skip to main content


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

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.
ORCiD logo [1] ; ORCiD logo [2] ; ORCiD logo [3] ;  [4]
  1. Australian National Univ., Canberra, ACT (Australia)
  2. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
  3. Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
  4. Univ. of Tokyo (Japan)
Publication Date:
Report Number(s):
Journal ID: ISSN 1070-664X; Australian Research Council Grant No. DP11010288; JSPS Grant No. KAKENHI 23224014.
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 24; Journal Issue: 4; Journal ID: ISSN 1070-664X
American Institute of Physics (AIP)
Research Org:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
Contributing Orgs:
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.
Country of Publication:
United States
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; hydromagnetic stability; magnetic reconnection; Taylor relaxation; vacuum systems; equilibria; pressure; discharge; principle; helicity
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1361799