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.

The MHD response and the penetration of a deuterium shattered pellet into a JET plasma is investigated via the non-linear reduced MHD code JOREK with the neutral gas shielding (NGS) ablation model. The dominant MHD destabilizing mechanism by the injection is identified as the local helical cooling at each rational surface, as opposed to the global current profile contraction. Thus the injected fragments destabilize each rational surface as they pass through them. The injection penetration is found to be much better compared to MGI, with the convective transport caused by core MHD instabilities (e.g. 1/1 kink) contributing significantly to the core penetration. Moreover, the injection with realistic JET SPI system configurations is simulated in order to provide some insights into future operations, and the impact on the total assimilation and penetration depth of varying injection parameters such as the injection velocity or fineness of shattering is assessed. Further, the effect of changing the target equilibrium temperature or q profile on the assimilation and penetration is also investigated. Such analysis will form the basis of further investigation into a desirable configuration for the future SPI system in ITER.

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.

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Impurity accumulation in the core plasma leads to fuel dilution and higher radiative losses that can lead to loss of the H-mode, to thermal collapse of the plasma, and eventually even to a disruption in tokamaks. In present experiments, it has been shown that Edge Localized Modes (ELMs) at sufficiently high frequency are required to prevent W accumulation in the core, by expelling impurities from the edge plasma region, thus preventing their penetration into the plasma core. We present a full-orbit particle extension of the MHD code JOREK suitable for simulating impurity transport during ELMs. This model has been applied to the simulation of an ELM crash in ASDEX Upgrade, where we have quantified the displacement of W particles across flux surfaces. The transport mechanism is shown to be the particle E × B-drifts due to the electric field created by the MHD instability underlying the ELM. In- and outward transport is observed as a series of interchange motions, leading to a superdiffusive behavior. This causes not only the particles near the plasma pedestal to move outwards but also the particles outside of the pedestal to move inwards. This has important consequences for operation with W in ITER, where it is expected to be screened in the pedestal, and ELMs are shown here to increase the core W density. A comparison with existing diffusive modeling is made, showing a qualitative agreement and the limitations of this simplified modeling approach.