Multi-region relaxed magnetohydrodynamics in plasmas with slowly changing boundaries -- Resonant response of a plasma slab

Dewar, R. L.; Hudson, S. R.; Bhattacharjee, A.; Yoshida, Z.

doi:10.1063/1.4979350

Title: Multi-region relaxed magnetohydrodynamics in plasmas with slowly changing boundaries -- Resonant response of a plasma slab

Journal Article · Mon Apr 03 00:00:00 EDT 2017 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4979350· OSTI ID:1358665

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^[2];

^[3]; Yoshida, Z. ^[4]

Australian National Univ., Canberra, ACT (Australia)
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Univ. of Tokyo (Japan)

The adiabatic limit of a recently proposed dynamical extension of Taylor relaxation, multi-region relaxed magnetohydrodynamics (MRxMHD), is summarized, with special attention to the appropriate definition of a relative magnetic helicity. The formalism is illustrated using a simple two-region, sheared-magnetic-field model similar to the Hahm-Kulsrud-Taylor (HKT) rippled-boundary slab model. In MRxMHD, a linear Grad-Shafranov equation applies, even at finite ripple amplitude. The adiabatic switching on of boundary ripple excites a shielding current sheet opposing reconnection at a resonant surface. The perturbed magnetic field as a function of ripple amplitude is calculated by invoking the conservation of magnetic helicity in the two regions separated by the current sheet. Here, at low ripple amplitude, "half islands" appear on each side of the current sheet, locking the rotational transform at the resonant value. Beyond a critical amplitude, these islands disappear and the rotational transform develops a discontinuity across the current sheet. Published by AIP Publishing.

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Research Organization:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES)

Contributing Organization:: Centre for Plasmas and Fluids, Research School of Physics and Engineering, The Australian National University, Canberra, ACT 2601, Australia; Graduate School of Frontier Sciences, University of Tokyo, Kashiwa, Chiba 277-8561, Japan; R.L.D. some travel support from Australian Research Council Grant No. DP11010288. The work of S.R.H. and A.B. was supported under U.S. DOE Grant No. DE-AC02-09CH11466 and that of Z.Y. was supported under JSPS Grant No. KAKENHI 23224014.

Grant/Contract Number:: AC02-09CH11466

OSTI ID:: 1358665

Alternate ID(s):: OSTI ID: 1361799

Report Number(s):: PPPL-5373; Australian Research Council Grant No. DP11010288; JSPS Grant No. KAKENHI 23224014.

Journal Information:: Physics of Plasmas, Vol. 24, Issue 4; ISSN 1070-664X

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

Country of Publication:: United States

Language:: English

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Cited by: 5 works

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References (50)

Current drive and helicity injection Jensen, T. H.; Chu, M. S. Physics of Fluids, Vol. 27, Issue 12 https://doi.org/10.1063/1.864602	journal	January 1984
An energy principle for hydromagnetic stability problems Bernstein, I. B.; Frieman, E. A.; Kruskal, Martin David Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 244, Issue 1236, p. 17-40 https://doi.org/10.1098/rspa.1958.0023	journal	February 1958
The topological properties of magnetic helicity Berger, Mitchell A.; Field, George B. Journal of Fluid Mechanics, Vol. 147, Issue -1 https://doi.org/10.1017/S0022112084002019	journal	October 1984
Verification of the ideal magnetohydrodynamic response at rational surfaces in the VMEC code Lazerson, Samuel A.; Loizu, Joaquim; Hirshman, Steven Physics of Plasmas, Vol. 23, Issue 1 https://doi.org/10.1063/1.4939881	journal	January 2016
Relaxed plasma-vacuum systems with pressure Spies, G. O. Physics of Plasmas, Vol. 10, Issue 7 https://doi.org/10.1063/1.1584047	journal	July 2003
Current density and plasma displacement near perturbed rational surfaces Boozer, Allen H.; Pomphrey, Neil Physics of Plasmas, Vol. 17, Issue 11 https://doi.org/10.1063/1.3507307	journal	November 2010
Preconditioned descent algorithm for rapid calculations of magnetohydrodynamic equilibria Hirshman, S. P.; Betancourt, O. Journal of Computational Physics, Vol. 96, Issue 1 https://doi.org/10.1016/0021-9991(91)90267-O	journal	September 1991
Relaxation and magnetic reconnection in plasmas Taylor, J. B. Reviews of Modern Physics, Vol. 58, Issue 3 https://doi.org/10.1103/RevModPhys.58.741	journal	July 1986
Representation of ideal magnetohydrodynamic modes White, R. B. Physics of Plasmas, Vol. 20, Issue 2 https://doi.org/10.1063/1.4791661	journal	February 2013
Rapid Change of Field line Connectivity and Reconnection in Stochastic Magnetic Fields Huang, Yi-Min; Bhattacharjee, A.; Boozer, Allen H. The Astrophysical Journal, Vol. 793, Issue 2 https://doi.org/10.1088/0004-637X/793/2/106	journal	September 2014
The relationship between the 'tangled discharge' and 'dynamo' models of the magnetic relaxation process Rusbridge, M. G. Plasma Physics and Controlled Fusion, Vol. 33, Issue 12 https://doi.org/10.1088/0741-3335/33/12/004	journal	October 1991
Hamilton–Jacobi theory for continuation of magnetic field across a toroidal surface supporting a plasma pressure discontinuity McGann, M.; Hudson, S. R.; Dewar, R. L. Physics Letters A, Vol. 374, Issue 33 https://doi.org/10.1016/j.physleta.2010.06.014	journal	July 2010
Exact axisymmetric Taylor states for shaped plasmas Cerfon, Antoine J.; O'Neil, Michael Physics of Plasmas, Vol. 21, Issue 6 https://doi.org/10.1063/1.4881466	journal	June 2014
Stepped pressure profile equilibria in cylindrical plasmas via partial Taylor relaxation Hole, M. J.; Hudson, S. R.; Dewar, R. L. Journal of Plasma Physics, Vol. 72, Issue 06 https://doi.org/10.1017/S0022377806005861	journal	December 2006
Magnetic islands and singular currents at rational surfaces in three-dimensional magnetohydrodynamic equilibria Loizu, J.; Hudson, S.; Bhattacharjee, A. Physics of Plasmas, Vol. 22, Issue 2 https://doi.org/10.1063/1.4906888	journal	February 2015
Interaction between Hydromagnetic Waves and a Time-Dependent, Inhomogeneous Medium Dewar, R. L. Physics of Fluids, Vol. 13, Issue 11 https://doi.org/10.1063/1.1692854	journal	January 1970
Relativistic helicity and link in Minkowski space-time Yoshida, Z.; Kawazura, Y.; Yokoyama, T. Journal of Mathematical Physics, Vol. 55, Issue 4 https://doi.org/10.1063/1.4872236	journal	April 2014
Tokamak plasma high field side response to an n = 3 magnetic perturbation: a comparison of 3D equilibrium solutions from seven different codes Reiman, A.; Ferraro, N. M.; Turnbull, A. Nuclear Fusion, Vol. 55, Issue 6 https://doi.org/10.1088/0029-5515/55/6/063026	journal	May 2015
Forced magnetic reconnection Hahm, T. S.; Kulsrud, R. M. Physics of Fluids, Vol. 28, Issue 8 https://doi.org/10.1063/1.865247	journal	January 1985
Existence and calculation of sharp boundary magnetohydrodynamic equilibrium in three-dimensional toroidal geometry Berk, H. L.; Freidberg, J. P.; Llobet, X. Physics of Fluids, Vol. 29, Issue 10 https://doi.org/10.1063/1.865845	journal	January 1986
Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics Dewar, R. L.; Yoshida, Z.; Bhattacharjee, A. Journal of Plasma Physics, Vol. 81, Issue 6 https://doi.org/10.1017/S0022377815001336	journal	November 2015
Plasmoid solutions of the Hahm–Kulsrud–Taylor equilibrium model Dewar, R. L.; Bhattacharjee, A.; Kulsrud, R. M. Physics of Plasmas, Vol. 20, Issue 8 https://doi.org/10.1063/1.4817276	journal	August 2013
Taylor relaxation in a torus of arbitrary aspect ratio and cross section Reiman, Allan Physics of Fluids, Vol. 24, Issue 5 https://doi.org/10.1063/1.863468	journal	January 1981
Minimum energy state of a toroidal discharge Reiman, Allan Physics of Fluids, Vol. 23, Issue 1 https://doi.org/10.1063/1.862857	journal	January 1980
Hydromagnetic stability of a diffuse linear pinch Newcomb, William A. Annals of Physics, Vol. 10, Issue 2 https://doi.org/10.1016/0003-4916(60)90023-3	journal	June 1960
Computation of multi-region relaxed magnetohydrodynamic equilibria Hudson, S. R.; Dewar, R. L.; Dennis, G. Physics of Plasmas, Vol. 19, Issue 11 https://doi.org/10.1063/1.4765691	journal	November 2012
Helical bifurcation and tearing mode in a plasma—a description based on Casimir foliation Yoshida, Z.; Dewar, R. L. Journal of Physics A: Mathematical and Theoretical, Vol. 45, Issue 36 https://doi.org/10.1088/1751-8113/45/36/365502	journal	August 2012
Motion of magnetic lines of force Newcomb, William A. Annals of Physics, Vol. 3, Issue 4 https://doi.org/10.1016/0003-4916(58)90024-1	journal	April 1958
Edge stability and transport control with resonant magnetic perturbations in collisionless tokamak plasmas Evans, Todd E.; Moyer, Richard A.; Burrell, Keith H. Nature Physics, Vol. 2, Issue 6 https://doi.org/10.1038/nphys312	journal	May 2006
Woltjer-Taylor State without Taylor’s Conjecture: Plasma Relaxation at all Wavelengths Qin, Hong; Liu, Wandong; Li, Hong Physical Review Letters, Vol. 109, Issue 23 https://doi.org/10.1103/PhysRevLett.109.235001	journal	December 2012
Formation of current singularity in a topologically constrained plasma Zhou, Yao; Huang, Yi-Min; Qin, Hong Physical Review E, Vol. 93, Issue 2 https://doi.org/10.1103/PhysRevE.93.023205	journal	February 2016
Saturation of the tearing mode White, Roscoe B.; Monticello, D. A.; Rosenbluth, Marshall N. Physics of Fluids, Vol. 20, Issue 5 https://doi.org/10.1063/1.861939	journal	January 1977
Pressure-driven amplification and penetration of resonant magnetic perturbations Loizu, J.; Hudson, S. R.; Helander, P. Physics of Plasmas, Vol. 23, Issue 5 https://doi.org/10.1063/1.4944818	journal	May 2016
Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets Loizu, J.; Hudson, S. R.; Bhattacharjee, A. Physics of Plasmas, Vol. 22, Issue 9 https://doi.org/10.1063/1.4931094	journal	September 2015
2-D, nonlinear spectral simulation of reconnective transitions on a periodic, planar current sheet with (1) smooth and (2) corrugated conducting wall boundary conditions with flow Parker, R. D.; Dewar, R. L. Computer Physics Communications, Vol. 59, Issue 1 https://doi.org/10.1016/0010-4655(90)90151-P	journal	May 1990
Toroidal Containment of a Plasma Grad, Harold Physics of Fluids, Vol. 10, Issue 1 https://doi.org/10.1063/1.1761965	journal	January 1967
Equilibria and stability in partially relaxed plasma–vacuum systems Hole, M. J.; Hudson, S. R.; Dewar, R. L. Nuclear Fusion, Vol. 47, Issue 8 https://doi.org/10.1088/0029-5515/47/8/004	journal	July 2007
Magnetohydrodynamic stability of plasmas with ideal and relaxed regions Mills, R. L.; Hole, M. J.; Dewar, R. L. Journal of Plasma Physics, Vol. 75, Issue 5 https://doi.org/10.1017/S0022377809008095	journal	October 2009
The spectrum of multi-region-relaxed magnetohydrodynamic modes in topologically toroidal geometry Dewar, R. L.; Tuen, L. H.; Hole, M. J. Plasma Physics and Controlled Fusion, Vol. 59, Issue 4 https://doi.org/10.1088/1361-6587/aa5b53	journal	February 2017
Hamilton's principle for a hydromagnetic fluid with a free boundary Dewar, R. L. Nuclear Fusion, Vol. 18, Issue 11 https://doi.org/10.1088/0029-5515/18/11/007	journal	November 1978
Relaxation of Toroidal Plasma and Generation of Reverse Magnetic Fields Taylor, J. B. Physical Review Letters, Vol. 33, Issue 19 https://doi.org/10.1103/PhysRevLett.33.1139	journal	November 1974
Preconditioned descent algorithm for rapid calculations of magnetohydrodynamic equilibria Hirshman, S. P.; Betancourt, O. Journal of Computational Physics, Vol. 91, Issue 1 https://doi.org/10.1016/0021-9991(90)90017-u	journal	November 1990
Hamilton's principle for a hydromagnetic fluid with a free boundary Dewar, R. L. https://doi.org/10.2172/5056964	report	March 1978
Forced Magnetic Reconnection Kulsrud, R. M.; Hahm, T. S. Physica Scripta, Vol. T2B https://doi.org/10.1088/0031-8949/1982/t2b/034	journal	January 1982
Magnetohydrodynamic Stability of Plasmas with Ideal and Relaxed Regions Mills, R. L.; Hole, M. J.; Dewar, R. L. arXiv https://doi.org/10.48550/arxiv.0902.2612	text	January 2009
Computation of multi-region relaxed magnetohydrodynamic equilibria Hudson, S. R.; Dewar, R. L.; Dennis, G. arXiv https://doi.org/10.48550/arxiv.1211.3072	text	January 2012
Relativistic helicity and link in Minkowski space-time Yoshida, Z.; Kawazura, Y.; Yokoyama, T. arXiv https://doi.org/10.48550/arxiv.1308.2455	text	January 2013
Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics Dewar, Robert L.; Yoshida, Zensho; Bhattacharjee, Amitava arXiv https://doi.org/10.48550/arxiv.1509.00240	text	January 2015
Formation of current singularity in a topologically constrained plasma Zhou, Yao; Huang, Yi-Min; Qin, Hong arXiv https://doi.org/10.48550/arxiv.1509.08163	text	January 2015
Spectrum of multi-region-relaxed magnetohydrodynamic modes in topologically toroidal geometry Dewar, Robert L.; Tuen, Li Huey; Hole, Matthew J. arXiv https://doi.org/10.48550/arxiv.1608.04939	text	January 2016

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