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Variational constructions of almost-invariant tori for 1 ½-D Hamiltonian systems Ìý

Bob Dewar

Plasma Research Laboratory,ÌýAustralian National University, Canberra, Australia

Date and time:Ìý

Thursday, November 7, 2013 - 2:00pm

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ECCR 257

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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, θ = θ(Θ,ζ), where θ and ζ (a time-like variable) are poloidal and toroidal angles, respectively, with Θ a new poloidal angle chosen to give pseudo-orbits that are (a) straight when plotted in the ζ-Θ 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)
[2] R.L. Dewar and S.R. Hudson and A.M. Gibson, Plasma Phys. Control. Fusion 55 014004 (2013)
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