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JOREK is a massively parallel fully implicit non-linear extended MHD code forrealistic tokamak X-point plasmas. It has become a widely used versatile codefor studying large-scale plasma instabilities and their control developed in aninternational community. This article gives a comprehensive overview of thephysics models implemented, numerical methods applied for solving the equationsand physics studies performed with the code. A dedicated section highlightssome of the verification work done for the code. A hierarchy of differentphysics models is available including a free boundary and resistive wallextension and hybrid kinetic-fluid models. The code allows for flux-surfacealigned iso-parametric finite element grids in single and double X-pointplasmas which can be extended to the true physical walls and uses a robustfully implicit time stepping. Particular focus is laid on plasma edge andscrape-off layer (SOL) physics as well as disruption related phenomena. Amongthe key results obtained with JOREK regarding plasma edge and SOL, are deepinsights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELMcontrol by resonant magnetic perturbations, pellet injection, as well as byvertical magnetic kicks. Also ELM free regimes, detachment physics, thegeneration and transport of impurities during an ELM, and electrostaticturbulence in the pedestal region are investigated. Regarding disruptions, thefocus is on the dynamics of the thermal quench and current quench triggered bymassive gas injection (MGI) and shattered pellet injection (SPI), runawayelectron (RE) dynamics as well as the RE interaction with MHD modes, andvertical displacement events (VDEs). Also the seeding and suppression oftearing modes (TMs), the dynamics of naturally occurring thermal quenchestriggered by locked modes, and radiative collapses are being studied.

The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas