April 15-17

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Author: Arunav Kumar
Requested Type: Poster
Submitted: 2019-02-24 22:57:00

Co-authors: Matthew.J.Hole, Robert L. Dewar, Stuart R. Hudson, Zhisong Qu, Markus Hegland

Contact Info:
the Australian National University
the Australian National Univer
Canberra, Acton   2601
Australia

Abstract Text:
A dynamical formulation of magnetohydrodynamics (MHD), Multi-Region Relaxed MHD (MRxMHD)[1], based on Hamilton’s principle of stationary action which applied to the MHD Lagrangian but using only a small subset of constraints build into ideal MHD has been recently developed. Unlike commonly used ideal-MHD[2] based methods, magnetic islands and chaotic fields may form whenever the physics dictates such that Beltrami fields (force-free fields) arise from the Taylor global relaxation variational principle, which postulates the minimization of total magnetic energy subject to constraints of conservation of global magnetic flux and global magnetic helicity. A numerical based equilibrium code SPEC[3],has been written to solve for MRxMHD fields by taking the partition as current sheets to be a discrete set of nested topological tori.

Moreover, as SPEC constructs Beltrami fields by Newton search based method for locating minimum constrained energy functional, the transition from primitive axisymmetric state to helical state dictates.So, as to implement helicity constraint in hessian (second variation of energy functional) throughout SPEC,one need to look for changes in parameter μ** within each relaxed region and then add the contribution to Hessian. Instabilities occurs when the hessian matrix has one or more negative eigenvalue(s).
With well-posed Taylor Relaxation Theory[4],resulting minimum constrained energy functional will be compared and process to include global helicity will discussed.

Time permitting, other constraints such as a fixed rotational transform (similar to ideal MHD) will also be discussed.
** an independent degree of freedom
[1] M.J.Hole,S.R.Hudson,and R.L.Dewar,Nucl.Fusion 47,746(2007)
[2] R.J.Hosking and R.L.Dewar,https://dx.doi.org/10.1007/978-981-287-600-3
[3] S.R.Hudson,R.L.Dewar,G.Dennis,M.J.Hole,M.McGann,G.von Nessi and S.Lazerson,Phys.Plasma 19,112502,2012
[4] J.B Taylor,Rev.Mod.Phys.58,741-763,1986

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