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

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.Peer ReviewedPostprint (published version

Non regression testing for the JOREK code

Non Regression Testing (NRT) aims to check if software modifications result in undesired behaviour. Suppose the behaviour of the application previously known, this kind of test makes it possible to identify an eventual regression, a bug. Improving and tuning a parallel code can be a time-consuming and difficult task, especially whenever people from different scientific fields interact closely. The JOREK code aims at investing Magnetohydrodynamic (MHD) instabilities in a Tokamak plasma. This paper describes the NRT procedure that has been tuned for this simulation code. Automation of the NRT is one keypoint to keeping the code healthy in a source code repository.Comment: No. RR-8134 (2012

First principles modelling of the edge and diveror physics of Edge Localized Modes (ELMs) suppression by Resonant Magnetic Perturbations (RMPs) in ITER

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MS45: "Numerical methods and HPC challenges in Magneto Hydro Dynamics (MHD) modelling in plasma physics"

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Non-linear MHD Simulations of ELMs in a High Recycling Divertor

International audienceITER plasmas will be characterized by a high density plasma (i.e. Greenwald fraction) at low collisionality inside the separatrix, a high density in the scrape-off layer combined with a high recycling detached divertor. ELMs in ITER are expected to be tolerable at low plasma current but need to be controlled at the full 15MA current. Whether ELMs are tolerable depends in part on the interaction of the ELM energy and density losses with the detached divertor, i.e. do (very) small ELMs burn through the detached divertor plasma. Since the ITER regime cannot be obtained in current experiments, numerical simulations of ELMs are required for the extrapolation to ITER. Presently in the nonlinear MHD code JOREK, a fluid model is used to describe the main plasma and the neutrals. The time evolution of the neutrals is described by a diffusion model combined with a boundary condition which reflects outgoing ions as incoming neutrals. This fluid model has been successfully used to simulate ELMs in the super-X divertor of MAST-U [1] and is applied below to ITER

Non-linear modeling of the threshold between ELM mitigation and ELM suppression by resonant magnetic perturbations in ASDEX upgrade ASDEX Upgrade

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Non-linear MHD simulations of QH-mode DIII-D plasmas and implications for ITER high Q scenarios

International audienceIn nonlinear MHD simulations of DIII-D QH-mode plasmas it has been found that low n kink/peeling modes (KPMs) are unstable and grow to a saturated external kink mode. The features of the dominant saturated KPMs, which are localized toroidally by non-linear coupling of harmonics, such as mode frequencies, density fluctuations and their effect on pedestal particle and energy transport, are in good agreement with the observations of the Edge Harmonic Oscillation (EHO) typically present in DIII-D QH-mode experiments. The non-linear evolution of MHD modes with toroidal mode numbers n from 0 to 10, including both kink-peeling modes and ballooning modes, is investigated through MHD simulations by varying the pedestal current and pressure relative to the initial conditions of DIII-D QH-mode plasma. The edge current and pressure at the pedestal are key parameters for the plasma either saturating to a QH-mode regime or a ballooning mode dominant regime. The influence of E×B flow and its shears on QH-mode plasma has been investigated. The behavior of QH-mode with different flow shear shows E×B rotation has strong stabilization effects on the medium to high-n modes but destabilizing for n=2. The QH-mode extrapolation results of an ITER Q=10 plasma show that the pedestal currents are large enough to destabilize an n=1-5 kink/peeling mode, leading to a saturated kink-peeling mode

Non-linear MHD modeling of edge localized mode cycles and mitigation by resonant magnetic perturbations

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Non-linear MHD modelling of Edge Localized Modes suppression by Resonant Magnetic Perturbations in ITER

International audienceEdge Localized Modes (ELMs) suppression by Resonant Magnetic Perturbations (RMPs) was studied with non-linear resistive MHD code JOREK for ITER H-mode scenarios 15MA,12.5MA,10MA/5.3T, obtained by the ASTRA code. • RMP spectra, optimized by the linear MHD MARS-F code, with main toroidal harmonics N=2, N=3, N=4 used as boundary conditions of the computational domain of JOREK including realistic RMP coils, plasma, divertor and wall geometry. The model includes all relevant plasma flows: toroidal rotation, two fluid diamagnetic effects and neoclassical poloidal friction. • The threshold for ELM suppression was found at a maximum RMP coils current of 45kAt-60kAt compared to the coils maximum capability of 90kAt. With RMPs, the main harmonic and the non-linearly coupled harmonics remain dominant at the plasma edge, producing continuous MHD turbulent transport and suppressing ELMs in all scenarios. • In the high beta poloidal steady-state 10MA/5.3T scenario a rotating QH-mode without ELMs was observed even without RMPs. N=3 RMPs induced a static QH-like mode, locked to the RMP fields in this scenario. • The 3D divertor heat and particle fluxes in the stationary RMP phase show the characteristic splitting with the main RMP toroidal symmetry. The radial extension of the footprints typically was ~20 cm in inner divertor and ~40 cm in outer divertor with heat fluxes decreasing further out from the initial strike point from ~6-5MW/m 2 to ~1MW/m 2 in the stationary regime with RMPs and total power in the divertor ~50MW. The footprints remain within the divertor target and baffle areas. However in transient regimes when RMPs are switched on, part of plasma thermal energy is lost and these heat fluxes can be much larger; optimization of RMP switch-on needs to be studied further with respect to the ensuing power fluxes and L-H access