The plasma response to Resonant Magnetic Perturbations (RMPs) in ASDEX Upgrade is modeled with the non-linear resistive MHD code JOREK, using input profiles that match those of the experiments as closely as possible. The RMP configuration for which Edge Localized Modes are best mitigated in experiments is related to the largest edge kink response observed near the X-point in modeling. On the edge resonant surfaces q = m/n, the coupling between the m + 2 kink component and the m resonant component is found to induce the amplification of the resonant magnetic perturbation. The ergodicity and the 3D-displacement near the X-point induced by the resonant amplification can only partly explain the density pumpout observed in experiments.

In this paper we present a rigorous derivation of the reduced MHD models with and without parallel velocity that are implemented in the non-linear MHD code JOREK. The model we obtain contains some terms that have been neglected in the implementation but might be relevant in the non-linear phase. These are necessary to guarantee exact conservation with respect to the full MHD energy.For the second part of this work, we have replaced the linearized time stepping of JOREK by a non-linear solver based on the Inexact Newton method including adaptive time stepping. We demonstrate that this approach is more robust especially with respect to numerical errors in the saturation phase of an instability and allows to use larger time steps in the non-linear phase. *

View the article online for updates and enhancements. Related content Toroidal mode number determination of ELM associated phenomena on ASDEX Upgrade Felician Mink, Elisabeth Wolfrum, Marc Maraschek et al.-High frequency magnetic fluctuations correlated with the inter-ELM pedestal evolution in ASDEX Upgrade F M Laggner, E Wolfrum, M Cavedon et al.-Recent progress in understanding the processes underlying the triggering of and energy loss associated with type I ELMs

The explanation of the existence of the rotating MHD modes in the pedestal region before Type I Edge Localized Mode (ELM) crash and in the inter-ELM periods (ELM precursors) observed in KSTAR is provided for the first time in the present paper. The dynamics of ELMs, observed using Electron Cyclotron Emission Imaging (ECEI) in KSTAR tokamak, is compared to the modelling results of the non-linear reduced resistive MHD code JOREK. The realistic KSTAR pulse parameters and geometry including X-point and Scrape Off Layer (SOL) were used. The full ELM crash modelling was performed using JOREK code for single and multi-harmonic representation and in multi-cycles ELMy regimes including relevant flows. The most unstable toroidal modes numbers (n=5-8), velocity (~5km/s for n=8 mode) and the direction of the mode rotation were reproduced in modelling. The two fluid diamagnetic effects and toroidal rotations included in the model were found to be the most important factors in explaining the experimentally observed rotation of the ballooning modes before the ELM crash and in the inter-ELM phase. In multi-harmonic multi-cycle simulations the spectrum of temperature fluctuations is similar to the experimental one in the inter-ELM phase, where several rotating modes with medium n numbers were detected in 5-30kHz frequency range. The rotating modes can contain single or several harmonics which last from 0.2ms to few ms in time, and can appear and disappear in the inter ELM period or persist until a new ELM crash. I.Introduction. The understanding of Edge Localized Modes (ELMs) physics is of particular importance for ITER where heat and particles fluxes due to ELMs represent a concern for the plasma facing components (PFC) [1]. The direct comparison of theory and modelling with experimental observations of ELM dynamics plays an important role not only in the theoretical understanding of ELMs. They are necessary for the reliable predictions of divertor heat and particle fluxes and for understanding of ELMs mitigation technics physics needed for their optimization in different ITER scenarios. The measurements performed with Electron Cyclotron Emission Imaging (ECEI) diagnostic on KSTAR [2,3,4] provided new surprising features of the Type I ELMy regimes on which the present paper is mainly focused. The