Variational constructions of almost-invariant tori for 1 1/2-D Hamiltonian systems

Professor Robert 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.
[1] 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
[2] 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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