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• W2004113863 endingPage "365502" @default.
• W2004113863 startingPage "365502" @default.
• W2004113863 abstract "The relation between the helical bifurcation of a Taylor relaxed state (a Beltrami equilibrium) and a tearing mode is analyzed in a Hamiltonian framework. Invoking an Eulerian representation of the Hamiltonian, the symplectic operator (defining a Poisson bracket) becomes non-canonical, i.e. the symplectic operator has a nontrivial cokernel (dual to its nullspace), foliating the phase space into level sets of Casimir invariants. A Taylor relaxed state is an equilibrium point on a Casimir (helicity) leaf. Changing the helicity, equilibrium points may bifurcate to produce helical relaxed states; a necessary and sufficient condition for bifurcation is derived. Tearing yields a helical perturbation on an unstable equilibrium, producing a helical structure approximately similar to a helical relaxed state. A slight discrepancy found between the helically bifurcated relaxed state and the linear tearing mode viewed as a perturbed, singular equilibrium state is attributed to a Casimir element (named ?helical flux?) pertinent to a ?resonance singularity? of the non-canonical symplectic operator. While the helical bifurcation can occur at discrete eigenvalues of the Beltrami parameter, the tearing mode, being a singular eigenfunction, exists for an arbitrary Beltrami parameter. Bifurcated Beltrami equilibria appearing on the same helicity leaf are isolated by the helical-flux Casimir foliation. The obstacle preventing the tearing mode to develop in the ideal limit turns out to be the shielding current sheet on the resonant surface, preventing the release of the ?potential energy?. When this current is dissipated by resistivity, reconnection is allowed and tearing instability occurs. The ?? criterion for linear tearing instability of Beltrami equilibria is shown to be directly related to the spectrum of the curl operator." @default.
• W2004113863 created "2016-06-24" @default.
• W2004113863 creator A5018585307 @default.
• W2004113863 creator A5022332391 @default.
• W2004113863 date "2012-08-22" @default.
• W2004113863 modified "2023-09-26" @default.
• W2004113863 title "Helical bifurcation and tearing mode in a plasma—a description based on Casimir foliation" @default.
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• W2004113863 doi "https://doi.org/10.1088/1751-8113/45/36/365502" @default.
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