**SMS scnews item created by Eduardo Altmann at Fri 7 Apr 2017 1701**

Type: Seminar

Distribution: World

Expiry: 5 May 2017

**Calendar1: 26 Apr 2017 1400-1500**

**CalLoc1: AGR Carslaw 829**

CalTitle1: Variational constructions of almost-invariant tori for 1 1/2-D Hamiltonian systems

Auth: ega@como.maths.usyd.edu.au

### Applied Maths Seminar

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

### Dewar

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

Seminars are held at 2:00 pm on Wednesdays in the Access Grid Room ( Carslaw Building, 8th floor), unless
otherwise noted.

See
http://www.maths.usyd.edu.au/u/SemConf/Applied.html