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The JOREK Code

The non-linear extended MHD code JOREK resolves realistic toroidal X-point geometries with a C1 continuous flux-surface aligned grid including main plasma, scrape-off layer and divertor region. It is based on robust fully implicit numerics, and includes divertor boundary conditions, 3D resistive wall effects, two-fluid effects and neoclassical flows.

The well established physics and numerics community around JOREK has strong connections to the relevant experiments, the ITER Organization and the respective ITPA Topical Groups.

Key Physics Applications

MAST ELM Simulation
  • Edge Localized Modes (ELMs)
  • Pellet triggering of Edge Localized Modes
  • Error field penetration for resonant magnetic perturbations (RMPs)
  • Mitigation / suppression of ELMs via RMP fields
  • Massive gas injection triggered disruptions
  • Stabilization of Tearing Modes via ECCD
  • Vertical Displacement Events
  • Resistive Wall Modes
  • QH-Mode

Physics Models

  • Reduced and full MHD models
  • Two-fluid and neoclassical effects
  • Divertor model
  • Pellet ablation model
  • Neutrals model for Deuterium MGI — impurity MGI model under development
  • Resistive wall extension — inclusion of Halo currents under development
  • Electron Cyclotron Current Drive (ECCD) model
  • Particle in cell model under development

X-Point Grid

Numerics

  • Flux-aligned 2D Bezier finite elements — generalization under development
  • Toroidal Fourier expansion — generalization under development
  • Fully implicit time stepping
  • GMRES and Newton iterations
  • Physics based preconditioning — Jacobian free preconditioning under development
  • Taylor-Galerkin stabilization
  • MPI + OpenMP parallelization

Selected Publications

  • Huysmans GTA and Czarny O. MHD stability in X-point geometry: simulation of ELMs. Nucl. Fusion 47, 659 (2007)
  • Czarny O and Huysmans G. Bézier surfaces and finite elements for MHD simulations. J. Comput. Phys. 227, 7423 (2008)
  • Nardon E, Bécoulet M, Huysmans G and Czarny O. Magnetohydrodynamics modelling of H-mode plasma response to external resonant magnetic perturbations. Phys. Plasmas 14, 092501 (2007)
  • Huysmans GTA, Pamela S, van der Plas E, and Ramet P, Non-linear MHD simulations of edge localized modes (ELMs). Plasma Phys. Control. Fusion 51 124012 (2009)
  • Pamela S, Huysmans G, Benkadda S. Influence of poloidal equilibrium rotation in MHD simulations of edge-localized modes. Plasma Phys. Control. Fusion 52, 075006 (2010)
  • Pamela SJP, Huysmans GTA, Beurskens MNA, Devaux S, Eich T, Benakadda S, JET EFDA contributors Nonlinear MHD simulations of edge-localized-modes in JET. Plasma Phys. Control. Fusion 53, 054014 (2011)
  • Hoelzl M, Günter S, Wenninger RP, Mueller W-C, Huysmans GTA, Lackner K, Krebs I, ASDEX Upgrade Team. Reduced-MHD Simulations of Toroidally and Poloidally Localized ELMs. Phys. Plasmas, 19, 082505 (2012)
  • Hoelzl M, Merkel P, Huysmans GTA, Nardon E, McAdams R, Chapman I. Coupling the JOREK and STARWALL Codes for Non-linear Resistive-wall Simulations. JPCS, 401, 012010 (2012)
  • Pamela SJP, Huijsmans GTA, Kirk A, Chapman IT, Harrison JR, Scannell R, Thornton AJ, Becoulet M, Orain F, MAST Team. Resistive MHD simulation of edge-localized-modes for double-null discharges in the MAST device. Plasma Phys. Control. Fusion 55, 095001 (2013)
  • Huijsmans GTA, Loarte A, Non-linear MHD simulation of ELM energy deposition, Nucl. Fusion 53, 123023 (2013)
  • Orain F, Bécoulet M, Dif-Pradalier G, Huijsmans G, Pamela S, Nardon E, Passeron C, Latu G, Grandgirard V, Fil A, Ratnani A, Chapman I, Kirk A, Thornton A, Hoelzl M, Cahyna P. Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations, Phys. Plasmas 20, 102510 (2013)
  • Krebs I, Hoelzl M, Lackner K, Günter S. Nonlinear excitation of low-n harmonics in reduced MHD simulations of edge-localized modes. Phys, Plasmas, 20, 082506 (2013)
  • Bécoulet M, Orain F, Huijsmans GTA, Pamela S, Cahyna P, Hoelzl M, Garbet X, Franck E, Sonnendrücker E, Dif-Pradalier G, Passeron C, Latu G, Morales J, Nardon E, Fil A, Nkonga B, Ratnani A, and Grandgirard V. Mechanism of Edge Localized Mode Mitigation by Resonant Magnetic Perturbations, Phys. Rev. Lett. 113, 115001 (2014)
  • Futatani S, Huijsmans G, Loarte A, Baylor LR, Commaux N, Jernigan TC, Fenstermacher ME, Lasnier C, Osborne TH, and Pegourié B. Non-linear MHD modelling of ELM triggering by pellet injection in DIII-D and implications for ITER. Nucl. Fusion 54 073008 (2014)
  • Pamela SJP, Huijsmans G, Kirk A, Chapman I, MAST Team. Proceedings 41st EPS Conference (2014)
  • Orain F, Bécoulet M, Huijsmans GTA, Dif-Pradalier G, Hoelzl M, Morales J, Garbet X, Nardon E, Pamela S, Passeron C, Latu G, Fil A, Cahyna P. First simulations of multi-ELM cycles in tokamak X-point plasmas. Phys. Rev. Lett. 114, 035001 (2015)
  • Fil A, Nardon E, Hoelzl M, Huijsmans GTA, Orain F, Bécoulet M, Beyer P, Dif-Pradalier G, Guirlet R, Koslowski HR, Lehnen M, Morales J, Pamela S, Passeron C, Reux C, Saint-Laurent F and JET contributors. Modeling a massive gas injection triggered disruption in JET with the JOREK code. Phys. Plasmas 22, 062509 (2015)
  • Huijsmans GTA, Chang CS, Ferraro N, Sugiyama L, Waelbroek F, Xu XQ, Loarte A, Futatani S. Modelling of edge localised modes and edge localised mode control. Phys. Plasmas 22, 021805 (2015)
  • Franck E, Hoelzl M, Lessig A, Sonnendrücker E. Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK code. ESAIM:M2AN 49, 133 | arxiv:1408.2099
  • Liu F., Huijsmans G.T.A., Loarte A., Garofalo A.M., Solomon W.M., Snyder P.B., Hoelzl M., Zeng L. Nonlinear MHD simulations of Quiescent H-mode plasmas in DIII-D. Nuclear Fusion 55, 113002 (2015)
  • P. Merkel, E. Strumberger. Linear MHD stability studies with the STARWALL code. arXiv:1508.04911 (2015)
  • Pamela S., Eich T., Frassinetti L., Sieglin B., Saarelma S., Huijsmans G., Hoelzl M., Becoulet M., Orain F., Devaux S., Chapman I., Lupelli I., Solano E., and JET Contributors. Nonlinear MHD Simulations of ELMs in JET and Quantitative Comparisons to Experiments. Plasma Physics and Controlled Fusion 58, 014026 (2015).
  • Zakharov L., Atanasiu C., Lackner K., Hoelzl M., Strumberger E. Electromagnetic Thin Wall Model for Simulations of Plasma Wall Touching Kink and Vertical Modes. Journal of Plasma Physics 81, 515810610 (2015).
  • Pamela S., Huijsmans G., Hoelzl M., Becoulet M., Orain F., Liu F., Fil A., Nardon E., Morales J., Lessig A., Krebs I. Non-Linear MHD Simulations with JOREK on HELIOS-CSC. 4th IFERC-CSC Review Meeting, Tohoku University, Sendai, Japan (15/03/2016). [Slides]
  • Nkonga B., Tarcisio-Costa J., Vides J. VMS Finite Elment for MHD and Reduced-MHD in Toikamak Plasmas. Research Report 8892, Inria Sophia Antipolis; Universite de Nice-Sophia Antipolis (2016). [PDF]
  • Haverkort J.W., de Blank H.J., Huysmans G.T.A., Pratt J., Koren B. Implementation of the full viscoresistive magnetohydrodynamic equations in a nonlinear finite element code Journal of Computational Physics 316, 281 (2016).
  • Morales J.A., Becoulet M., Garbet X., Dif-Pradalier G., Fil A., Nardon E., Passeron C., Latu G., Orain F., Hoelzl M., Pamela S., Cahyna P., Huijsmans G.T.A. Edge Localized Modes Rotation and Filaments Nonlinear Dynamics. Physics of Plasmas 23, 042513 (2016).
JOREK Team 2016

The Present JOREK Team (alphabetical)


  • Artola Such Javier
  • Atanasiu Calin
  • Becoulet Marina
  • Cahyna Pavel
  • Caldini-Queiros Celine (website)
  • Costa Jose
  • Estibals Elise
  • Franck Emmanuel (website)
  • Futatani Shimpei
  • Guillard Herve
  • Hindenlang Florian
  • Hoelzl Matthias (website)
  • Huijsmans Guido (website)
  • Iaagoubi Ayoub
  • Kanjanaput Wittawat
  • Latu Guillaume (website)
  • Lessig Alexander
  • Liu Feng
  • Meshcheriakov Dmytro
  • Mochalskyy Serhiy
  • Morales Jorge
  • Nardon Eric
  • Nkonga Boniface
  • Orain Francois
  • Pamela Stanislas
  • Passeron Chantal
  • Pautasso Gabriella
  • Pinches Simon
  • Pratt Jane (website)
  • Ratnani Ahmed (website)
  • Sangam Afeintou
  • Seidl Jakub
  • Sommariva Cristian
  • Sonnendruecker Eric (website)
  • Strumberger Erika
  • van Vugt Daan
  • Verbeek Mark
  • Westerhof Egbert

Involved Institutes (alphabetical)

  • Barcelona Supercomputing Center, Department of Computer Applications in Science and Engineering (CASE), 08034 Barcelona, Spain
  • CCFE, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK
  • CEA, IRFM, F-13108 St. Paul-lez-Durance cedex, France
  • Eindhoven University of Technology, The Netherlands
  • FOM Institute DIFFER - Dutch Institute for Fundamental Energy Research, Eindhoven, the Netherlands
  • INRIA Nancy - Grand Est & IRMA - Institut de Recherche Mathématique Avancée, Strasbourg, France
  • INRIA Sophia Antipolis - Méditerranée & Université de Nice-Sophia Antipolis, France
  • Institute of Plasma Physics ASCR, 182 00 Prague 8, Czech Republic
  • ITER Organization, Route de Vinon sur Verdon, 13115 Saint Paul Lez Durance, France
  • Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching b. M., Germany
  • National Institute for Laser, Plasma and Radiation Physics, Atomistilor 409, 077125 Magurele, Bucharest, Romania
  • (not yet complete)

Acknowledgements

Some of this work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.

Some of this work was done by ITER Organization or in collaboration with it. The opinions expressed herein do not necessarily reflect those of the ITER Organization.

Some of this work was carried out using the following supercomputers: Marconi-Fusion (Italy), IFERC-CSC HELIOS (Amori, Japan), Hydra (Garching, Germany), Idris (CNRS-France), Curie-Prace (France), Archer (UK), Jade-Cines (France), HPC-FF (Jülich, Germany).

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