Abstract
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.
Highlights
The present article provides a comprehensive overview of the non-linear extended magneto-hydrodynamic (MHD) code JOREK, which is among the leading simulation codes worldwide for studying large scale plasma instabilities and their control in realistic divertor tokamaks
Reference [3] contains an overview of modelling activities worldwide regarding edge localized modes (ELMs) and ELM control based on many different simulation codes, and references [4,5,6] provide a partial overview of JOREK activities regarding plasma edge and scrape off layer
In spite of some differences, the benchmark demonstrates that the very different numerical descriptions of the resistive wall structures used in the codes lead to comparable results for such a violent 3D vertical displacement event (VDE) case and that the ansatz based reduced MHD model used here for the JOREK simulation is capturing the 3D dynamics of the wall currents, even for the large β spherical plasma considered here
Summary
The present article provides a comprehensive overview of the non-linear extended magneto-hydrodynamic (MHD) code JOREK, which is among the leading simulation codes worldwide for studying large scale plasma instabilities and their control in realistic divertor tokamaks. The article provides a detailed description of the physics models, numerical methods, and physics applications of the code. Localized modes (ELMs) and ELM control based on many different simulation codes, and references [4,5,6] provide a partial overview of JOREK activities regarding plasma edge and scrape off layer. The rest of the article is organized as follows: section 2 provides a detailed overview of the physics models available in JOREK and section 3 describes the numerical methods employed for solving the equations. After this ‘technical’ part, a detailed picture is drawn of the physics studies and validation activities performed in particular in the fields of plasma edge and scrape off layer physics (section 5) as well as disruption physics (section 6). Additional details on the coordinate systems, finite element basis, normalization of quantities, and time stepping scheme are provided in appendices A–C
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