over “antenna-scale” 2D (toroidal/radial) domains, via non-linear RF and DC sheath boundary conditions (SBCs) applied at shaped plasma-facing boundaries. For the different modules and associated SBCs, more elaborate basic research in RF-sheath physics, SOL turbulent transport and applied mathematics, generally over smaller spatial scales, guides code improvement. The available simulation tools were applied to interpret experimental observations on various tokamaks. We focus on robust qualitative results common to several devices: the spatial distribution of RF-induced DC bias; left-right asymmetries over strap power unbalance; parametric dependence and antenna electrical tuning; DC SOL biasing far from the antennas, and RF-induced density modifications. From these results we try to identify the relevant physical ingredients necessary to reproduce the measurements, e.g. accurate radiated field maps from 3D antenna codes, spatial proximity effects from wave evanescence in the near RF field, or DC current transport. Pending issues towards quantitative predictions are also outlined