Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK code

Franck, Emmanuel; Hölzl, M.; Lessig, A.; Sonnendrücker, Éric

doi:10.1051/m2an/2015014

Cited by 26 publications

(52 citation statements)

References 24 publications

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“…Results presented in this paper are based on a reduced MHD physics model, including neo‐classical and diamagnetic effects, which fulfils the energy conservation properties . Full MHD equations are available and presently being extended by two‐fluid effects, sheath boundary conditions, and stabilization methods.…”

Section: The Jorek Codementioning

confidence: 99%

Insights into type‐I edge localized modes and edge localized mode control from JOREK non‐linear magneto‐hydrodynamic simulations

Hoelzl

Huijsmans

Orain

et al. 2018

Contributions to Plasma Physics

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Edge localized modes (ELMs) are repetitive instabilities driven by the large pressure gradients and current densities in the edge of H‐mode plasmas. Type‐I ELMs lead to a fast collapse of the H‐mode pedestal within several hundred microseconds to a few milliseconds. Localized transient heat fluxes to divertor targets are expected to exceed tolerable limits for ITER, requiring advanced insights into ELM physics and applicable mitigation methods. This paper describes how non‐linear magneto‐hydrodynamic (MHD) simulations can contribute to this effort. The JOREK code is introduced, which allows the study of large‐scale plasma instabilities in tokamak X‐point plasmas covering the main plasma, the scrape‐off layer, and the divertor region with its finite element grid. We review key physics relevant for type‐I ELMs and show to what extent JOREK simulations agree with experiments and help reveal the underlying mechanisms. Simulations and experimental findings are compared in many respects for type‐I ELMs in ASDEX Upgrade. The role of plasma flows and non‐linear mode coupling for the spatial and temporal structure of ELMs is emphasized, and the loss mechanisms are discussed. An overview of recent ELM‐related research using JOREK is given, including ELM crashes, ELM‐free regimes, ELM pacing by pellets and magnetic kicks, and mitigation or suppression by resonant magnetic perturbation coils (RMPs). Simulations of ELMs and ELM control methods agree in many respects with experimental observations from various tokamak experiments. On this basis, predictive simulations become more and more feasible. A brief outlook is given, showing the main priorities for further research in the field of ELM physics and further developments necessary.

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Section: The Jorek Codementioning

confidence: 99%

Insights into type‐I edge localized modes and edge localized mode control from JOREK non‐linear magneto‐hydrodynamic simulations

Hoelzl

Huijsmans

Orain

et al. 2018

Contributions to Plasma Physics

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“…To separate the three MHD waves, Izzo et al 11 and Breslau et al 12 used a threeterm expansion of the velocity, with each wave contained in a specific term. We generalize their expression to the case of χ = F 0 φ while keeping the first two terms consistent with 1, 13 :…”

Section: Magnetic Field and Velocity Representationsmentioning

confidence: 99%

“…Izzo et al used a similar ansatz in their study 11 . Later papers also adopt an ansatz for the magnetic field that eliminates field compression 12,13 . The ansatz approach allows one to make less assumptions (although, as we will show, an assumption on the relative magnitude of the induced magnetic field still needs to be made to eliminate fast waves) and keep more physical effects, while generally resulting in more complicated equations than the ordering approach.…”

Section: Introductionmentioning

confidence: 99%

A three-dimensional reduced MHD model consistent with full MHD

et al. 2019

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Within the context of a viscoresistive magnetohydrodynamic (MHD) model with anisotropic heat transport and cross-field mass diffusion, we introduce novel three-term representations for the magnetic field (background vacuum field, field line bending and field compression) and velocity ( E × B flow, field-aligned flow and fluid compression), which are amenable to three-dimensional treatment. Once the representations are inserted into the MHD equations, appropriate projection operators are applied to Faradays law and the Navier-Stokes equation to obtain a system of scalar equations that is closed by the continuity and energy equations. If the background vacuum field is sufficiently strong and the β is low, MHD waves are approximately separated by the three terms in the velocity representation, with each term containing a specific wave. Thus, by setting the appropriate term to zero, we eliminate fast magnetosonic waves, obtaining a reduced MHD model. We also show that the other two velocity terms do not compress the magnetic field, which allows us to set the field compression term to zero within the same reduced model. Dropping also the field-aligned flow, a further simplified model is obtained, leading to a fully consistent hierarchy of reduced and full MHD models for 3D plasma configurations. Finally, we discuss the conservation properties and derive the conditions under which the reduction approximation is valid. We also show that by using an ordering approach, reduced MHD equations similar to what we got from the ansatz approach can be obtained by means of a physics-based asymptotic expansion.

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“…The toroidal magnetic field B / ¼ F 0 =R is held constant; when the toroidal magnetic field is large, the reduced MHD formalism is accurate. 31,32 The evolution equations 33 for the poloidal magnetic flux w, and the velocity v are…”

Section: B a Reduced Mhd Fluid Model In The Jorek Codementioning

confidence: 99%

“…21 In the toroidal direction, a spectral method is used. For further details of the numerical models in the current JOREK code, we refer to Franck et al, 32 H€ olzl et al…”

Section: B a Reduced Mhd Fluid Model In The Jorek Codementioning

confidence: 99%

Early evolution of electron cyclotron driven current during suppression of tearing modes in a circular tokamak

2016

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When electron cyclotron (EC) driven current is first applied to the inside of a magnetic island, the current spreads throughout the island and after a short period achieves a steady level. Using a two equation fluid model for the EC current that allows us to examine this early evolution in detail, we analyze high-resolution simulations of a 2/1 classical tearing mode in a low-beta large aspectratio circular tokamak. These simulations use a nonlinear 3D reduced-MHD fluid model and the JOREK code. During the initial period where the EC driven current grows and spreads throughout the magnetic island, it is not a function of the magnetic flux. However, once it has reached a steady-state, it should be a flux function. We demonstrate numerically that if sufficiently resolved toroidally, the steady-state EC driven current becomes approximately a flux function. We discuss the physics of this early period of EC evolution and its impact on the size of the magnetic island.

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Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK code

Cited by 26 publications

References 24 publications

Insights into type‐I edge localized modes and edge localized mode control from JOREK non‐linear magneto‐hydrodynamic simulations

Insights into type‐I edge localized modes and edge localized mode control from JOREK non‐linear magneto‐hydrodynamic simulations

A three-dimensional reduced MHD model consistent with full MHD

Early evolution of electron cyclotron driven current during suppression of tearing modes in a circular tokamak

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