1,089 research outputs found
The surprising attractiveness of tearing mode locking in tokamaks
Tearing modes in tokamaks typically rotate while small and then lock at a
fixed location when larger. Research on present-day devices has focused almost
exclusively on stabilisation of rotating modes, as it has been considered
imperative to avoid locked modes. However, in larger devices, such as those
contemplated for tokamak reactors, the locking occurs at a smaller island size,
and the island can be safely stabilised after locking. The stabilisation of
small locked modes can be performed at lower wave power and broader deposition
compared to rotating islands. On large devices, it thus becomes surprisingly
advantageous to allow the mode to grow and lock naturally before stabilising
it. Calculations indicate that the ITER international megaproject would be best
stabilised through this approach.Comment: 6 pages, 4 figure
Strong "quantum" chaos in the global ballooning mode spectrum of three-dimensional plasmas
The spectrum of ideal magnetohydrodynamic (MHD) pressure-driven (ballooning)
modes in strongly nonaxisymmetric toroidal systems is difficult to analyze
numerically owing to the singular nature of ideal MHD caused by lack of an
inherent scale length. In this paper, ideal MHD is regularized by using a
-space cutoff, making the ray tracing for the WKB ballooning formalism a
chaotic Hamiltonian billiard problem. The minimum width of the toroidal Fourier
spectrum needed for resolving toroidally localized ballooning modes with a
global eigenvalue code is estimated from the Weyl formula. This
phase-space-volume estimation method is applied to two stellarator cases.Comment: 4 pages typeset, including 2 figures. Paper accepted for publication
in Phys. Rev. Letter
Darboux Coordinates and Liouville-Arnold Integration in Loop Algebras
Darboux coordinates are constructed on rational coadjoint orbits of the
positive frequency part \wt{\frak{g}}^+ of loop algebras. These are given by
the values of the spectral parameters at the divisors corresponding to
eigenvector line bundles over the associated spectral curves, defined within a
given matrix representation. A Liouville generating function is obtained in
completely separated form and shown, through the Liouville-Arnold integration
method, to lead to the Abel map linearization of all Hamiltonian flows induced
by the spectral invariants. Serre duality is used to define a natural
symplectic structure on the space of line bundles of suitable degree over a
permissible class of spectral curves, and this is shown to be equivalent to the
Kostant-Kirillov symplectic structure on rational coadjoint orbits. The general
construction is given for or , with
reductions to orbits of subalgebras determined as invariant fixed point sets
under involutive automorphisms. The case is shown to reproduce
the classical integration methods for finite dimensional systems defined on
quadrics, as well as the quasi-periodic solutions of the cubically nonlinear
Schr\"odinger equation. For , the method is applied to the
computation of quasi-periodic solutions of the two component coupled nonlinear
Schr\"odinger equation.Comment: 61 pg
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