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

Abstract

JOREK is a massively parallel fully implicit non-linear extended MHD code for realistic tokamak X-point plasmas. It has become a widely used versatile code for studying large-scale plasma instabilities and their control developed in an international community. 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 and current quench triggered by massive gas injection (MGI) and shattered pellet injection (SPI), runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events (VDEs). Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring thermal quenches triggered by locked modes, and radiative collapses are being studied.

Comprehensive review published as special topic article in Nuclear Fusion

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Cited by in corpus (45)

• A quasi-continuous exhaust scenario for a fusion reactor: the renaissance of small edge localized modes
• Plasma Surrogate Modelling using Fourier Neural Operators
• Complete 3D MHD simulations of the current quench phase of ITER mitigated disruptions
• 3D simulations of vertical displacement events in tokamaks: A benchmark of M3D-C${}^1$, NIMROD and JOREK
• First predictive simulations for deuterium shattered pellet injection in ASDEX Upgrade
• MHD simulations of small ELMs at low triangularity in ASDEX Upgrade
• Fast Dynamic 1D Simulation of Divertor Plasmas with Neural PDE Surrogates
• JOREK3D: An extension of the JOREK nonlinear MHD code to stellarators
• FLARE: field line analysis and reconstruction for 3D plasma boundary modeling
• Comparing spontaneous and pellet-triggered ELMs via non-linear extended MHD simulations
• MHD simulations of formation, sustainment and loss of Quiescent H-mode in the all-tungsten ASDEX Upgrade
• Probing non-linear MHD stability of the EDA H-mode in ASDEX Upgrade
• Plasmoid drift and first wall heat deposition during ITER H-mode dual-SPIs in JOREK simulations
• A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume/finite element scheme for the incompressible MHD equations
• Runaway dynamics in disruptions with current relaxation
• Development and application of a hybrid MHD-kinetic model in JOREK
• Axisymmetric predictions for mitigated and vertically unstable disruptions in ITER with runaway electrons
• Radiated energy fraction of SPI-induced disruptions at ASDEX Upgrade
• Accelerating the convergence of Newton's method for nonlinear elliptic PDEs using Fourier neural operators
• Efficient kinetic Lattice Boltzmann simulation of three-dimensional Hall-MHD Turbulence
• Testing of the new JOREK stellarator-capable model in the tokamak limit
• Enhanced Preconditioner for JOREK MHD Solver
• The rapid destruction of toroidal magnetic surfaces
• Plasmoid-mediated reconnection during nonlinear peeling-ballooning edge-localized modes
• 3D MHD modelling of plasmoid drift following massive material injection in a tokamak
• Neural-Parareal: Dynamically Training Neural Operators as Coarse Solvers for Time-Parallelisation of Fusion MHD Simulations
• Mesh Refinement for Anisotropic Diffusion in Magnetized Plasmas
• Uncertainty Quantification of Surrogate Models using Conformal Prediction
• An E & B Gyrokinetic Simulation Model for Kinetic Alfvén Waves inTokamak Plasmas
• Reduced kinetic modelling of shattered pellet injection in ASDEX Upgrade
• Going Beyond the MHD Approximation: Physics-Based Numerical Solution of the CGL Equations
• Nonlinear MHD simulations of external kinks in quasi-axisymmetric stellarators using an axisymmetric external rotational transform approximation
• Hot-tail electrons' impact on assimilation and injection penetration of D2 Shattered Pellet Injections
• Direct prediction of saturated neoclassical tearing modes in slab using an equilibrium approach
• Filamentary plasma eruptions and the heating and acceleration of electrons
• The impact of fusion-born alpha particles on runaway electron dynamics in ITER disruptions
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• How well can VMEC predict the initial saturation of external kink modes in near circular tokamaks and $l=2$ stellarators?
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• Collisional-radiative non-equilibrium impurity treatment for JOREK simulations
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