Are ghost surfaces quadratic-flux-minimizing?

Details Are ghost surfaces quadratic-flux-minimizing? Are ghost surfaces quadratic-flux-minimizing?

2009-09-11

arxiv.org/abs/0909.2096v2

Phys. Letts. A 373, 4409--4415 (2009)

Physics

Plasma Physics

8 pages, 3 figures. Revised version includes post-publication corrections in text, as described in Appendix C Erratum

Scientific paper

10.1016/j.physleta.2009.10.005

Two candidates for "almost-invariant" toroidal surfaces passing through magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost surfaces, use families of periodic pseudo-orbits (i.e. paths for which the action is not exactly extremal). QFMin pseudo-orbits, which are coordinate-dependent, are field lines obtained from a modified magnetic field, and ghost-surface pseudo-orbits are obtained by displacing closed field lines in the direction of steepest descent of magnetic action, $\oint \vec{A}\cdot\mathbf{dl}$. A generalized Hamiltonian definition of ghost surfaces is given and specialized to the usual Lagrangian definition. A modified Hamilton's Principle is introduced that allows the use of Lagrangian integration for calculation of the QFMin pseudo-orbits. Numerical calculations show QFMin and Lagrangian ghost surfaces give very similar results for a chaotic magnetic field perturbed from an integrable case, and this is explained using a perturbative construction of an auxiliary poloidal angle for which QFMin and Lagrangian ghost surfaces are the same up to second order. While presented in the context of 3-dimensional magnetic field line systems, the concepts are applicable to defining almost-invariant tori in other $1{1/2}$ degree-of-freedom nonintegrable Lagrangian/Hamiltonian systems.

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