•Novel FEM method: G-continuous Bezier elements.•Non-linear MHD simulations of fusion plasmas in realistic geometry.•Numerical methods for non-linear simulations.
The international tokamak ITER is ...progressing towards assembly completion and first-plasma operation, which will be a physics and engineering challenge for the fusion community. In the preparation for ITER experimental scenarios, non-linear MHD simulations are playing an essential role to actively understand and predict the behaviour and stability of tokamak plasmas in future fusion power plant. The development of MHD codes like JOREK is a key aspect of this research effort, and provides invaluable insight into the plasma stability and the control of global and localised plasma events, like Edge-Localised-Mode and disruptions. In this paper, we present an operational implementation of a new, generalised formulation of Bezier finite-elements applied to the JOREK code, a significant advancement from the previously G1-continuous bi-cubic Bezier elements. This new mathematical method enables any polynomial order of Bezier elements, with a guarantee of G-continuity at the level of (n−1)/2, for any odd n, where n is the order of the Bezier polynomials. The generalised method is defined, and a rigorous mathematical proof is provided for the G-continuity requirement. Key details on the code implementation are mentioned, together with a suite of tests to demonstrate the mathematical reliability of the finite-element method, as well as the practical usability for typical non-linear tokamak MHD simulations. A demonstration for a state-of-the-art simulation of an Edge-Localised-Mode instability in the future ITER tokamak, with realistic grid geometry, finalises the study.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPUK, ZAGLJ, ZRSKP
A possible mechanism of edge localized modes (ELMs) mitigation by resonant magnetic perturbations (RMPs) is proposed based on the results of nonlinear resistive magnetohydrodynamic modeling using the ...jorek code, realistic JET-like plasma parameters and an RMP spectrum of JET error-field correction coils (EFCC) with a main toroidal number n=2 were used in the simulations. Without RMPs, a large ELM relaxation is obtained mainly due to the most unstable medium-n ballooning mode. The externally imposed RMP drives nonlinearly the modes coupled to n=2 RMP which produce small multimode relaxations, mitigated ELMs. The modes driven by RMPs exhibit a tearinglike structure and produce additional islands. Mitigated ELMs deposit energy into the divertor mainly in the structures ("footprints") created by n=2 RMPs, however, slightly modulated by other nonlinearly driven even harmonics. The divertor power flux during a ELM phase mitigated by RMPs is reduced almost by a factor of 10. The mechanism of ELM mitigation by RMPs proposed here reproduces generic features of high collisionality RMP experiments, where large ELMs are replaced by small, much more frequent ELMs or magnetic turbulence. Total ELM suppression was also demonstrated in modeling at higher RMP amplitude.
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CMK, CTK, FMFMET, IJS, NUK, PNG, UM
Progress in the definition of the requirements for edge localized mode (ELM) control and the application of ELM control methods both for high fusion performance DT operation and non-active ...low-current operation in ITER is described. Evaluation of the power fluxes for low plasma current H-modes in ITER shows that uncontrolled ELMs will not lead to damage to the tungsten (W) divertor target, unlike for high-current H-modes in which divertor damage by uncontrolled ELMs is expected. Despite the lack of divertor damage at lower currents, ELM control is found to be required in ITER under these conditions to prevent an excessive contamination of the plasma by W, which could eventually lead to an increased disruptivity. Modelling with the non-linear MHD code JOREK of the physics processes determining the flow of energy from the confined plasma onto the plasma-facing components during ELMs at the ITER scale shows that the relative contribution of conductive and convective losses is intrinsically linked to the magnitude of the ELM energy loss. Modelling of the triggering of ELMs by pellet injection for DIII-D and ITER has identified the minimum pellet size required to trigger ELMs and, from this, the required fuel throughput for the application of this technique to ITER is evaluated and shown to be compatible with the installed fuelling and tritium re-processing capabilities in ITER. The evaluation of the capabilities of the ELM control coil system in ITER for ELM suppression is carried out (in the vacuum approximation) and found to have a factor of ∼2 margin in terms of coil current to achieve its design criterion, although such a margin could be substantially reduced when plasma shielding effects are taken into account. The consequences for the spatial distribution of the power fluxes at the divertor of ELM control by three-dimensional (3D) fields are evaluated and found to lead to substantial toroidal asymmetries in zones of the divertor target away from the separatrix. Therefore, specifications for the rotation of the 3D perturbation applied for ELM control in order to avoid excessive localized erosion of the ITER divertor target are derived. It is shown that a rotation frequency in excess of 1 Hz for the whole toroidally asymmetric divertor power flux pattern is required (corresponding to n Hz frequency in the variation of currents in the coils, where n is the toroidal symmetry of the perturbation applied) in order to avoid unacceptable thermal cycling of the divertor target for the highest power fluxes and worst toroidal power flux asymmetries expected. The possible use of the in-vessel vertical stability coils for ELM control as a back-up to the main ELM control systems in ITER is described and the feasibility of its application to control ELMs in low plasma current H-modes, foreseen for initial ITER operation, is evaluated and found to be viable for plasma currents up to 5-10 MA depending on modelling assumptions.
A triggering mechanism responsible for the explosive onset of edge localised modes (ELMs) in fusion plasmas is identified by performing, for the first time, non-linear magnetohydrodynamic simulations ...of repetitive type-I ELMs. Briefly prior to the ELM crash, destabilising and stabilising terms are affected at different timescales by an increasingly ergodic magnetic field caused by non-linear interactions between the axisymmetric background plasma and growing non-axisymmetric perturbations. The separation of timescales prompts the explosive, i.e. faster than exponential, growth of an ELM crash which lasts ∼500 μs. The duration and size of the simulated ELM crashes compare qualitatively well with type-I ELMs in ASDEX Upgrade. As expected for type-I ELMs, a direct proportionality between the heating power in the simulations and the ELM repetition frequency is obtained. The simulations presented here are a major step forward towards predictive modelling of ELMs and of the assessment of mitigation techniques in ITER and other future tokamaks.
The radiation response and the MHD destabilization during the thermal quench after a mixed species shattered pellet injection with impurity species neon and argon are investigated via 3D non-linear ...MHD simulation using the JOREK code. Both the n = 0 global current profile contraction and the local helical cooling at each rational surface caused by the pellet fragments are found to be responsible for MHD destabilization after the injection. Significant current driven mode growth is observed as the fragments cross low order rational surfaces, resulting in rapidly inward propagating stochastic magnetic field, ultimately causing the core temperature collapse. The thermal quench (TQ) is triggered as the fragments arrive on the q = 1 or q = 2 surface depending on the exact q profile and thus mode structure. When injecting from a single toroidal location, strong radiation asymmetry is found before and during the TQ as a result of the unrelaxed impurity density profile along the field line and asymmetric outward heat flux. Such asymmetry gradually relaxes over the course of the TQ, and is entirely eliminated by the end of it. Simulation results indicate that the aforementioned asymmetric radiation behavior could be significantly mitigated by injection from toroidally opposite locations, provided that the time delay between the two injectors is shorter than 1 ms. It is also found that the MHD response are sensitive to the relative timing and injection configuration in these multiple injection cases.
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.
The mechanisms of edge-localized mode (ELM) energy deposition are studied by means of non-linear magnetohydrodynamic (MHD) simulation of ELMs. The footprint of the ELM heat flux at the divertor is ...found to increase approximately linearly with the total ELM energy loss for JET-scale plasmas, which is similar to the experimentally observed broadening of the ELM energy deposition with ELM energy loss. For these relatively large ELMs, in which conductive losses dominate, the divertor footprint broadening is due to an increase in the magnetic perturbation of the ballooning mode with increasing ELM energy loss, which results in a widening of the homoclinic tangles intersecting the target. The first results from ELM simulations in the ITER Q = 10 scenario indicate that on the ITER scale the broadening is similar for conductive and convective ELMs at least up to an ELM energy loss of 4 MJ. For the larger conductive-type ELMs the magnetic perturbation and its homoclinic tangles determine the pattern of the ELM heat flux at the divertor target similar to the JET-scale results. For the smaller convective ELMs, the ELM footprint is determined by the radial distance travelled by plasma filaments expelled by the ELM and the loss of the plasma energy in the filaments along the magnetic field lines.