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The confinement of neutral beam injection (NBI) particles in the presence of n = 3 resonant magnetic perturbations (RMPs) in 15 MA ITER DT plasmas has been studied using full orbit ASCOT simulations. Realistic NBI distribution functions, and 3D wall and equilibria, including the plasma response to the externally applied 3D fields calculated with MARS-F, have been employed. The observed total fast-ion losses depend on the poloidal spectra of the applied n = 3 RMP as well as on the absolute toroidal phase of the applied perturbation with respect to the NBI birth distribution. The absolute toroidal phase of the RMP perturbation does not affect the ELM control capabilities, which makes it a key parameter in the confinement optimization. The physics mechanisms underlying the observed fast-ion losses induced by the applied 3D fields have been studied in terms of the variation of the particle canonical angular momentum (δP ϕ ) induced by the applied 3D fields. The presented simulations indicate that the transport is located in an edge resonant transport layer as observed previously in ASDEX upgrade studies. Similarly, our results indicate that an overlapping of several linear and nonlinear resonances at the edge of the plasma might be responsible for the observed fast-ion losses. The results presented here may help to optimize the RMP configuration with respect to the NBI confinement in future ITER discharges.

The data collected during ASDEX Upgrade experiments in which external 3D fields have been deployed in the attempt of mitigating runaway electrons (RE) are interpreted by a numerical test particle approach. To this end the Hamiltonian guiding center code ORBIT has been used, with the implementation of the magnetic perturbation spectrum modeled by the code MARS-F, which also takes into account the plasma response to the applied 3D fields. In agreement with the observed phenomenology, ORBIT simulations show that the configuration of the currents in the top/bottom arrays of error field coils, which maximizes the plasma response to the external perturbations, is the one that most affects the high energy test electron trajectories in the edge region, thus leading to an enhancement of the energetic electron losses. This occurs in particular during the disruption, i.e. taking into account the increased toroidal electric field associated with the fast plasma cooling. Used in a predictive way, the numerical results suggest which coil configuration could further improve the RE mitigation.

The plasma response from an external n = 2 magnetic perturbation field in ASDEX Upgrade has been measured using mainly electron cyclotron emission (ECE) diagnostics and a rigid rotating field. To interpret ECE and ECE-imaging (ECE-I) measurements accurately, forward modeling of the radiation transport has been combined with ray tracing. The measured data is compared to synthetic ECE data generated from a 3D ideal magnetohydrodynamics (MHD) equilibrium calculated by VMEC. The measured amplitudes of the helical displacement around the low field side midplane are in reasonable agreement with the one from the synthetic VMEC diagnostics. Both exceed the prediction from the vacuum field calculations and indicate the presence of a kink response at the edge, which amplifies the perturbation. VMEC and MARS-F have been used to calculate the properties of this kink mode. The poloidal mode structure of the magnetic perturbation of this kink mode at the edge peaks at poloidal mode numbers larger than the resonant components |m| > |nq|, whereas the poloidal mode structure of its displacement is almost resonant |m| ~ |nq|. This is expected from ideal MHD in the proximity of rational surfaces. The displacement measured by ECE-I confirms this resonant response., 34 pages, 19 figures. This is an author-created, un-copyedited version of an article submitted for publication in Plasma Physics and Controlled Fusion. IoP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

Disruption-generated runaway electron (RE) beams represent a severe threat for tokamak plasma-facing components in high current devices like ITER, thus motivating the search of mitigation techniques. The application of 3D fields might aid this purpose and recently was investigated also in the ASDEX Upgrade experiment by using the internal active saddle coils (termed B-coils). Resonant magnetic perturbations (RMPs) with dominant toroidal mode number n = 1 have been applied by the B-coils, in a RE specific scenario, before and during disruptions, which are deliberately created via massive gas injection. The application of RMPs affects the electron temperature profile and seemingly changes the dynamics of the disruption; this results in a significantly reduced current and lifetime of the generated RE beam. A similar effect is observed also in the hard-x-ray (HXR) spectrum, associated to RE emission, characterized by a partial decrease of the energy content below 1 MeV when RMPs are applied. The strength of the observed effects strongly depends on the upper-to-lower B-coil phasing, i.e. on the poloidal spectrum of the applied RMPs, which has been reconstructed including the plasma response by the code MARS-F. A crude vacuum approximation fails in the interpretation of the experimental findings: despite the relatively low β () of these discharges, a modest amplification (factor of ) of the edge kink response occurs, which has to be considered to explain the observed suppression effects. © 2017 Universitá di Padova.

Edge Localised Modes (ELMs) are a repetitive MHD instability, which may be mitigated or suppressed by the application of resonant magnetic perturbations (RMPs). In tokamaks which have an upper and lower set of RMP coils, the applied spectrum of the RMPs can be tuned for optimal ELM control, by introducing a toroidal phase difference ∆Φ between the upper and lower rows. The outermost resonant component of the RMP field b1res (numerous other criteria have also been devised, as discussed herein) has been shown experimentally to correlate with mitigated ELM frequency, and to be controllable by ∆Φ (Kirk et al 2013 Plas. Phys. Cont. Fus. 53 043007). This suggests that ELM mitigation may be optimised by choosing ∆Φ = ∆Φopt, such that b1res is maximal. However it is currently impractical to compute ∆Φopt in advance of experiments. This motivates this computational study of the dependence of the optimal coil phase difference ∆Φopt, on plasma parameters βN and q95, in order to produce a simple parametrisation of ∆Φopt. In this work, a set of tokamak equilibria spanning a wide range of (βN , q95) is produced, based on a reference equilibrium from an ASDEX Upgrade RMP experiment. The MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681) is then used to compute ∆Φopt across this equilibrium set for toroidal mode numbers n = 1 − 4, both for the vacuum field and including the plasma response. The computational scan finds that for fixed plasma boundary shape, rotation profiles and toroidal mode number n, ∆Φopt is a smoothly varying function of (βN , q95). A 2D quadratic function in (βN , q95) is used to parametrise ∆Φopt, such that for given (βN , q95) and n an estimate of ∆Φopt may be made, without requiring a plasma response computation. In order to quantify the uncertainty of the parametrisation relative to a plasma response computation, ∆Φopt is also computed using MARS-F for a set of validation points. Each validation point consists of a distinct free boundary equilibrium reconstructed from an ASDEX Upgrade RMP experiment, and set of experimental kinetic profiles and coil currents. Comparing the MARS-F computed ∆Φopt for these validation points to ∆Φopt computed with the 2D quadratic, shows that relative to a plasma response computation with MARS-F the 2D quadratic is accurate to 26.5 degrees for n = 1, and 20.6 degrees for n = 2. Potential sources for uncertainty are then assessed

Toroidal computations are performed using the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681), in order to understand correlations between the plasma response and the observed mitigation of the edge localized modes (ELM) using resonant magnetic perturbation fields in ASDEX Upgrade. In particular, systematic numerical scans of the edge safety factor reveal that the amplitude of the resonant poloidal harmonic of the response radial magnetic field near the plasma edge, as well as the plasma radial displacement near the X-point, can serve as good indicators for predicting the optimal toroidal phasing between the upper and lower rows of coils in ASDEX Upgrade. The optimal coil phasing scales roughly linearly with the edge safety factor q 95 , for various choices of the toroidal mode number n = 1–4 of the coil configuration. The optimal coil phasing is also predicted to vary with the upper triangularity of the plasma shape in ASDEX Upgrade. Furthermore, multiple resonance effects of the plasma response, with continuously varying q 95 , are computationally observed and investigated.

Experimental measurements with Langmuir probe and laser photodetachment in beam extraction region of a cesium-seeded negative ion source for NBI has been conducted in order to investigate the response of charged particles to applied external field. The profiles of probe saturation current and H− ion density in the direction normal to the plasma grid (PG) surface were measured by scanning the tip position. By comparing the results before and during beam extraction, the charged particle responses due to the beam extraction have been analyzed. During beam extraction, probe saturation current increases since H− ions are extracted and electrons flow into the extracting region for charge neutrality. The maximum increment of the probe saturation current due to electron flow appears in the range of 15 - 25 mm apart from the PG surface. Meanwhile, the maximum decrement of the H− ion density is at around 18 mm from the PG. In the region far from the PG, probe saturation current increment is low as well as the decrement of the H− ion density. The extrapolations of the profiles suggest that the depth of the influence on the plasma by beam extraction is 42 mm from the plasma grid surface.

The plasma response to the vacuum resonant magnetic perturbation (RMP) fields, produced by the ELM control coils in ASDEX Upgrade experiments, is computationally modelled using the MARS-F/K codes (Liu et al 2000 Phys. Plasmas 7 3681, Liu et al 2008 Phys. Plasmas 15 112503). A systematic investigation is carried out, considering various plasma and coil configurations as in the ELM control experiments. The low q plasmas, with q 95 ∼ 3.8 (q 95 is the safety factor q value at 95% of the equilibrium poloidal flux), responding to low n (n is the toroidal mode number) field perturbations from each single row of the ELM coils, generates a core kink amplification effect. Combining two rows, with different toroidal phasing, thus leads to either cancellation or reinforcement of the core kink response, which in turn determines the poloidal location of the peak plasma surface displacement. The core kink response is typically weak for the n = 4 coil configuration at low q, and for the n = 2 configuration but only at high q ( q 95 ∼ 5.5 ). A phase shift of around 60 degrees for low q plasmas, and around 90 degrees for high q plasmas, is found in the coil phasing, between the plasma response field and the vacuum RMP field, that maximizes the edge resonant field component. This leads to an optimal coil phasing of about 100 (−100) degrees for low (high) q plasmas, that maximizes both the edge resonant field component and the plasma surface displacement near the X-point of the separatrix. This optimal phasing closely corresponds to the best ELM mitigation observed in experiments. A strong parallel sound wave damping moderately reduces the core kink response but has minor effect on the edge peeling response. For low q plasmas, modelling shows that both the resonant electromagnetic torque and the neoclassical toroidal viscous (NTV) torque (due to the presence of 3D magnetic field perturbations) contribute to the toroidal flow damping, in particular near the plasma edge region. For high q plasmas, however, significant amount of torque is also produced in the bulk plasma region, and the contributions from the electromagnetic, the NTV, and the torque associated with the Reynolds stress, all play significant roles.