Relaxed MHD model for island formation by forced reconnection in a rippled-boundary plasma slab

Ideal MHD motions are strongly constrained by an infinite number of microscopic constraints or \textit{Casimir invariants}. To generalize Taylor relaxation theory [1] we retain a subset of these constraints on isolated surfaces (current sheets or \textit{singular Casimirs} [2]) that prevent total relaxation. We call this approach \textit{Relaxed MHD }(RXMHD), and when the current sheet surfaces partition the plasma into disjoint regions we call this \textit{MultiRegion Relaxed MHD} (MRXMHD). E.g. in the SPEC 3-D equilibrium code [3] these current sheets are taken to be tori. Another application is to the shielding current sheets formed in resonant forced reconnection, which are most simply examined in the Hahm--Kulsrud--Taylor [4] model. Recently [5] a sequence of analytic ``plasmoid'' equilibria continuously connecting the two solutions found in [4] have been found. By imposing conservation of toroidal flux and helicity on these new solutions we construct a sequence of intermediate states arising as gaps open up in the initially continuous shielding current sheet on the $y$-axis and an island forms. [1] J. B. Taylor \textit{Rev. Mod. Phys.} \textbf{58} 741 (1986) [2] Z. Yoshida {\&} R.~L. Dewar\textit{ J. Phys. A: Math. Gen. }\textbf{45 }365502 (2012) [3] S. R. Hudson, R. L. Dewar, G. Dennis, M. J. Hole, M. McGann, G. von Nessi, {\&} S. Lazerson \textit{Phys. Plasmas} \textbf{19} 112502 (2012) [4] T. S. Hahm {\&} R. M. Kulsrud \textit{Phys. Fluids} \textbf{28} 2412 (1985) [5] R.~L. Dewar, A. Bhattacharjee, R.~M. Kulsrud {\&} A.~M. Wright, \underline {arxiv:1304.6273} (accepted Phys. Plasmas 2013)