On Ohm’s law in reduced plasma fluid models
Abstract
Drift-reduced MHD models are widely used to study magnetised plasma phenomena, in particular for magnetically confined fusion applications, as well as in solar and astrophysical research. This letter discusses the choice of Ohm's law in these models, the resulting dispersion relations for the dynamics parallel to the magnetic field, and the implications for numerical simulations. We find that if electron pressure is included in Ohm's law, then both electromagnetic and finite electron mass effects must also be included in order to obtain physical dispersion relations. A simple modification to the plasma vorticity is also found which improves handling of low density regions, of particular relevance to the simulation of the boundary region of magnetised plasmas.
- Authors:
-
- Univ. of York (United Kingdom); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Culham Centre for Fusion Energy, Oxon (United Kingdom)
- Culham Centre for Fusion Energy, Oxon (United Kingdom); Univ. of Exeter (United Kingdom)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1840134
- Report Number(s):
- LLNL-JRNL-826562
Journal ID: ISSN 0741-3335; 1041291; TRN: US2301180
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Plasma Physics and Controlled Fusion
- Additional Journal Information:
- Journal Volume: 63; Journal Issue: 12; Journal ID: ISSN 0741-3335
- Publisher:
- IOP Science
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; dispersion; fluid model; tokamak edge; numerical simulation; Ohm’s law
Citation Formats
Dudson, Benjamin D., Newton, S. L., Omotani, J. T., and Birch, J.. On Ohm’s law in reduced plasma fluid models. United States: N. p., 2021.
Web. doi:10.1088/1361-6587/ac2af9.
Dudson, Benjamin D., Newton, S. L., Omotani, J. T., & Birch, J.. On Ohm’s law in reduced plasma fluid models. United States. https://doi.org/10.1088/1361-6587/ac2af9
Dudson, Benjamin D., Newton, S. L., Omotani, J. T., and Birch, J.. Tue .
"On Ohm’s law in reduced plasma fluid models". United States. https://doi.org/10.1088/1361-6587/ac2af9. https://www.osti.gov/servlets/purl/1840134.
@article{osti_1840134,
title = {On Ohm’s law in reduced plasma fluid models},
author = {Dudson, Benjamin D. and Newton, S. L. and Omotani, J. T. and Birch, J.},
abstractNote = {Drift-reduced MHD models are widely used to study magnetised plasma phenomena, in particular for magnetically confined fusion applications, as well as in solar and astrophysical research. This letter discusses the choice of Ohm's law in these models, the resulting dispersion relations for the dynamics parallel to the magnetic field, and the implications for numerical simulations. We find that if electron pressure is included in Ohm's law, then both electromagnetic and finite electron mass effects must also be included in order to obtain physical dispersion relations. A simple modification to the plasma vorticity is also found which improves handling of low density regions, of particular relevance to the simulation of the boundary region of magnetised plasmas.},
doi = {10.1088/1361-6587/ac2af9},
journal = {Plasma Physics and Controlled Fusion},
number = 12,
volume = 63,
place = {United States},
year = {2021},
month = {10}
}
Works referenced in this record:
Nonlinear, three-dimensional magnetohydrodynamics of noncircular tokamaks
journal, January 1976
- Strauss, H. R.
- Physics of Fluids, Vol. 19, Issue 1
Hamiltonian four-field model for nonlinear tokamak dynamics
journal, January 1987
- Hazeltine, R. D.; Hsu, C. T.; Morrison, P. J.
- Physics of Fluids, Vol. 30, Issue 10
Numerical studies of nonlinear evolution of kink modes in tokamaks
journal, January 1976
- Rosenbluth, Marshall N.; Monticello, D. A.; Strauss, H. R.
- Physics of Fluids, Vol. 19, Issue 12
Collisional drift fluid equations and implications for drift waves
journal, January 1996
- Pfirsch, Dieter; Correa-Restrepo, Darío
- Plasma Physics and Controlled Fusion, Vol. 38, Issue 1
Interplanetary and interstellar plasma turbulence
journal, March 2007
- Schekochihin, A. A.; Cowley, S. C.; Dorland, W.
- Plasma Physics and Controlled Fusion, Vol. 49, Issue 5A
Shell Models of RMHD Turbulence and the Heating of Solar Coronal Loops
journal, June 2007
- Buchlin, E.; Velli, M.
- The Astrophysical Journal, Vol. 662, Issue 1
Fluid formalism for collisionless magnetized plasmas
journal, May 2005
- Ramos, J. J.
- Physics of Plasmas, Vol. 12, Issue 5
Numerical investigation of isolated filament motion in a realistic tokamak geometry
journal, September 2015
- Walkden, N. R.; Dudson, B. D.; Easy, L.
- Nuclear Fusion, Vol. 55, Issue 11
Shear-Alfvén dynamics of toroidally confined plasmas
journal, May 1985
- Hazeltine, R. D.; Meiss, J. D.
- Physics Reports, Vol. 121, Issue 1-2
BOUT++: A framework for parallel plasma fluid simulations
journal, September 2009
- Dudson, B. D.; Umansky, M. V.; Xu, X. Q.
- Computer Physics Communications, Vol. 180, Issue 9
Modeling of large amplitude plasma blobs in three-dimensions
journal, January 2014
- Angus, Justin R.; Umansky, Maxim V.
- Physics of Plasmas, Vol. 21, Issue 1
Dynamics of scrape-off layer filaments in high β plasmas
journal, September 2019
- Hoare, D.; Militello, F.; Omotani, J. T.
- Plasma Physics and Controlled Fusion, Vol. 61, Issue 10
TOKAM-3D: A 3D fluid code for transport and turbulence in the edge plasma of Tokamaks
journal, January 2010
- Tamain, P.; Ghendrih, Ph.; Tsitrone, E.
- Journal of Computational Physics, Vol. 229, Issue 2
Upstream and divertor ion temperature measurements on MAST by retarding field energy analyser
journal, May 2012
- Elmore, S.; Allan, S. Y.; Kirk, A.
- Plasma Physics and Controlled Fusion, Vol. 54, Issue 6
Three-dimensional computation of drift Alfvén turbulence
journal, October 1997
- Scott, B.
- Plasma Physics and Controlled Fusion, Vol. 39, Issue 10
Is it necessary to resolve the Debye length in standard or δ f PIC codes?
journal, May 2020
- McMillan, B. F.
- Physics of Plasmas, Vol. 27, Issue 5
Simulation of plasma turbulence in scrape-off layer conditions: the GBS code, simulation results and code validation
journal, November 2012
- Ricci, P.; Halpern, F. D.; Jolliet, S.
- Plasma Physics and Controlled Fusion, Vol. 54, Issue 12
Nonlinear reduced fluid equations for toroidal plasmas
journal, January 1984
- Drake, J. F.; Antonsen, Thomas M.
- Physics of Fluids, Vol. 27, Issue 4
A generalized reduced fluid model with finite ion-gyroradius effects
journal, January 1986
- Hsu, C. T.; Hazeltine, R. D.; Morrison, P. J.
- Physics of Fluids, Vol. 29, Issue 5
Electromagnetic effects on dynamics of high-beta filamentary structures
journal, January 2015
- Lee, Wonjae; Umansky, Maxim V.; Angus, J. R.
- Physics of Plasmas, Vol. 22, Issue 1
Ion temperature measurements of L-mode filaments in MAST by retarding field energy analyser
journal, February 2016
- Allan, S. Y.; Elmore, S.; Fishpool, G.
- Plasma Physics and Controlled Fusion, Vol. 58, Issue 4
Reduced MHD equations for mirror machines
journal, July 1982
- Strauss, H. R.
- Nuclear Fusion, Vol. 22, Issue 7
Three dimensional simulations of plasma filaments in the scrape off layer: A comparison with models of reduced dimensionality
journal, December 2014
- Easy, L.; Militello, F.; Omotani, J.
- Physics of Plasmas, Vol. 21, Issue 12
Gyrokinetic particle simulation model
journal, September 1987
- Lee, W. W.
- Journal of Computational Physics, Vol. 72, Issue 1
Application of Parallel Implicit Methods to Edge-Plasma Numerical Simulations
journal, January 2002
- Rognlien, T. D.; Xu, X. Q.; Hindmarsh, A. C.
- Journal of Computational Physics, Vol. 175, Issue 1
Transport Equations of Plasma in a Curvilinear Magnetic Field
journal, January 1984
- Mikhailovskii, A. B.; Tsypin, V. S.
- Beiträge aus der Plasmaphysik, Vol. 24, Issue 4
Generalized reduced magnetohydrodynamic equations
journal, December 1998
- Kruger, S. E.; Hegna, C. C.; Callen, J. D.
- Physics of Plasmas, Vol. 5, Issue 12
Status and verification of edge plasma turbulence code BOUT
journal, June 2009
- Umansky, M. V.; Xu, X. Q.; Dudson, B.
- Computer Physics Communications, Vol. 180, Issue 6
�ber die partiellen Differenzengleichungen der mathematischen Physik
journal, December 1928
- Courant, R.; Friedrichs, K.; Lewy, H.
- Mathematische Annalen, Vol. 100, Issue 1
Energy-conserving finite-β electromagnetic drift-fluid equations
journal, September 2005
- Brizard, A. J.
- Physics of Plasmas, Vol. 12, Issue 9
Three-dimensional plasma edge turbulence simulations of the Mega Ampere Spherical Tokamak and comparison with experimental measurements
journal, August 2019
- Riva, Fabio; Militello, Fulvio; Elmore, Sarah
- Plasma Physics and Controlled Fusion, Vol. 61, Issue 9
Simulations of drift resistive ballooning L-mode turbulence in the edge plasma of the DIII-D tokamak
journal, May 2013
- Cohen, B. I.; Umansky, M. V.; Nevins, W. M.
- Physics of Plasmas, Vol. 20, Issue 5
Drift-ordered fluid equations for field-aligned modes in low-β collisional plasma with equilibrium pressure pedestals
journal, December 2003
- Simakov, Andrei N.; Catto, Peter J.
- Physics of Plasmas, Vol. 10, Issue 12
Revisited global drift fluid model for linear devices
journal, July 2012
- Reiser, Dirk
- Physics of Plasmas, Vol. 19, Issue 7
Heating of the Solar Chromosphere and Corona by AlfvÉN wave Turbulence
journal, June 2011
- van Ballegooijen, A. A.; Asgari-Targhi, M.; Cranmer, S. R.
- The Astrophysical Journal, Vol. 736, Issue 1
Review of implicit methods for the magnetohydrodynamic description of magnetically confined plasmas
journal, February 2012
- Jardin, S. C.
- Journal of Computational Physics, Vol. 231, Issue 3
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
journal, September 2005
- Hindmarsh, Alan C.; Brown, Peter N.; Grant, Keith E.
- ACM Transactions on Mathematical Software, Vol. 31, Issue 3