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

Comparing spontaneous and pellet-triggered ELMs via non-linear extended MHD simulations

Injecting frozen deuterium pellets into an ELMy H-mode plasma is a well established scheme for triggering edge localized modes (ELMs) before they naturally occur. This paper presents non-linear simulations of spontaneous type-I ELMs and pellet-triggered ELMs in ASDEX Upgrade performed with the extended MHD code JOREK. A thorough comparison of the non-linear dynamics of these events is provided. In particular, pellet-triggered ELMs are simulated by injecting deuterium pellets into different time points during the pedestal build-up described in A Cathey et al (2020 Nuclear Fusion 60 124007). Realistic ExB and diamagnetic background plasma flows as well as the time dependent bootstrap current evolution are included during the build-up to accurately capture the balance between stabilising and destabilising terms for the edge instabilities. Dependencies on the pellet size and injection times are studied. The spatio-temporal structures of the modes and the resulting divertor heat fluxes are compared in detail between spontaneous and triggered ELMs. We observe that the premature excitation of ELMs by means of pellet injection is caused by a helical perturbation described by a toroidal mode number of n¿=¿1. In accordance with experimental observations, the pellet-triggered ELMs show reduced thermal energy losses and a narrower divertor wetted area with respect to spontaneous ELMs. The peak divertor energy fluence is seen to decrease when ELMs are triggered by pellets injected earlier during the pedestal build-up.Peer ReviewedPostprint (published version

Recent progress in the quantitative validation of JOREK simulations of ELMs in JET

Future devices like JT-60SA, ITER and DEMO require quantitative predictions of pedestal density and temperature levels, as well as inter-ELM and ELM divertor heat fluxes, in order to improve global confinement capabilities while preventing divertor erosion/melting in the planning of future experiments. Such predictions can be obtained from dedicated pedestal models like EPED, and from non-linear MHD codes like JOREK, for which systematic validation against current experiments is necessary. In this paper, we show progress in the quantitative validation of the JOREK code using JET simulations. Results analyse the impact of diamagnetic terms on the dynamics and size of the ELMs, and evidence is provided that the onset of type-I ELMs is not governed by linear MHD stability alone, but that a nonlinear threshold could be responsible for large MHD events at the plasma edge.Peer ReviewedPostprint (published version

Transition from no-ELM response to pellet ELM triggering during pedestal build-up - insights from extended MHD simulations

Pellet edge localized mode (ELM) triggering is a well-established scheme for decreasing the time between two successive ELM crashes below its natural value. Reliable ELM pacing has been demonstrated experimentally in several devices, increasing the ELM frequency considerably. However, it was also shown that the frequency cannot be increased arbitrarily due to a so-called lag-time. During this time, after a preceding natural or triggered ELM crash, neither a natural ELM crash occurs nor is it possible to trigger an ELM crash by pellet injection. For this article, pellet ELM triggering simulations are advanced beyond previous studies in two ways. Firstly, realistic E × B and diamagnetic background flows are included. And secondly, the pellet is injected at different stages of the pedestal build-up. This allows us to recover the lag time for the first time in simulations and investigate it in detail. A series of nonlinear extended MHD simulations is performed to investigate the plasma dynamics resulting from an injection at different time points during the pedestal build-up. The experimentally observed lag-time is qualitatively reproduced. In particular, a sharp transition is observed between the regime where no ELMs can be triggered and the regime where pellet injection causes an ELM crash. Via variations of pellet parameters and injection time, the two regimes are studied and compared in detail, revealing pronounced differences in the nonlinear dynamics. The toroidal mode spectrum is significantly broader when an ELM crash is triggered, enhancing the stochasticity and therefore also the losses of thermal energy along magnetic field lines. In the heat fluxes to the divertor targets, pronounced toroidal asymmetries are observed. In the case of high injection velocities leading to deep penetration, the excitation of core modes like the 2/1 neoclassical tearing mode is also observed.Peer ReviewedPostprint (published version

Experimental studies of plasma-antenna coupling with the JET Alfvén Eigenmode Active Diagnostic

This paper presents a dedicated study of plasma-antenna (PA) coupling with the Alfvén Eigenmode Active Diagnostic (AEAD) in JET. Stable AEs and their resonant frequencies f, damping rates γ < 0, and toroidal mode numbers n are measured for various PA separations and limiter versus X-point magnetic configurations. Two stable AEs are observed to be resonantly excited at distinct low and high frequencies in limiter plasmas. The values of f and n do not vary with PA separation. However, |γ| increases with PA separation for the low-f, but not high-f, mode, yet this may be due to slightly different edge conditions. The high-f AE is detected throughout the transition from limiter to X-point configuration, though its damping rate increases; the low-f mode, on the other hand, becomes unidentifiable. The linear resistive MHD code CASTOR is used to simulate the frequency scan of an AEAD-like external antenna. For the limiter pulses, the high-f mode is determined to be an n = 0 GAE, while the low-f mode is likely an n = 2 TAE. During the transition from limiter to X-point configuration, CASTOR indicates that n = 1 and 2 EAEs are excited in the edge gap. These results extend previous experimental studies in JET and Alcator C-Mod; validate the computational work performed by Dvornova et al 2020 Phys. Plasmas 27 012507; and provide guidance for the optimization of PA coupling in upcoming JET energetic particle experiments, for which the AEAD will aim to identify the contribution of alpha particles to AE drive during the DT campaign