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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, ITER Organization and the respective ITPA Topical Groups.

This page briefly describes key physics applications, physics models, numerics methods and contains lists of selected references, team members, and science institutes involved in this work.

Key Physics Applications

MAST ELM Simulation
  • Edge Localized Modes (ELMs) including pellet ELM triggering, ELM mitigation and suppression via RMP fields, vertical kick ELM triggering, QH-Mode, impurity transport
  • Disruptions including massive gas injection, shattered pellets, vertical displacement events (VDEs), runaway electrons, tearing mode seeding and suppression

Physics Models

  • Reduced and full MHD models
  • Two-fluid and neoclassical effects
  • Divertor model
  • Neutrals model
  • Pellet ablation model
  • Free boundary / resistive wall model
  • Full orbit and guiding center particle models

X-Point Grid


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

Main References for the JOREK Code

  • Huysmans GTA and Czarny O MHD stability in X-point geometry: simulation of ELMs NF 47, 659 (2007)
  • Czarny O and Huysmans G Bézier surfaces and finite elements for MHD simulations JCP 227, 7423 (2008)

Selected Publications

  • Nardon E, Bécoulet M, Huysmans G and Czarny O Magnetohydrodynamics modelling of H-mode plasma response to external resonant magnetic perturbations PoP 14, 092501 (2007)
  • Huysmans GTA, Pamela S, van der Plas E, and Ramet P Non-linear MHD simulations of edge localized modes (ELMs) PPCF 51, 124012 (2009)
  • Pamela S, Huysmans G, Benkadda S Influence of poloidal equilibrium rotation in MHD simulations of edge-localized modes PPCF 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 PPCF 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 PoP 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 PPCF 55, 095001 (2013)
  • Huijsmans GTA, Loarte A Non-linear MHD simulation of ELM energy deposition NF 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 PoP 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 PoP 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 PRL 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 NF 54, 073008 (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 PRL 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 PoP 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 PoP 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 (2015) arxiv:1408.2099
  • Liu F, Huijsmans GTA, Loarte A, Garofalo AM, Solomon WM, Snyder PB, Hoelzl M, Zeng L Nonlinear MHD simulations of Quiescent H-mode plasmas in DIII-D NF 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 PPCF 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, Japan (15/03/2016) [Slides]
  • Nkonga B, Tarcisio-Costa J, Vides J VMS Finite Element for MHD and Reduced-MHD in Toikamak Plasmas Inria Research Report 8892 (2016)
  • Haverkort JW, de Blank HJ, Huysmans GTA, Pratt J, Koren B Implementation of the full viscoresistive magnetohydrodynamic equations in a nonlinear finite element code JCP 316, 281 (2016)
  • Morales JA, Becoulet M, Garbet X, Dif-Pradalier G, Fil A, Nardon E, Passeron C, Latu G, Orain F, Hoelzl M, Pamela S, Cahyna P, Huijsmans GTA Edge Localized Modes Rotation and Filaments Nonlinear Dynamics PoP 23, 042513 (2016)
  • Orain F, Hoelzl M, Viezzer E, Dunne M, Willensdorfer M, Suttrop W, Strumberger E, Guenter S, Lessig A, ASDEX Upgrade Team, Becoulet M, Huijsmans GTA, Morales J, Kirk A, Pamela S, Cahyna P, EUROfusion MST1 Team Non-linear modeling of the plasma response to RMPs in ASDEX Upgrade NF 57, 022013 (2016)
  • Nardon E, Fil A, Hoelzl M, Huijsmans G, JET Contributors Progress in understanding disruptions triggered by massive gas injection via 3D non-linear MHD modelling with JOREK PPCF 59, 014006 (2016)
  • Liu F, Huijsmans GTA, Loarte A, Garofalo AM, Solomon WM, Hoelzl M, Pamela S, Becoulet M, Orain F Nonlinear MHD simulations of Quiescent H-mode pedestal in DIII-D and implications for ITER. 26th IAEA Fusion Energy Conference, Kyoto, Japan (10/2016)
  • Bécoulet M, Kim M, Yun G, Pamela S, Huijsmans GTA, Morales J, Garbet X, Passeron C, Fevrier O, Hoelzl M, Lessig A, Orain F Non-linear MHD modelling of Edge Localized Modes dynamics. 26th IAEA Fusion Energy Conference, Kyoto, Japan (10/2016)
  • Orain F, Hoelzl M, Viezzer E, Dunne M, Becoulet M, Cahyna P, Huijsmans GTA, Willensdorfer M, Suttrop W, Kirk A, Pamela S, Guenter S, Strumberger E, Lessig A, ASDEX Upgrade Team, EUROfusion MST1 Team. Non-linear modeling of the Edge Localized Mode control by Resonant Magnetic Perturbations in ASDEX Upgrade. 26th IAEA Fusion Energy Conference, Kyoto, Japan (10/2016)
  • Futatani S, Huijsmans GTA, Loarte A, Pamela S, Hoelzl M, Lang PT, Garzotti L, Kocsis G, Orain F, Frigione D, Dunne M, Lessig A, Mantsinen M, EUROfusion MST1 Team, ASDEX Upgrade Team, JET Contributors. Non-linear MHD Simulations of pellet triggered ELMs. 26th IAEA Fusion Energy Conference, Kyoto, Japan (10/2016)
  • Pamela S, Huijsmans G, Eich T, Saarelma S, Lupelli I, Maggi C, Giroud C, Chapman I, Smith S, Frassineti L, Becoulet M, Hoelzl M, Orain F, Futatani S Recent Progress in the Quantitative Validation of JOREK Simulations of ELMs in JET. NF 57, 076006 (2017)
  • Pratt J, Huijsmans GTA, Westerhof E Early evolution of electron cyclotron driven current during suppression of tearing modes in a circular tokamak. PoP (submitted)
    arXiv:1609.08850 | [PDF]


(not a complete list)
  • Pamela S Simulation Magnéto-Hydro-Dynamiques des Edge-Localised-Modes dans un tokamak PhD Thesis (2010)
  • Krebs I Non-Linear reduced MHD Simulations of Edge-Localized Modes in Realistic ASDEX Upgrade Geometry Master Thesis (2012)
  • McAdams R Non-linear Magnetohydrodynamic Instabilities in Advanced Tokamak Plasmas PhD Thesis (2014)
  • Orain F Edge Localized Mode control by Resonant Magnetic Perturbations in tokamak plasmas PhD Thesis (2014)
  • Fil A Modeling of massive gas injection triggered disruptions in tokamak plasmas PhD Thesis (2015)
JOREK Team 2016

The Present JOREK Team (alphabetical)

  • Artola Such Javier
  • Atanasiu Calin
  • Becoulet Marina
  • Estibals Elise
  • Franck Emmanuel (website)
  • Futatani Shimpei
  • Guillard Herve
  • Hindenlang Florian
  • Hoelzl Matthias (website)
  • Huijsmans Guido (website)
  • Hu Di
  • 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
  • Pratt Jane (website)
  • Ratnani Ahmed (website)
  • Sangam Afeintou
  • Sommariva Cristian
  • Sonnendruecker Eric (website)
  • van Vugt Daan
  • 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
  • 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)


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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