The interaction of static Resonant Magnetic Perturbations (RMPs) with the plasma flows is modeled in toroidal geometry, using the non-linear resistive MHD code JOREK, which includes the X-point and the Scrape-Off-Layer. Two-fluid diamagnetic effects, the neoclassical poloidal friction and a source of toroidal rotation are introduced in the model to describe realistic plasma flows. RMP penetration is studied taking self-consistently into account the effects of these flows and the radial electric field evolution. JET-like, MAST and ITER parameters are used in modeling. For JET-like parameters, three regimes of plasma response are found depending on the plasma resistivity and the diamagnetic rotation: at high resistivity and slow rotation, the islands generated by the RMPs at the edge resonant surfaces rotate in the ion diamagnetic direction and their size oscillates. At faster rotation, the generated islands are static and are more screened by the plasma. An intermediate regime with static islands which slightly oscillate is found at lower resistivity. In ITER simulations, the RMPs generate static islands, which forms an ergodic layer at the very edge (ψ ≥ 0.96) characterized by lobe structures near the X-point and results in a small strike point splitting on the divertor targets. In MAST DND geometry, lobes are also found near the X-point and the 3D-deformation of the density and temperature profiles is observed.

JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.

3D non-linear MHD simulations of a D 2 massive gas injection (MGI) triggered disruption in JET with the JOREK code provide results which are qualitatively consistent with experimental observations and shed light on the physics at play. In particular, it is observed that the gas destabilizes a large m/n = 2/1 tearing mode, with the island O-point coinciding with the gas deposition region, by enhancing the plasma resistivity via cooling. When the 2/1 island gets so large that its inner side reaches the q = 3/2 surface, a 3/2 tearing mode grows. Simulations suggest that this is due to a steepening of the current profile right inside q = 3/2. Magnetic field stochastization over a large fraction of the minor radius as well as the growth of higher n modes ensue rapidly, leading to the thermal quench (TQ). The role of the 1/1 internal kink mode is discussed. An I p spike at the TQ is obtained in the simulations but with a smaller amplitude than in the experiment. Possible reasons are discussed.

PACS numbers: 52.25.Xz; 52.30.Cv; 52.25.Fi.A possible mechanism of Edge Localized Modes (ELMs) mitigation by Resonant Magnetic Perturbations (RMPs) is proposed based on the results of non-linear resistive MHD modelling using the JOREK code, Realistic JET-like plasma parameters and RMP spectrum of JET error-field correction coils (EFCC) with main toroidal number n=2 were used in the simulations. Without RMPs, a large ELM relaxation is obtained mainly due to the most unstable medium-n ballooning mode. The externally imposed RMP drives non-linearly the modes coupled to n=2 RMP which produce small multi-mode relaxations, mitigated ELMs. The modes driven by RMPs exhibit a tearing-like structure and produce additional islands. Mitigated ELMs deposit energy into the divertor mainly in the structures ("footprints") created by n=2 RMPs, however, slightly modulated by other nonlinearly driven even harmonics. The divertor power flux during ELMy phase mitigated by RMPs is reduced almost by a factor of ten. The mechanism of ELM mitigation by RMPs proposed here reproduces generic features of high collisionality RMP experiments, where large ELMs are replaced by small much more frequent ELMs or magnetic turbulence. Total ELMs suppression was also demonstrated in modelling at higher RMP amplitude.1.Introduction. The aim of the ITER project is the demonstration of the scientific feasibility of nuclear fusion reactor based on a magnetic confinement concept as a future source of energy [1]. Plasma edge magneto-hydro-dynamic (MHD) instabilities, such as ELMs driven by the pressure gradient and the plasma current produce quasi-periodic relaxations of the edge density and temperature profiles on few hundred microseconds time scale. ELMs in ITER are predicted to lead to the transient heat fluxes reaching tens of GWm -2 which would cause strong erosion of the PFC materials [1-2], hence ELMs control is mandatory in ITER. Recently the application of Resonant Magnetic Perturbations (RMPs) demonstrated the possibility of total ELMs suppression or strong mitigation of their size [3][4][5][6][7][8][9], motivating the use of this method in ITER [1]. In the last decade, the non-linear MHD theory and modeling have made a significant progress to refine the understanding of ELM [10][11][12][13][14] and RMP [15][16][17][18][19][20] physics. However the understanding of RMP interaction with ELMs is still missing and was not modeled so far, motivating work we are presenting here. One can clearly distinguish two groups of RMP experiments. At high collisionality the application of RMPs usually leads to the replacement of large ELMs by small frequent ELMs or MHD turbulence, the divertor power loads are reduced by RMPs. Small changes in edge pressure gradient and MHD stability are reported [3][4][5][6][7][8]. On the other hand, at low collisionality resulting from strong density pump-out due to RMPs, ELMs have been totally suppressed in DIII-D and the plasma edge appears to be stable to peeling/ballooning modes [9]. In the present Letter we report on the...

The radiation response and the MHD destabilization during the thermal quench after a mixed species shattered pellet injection with impurity species neon and argon are investigated via 3D non-linear MHD simulation using the JOREK code. Both the n = 0 global current profile contraction and the local helical cooling at each rational surface caused by the pellet fragments are found to be responsible for MHD destabilization after the injection. Significant current driven mode growth is observed as the fragments cross low order rational surfaces, resulting in rapidly inward propagating stochastic magnetic field, ultimately causing the core temperature collapse. The thermal quench (TQ) is triggered as the fragments arrive on the q = 1 or q = 2 surface depending on the exact q profile and thus mode structure. When injecting from a single toroidal location, strong radiation asymmetry is found before and during the TQ as a result of the unrelaxed impurity density profile along the field line and asymmetric outward heat flux. Such asymmetry gradually relaxes over the course of the TQ, and is entirely eliminated by the end of it. Simulation results indicate that the aforementioned asymmetric radiation behavior could be significantly mitigated by injection from toroidally opposite locations, provided that the time delay between the two injectors is shorter than 1 ms. It is also found that the MHD response are sensitive to the relative timing and injection configuration in these multiple injection cases.