Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing

Furukawa, M.; Watanabe, Takahiro; Morrison, P. J.; Ichiguchi, K.

doi:10.1063/1.5038043

Title: Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing

Journal Article · 06 August 2018 · Physics of Plasmas

DOI: https://doi.org/10.1063/1.5038043 · OSTI ID:1540226

^[1]; Watanabe, Takahiro ^[1];

^[2];

^[3]

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)

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.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG05-80ET53088

OSTI ID:: 1540226

Alternate ID(s):: OSTI ID: 1463054

Journal Information:: Physics of Plasmas, Vol. 25, Issue 8; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 3 works

Citation information provided by
Web of Science

References (27)

Noncanonical Hamiltonian Density Formulation of Hydrodynamics and Ideal Magnetohydrodynamics Morrison, Philip J.; Greene, John M. Physical Review Letters, Vol. 45, Issue 10 https://doi.org/10.1103/PhysRevLett.45.790	journal	September 1980
Nonlinear, three-dimensional magnetohydrodynamics of noncircular tokamaks Strauss, H. R. Physics of Fluids, Vol. 19, Issue 1 https://doi.org/10.1063/1.861310	journal	January 1976
Hamiltonian–Dirac simulated annealing: Application to the calculation of vortex states Flierl, G. R.; Morrison, P. J. Physica D: Nonlinear Phenomena, Vol. 240, Issue 2 https://doi.org/10.1016/j.physd.2010.08.011	journal	January 2011
Variational principle for three-dimensional steady-state flows of an ideal fluid Arnol'd, V. I. Journal of Applied Mathematics and Mechanics, Vol. 29, Issue 5 https://doi.org/10.1016/0021-8928(65)90119-X	journal	January 1965
Ideal magnetohydrodynamic equilibria with helical symmetry and incompressible flows Throumoulopoulos, G. N.; Tasso, H. Journal of Plasma Physics, Vol. 62, Issue 4 https://doi.org/10.1017/S0022377899008041	journal	October 1999
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
Dynamics of high β tokamaks Strauss, H. R. Physics of Fluids, Vol. 20, Issue 8 https://doi.org/10.1063/1.862018	journal	January 1977
Stationary toroidal equilibria at finite beta Zehrfeld, H. P.; Green, B. J. Nuclear Fusion, Vol. 12, Issue 5 https://doi.org/10.1088/0029-5515/12/5/005	journal	September 1972
Extremal energy properties and construction of stable solutions of the Euler equations Vallis, G. K.; Carnevale, G. F.; Young, W. R. Journal of Fluid Mechanics, Vol. 207 https://doi.org/10.1017/S0022112089002533	journal	October 1989
Pseudo-advective relaxation to stable states of inviscid two-dimensional fluids Carnevale, G. F.; Vallis, G. K. Journal of Fluid Mechanics, Vol. 213, Issue -1 https://doi.org/10.1017/S0022112090002440	journal	April 1990
A general method for finding extremal states of Hamiltonian dynamical systems, with applications to perfect fluids Shepherd, Theodore G. Journal of Fluid Mechanics, Vol. 213, Issue -1 https://doi.org/10.1017/S0022112090002452	journal	April 1990
Simulated annealing applied to two-dimensional low-beta reduced magnetohydrodynamics Chikasue, Y.; Furukawa, M. Physics of Plasmas, Vol. 22, Issue 2 https://doi.org/10.1063/1.4913234	journal	February 2015
The effect of plasma flow on the toroidal equilibrium shift Green, B. J.; Zehrfeld, H. P. Nuclear Fusion, Vol. 13, Issue 5 https://doi.org/10.1088/0029-5515/13/5/014	journal	October 1973
Hamiltonian formulation of reduced magnetohydrodynamics Morrison, P. J.; Hazeltine, R. D. Physics of Fluids, Vol. 27, Issue 4 https://doi.org/10.1063/1.864718	journal	January 1984
Simulated annealing for three-dimensional low-beta reduced MHD equilibria in cylindrical geometry Furukawa, M.; Morrison, P. J. Plasma Physics and Controlled Fusion, Vol. 59, Issue 5 https://doi.org/10.1088/1361-6587/aa5863	journal	March 2017
Fluids and Plasmas: Geometry and Dynamics Marsden, Jerrold E. Contemporary Mathematics https://doi.org/10.1090/conm/028	book	January 1984
On the Stability of Plasma in Static Equilibrium Kruskal, M. D.; Oberman, C. R. Physics of Fluids, Vol. 1, Issue 4 https://doi.org/10.1063/1.1705885	journal	January 1958
Hamiltonian description of the ideal fluid Morrison, P. J. Reviews of Modern Physics, Vol. 70, Issue 2 https://doi.org/10.1103/RevModPhys.70.467	journal	April 1998
Structure and structure-preserving algorithms for plasma physics Morrison, P. J. Physics of Plasmas, Vol. 24, Issue 5 https://doi.org/10.1063/1.4982054	journal	April 2017
Hamiltonian magnetohydrodynamics: Helically symmetric formulation, Casimir invariants, and equilibrium variational principles Andreussi, T.; Morrison, P. J.; Pegoraro, F. Physics of Plasmas, Vol. 19, Issue 5 https://doi.org/10.1063/1.4714761	journal	May 2012
Toroidal magnetohydrodynamic equilibrium with toroidal flow Strauss, H. R. Physics of Fluids, Vol. 16, Issue 8 https://doi.org/10.1063/1.1694526	journal	January 1973
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 Chikasue, Y.; Furukawa, M. Journal of Fluid Mechanics, Vol. 774 https://doi.org/10.1017/jfm.2015.263	journal	June 2015
The equilibrium and stability of rotating plasmas Hameiri, Eliezer Physics of Fluids, Vol. 26, Issue 1 https://doi.org/10.1063/1.864012	journal	January 1983
Two-fluid equilibrium with flow: FLOW2 Guazzotto, L.; Betti, R. Physics of Plasmas, Vol. 22, Issue 9 https://doi.org/10.1063/1.4929854	journal	September 2015
On the stability of plasma in static equilibrium Kruskal, M.; Oberman, C. Journal of Nuclear Energy (1954), Vol. 7, Issue 3-4 https://doi.org/10.1016/0891-3919(58)90119-0	journal	September 1958
Hamiltonian magnetohydrodynamics: symmetric formulation, Casimir invariants, and equilibrium variational principles Andreussi, Tommaso; Morrison, Philip J.; Pegoraro, Francesco arXiv https://doi.org/10.48550/arxiv.1202.0468	text	January 2012
Simulated annealing for three-dimensional low-beta reduced MHD equilibria in cylindrical geometry Furukawa, M.; Morrison, P. J. arXiv https://doi.org/10.48550/arxiv.1609.01023	text	January 2016

Similar Records

Aspect ratio scaling of toroidal plasma equilibria and the tokamak bootstrap effect

Journal Article · 1997 · Physics of Plasmas · OSTI ID:560611

Weening, R H

Calculation of continuum damping of Alfvén eigenmodes in tokamak and stellarator equilibria

Journal Article · 2015 · Physics of Plasmas · OSTI ID:22490136

Bowden, G. W.; Hole, M. J.; Könies, A.

Toroidal and poloidal flows in single-fluid and two-fluid tokamak equilibria

Journal Article · 2006 · Physics of Plasmas · OSTI ID:20787362

Thyagaraja, A; McClements, K G

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Physics

Title: Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing

Citation Formats

References (27)

Similar Records

Related Subjects