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 magnetohydrodynamic simulations of a disruption triggered by a massive injection of argon gas in JET are performed with the JOREK code. The key role of the thermal drive of the m = 2, n = 1 tearing mode (i.e. the drive from helical cooling inside the island) in the disruption process is highlighted by varying the amplitude and position of the argon source across simulations, and also during a simulation. In cases where this drive persists in spite of the development of magnetic stochasticity, which is favoured by moving the argon source in an ad hoc way from the plasma edge into the 2/1 island at some point in the simulation, a relaxation in the region q ⩽ 2 (roughly) takes place. This relaxation generates a plasma current spike comparable to the experimental one. Simulations are compared in detail to measurements via synthetic diagnostics, validating the model to some degree.

Non-axisymmetric simulations of the current quench phase of ITER disruptions are key to predict asymmetric forces acting into the ITER wall. We present for the first time such simulations for ITER mitigated disruptions at realistic Lundquist numbers. For these strongly mitigated disruptions, we find that the edge safety factor remains above 2 and the maximal integral horizontal forces remain below 1 MN. The maximal integral vertical force is found to be 13 MN and arises in a time scale given by the resistive wall time as expected from theoretical considerations. In this respect, the vertical force arises after the plasma current has completely decayed, showing the importance of continuing the simulations also in the absence of plasma current. We conclude that the horizontal wall force rotation is not a concern for these strongly mitigated disruptions in ITER, since when the wall forces form, there are no remaining sources of rotation.

Hot Vertical Displacement Events (VDEs) are one of the worst case scenarios for high current tokamaks as they are associated with large heat loads and electro-magnetic forces. 
Non-linear magneto-hydrodynamic (MHD) simulations of the thermal and current quench can help to understand their dynamics and consequences. 
In order to make predictions for future devices, the validation of codes against present machines is crucial.
Dedicated experiments were performed in ASDEX Upgrade to provide a basis for simulations with the non-linear extended MHD code JOREK. 
2D as well as non-axisymmetric simulations at realistic parameters can reproduce quantities like the edge safety factor $q_{95}$ at the thermal quench (TQ) onset, the halo current magnitude and the level of vertical forces, while the exact width of the halo current area requires more sophisticated boundary conditions and is left for future work. Small horizontal forces are observed during the hot VDEs in the experiment as well as in the simulations.