Axisymmetric simulations of vertical displacement events in tokamaks: A benchmark of M3D-C1, NIMROD, and JOREK

Krebs, I.; Artola, F. J.; Sovinec, C. R.; Jardin, S.C.; Bunkers, K. J.; Hoelzl, M.; Ferraro, N.M.

doi:10.1063/1.5127664

Cited by 31 publications

(40 citation statements)

References 20 publications

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“…The obtained δI p /I p0 and ind in the simulations are shown together with the analytical prediction given by equations (13) and (14) in figure 4. The change of safety factor is shown in figure 5 where the analytical prediction is given by equation (15). The results show an excellent agreement between theory and simulations which validates the analytical model.…”

Section: Limit For a Circular Plasma With Large Aspect Ratiosupporting

confidence: 65%

“…The results show an excellent agreement between theory and simulations which validates the analytical model. More complex JOREK simulations also show this behaviour as it can be observed in the following VDE simulation where a hot NSTX plasma enters in contact with a highly resistive wall (see figure 6), which has also been used in benchmarks with other non-linear MHD codes recently in [15]. During the simulation, a Spitzer-like resistivity profile η = η 0 (T e0 )(T e0 /T e ) 3/2 is chosen where the core electron temperature is T e0 = 1 keV.…”

Section: Limit For a Circular Plasma With Large Aspect Ratiomentioning

confidence: 58%

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Understanding the reduction of the edge safety factor during hot VDEs and fast edge cooling events

et al. 2020

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In the present work a simple analytical approach is presented in order to clarify the physics behind the edge current density behaviour of a hot plasma entering in contact with a resistive conductor. As it has been observed in recent simulations [1], when a plasma enters in contact with a highly resistive wall, large current densities appear at the edge of the plasma. The model shows that this edge current originates from the plasma response, which attempts to conserve the poloidal magnetic flux (Ψ) when the outer current is being lost. The loss of outer current is caused by the high resistance of the outer current path compared to the plasma core resistance. The resistance of the outer path may be given by plasma contact with a very resistive structure or by a sudden decrease of the outer plasma temperature (e.g. due to a partial thermal quench or due to a cold front penetration caused by massive gas injection). For general plasma geometries and current density profiles the model shows that given a small change of minor radius (δa) the plasma current is conserved to first order (δI p = 0 + O(δa 2 )). This conservation comes from the fact that total inductance remains constant (δL = 0) due to an exact compensation of the change of external inductance with the change of internal inductance (δL ext + δL int = 0). As the total current is conserved and the plasma volume is reduced, the edge safety factor drops according to q a ∝ a 2 /I p . Finally the consistency of the resulting analytical predictions is checked with the help of free-boundary MHD simulations.

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Section: Limit For a Circular Plasma With Large Aspect Ratiosupporting

confidence: 65%

Section: Limit For a Circular Plasma With Large Aspect Ratiomentioning

confidence: 58%

Understanding the reduction of the edge safety factor during hot VDEs and fast edge cooling events

et al. 2020

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“…An international benchmark [96,170] between the JOREK, M3D-C 1 and NIMROD codes for an axisymmetric VDE in an NSTX-like plasma has shown excellent agreement not only on the growth rate of the instability, the evolution of the radial and vertical position of the magnetic axis as well as of the toroidal plasma and wall currents, but also on the spatial structure of the halo currents flowing into the wall (see figure 26(b)). The agreement is remarkable in particular, since the models implemented in the codes differ significantly (e.g., full MHD versus reduced MHD; Greens functions approach versus a direct discretization of the vacuum region with conductors in the computational domain).…”

Section: Free Boundary Simulationsmentioning

confidence: 99%

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

et al. 2021

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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.

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“…Previous studies for massive gas and shattered pellet injection [7][8][9][10][11][12] demonstrate some of the capabilities. The code allows also to study the dynamics of runaway electrons [13,14] and vertical displacement events [15,16] which are closely related to (mitigated) disruptions. In the present article, only a small subset of the code features is invoked to perform first predictive simulations for deuterium SPI into an ASDEX Upgrade H-mode plasma.…”

Section: Introductionmentioning

confidence: 99%

First predictive simulations for deuterium shattered pellet injection in ASDEX Upgrade

Hoelzl

Nardon

et al. 2020

Physics of Plasmas

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First simulations of deuterium shattered pellet injection (SPI) into an ASDEX Upgrade H-Mode plasma with the JOREK MHD code are presented. Resistivity is increased by one order of magnitude in most simulations to reduce computational costs and allow for extensive parameter scans. The effect of various physical parameters onto MHD activity and thermal quench (TQ) dynamics is studied and the influence of MHD onto ablation is shown. TQs are obtained quickly after injection in most simulations with a typical duration of 100 microseconds, which slows down at lower resistivity. Although the n=1 magnetic perturbation dominates in the simulations, toroidal harmonics up to n=10 contribute to stochastization and stochastic transport in the plasma core. The post-TQ density profile remains hollow for a few hundred microseconds. However, when flux surfaces re-form around the magnetic axis, the density has become monotonic again suggesting a beneficial behaviour for runaway electron avoidance/mitigation. With 10 21 atoms injected, the TQ is typically incomplete and triggered when the shards reach the q=2 rational surface. At a larger number of injected atoms, the TQ can set in even before the shards reach this surface. For low field side injection considered here, repeated formation of outward convection cells is observed in the ablation region reducing material assimilation. Responsible is a sudden rise of pressure in the high density cloud when the stochastic region expands further releasing heat from the hot core. After the TQ, strong sheared poloidal rotation is created by Maxwell stress, which contributes to re-formation of flux surfaces.

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Axisymmetric simulations of vertical displacement events in tokamaks: A benchmark of M3D-C1, NIMROD, and JOREK

Cited by 31 publications

References 20 publications

Understanding the reduction of the edge safety factor during hot VDEs and fast edge cooling events

Understanding the reduction of the edge safety factor during hot VDEs and fast edge cooling events

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

First predictive simulations for deuterium shattered pellet injection in ASDEX Upgrade

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