skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Journal Article · · Nuclear Fusion
ORCiD logo [1];  [2];  [3];  [4];  [4];  [5];  [6];  [7]; ORCiD logo [1];  [6]; ORCiD logo [8]; ORCiD logo [9];  [10];  [4];  [9];  [3];  [11]; ORCiD logo [12];  [13];  [6] more »;  [14];  [15]; ORCiD logo [16];  [17];  [18]; ORCiD logo [19];  [20];  [21];  [4];  [4];  [1];  [1];  [9];  [1]; ORCiD logo [4];  [22];  [9];  [1];  [23];  [24];  [25];  [4]; ORCiD logo [1];  [1];  [1]; ORCiD logo [3];  [26];  [1];  [18];  [18];  [20];  [9];  [27] « less
  1. Max Planck Institute for Plasma Physics, Garching (Germany)
  2. Alternative Energies and Atomic Energy Commission (CEA), Saint-Paul-Lez-Durance (France); Eindhoven Univ. of Technology (Netherlands)
  3. Culham Science Centre, Abingdon (United Kingdom). Culham Centre for Fusion Energy (CCFE)
  4. Alternative Energies and Atomic Energy Commission (CEA), Saint-Paul-Lez-Durance (France)
  5. Max Planck Institute for Plasma Physics, Garching (Germany); ITER Organization, St. Paul Lez Durance (France)
  6. Université Côte d'Azur, Nice (France)
  7. National Institute for Laser, Plasma and Radiation Physics, Magurele-Bucharest (Romania)
  8. Università di Padova (Italy)
  9. Max Planck Institute for Plasma Physics, Garching (Germany); Technical Univ. of Munich (Germany)
  10. Framatome, Lyon (France)
  11. Institute for Advanced Mathematical Research (IRMA), Strasbourg (France)
  12. Univ. Politecnica de Catalunya (Spain)
  13. Institute of Plasma Physics and Laser Microfusion, Warsaw (Poland)
  14. Delft Univ. of Technology (Netherlands)
  15. Max Planck Institute for Plasma Physics, Garching (Germany); Technical Univ. of Munich (Germany); Max Planck Computing and Data Facility, Garching (Germany)
  16. Beihang University, Beijing (China)
  17. Princeton Univ., NJ (United States)
  18. Eindhoven Univ. of Technology (Netherlands)
  19. University of Ljubljana (Slovenia)
  20. Dutch Institute for Fundamental Energy Research (DIFFER), Eindhoven (Netherlands)
  21. Institute of Plasma Physics, Prague (Czech Republic)
  22. Max Planck Institute for Plasma Physics, Garching (Germany); Princeton Univ., NJ (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
  23. Georgia State Univ., Atlanta, GA (United States)
  24. Max Planck Institute for Plasma Physics, Garching (Germany); Technical Univ. of Munich (Germany); Princeton Univ., NJ (United States)
  25. Université de Bordeaux, Talence (France)
  26. Ecole Polytechnique Federale Lausanne (Switzerland)
  27. Univ. of Saskatchewan, Saskatoon, SK (Canada)

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.

Research Organization:
Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
Sponsoring Organization:
USDOE; EUROfusion; ITER
Grant/Contract Number:
633053
OSTI ID:
1809091
Journal Information:
Nuclear Fusion, Vol. 61, Issue 6; ISSN 0029-5515
Publisher:
IOP ScienceCopyright Statement
Country of Publication:
United States
Language:
English

References (200)

Nonlinear MHD simulations of external kinks in quasi-axisymmetric stellarators using an axisymmetric external rotational transform approximation journal June 2021
Overview of KSTAR research progress and future plans toward ITER and K-DEMO journal July 2019
Solitary magnetic perturbations at the ELM onset journal October 2012
MHD stability in X-point geometry: simulation of ELMs journal June 2007
ELM-induced cold pulse propagation in ASDEX Upgrade journal February 2019
Filamentary plasma eruptions and their control on the route to fusion energy journal February 2020
Modeling of diamagnetic stabilization of ideal magnetohydrodynamic instabilities associated with the transport barrier journal October 2001
ELM pacing and high-density operation using pellet injection in the ASDEX Upgrade all-metal-wall tokamak journal June 2014
Scaling of the MHD perturbation amplitude required to trigger a disruption and predictions for ITER journal December 2015
Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK code journal August 2015
Magnetohydrodynamics modelling of H-mode plasma response to external resonant magnetic perturbations journal September 2007
Volume-preserving algorithm for secular relativistic dynamics of charged particles journal April 2015
Dynamics of high β tokamaks journal January 1977
Cross-code gyrokinetic verification and benchmark on the linear collisionless dynamics of the geodesic acoustic mode journal June 2017
3D two-temperature magnetohydrodynamic modeling of fast thermal quenches due to injected impurities in tokamaks journal November 2018
Modeling of lithium granule injection in NSTX with M3D-C1 journal August 2017
Non-linear MHD simulation of ELM energy deposition journal November 2013
Kinetic modeling of ELM-induced tungsten transport in a tokamak plasma journal April 2019
PT-Scotch: A tool for efficient parallel graph ordering journal July 2008
Non-linear extended MHD simulations of type-I edge localised mode cycles in ASDEX Upgrade and their underlying triggering mechanism journal November 2020
Promising High-Confinement Regime for Steady-State Fusion journal June 2019
Reduction of asymmetric wall force in JET and ITER disruptions including runaway electrons journal February 2020
Hybrid parallelization of the XTOR-2F code for the simulation of two-fluid MHD instabilities in tokamaks journal March 2017
Nonlinear magnetohydrodynamics simulation using high-order finite elements journal March 2004
ELMs and constraints on the H-mode pedestal: peeling–ballooning stability calculation and comparison with experiment journal January 2004
Recent advances in direct methods for solving unsymmetric sparse systems of linear equations journal September 2002
Formation and termination of runaway beams in ITER disruptions journal April 2017
Radiation asymmetry and MHD destabilization during the thermal quench after impurity shattered pellet injection journal January 2021
A mathematical model for calculation of the influence of ferromagnetic components in Vertical Displacement Events and stability simulations of tokamak plasmas journal January 2021
Numerical study of tearing mode seeding in tokamak X-point plasma journal April 2019
Testing of the new JOREK stellarator-capable model in the tokamak limit journal May 2021
Impurity mixing and radiation asymmetry in massive gas injection simulations of DIII-D journal May 2013
Stellarator equations of motion journal July 1980
Advances in the physics basis for the European DEMO design journal April 2015
A new cloud-based hp finite element method journal January 1998
The effect of ITER-like wall on runaway electron generation in JET journal November 2013
Model of vertical plasma motion during the current quench journal October 2017
Nonlinear excitation of low-n harmonics in reduced magnetohydrodynamic simulations of edge-localized modes journal August 2013
3D non-linear MHD simulation of the MHD response and density increase as a result of shattered pellet injection journal October 2018
Reduced models for parallel magnetic field fluctuations and their impact on pressure gradient driven MHD instabilities in axisymmetric toroidal plasmas journal August 2019
Test particles dynamics in the JOREK 3D non-linear MHD code and application to electron transport in a disruption simulation journal December 2017
Modeling of 3D magnetic equilibrium effects on edge turbulence stability during RMP ELM suppression in tokamaks journal July 2017
Assessing energy dependence of the transport of relativistic electrons in perturbed magnetic fields with orbit-following simulations journal November 2020
Multiple timescale calculations of sawteeth and other global macroscopic dynamics of tokamak plasmas journal January 2012
Fast-ion redistribution and loss due to edge perturbations in the ASDEX Upgrade, DIII-D and KSTAR tokamaks journal November 2013
Alternating Direction Implicit Methods for Parabolic Equations with a Mixed Derivative journal March 1980
Early evolution of electron cyclotron driven current during suppression of tearing modes in a circular tokamak journal October 2016
Reduced equations for finite beta tearing modes in tokamaks journal January 1985
The effect of resonant magnetic perturbations on the divertor heat and particle fluxes in MAST journal May 2014
A predictive model for the tokamak density limit journal July 2016
Scaling of the toroidal structure and nonlinear dynamics of ELMs on ASDEX Upgrade journal November 2018
Non-linear MHD modelling of ELM triggering by pellet injection in DIII-D and implications for ITER journal April 2014
Non-linear modeling of the plasma response to RMPs in ASDEX Upgrade journal September 2016
Linear and nonlinear particle-magnetohydrodynamic simulations of the toroidal Alfvén eigenmode journal May 1998
Reduced-magnetohydrodynamic simulations of toroidally and poloidally localized edge localized modes journal August 2012
Overview of the JET results in support to ITER journal June 2017
Fast-ion losses induced by ELMs and externally applied magnetic perturbations in the ASDEX Upgrade tokamak journal November 2013
A simple stabilized finite element method for solving two phase compressible–incompressible interface flows journal February 2011
Modeling of TAE mode excitation with an antenna in realistic X-point geometry journal January 2020
Modelling of edge localised modes and edge localised mode control journal February 2015
Implementation of the full viscoresistive magnetohydrodynamic equations in a nonlinear finite element code journal July 2016
Linear stability studies for a quasi-axisymmetric stellarator configuration including effects of parallel viscosity, plasma flow, and resistive walls journal August 2019
Relationship between locked modes and thermal quenches in DIII-D journal March 2018
Post-processing for ITER Scrape-Off Layer Plasma Simulations (SOLPS-ITER) in IMAS Framework journal May 2020
MHD modeling of a DIII-D low-torque QH-mode discharge and comparison to observations journal May 2017
Type-I ELM substructure on the divertor target plates in ASDEX Upgrade journal May 2005
Finite-aspect-ratio MHD equations for tokamaks journal May 1983
Non-linear saturation of the internal kink mode journal September 1980
Non-linear Simulations of MHD Instabilities in Tokamaks Including Eddy Current Effects and Perspectives for the Extension to Halo Currents journal November 2014
Design and first applications of the ITER integrated modelling & analysis suite journal October 2015
The Boltzmann equation an d the one-fluid hydromagnetic equations in the absence of particle collisions
  • Chew, G. F.; Goldberger, M. L.; Low, F. E.
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 236, Issue 1204, p. 112-118 https://doi.org/10.1098/rspa.1956.0116
journal July 1956
Progress in understanding disruptions triggered by massive gas injection via 3D non-linear MHD modelling with JOREK journal October 2016
Comparisons and physics basis of tokamak transport models and turbulence simulations journal March 2000
Non-linear MHD modelling of edge localized modes dynamics in KSTAR journal August 2017
Comparison of kinetic and extended magnetohydrodynamics computational models for the linear ion temperature gradient instability in slab geometry journal June 2013
Hybrid scheduling for the parallel solution of linear systems journal February 2006
Benchmark of gyrokinetic, kinetic MHD and gyrofluid codes for the linear calculation of fast particle driven TAE dynamics journal October 2018
Regime of Improved Confinement and High Beta in Neutral-Beam-Heated Divertor Discharges of the ASDEX Tokamak journal November 1982
Numerical modeling of the thermal force in a plasma for test-ion transport simulation based on a Monte Carlo Binary Collision Model (II) – Thermal forces due to temperature gradients parallel and perpendicular to the magnetic field journal October 2013
Comparing spontaneous and pellet-triggered ELMs via non-linear extended MHD simulations journal June 2021
PaStiX: a high-performance parallel direct solver for sparse symmetric positive definite systems journal February 2002
On particle movers in cylindrical geometry for Particle-In-Cell simulations journal November 2013
Reduced MHD in Astrophysical Applications: Two-dimensional or Three-dimensional? journal April 2017
Influence of massive material injection on avalanche runaway generation during tokamak disruptions journal June 2019
One-step Taylor–Galerkin methods for convection–diffusion problems journal July 2007
Thermal quench and current profile relaxation dynamics in massive-material-injection-triggered tokamak disruptions journal September 2021
Scattering of ion cyclotron range of frequency waves by filaments and ELMs journal July 2020
Simulations of particle and heat fluxes in an ELMy H-mode discharge on EAST using BOUT++ code journal March 2018
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling journal January 2001
Multi-region approach to free-boundary three-dimensional tokamak equilibria and resistive wall instabilities journal May 2016
Tokamak coordinate conventions: journal February 2013
XTOR-2F: A fully implicit Newton–Krylov solver applied to nonlinear 3D extended MHD in tokamaks journal October 2010
Validation of the model for ELM suppression with 3D magnetic fields using low torque ITER baseline scenario discharges in DIII-D journal October 2017
Fast plasma dilution in ITER with pure deuterium shattered pellet injection journal October 2020
A three-dimensional reduced MHD model consistent with full MHD journal October 2019
Toward integrated multi-scale pedestal simulations including edge-localized-mode dynamics, evolution of edge-localized-mode cycles, and continuous fluctuations journal May 2016
Reduced fluid simulation of runaway electron generation in the presence of resistive kink modes journal May 2017
Finite element and higher order difference formulations for modelling heat transport in magnetised plasmas journal October 2007
Understanding the reduction of the edge safety factor during hot VDEs and fast edge cooling events journal March 2020
Pellet driven disruptions in tokamaks journal January 2000
Plasma simulation studies using multilevel physics models journal May 1999
The XTOR code for nonlinear 3D simulations of MHD instabilities in tokamak plasmas journal July 2008
Extended full-MHD simulation of non-linear instabilities in tokamak plasmas journal October 2020
Cross-verification of the global gyrokinetic codes GENE and XGC journal June 2018
Bézier surfaces and finite elements for MHD simulations journal August 2008
Simulations of edge localised mode instabilities in MAST-U Super-X tokamak plasmas journal May 2020
Recent progress in the quantitative validation of JOREK simulations of ELMs in JET journal May 2017
A Taylor-Galerkin method for convective transport problems journal January 1984
A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries journal April 2017
Parametric decay instabilities near the second-harmonic upper hybrid resonance in fusion plasmas journal September 2020
Nonlinear MHD simulations of Quiescent H-mode plasmas in DIII-D journal September 2015
Three-dimensional non-linear magnetohydrodynamic modeling of massive gas injection triggered disruptions in JET journal June 2015
Non-linear MHD modeling of edge localized mode cycles and mitigation by resonant magnetic perturbations journal November 2014
3D simulations of vertical displacement events in tokamaks: A benchmark of M3D-C 1 , NIMROD, and JOREK journal May 2021
A high-order implicit finite element method for integrating the two-fluid magnetohydrodynamic equations in two dimensions journal October 2007
Axisymmetric benchmarks of impurity dynamics in extended-magnetohydrodynamic simulations journal April 2019
Existence of Electromagnetic-Hydrodynamic Waves journal October 1942
The role of edge resonant magnetic perturbations in edge-localized-mode suppression and density pump-out in low-collisionality DIII-D plasmas journal May 2020
A four-field model for tokamak plasma dynamics journal January 1985
Comment on ‘Plasma current spikes due to internal reconnection during tokamak disruptions’ journal April 2010
Insights into type-I edge localized modes and edge localized mode control from JOREK non-linear magneto-hydrodynamic simulations journal April 2018
A Robust Parallel Preconditioner for Indefinite Systems Using Hierarchical Matrices and Randomized Sampling conference May 2017
Disruptions in ITER and strategies for their control and mitigation journal August 2015
Transition from no-ELM response to pellet ELM triggering during pedestal build-up—insights from extended MHD simulations journal March 2021
Simulation of the electromagnetic wall response during Vertical Displacement Events (VDE) in ITER tokamak journal December 2018
Nonlinear, three-dimensional magnetohydrodynamics of noncircular tokamaks journal January 1976
Effect of transonic flow in the ablation cloud on the lifetime of a solid hydrogen pellet in a plasma journal January 1978
Edge localized mode rotation and the nonlinear dynamics of filaments journal April 2016
Nonlinear simulation of edge localized mode with pressure profile modified by pellet injection through a BOUT++ three-field MHD model journal March 2021
BOUT++: A framework for parallel plasma fluid simulations journal September 2009
M3D-C1 simulations of the plasma response to RMPs in NSTX-U single-null and snowflake divertor configurations journal May 2017
The influence of boundary and edge-plasma modeling in computations of axisymmetric vertical displacement journal November 2020
A binary collision model for plasma simulation with a particle code journal November 1977
CASTOR3D: linear stability studies for 2D and 3D tokamak equilibria journal November 2016
Presentation of the New SOLPS-ITER Code Package for Tokamak Plasma Edge Modelling journal January 2016
Global simulations of ion turbulence with magnetic shear reversal journal June 2001
Nonlinear modeling of the effect of n   =  2 resonant magnetic field perturbation on peeling-ballooning modes in KSTAR journal January 2020
Guiding-centre theory for kinetic-magnetohydrodynamic modes in strongly flowing plasmas journal May 2019
Analytic modeling of axisymmetric disruption halo currents journal July 1999
Simulation of surface currents excited by plasma Wall-Touching Kink and vertical modes in tokamak conference June 2016
Overview of recent physics results from MAST journal June 2017
Electron acceleration in a JET disruption simulation journal August 2018
Non-linear modeling of the threshold between ELM mitigation and ELM suppression by resonant magnetic perturbations in ASDEX upgrade journal April 2019
Nonlinear three-dimensional verification of the SPECYL and PIXIE3D magnetohydrodynamics codes for fusion plasmas journal August 2010
Resistive MHD simulation of edge-localized-modes for double-null discharges in the MAST device journal July 2013
Sputtering yields journal May 2008
First predictive simulations for deuterium shattered pellet injection in ASDEX Upgrade journal February 2020
Neoclassical conductivity and bootstrap current formulas for general axisymmetric equilibria and arbitrary collisionality regime journal July 1999
Nonlinear reconnecting edge localized modes in current-carrying plasmas journal May 2017
Magnetohydrodynamic simulations of massive gas injection into Alcator C-Mod and DIII-D plasmas journal May 2008
Nonlinear MHD simulations of QH-mode DIII-D plasmas and implications for ITER high Q scenarios journal November 2017
Effects of density gradients and fluctuations at the plasma edge on ECEI measurements at ASDEX Upgrade journal February 2018
Global ITG eigenmodes: From ballooning angle and radial shift to Reynolds stress and nonlinear saturation journal July 2020
The role of MHD in 3D aspects of massive gas injection journal June 2015
Development and testing of an unstructured mesh method for whole plasma gyrokinetic simulations in realistic tokamak geometry journal December 2019
Non-linear magnetohydrodynamic simulations of edge localised mode triggering via vertical position oscillations in ITER journal July 2018
Coupling JOREK and STARWALL Codes for Non-linear Resistive-wall Simulations journal December 2012
Influence of poloidal equilibrium rotation in MHD simulations of edge-localized modes journal June 2010
Reduced MHD in nearly potential magnetic fields journal January 1997
Magnetic surface loss and electron runaway journal January 2019
Non-linear magnetohydrodynamic simulations of pellet triggered edge-localized modes in JET journal December 2019
Shattered pellet injection simulations with NIMROD journal April 2019
Determination of Hydromagnetic Equilibria journal January 1961
ELM divertor peak energy fluence scaling to ITER with data from JET, MAST and ASDEX upgrade journal August 2017
Characteristics of type I ELM energy and particle losses in existing devices and their extrapolation to ITER journal August 2003
Closure of the single fluid magnetohydrodynamic equations in presence of electron cyclotron current drive journal October 2014
Reconnection processes and scaling laws in reversed field pinch magnetohydrodynamics journal May 1996
Physics of runaway electrons in tokamaks journal June 2019
Simulation of MHD instabilities with fluid runaway electron model in M3D-C1 journal May 2020
Edge localized modes (ELMs) journal February 1996
Nonlinear MHD simulations of edge-localized-modes in JET journal April 2011
Overview of physics studies on ASDEX Upgrade journal July 2019
Hamiltonian formalism of extended magnetohydrodynamics journal May 2015
Non-linear MHD simulations of ELMs in JET and quantitative comparisons to experiments journal November 2015
External kink (peeling) modes in x-point geometry journal October 2005
Free boundary resistive modes in tokamaks journal May 1993
Axisymmetric simulations of vertical displacement events in tokamaks: A benchmark of M3D-C 1 , NIMROD, and JOREK journal February 2020
Magnetohydrodynamic simulations of runaway electron beam termination in JET journal January 2021
Some properties of the M3D-C1 form of the three-dimensional magnetohydrodynamics equations journal September 2009
ITER cold VDEs in the limit of perfectly conducting walls journal January 2021
Non-linear MHD simulations of edge localized modes (ELMs) journal November 2009
Experimental study of ELM induced fast-ion transport using passive FIDA spectroscopy at the ASDEX Upgrade tokamak journal March 2021
Simulation of edge localized modes using BOUT++ journal April 2011
Heuristic closures for numerical simulations of neoclassical tearing modes journal February 2002
Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations journal October 2013
Generalized reduced magnetohydrodynamic equations journal December 1998
Mode locking in tokamaks journal December 1990
Nonlinear coupling induced toroidal structure of edge localized modes journal December 2017
Edge-localized modes - physics and theory journal May 1998
A wall-aligned grid generator for non-linear simulations of MHD instabilities in tokamak plasmas journal October 2019
Dependence on plasma shape and plasma fueling for small edge-localized mode regimes in TCV and ASDEX Upgrade journal June 2019
Tokamak halo currents journal August 2013
Influence of resistive internal kink on runaway current profile journal January 2015
Studies of the impurity pellet ablation in the high-temperature plasma of magnetic confinement devices journal May 2006
Electromagnetic thin-wall model for simulations of plasma wall-touching kink and vertical modes journal December 2015
The physics of edge localized modes (ELMs) and their role in power and particle exhaust journal August 1996
The Plasma Boundary of Magnetic Fusion Devices book January 2000
Non-linear Simulations of MHD Instabilities in Tokamaks Including Eddy Current Effects and Perspectives for the Extension to Halo Currents text January 2014
Linear MHD stability studies with the STARWALL code preprint January 2015
ELM-induced cold pulse propagation in ASDEX Upgrade text January 2019

Similar Records

3D simulations of vertical displacement events in tokamaks: A benchmark of M3D-C1, NIMROD, and JOREK
Journal Article · Mon May 24 00:00:00 EDT 2021 · Physics of Plasmas · OSTI ID:1809091

DIII-D Studies of Massive Gas Injection Fast Shutdowns for Disruption Mitigation
Conference · Fri Sep 29 00:00:00 EDT 2006 · OSTI ID:1809091

DIII-D Studies of Massive Gas Injection Fast Shutdowns for Disruption Mitigation
Journal Article · Mon Jun 19 00:00:00 EDT 2006 · Proceedings of the 33rd EPS Conference on Plasma Physics, vol. 30I, n/a, December 31, 2006, P5.136 · OSTI ID:1809091