Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing
Abstract
A simulated annealing (SA) relaxation method is used for the calculation of high-beta reduced magnetohydrodynamics (MHD) equilibria in toroidal geometry. The SA method, based on artificial dynamics derived from the MHD Hamiltonian structure, is used to calculate equilibria of large-aspect-ratio and circular-cross-section tokamaks as well as toroidally averaged stellarators. Tokamak equilibria including incompressible poloidal rotations are obtained and the Shafranov shift is seen to increase nearly quadratically in the rotation speed. A mapping procedure between non-rotating and poloidally rotating equilibria is shown to explain the quadratic dependence of equilibria shift on rotation. Calculated stellarator equilibria are seen to agree reasonably with previous results. The numerical results demonstrate the first successful application of the SA method to obtain toroidal equilibria.
- Authors:
-
- Tottori Univ., Tottori (Japan)
- Univ. of Texas at Austin, Austin, TX (United States)
- National Institute for Fusion Science, Toki (Japan); SOKENDAI, The Graduate Univ. for Advanced Studies, Toki (Japan)
- Publication Date:
- Research Org.:
- Univ. of Texas, Austin, TX (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1540226
- Alternate Identifier(s):
- OSTI ID: 1463054
- Grant/Contract Number:
- FG05-80ET53088
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 8; Journal ID: ISSN 1070-664X
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Physics
Citation Formats
Furukawa, M., Watanabe, Takahiro, Morrison, P. J., and Ichiguchi, K. Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing. United States: N. p., 2018.
Web. doi:10.1063/1.5038043.
Furukawa, M., Watanabe, Takahiro, Morrison, P. J., & Ichiguchi, K. Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing. United States. https://doi.org/10.1063/1.5038043
Furukawa, M., Watanabe, Takahiro, Morrison, P. J., and Ichiguchi, K. Mon .
"Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing". United States. https://doi.org/10.1063/1.5038043. https://www.osti.gov/servlets/purl/1540226.
@article{osti_1540226,
title = {Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing},
author = {Furukawa, M. and Watanabe, Takahiro and Morrison, P. J. and Ichiguchi, K.},
abstractNote = {A simulated annealing (SA) relaxation method is used for the calculation of high-beta reduced magnetohydrodynamics (MHD) equilibria in toroidal geometry. The SA method, based on artificial dynamics derived from the MHD Hamiltonian structure, is used to calculate equilibria of large-aspect-ratio and circular-cross-section tokamaks as well as toroidally averaged stellarators. Tokamak equilibria including incompressible poloidal rotations are obtained and the Shafranov shift is seen to increase nearly quadratically in the rotation speed. A mapping procedure between non-rotating and poloidally rotating equilibria is shown to explain the quadratic dependence of equilibria shift on rotation. Calculated stellarator equilibria are seen to agree reasonably with previous results. The numerical results demonstrate the first successful application of the SA method to obtain toroidal equilibria.},
doi = {10.1063/1.5038043},
journal = {Physics of Plasmas},
number = 8,
volume = 25,
place = {United States},
year = {Mon Aug 06 00:00:00 EDT 2018},
month = {Mon Aug 06 00:00:00 EDT 2018}
}
Web of Science
Works referenced in this record:
Noncanonical Hamiltonian Density Formulation of Hydrodynamics and Ideal Magnetohydrodynamics
journal, September 1980
- Morrison, Philip J.; Greene, John M.
- Physical Review Letters, Vol. 45, Issue 10
Nonlinear, three-dimensional magnetohydrodynamics of noncircular tokamaks
journal, January 1976
- Strauss, H. R.
- Physics of Fluids, Vol. 19, Issue 1
Hamiltonian–Dirac simulated annealing: Application to the calculation of vortex states
journal, January 2011
- Flierl, G. R.; Morrison, P. J.
- Physica D: Nonlinear Phenomena, Vol. 240, Issue 2
Variational principle for three-dimensional steady-state flows of an ideal fluid
journal, January 1965
- Arnol'd, V. I.
- Journal of Applied Mathematics and Mechanics, Vol. 29, Issue 5
Ideal magnetohydrodynamic equilibria with helical symmetry and incompressible flows
journal, October 1999
- Throumoulopoulos, G. N.; Tasso, H.
- Journal of Plasma Physics, Vol. 62, Issue 4
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
journal, July 1986
- Saad, Youcef; Schultz, Martin H.
- SIAM Journal on Scientific and Statistical Computing, Vol. 7, Issue 3
Dynamics of high β tokamaks
journal, January 1977
- Strauss, H. R.
- Physics of Fluids, Vol. 20, Issue 8
Stationary toroidal equilibria at finite beta
journal, September 1972
- Zehrfeld, H. P.; Green, B. J.
- Nuclear Fusion, Vol. 12, Issue 5
Extremal energy properties and construction of stable solutions of the Euler equations
journal, October 1989
- Vallis, G. K.; Carnevale, G. F.; Young, W. R.
- Journal of Fluid Mechanics, Vol. 207
Pseudo-advective relaxation to stable states of inviscid two-dimensional fluids
journal, April 1990
- Carnevale, G. F.; Vallis, G. K.
- Journal of Fluid Mechanics, Vol. 213, Issue -1
A general method for finding extremal states of Hamiltonian dynamical systems, with applications to perfect fluids
journal, April 1990
- Shepherd, Theodore G.
- Journal of Fluid Mechanics, Vol. 213, Issue -1
Simulated annealing applied to two-dimensional low-beta reduced magnetohydrodynamics
journal, February 2015
- Chikasue, Y.; Furukawa, M.
- Physics of Plasmas, Vol. 22, Issue 2
The effect of plasma flow on the toroidal equilibrium shift
journal, October 1973
- Green, B. J.; Zehrfeld, H. P.
- Nuclear Fusion, Vol. 13, Issue 5
Hamiltonian formulation of reduced magnetohydrodynamics
journal, January 1984
- Morrison, P. J.; Hazeltine, R. D.
- Physics of Fluids, Vol. 27, Issue 4
Simulated annealing for three-dimensional low-beta reduced MHD equilibria in cylindrical geometry
journal, March 2017
- Furukawa, M.; Morrison, P. J.
- Plasma Physics and Controlled Fusion, Vol. 59, Issue 5
On the Stability of Plasma in Static Equilibrium
journal, January 1958
- Kruskal, M. D.; Oberman, C. R.
- Physics of Fluids, Vol. 1, Issue 4
Hamiltonian description of the ideal fluid
journal, April 1998
- Morrison, P. J.
- Reviews of Modern Physics, Vol. 70, Issue 2
Structure and structure-preserving algorithms for plasma physics
journal, April 2017
- Morrison, P. J.
- Physics of Plasmas, Vol. 24, Issue 5
Hamiltonian magnetohydrodynamics: Helically symmetric formulation, Casimir invariants, and equilibrium variational principles
journal, May 2012
- Andreussi, T.; Morrison, P. J.; Pegoraro, F.
- Physics of Plasmas, Vol. 19, Issue 5
Toroidal magnetohydrodynamic equilibrium with toroidal flow
journal, January 1973
- Strauss, H. R.
- Physics of Fluids, Vol. 16, Issue 8
Adjustment of vorticity fields with specified values of Casimir invariants as initial condition for simulated annealing of an incompressible, ideal neutral fluid and its MHD in two dimensions
journal, June 2015
- Chikasue, Y.; Furukawa, M.
- Journal of Fluid Mechanics, Vol. 774
The equilibrium and stability of rotating plasmas
journal, January 1983
- Hameiri, Eliezer
- Physics of Fluids, Vol. 26, Issue 1
Two-fluid equilibrium with flow: FLOW2
journal, September 2015
- Guazzotto, L.; Betti, R.
- Physics of Plasmas, Vol. 22, Issue 9
On the stability of plasma in static equilibrium
journal, September 1958
- Kruskal, M.; Oberman, C.
- Journal of Nuclear Energy (1954), Vol. 7, Issue 3-4
Hamiltonian magnetohydrodynamics: symmetric formulation, Casimir invariants, and equilibrium variational principles
text, January 2012
- Andreussi, Tommaso; Morrison, Philip J.; Pegoraro, Francesco
- arXiv
Simulated annealing for three-dimensional low-beta reduced MHD equilibria in cylindrical geometry
text, January 2016
- Furukawa, M.; Morrison, P. J.
- arXiv