The three-dimensional plasma boundary displacements induced by applied non-axisymmetric magnetic perturbations have been measured in ASDEX Upgrade, DIII-D, JET, MAST and NSTX. The displacements arising from applied resonant magnetic perturbations (RMPs) are measured up to ±5% of the minor radius in present-day machines. Good agreement can be found between different experimental measurements and a range of models-be it vacuum field line tracing, ideal three-dimensional MHD equilibrium modelling, or nonlinear plasma amplification. The agreement of the various experimental measurements with the different predictions from these models is presented, and the regions of applicability of each discussed. The measured displacement of the outboard boundary from various machines is found to correlate approximately linearly with the applied resonant field predicted by vacuum modelling (though it should be emphasized that one should not infer that vacuum modelling accurately predicts the displacement inside the plasma). The RMP-induced displacements foreseen in ITER are expected to lie within the range of those predicted by the different models, meaning less than ±1.75% (±3.5 cm) of the minor radius in the H-mode baseline and less than ±2.5% (±5 cm) in a 9 MA plasma. Whilst a displacement of 7 cm peak-to-peak in the baseline scenario is marginally acceptable from both a plasma control and heat loading perspective, it is important that ITER adopts a plasma control system which can account for a three-dimensional boundary corrugation to avoid an n = 0 correction which would otherwise locally exacerbate the displacement caused by the applied fields.
Wendelstein 7-X is an optimized stellarator with superconducting magnetic field coils that just started plasma operation at Max-Planck-Institut für Plasmaphysik (IPP) Greifswald. Utilizing the electron beam technique the first vacuum flux surface measurements were performed during the commissioning of the magnet system. For the magnetic configurations investigated so far the existence of closed and nested flux surfaces has been validated. All features of the configuration designed for the initial plasma operation phase, including a predicted island chain, were confirmed. No evidence on significant magnetic field errors was found. Furthermore, the effect of the elastic deformation of the non-planar coils was confirmed by the measurements.
The mitigation and suppression of edge localized modes (ELMs) through application of resonant magnetic perturbations (RMPs) in Tokamak plasmas is a well documented phenomenon (142603) in DIII-D. In these codes, a self-consistent calculation of the plasma response due to the RMP coils is calculated. The VMEC code globally enforces the constraints of ideal MHD; consequently, a continuously nested family of flux surfaces is enforced throughout the plasma domain. This approach necessarily precludes the observation of islands or field-line chaos. The SPEC code relaxes the constraints of ideal MHD locally, and allows for islands and field line chaos at or near the rational surfaces. Equilibria with finite pressure gradients are approximated by a set of discrete 'ideal-interfaces' at the most irrational flux surfaces and where the strongest pressure gradients are observed. Both the VMEC and SPEC calculations are initialized from EFIT reconstructions of the plasma that are consistent with the experimental pressure and current profiles. A 3D reconstruction using the STELLOPT code, which fits VMEC equilibria to experimental measurements, has also been performed. Comparisons between the equilibria generated by the 3D codes and between STELLOPT and EFIT are presented.
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