Dewar (Research School of Physics & Eng., Australian National Univ., Canberra)
Title:Variational constructions of almost-invariant tori for 1 1/2-D Hamiltonian systems
Abstract: Action-angle variables are normally defined only for integrable systems, but in order to describe 3D magnetic field systems a generalization of this concept was proposed recently [1,2] that unified the concepts of ghost surfaces and quadratic-flux-minimizing (QFMin) surfaces (two strategies for minimizing action gradient). This was based on a simple canonical transformation generated by a change of variable, $\theta = \theta(\Theta ,\zeta)$, where $\theta$ and $\zeta$ (a time-like variable) are poloidal and toroidal angles, respectively, with $\Theta$ a new poloidal angle chosen to give pseudo-orbits that are (a) straight when plotted in the $\zeta,\Theta$ plane and (b) QFMin pseudo-orbits in the transformed coordinate. These two requirements ensure that the pseudo-orbits are also (c) ghost pseudo-orbits, but they do not uniquely specify the transformation owing to a relabelling symmetry. Variational methods of solution that remove this lack of uniqueness are discussed.
 R.L. Dewar and S.R. Hudson and A.M. Gibson, Commun. Nonlinear Sci. Numer. Simulat. 17, 2062 (2012) http://dx.doi.org/10.1016/j.cnsns.2011.04.022
 R.L. Dewar and S.R. Hudson and A.M. Gibson, Plasma Phys. Control. Fusion 55, 014004 (2013) http://dx.doi.org/10.1088/0741-3335/55/1/014004
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