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MHD equilibrium: Difference between revisions
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Assuming an initial situation with nested magnetic surfaces, the [[Rotational transform|rotational transform]] of the field line on the surface may either be irrational so that the field line covers the surface entirely (ergodically), or rational. | Assuming an initial situation with nested magnetic surfaces, the [[Rotational transform|rotational transform]] of the field line on the surface may either be irrational so that the field line covers the surface entirely (ergodically), or rational. | ||
In the latter case, the field line does not cover a surface but constitutes a one-dimensional structure. | In the latter case, the field line does not cover a surface but constitutes a one-dimensional structure. | ||
Physically, a rational surface is sensitive to small perturbations and flute-like instabilities may develop that lead to the formation of ''magnetic islands'' and ''stochastic regions'' (assuming non-zero resistivity). | Physically, a rational surface is sensitive to small perturbations and flute-like instabilities may develop that lead to the formation of ''[[Magnetic island|magnetic islands]]'' and ''stochastic regions'' (assuming non-zero resistivity). | ||
Since the field line trajectories are described by Hamiltonian equations, the [[:Wikipedia:Kolmogorov-Arnold-Moser_theorem|KAM theorem]] is relevant. | Since the field line trajectories are described by Hamiltonian equations, the [[:Wikipedia:Kolmogorov-Arnold-Moser_theorem|KAM theorem]] is relevant. | ||