A BOUT++ extension for full annular tokamak edge MHD and turbulence simulations

Seto, Haruki; Dudson, Benjamin D.; Xu, Xue-Qiao; Yagi, Masatoshi

doi:10.1016/j.cpc.2022.108568

A BOUT++ extension for full annular tokamak edge MHD and turbulence simulations

Journal Article · Mon Oct 24 00:00:00 EDT 2022 · Computer Physics Communications

DOI:https://doi.org/10.1016/j.cpc.2022.108568· OSTI ID:2203615

^[1]; Dudson, Benjamin D. ^[2]; Xu, Xue-Qiao ^[3]; Yagi, Masatoshi ^[1]

National Institutes for Quantum Science and Technology (Japan)
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Univ. of York (United Kingdom)
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

For tokamak edge plasma simulation, a plasma simulation framework BOUT++ employs a dual coordinate system to simulate moderate-n and high-n plasma instability with reasonable computational cost, where n is the toroidal mode number. This coordinate system however limits the computational domain to the toroidal wedge (full torus divided into N parts in the toroidal direction) for computational efficiency and the use of flute-ordering approximation in the field solver calculating the flow potential from the vorticity which may not be valid for low-n modes. Improving numerical treatment of low-n modes is however indispensable to address simulations of low-n current-driven edge localized mode (ELM), ELM control by resonant magnetic perturbations (RMPs), edge turbulence with RMPs and so on. In this work, BOUT++ is extended to simulate the interplay between $n=0$, low-n and high-n plasma components in a full annular tokamak edge domain through hybrid modeling of the flow potential and the vorticity. Low-n modes of flow potential are calculated in an orthogonal flux surface coordinate and high-n modes in the dual coordinate system separately in Fourier space. Finally, the proposed scheme can capture an interplay between $n=1$ global modes and high-n turbulence during pedestal collapse in a full annular torus domain with a circular cross section.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2203615

Report Number(s):: LLNL--JRNL-837012; 1056665

Journal Information:: Computer Physics Communications, Journal Name: Computer Physics Communications Vol. 283; ISSN 0010-4655

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (42)

GATO: An MHD stability code for axisymmetric plasmas with internal separatrices Bernard, L. C.; Helton, F. J.; Moore, R. W. Computer Physics Communications, Vol. 24, Issue 3-4 https://doi.org/10.1016/0010-4655(81)90160-0	journal	December 1981
Shear-Alfvén dynamics of toroidally confined plasmas Hazeltine, R. D.; Meiss, J. D. Physics Reports, Vol. 121, Issue 1-2 https://doi.org/10.1016/0370-1573(85)90083-3	journal	May 1985
BOUT++: A framework for parallel plasma fluid simulations Dudson, B. D.; Umansky, M. V.; Xu, X. Q. Computer Physics Communications, Vol. 180, Issue 9 https://doi.org/10.1016/j.cpc.2009.03.008	journal	September 2009
Drift reduced Landau fluid model for magnetized plasma turbulence simulations in BOUT++ framework Zhu, Ben; Seto, Haruki; Xu, Xue-qiao Computer Physics Communications, Vol. 267 https://doi.org/10.1016/j.cpc.2021.108079	journal	October 2021
Finalizing the ITER divertor design: The key role of SOLPS modeling Kukushkin, A. S.; Pacher, H. D.; Kotov, V. Fusion Engineering and Design, Vol. 86, Issue 12 https://doi.org/10.1016/j.fusengdes.2011.06.009	journal	December 2011
Nonlinear magnetohydrodynamics simulation using high-order finite elements Sovinec, C. R.; Glasser, A. H.; Gianakon, T. A. Journal of Computational Physics, Vol. 195, Issue 1 https://doi.org/10.1016/j.jcp.2003.10.004	journal	March 2004
Bézier surfaces and finite elements for MHD simulations Czarny, Olivier; Huysmans, Guido Journal of Computational Physics, Vol. 227, Issue 16 https://doi.org/10.1016/j.jcp.2008.04.001	journal	August 2008
Shifted metric procedure for flux tube treatments of toroidal geometry: Avoiding grid deformation Scott, B. Physics of Plasmas, Vol. 8, Issue 2 https://doi.org/10.1063/1.1335832	journal	February 2001
Edge localized modes and the pedestal: A model based on coupled peeling–ballooning modes Snyder, P. B.; Wilson, H. R.; Ferron, J. R. Physics of Plasmas, Vol. 9, Issue 5 https://doi.org/10.1063/1.1449463	journal	May 2002
Numerical studies of edge localized instabilities in tokamaks Wilson, H. R.; Snyder, P. B.; Huysmans, G. T. A. Physics of Plasmas, Vol. 9, Issue 4 https://doi.org/10.1063/1.1459058	journal	April 2002
Tearing mode in the cylindrical tokamak Furth, H. P. Physics of Fluids, Vol. 16, Issue 7 https://doi.org/10.1063/1.1694467	journal	January 1973
Finite-Resistivity Instabilities of a Sheet Pinch Furth, Harold P.; Killeen, John; Rosenbluth, Marshall N. Physics of Fluids, Vol. 6, Issue 4 https://doi.org/10.1063/1.1706761	journal	January 1963
Edge localized linear ideal magnetohydrodynamic instability studies in an extended-magnetohydrodynamic code Burke, B. J.; Kruger, S. E.; Hegna, C. C. Physics of Plasmas, Vol. 17, Issue 3 https://doi.org/10.1063/1.3309732	journal	March 2010
Ideal and resistive edge stability calculations with M3D-C1 Ferraro, N. M.; Jardin, S. C.; Snyder, P. B. Physics of Plasmas, Vol. 17, Issue 10 https://doi.org/10.1063/1.3492727	journal	October 2010
CVODE, A Stiff/Nonstiff ODE Solver in C Cohen, Scott D.; Hindmarsh, Alan C.; Dubois, Paul F. Computers in Physics, Vol. 10, Issue 2 https://doi.org/10.1063/1.4822377	journal	January 1996
Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations Orain, F.; Bécoulet, M.; Dif-Pradalier, G. Physics of Plasmas, Vol. 20, Issue 10 https://doi.org/10.1063/1.4824820	journal	October 2013
The impact of pedestal turbulence and electron inertia on edge-localized-mode crashes Xi, P. W.; Xu, X. Q.; Diamond, P. H. Physics of Plasmas, Vol. 21, Issue 5 https://doi.org/10.1063/1.4875332	journal	May 2014
Interplay between fluctuation driven toroidal axisymmetric flows and resistive ballooning mode turbulence Seto, H.; Xu, X. Q.; Dudson, B. D. Physics of Plasmas, Vol. 26, Issue 5 https://doi.org/10.1063/1.5086998	journal	May 2019
Generalized gyroviscous force and its effect on the momentum balance equation Chang, Zuoyang; Callen, J. D. Physics of Fluids B: Plasma Physics, Vol. 4, Issue 7 https://doi.org/10.1063/1.860032	journal	March 1992
Field‐aligned coordinates for nonlinear simulations of tokamak turbulence Beer, M. A.; Cowley, S. C.; Hammett, G. W. Physics of Plasmas, Vol. 2, Issue 7 https://doi.org/10.1063/1.871232	journal	August 1995
Integration of Stiff Equations Curtiss, C. F.; Hirschfelder, J. O. Proceedings of the National Academy of Sciences, Vol. 38, Issue 3 https://doi.org/10.1073/pnas.38.3.235	journal	March 1952
Hot particle stabilization of ballooning modes in tokamaks Miller, R. L.; Van Dam, J. W. Nuclear Fusion, Vol. 27, Issue 12 https://doi.org/10.1088/0029-5515/27/12/010	journal	December 1987
Chapter 4: Power and particle control Loarte, A.; Lipschultz, B.; Kukushkin, A. S. Nuclear Fusion, Vol. 47, Issue 6 https://doi.org/10.1088/0029-5515/47/6/S04	journal	June 2007
MHD stability in X-point geometry: simulation of ELMs Huysmans, G. T. A.; Czarny, O. Nuclear Fusion, Vol. 47, Issue 7 https://doi.org/10.1088/0029-5515/47/7/016	journal	June 2007
The physics and technology basis entering European system code studies for DEMO Wenninger, R.; Kembleton, R.; Bachmann, C. Nuclear Fusion, Vol. 57, Issue 1 https://doi.org/10.1088/0029-5515/57/1/016011	journal	October 2016
The role of the electric field in confinement Itoh, Kimitaka; Itoh, Sanae-I Plasma Physics and Controlled Fusion, Vol. 38, Issue 1 https://doi.org/10.1088/0741-3335/38/1/001	journal	January 1996
The physics of edge localized modes (ELMs) and their role in power and particle exhaust Zohm, Hartmut Plasma Physics and Controlled Fusion, Vol. 38, Issue 8 https://doi.org/10.1088/0741-3335/38/8/012	journal	August 1996
Quiescent H-mode plasmas in the DIII-D tokamak Burrell, K. H.; Austin, M. E.; Brennan, D. P. Plasma Physics and Controlled Fusion, Vol. 44, Issue 5A https://doi.org/10.1088/0741-3335/44/5A/325	journal	April 2002
Simulation of edge localized modes using BOUT++ Dudson, B. D.; Xu, X. Q.; Umansky, M. V. Plasma Physics and Controlled Fusion, Vol. 53, Issue 5 https://doi.org/10.1088/0741-3335/53/5/054005	journal	April 2011
Connection between plasma response and resonant magnetic perturbation (RMP) edge localized mode (ELM) suppression in DIII-D Wingen, A.; Ferraro, N. M.; Shafer, M. W. Plasma Physics and Controlled Fusion, Vol. 57, Issue 10 https://doi.org/10.1088/0741-3335/57/10/104006	journal	September 2015
Hermes: global plasma edge fluid turbulence simulations Dudson, B. D.; Leddy, J. Plasma Physics and Controlled Fusion, Vol. 59, Issue 5 https://doi.org/10.1088/1361-6587/aa63d2	journal	April 2017
Surface heat loads on the ITER divertor vertical targets Gunn, J. P.; Carpentier-Chouchana, S.; Escourbiac, F. Nuclear Fusion, Vol. 57, Issue 4 https://doi.org/10.1088/1741-4326/aa5e2a	journal	March 2017
The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas Hoelzl, Matthias; Huijsmans, Guido; Pamela, Stanislas Nuclear Fusion https://doi.org/10.1088/1741-4326/abf99f	journal	April 2021
Iterative methods for solving partial difference equations of elliptic type Young, David Transactions of the American Mathematical Society, Vol. 76, Issue 1 https://doi.org/10.1090/S0002-9947-1954-0059635-7	journal	January 1954
Fluid simulations of tokamak turbulence in quasiballooning coordinates Dimits, A. M. Physical Review E, Vol. 48, Issue 5 https://doi.org/10.1103/PhysRevE.48.4070	journal	November 1993
Quiescent H-Mode Plasmas with Strong Edge Rotation in the Cocurrent Direction Burrell, K. H.; Osborne, T. H.; Snyder, P. B. Physical Review Letters, Vol. 102, Issue 15 https://doi.org/10.1103/PhysRevLett.102.155003	journal	April 2009
Nonlinear Simulations of Peeling-Ballooning Modes with Anomalous Electron Viscosity and their Role in Edge Localized Mode Crashes Xu, X. Q.; Dudson, B.; Snyder, P. B. Physical Review Letters, Vol. 105, Issue 17 https://doi.org/10.1103/PhysRevLett.105.175005	journal	October 2010
Phase Dynamics Criterion for Fast Relaxation of High-Confinement-Mode Plasmas Xi, P. W.; Xu, X. Q.; Diamond, P. H. Physical Review Letters, Vol. 112, Issue 8 https://doi.org/10.1103/PhysRevLett.112.085001	journal	February 2014
Resistive Reduced MHD Modeling of Multi-Edge-Localized-Mode Cycles in Tokamak X -Point Plasmas Orain, F.; Bécoulet, M.; Huijsmans, G. T. A. Physical Review Letters, Vol. 114, Issue 3 https://doi.org/10.1103/PhysRevLett.114.035001	journal	January 2015
Regime of Improved Confinement and High Beta in Neutral-Beam-Heated Divertor Discharges of the ASDEX Tokamak Wagner, F.; Becker, G.; Behringer, K. Physical Review Letters, Vol. 49, Issue 19 https://doi.org/10.1103/PhysRevLett.49.1408	journal	November 1982
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems Saad, Youcef; Schultz, Martin H. SIAM Journal on Scientific and Statistical Computing, Vol. 7, Issue 3 https://doi.org/10.1137/0907058	journal	July 1986
Convergence Rates of Iterative Treatments of Partial Differential Equations Frankel, Stanley P. Mathematical Tables and Other Aids to Computation, Vol. 4, Issue 30 https://doi.org/10.2307/2002770	journal	April 1950

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A BOUT++ extension for full annular tokamak edge MHD and turbulence simulations

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