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The JOREK non-linear MHD Code

  • The non-linear extended MHD code JOREK resolves realistic toroidal tokamak 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 sheath boundary conditions, resistive wall effects, two-fluid effects and neoclassical flows, kinetic particle models, and further extensions. Main physics applications are the physics and control of disruptions and edge localized modes (ELMs).
  • The well established physics and numerics community around JOREK has strong connections to the relevant experiments, ITER Organization and the respective ITPA Topical Groups.
  • 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)
    • M Hoelzl, GTA Huijsmans, SJP Pamela, M Becoulet, E Nardon, FJ Artola, B Nkonga, et al The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas NF 61, 065001 (2021)
  • Below: applications | methods and models | publications | thesis | acknowledgements

Key Physics Applications

Large scale plasma instabilities in magnetically confined fusion devices, in particular: MAST Upgrade ELM Simulation

Edge Localized Modes (ELMs)

  • natural type-I ELM cycles
  • small ELM and ELM free regimes
  • pellet ELM triggering
  • ELM mitigation and suppression via resonant magnetic perturbation fields (RMPs)
  • vertical kick ELM triggering
  • detachment and burn-through
  • impurity sputtering and transport
ASDEX Upgrade Simulation


  • neoclassical tearing modes (NTMs) and mode locking
  • mitigation by massive gas injection (MGI) and shattered pellet injection (SPI)
  • vertical displacement events (VDEs)
  • eddy and halo currents
  • runaway electrons (REs)
  • vertical kick ELM triggering
  • density limit disruptions
X-Point Grid

Methods and models

Numerical Methods

  • 2D Bezier finite elements
  • Toroidal Fourier expansion
  • Flux surface aligned grid with option to extend to the first wall
  • Fully implicit time stepping
  • Iterative solver with physics based preconditioner
  • Taylor-Galerkin and VMS stabilization
  • MPI + OpenMP hybrid parallelization

Physics Models

  • Reduced and full MHD models with various extensions, e.g.
  • Free boundary extension including 3D resistive walls and coils
  • Two-fluid and neoclassical effects
  • Sheath boundary conditions
  • Fluid and kinetic neutrals models
  • Fluid and kinetic impurity models
  • Pellet and shattered pellet models
  • Full orbit and guiding center kinetic particles
  • Relativistic full orbit and guiding center kinetic particles
  • Runaway electron fluid model

Selected Publications


  • Cathey A., Hoelzl M., Futatani S., Lang P.T., Lackner K., Huijsmans G.T.A., Pamela S.J.P., Günter S., JOREK Team, ASDEX Upgrade Team, EUROfusion MST1 Team. Comparing spontaneous and pellet-triggered ELMs via non-linear extended MHD simulations. PPCF 63, 075016 (2021) doi:10.1088/1361-6587/abf80b | arXiv
  • Hoelzl M., Huijsmans G.T.A., Pamela S.J.P., Becoulet M., Nardon E., Artola F.J., Nkonga B., Atanasiu C.V., Bandaru V., Bhole A., Bonfiglio D., Cathey A., Czarny O., Dvornova A., Feher T., Fil A., Franck E., Futatani S., Gruca M., Guillard H., Haverkort J.W., Holod I., Hu D., Kim S.K., Korving S.Q., Kos L., Krebs I., Kripner L., Latu G., Liu F., Merkel P., Meshcheriakov D., Mitterauer V., Mochalskyy S., Morales J.A., Nies R., Nikulsin N., Orain F., Pratt J., Ramasamy R., Ramet P., Reux C., Särkimäki K., Schwarz N., Singh Verma P., Smith S.F., Sommariva C., Strumberger E., van Vugt D.C., Verbeek M., Westerhof E., Wieschollek F., Zielinski J.. The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas. NF 61, 065001 (2021) doi:10.1088/1741-4326/abf99f | arXiv
  • Artola F.J.,Sovinec C.R., Jardin S.C., Hoelzl M., Krebs I., Clauser C. 3D simulations of vertical displacement events in tokamaks: A benchmark of M3D-C1, NIMROD, and JOREK. PoP 28, 052511 (2021) doi:10.1063/5.0037115 | arXiv
  • Nikulsin N., Hoelzl M., Zocco A., Lackner K., Günter S., JOREK Team. Testing of the new JOREK stellarator-capable model in the tokamak limit. JPP 87, 855870301 (2021) doi:10.1017/S0022377821000477 | arXiv
  • Artola F.J., Loarte A., Matveeva E., Havlicek J., Markovic T., Adamek J., Cavalier J., Kripner L., Huijsmans G.T.A., Lehnen M., Hoelzl M., Panek R., COMPASS Team, JOREK Team. Simulations of COMPASS vertical displacement events with a self-consistent model for halo currents including neutrals and sheath boundary conditions. PPCF 63, 064004 (2021) doi:10.1088/1361-6587/abf620 | arXiv
  • Reux C, Paz-Soldan C, Aleynikov P, Bandaru V, Ficker O, Silburn S, Hoelzl M, Jachmich S, Eidietis N, Lehnen M, Sridhar S, JET Contributors. Demonstration of Safe Termination of Megaampere Relativistic Electron Beams in Tokamaks. PRL 126, 175001 (2021) doi:10.1103/PhysRevLett.126.175001
  • Futatani S, Cathey A, Hoelzl M, Lang PT, Huijsmans GTA, Dunne M, JOREK Team, ASDEX Upgrade Team, EUROfusion MST1 Team. Transition from no-ELM response to pellet ELM triggering during pedestal build-up - insights from extended MHD simulations.. Nuclear Fusion 61, 046043 (2021) doi:10.1088/1741-4326/abdfb4 | arXiv
  • JET simulation Bandaru V, Hoelzl M, Reux C, Ficker O, Silburn S, Lehnen M, Eidietis N,JOREK Team and JET Contributors. Magnetohydrodynamic simulations of runaway electron beam termination in JET. Plasma Physics and Controlled Fusion 63, 035024 (2021) doi:10.1088/1361-6587/abdbcf
  • Hu D, Nardon E, Hoelzl M, Wieschollek F, Lehnen M, Huijsmans GTA, van Vugt DC, Kim S-H, JET Contributors, JOREK Team. Radiation asymmetry and MHD destabilization during the thermal quench after impurity shattered pellet injection. Nuclear Fusion 61, 026015 (2021) doi:10.1088/1741-4326/abcbcb | arXiv



  • Nikulsin N., Hoelzl M., Zocco A., Lackner K., Günter S.. A three-dimensional reduced MHD model consistent with full MHD. Physics of Plasmas 26, 102109 (2019) doi:10.1063/1.5122013 | arXiv
  • Nies R. and Hoelzl M. Testing performance with and without Block Low Rank Compression in MUMPS and the new PaStiX 6.0 for JOREK nonlinear MHD simulations. arXiv:1907.13442 (2019)
  • Bandaru V., Hoelzl M., Artola F.J., Papp G., and Huijsmans G.T.A. Simulating the nonlinear interaction of relativistic electrons and tokamak plasma instabilities: Implementation and validation of a fluid model. Physical Review E 99, 063317 (2019) doi:10.1103/PhysRevE.99.063317
  • Pamela S., Huijsmans G., Thornton A.J., Kirk A., Smith S.F., Hoelzl M., Eich T., JET Contributors, MAST Team, JOREK Team. A wall-aligned grid generator for non-linear simulations of MHD instabilities in tokamak plasmas. Computer Physics Communications 243, 41 (2019) doi:10.1016/j.cpc.2019.05.007
  • Orain F., Hoelzl M., Mink F., Willensdorfer M., Dunne M., Viezzer E., Becoulet M., Huijsmans G., Pamela S., Suttrop W., Günter S., Lackner K., ASDEX Upgrade Team, EUROfusion MST1 Team. Non-linear modeling of the threshold between ELM mitigation and ELM suppression by resonant magnetic perturbations in ASDEX Upgrade. Physics of Plasmas 26, 042503 (2019) doi:10.1063/1.5091843 | arXiv
  • Meshcheriakov D., Hoelzl M., Igochine V., Fietz S., Orain F., Huijsmans G.T.A., Maraschek M., Dunne M., McDermott R., Zohm H., Lackner K., Günter S., ASDEX Upgrade Team, EUROfusion MST1 Team. Numerical study of tearing mode seeding in tokamak X-point plasma. Physics of Plasmas 26, 042504 (2019) doi:10.1063/1.5086402 | arXiv
  • van Vugt D.C., Huijsmans G.T.A., Hoelzl M., Loarte A., Lopes Cardozo N.J. Kinetic modelling of ELM-induced W transport in ASDEX Upgrade. Physics of Plasmas 26, 042508 (2019) doi:10.1063/1.5092319


  • Sommariva C., Nardon E., Beyer P., Hoelzl M., Huysmans G.T.A., van Vugt D., JET Contributors. Test particles dynamics in the JOREK 3D non-linear MHD code and application to electron transport in a disruption simulation. Nuclear Fusion 58, 016043 (2018) doi:10.1088/1741-4326/aa95cd | arXiv
  • Liu F., Huijsmans G.T.A., Loarte A., Garofalo A.M., Solomon W.M., Hoelzl M., Nkonga B., Pamela S., Becoulet M., Orain F., van Vugt D.. Non-linear MHD simulations of QH-mode DIII-D plasmas and implications for ITER high Q scenarios. Plasma Physics and Controlled Fusion 60, 014039 (2018) doi:10.1088/1361-6587/aa934f
  • Mink F., Hoelzl M., Wolfrum E., Orain F., Dunne M., Lessig A., Pamela S., Manz P., Maraschek M., Huijsmans G.T.A., Becoulet M., Laggner F.M., Cavedon M., Lackner K., Guenter S., Stroth U.. Nonlinear coupling induced toroidal structure of edge localized modes. Nuclear Fusion 58, 026011 (2018) doi:10.1088/1741-4326/aa98f7
  • Hoelzl M., Huijsmans G.T.A., Orain F., Artola F.J., Pamela S., Becoulet M., van Vugt D., Liu F., Futatani S., Lessig A., Wolfrum E., Mink F., Trier E., Dunne M., Viezzer E., Eich T., Vanovac B., Frassinetti L., Guenter S., Lackner K., Krebs I., ASDEX Upgrade Team, EUROfusion MST1 Team. Insights into type-I ELMs and ELM control methods from JOREK MHD simulations. Contributions to Plasma Physics 58, 518 (2018) doi:10.1002/ctpp.201700142
  • Artola F.J., Huijsmans G.T.A., Hoelzl M., Beyer P., Loarte A., Gribov Y. Non-linear magnetohydrodynamic simulations of Edge Localised Modes triggering via vertical oscillations. Nuclear Fusion 58, 096018 (2018) doi:10.1088/1741-4326/aace0e
  • Sommariva C., Nardon E., Beyer P., Hoelzl M., Huijsmans G.T.A. and JET Contributors. Electron acceleration during a simulated JET-like disruption thermal quench. Nuclear Fusion 58, 106022 (2018) doi:10.1088/1741-4326/aad47d | arXiv
  • Feher T., Hoelzl M., Latu G., Huijsmans G.T.A. Performance analysis and optimization of the JOREK code for many-core CPUs. , (2018) | arXiv
  • D. Hu, E. Nardon, M. Lehnen, G.T.A. Huijsmans, D.C. van Vugt, and JET Contributors. 3D non-linear MHD simulation of the MHD response and density increase as a result of shattered pellet injection. Nuclear Fusion 58, 126025 (2018) doi:10.1088/1741-4326/aae614


  • 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)
  • Bécoulet M., Kim M., Yun G., Pamela S., Morales J., Garbet X., Huijsmans G.T.A., Passeron C., Fevrier O., Hoelzl M., Lessig A., Orain F.. Non-linear MHD modelling of Edge Localized Modes dynamics in KSTAR.. Nuclear Fusion 57, 116059 (2017) doi:10.1088/1741-4326/aa8142
  • Mochalskyy S., Hoelzl M., Hatzky R.. Parallelization of JOREK-STARWALL for non-linear MHD simulations including resistive walls. , (2017) | arXiv


  • 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)
  • J Pratt, GTA Huijsmans, E Westerhof. Early evolution of electron cyclotron driven current during suppression of tearing modes in a circular tokamak. Physics of Plasmas 23, 102507 (2016) doi:10.1063/1.4964785 | arXiv


  • 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)

2013 – 2014

  • 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)
  • 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)

2007 – 2012

  • 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, 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)
  • Pamela S, Huysmans G, Benkadda S Influence of poloidal equilibrium rotation in MHD simulations of edge-localized modes PPCF 52, 075006 (2010)
  • Czarny O and Huysmans G Bézier surfaces and finite elements for MHD simulations JCP 227, 7423 (2008)
  • Huysmans GTA, Pamela S, van der Plas E, and Ramet P Non-linear MHD simulations of edge localized modes (ELMs) PPCF 51, 124012 (2009)
  • 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 and Czarny O MHD stability in X-point geometry: simulation of ELMs NF 47, 659 (2007)

Thesis (not a complete list)

  • Schwarz N Vertical Displacement Events in ASDEX Upgrade master Thesis (2020)
  • Kim SK On the mechanism of RMP-driven pedestal transport and ELM suppression in KSTAR PhD Thesis (2020)
  • Siobhan Faye Smith Numerical simulations of edge localised mode instabilities in the MAST-U Super-X tokamak PhD Thesis (2020)
  • van Vugt DC Nonlinear coupled MHD-kinetic particle simulations of heavy impurities in tokamak plasmas PhD Thesis (2019)
  • Artola Such FJ Free boundary simulations of MHD plasma instabilities in tokamaks PhD Thesis (2018)
  • Sommariva C Test particle dynamics in 3D non-linear magnetohydrodynamics simulations and application to runaway formation in tokamak disruptions PhD Thesis (2017)
  • Fil A Modeling of massive gas injection triggered disruptions in tokamak plasmas PhD Thesis (2015)
  • Orain F Edge Localized Mode control by Resonant Magnetic Perturbations in tokamak plasmas PhD Thesis (2014)
  • McAdams R Non-linear Magnetohydrodynamic Instabilities in Advanced Tokamak Plasmas PhD Thesis (2014)
  • Haverkort JW Magnetohydrodynamic waves and instabilities in rotating tokamak plasmas. PhD Thesis (2013)
  • Krebs I Non-Linear reduced MHD Simulations of Edge-Localized Modes in Realistic ASDEX Upgrade Geometry Master Thesis (2012)
  • Pamela S Simulation Magnéto-Hydro-Dynamiques des Edge-Localised-Modes dans un tokamak PhD Thesis (2010)
  • Nardon E Edge localized modes control by resonant magnetic perturbations PhD Thesis (2007)

The JOREK Team

  • For a list of team members, please refer to the author list of our submitted review article.
  • In case you are interested in a master, PhD, or postdoc project, send us an e-mail to discuss possible opportunities.


  • 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 and 2019-2020 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), MareNostrum (Spain), JFRS-1 (Japan), Cobra (Germany), Archer (UK).
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