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MHD equilibrium: Difference between revisions
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In three dimensions, the existence of flux surfaces (nested or not) is not guaranteed. | In three dimensions, the existence of flux surfaces (nested or not) is not guaranteed. | ||
<ref>[http://dx.doi.org/10.1063/1.1761965 H. Grad, ''Toroidal Containment of a Plasma'', Phys. Fluids '''10''' (1967) 137]</ref> | <ref>[http://dx.doi.org/10.1063/1.1761965 H. Grad, ''Toroidal Containment of a Plasma'', Phys. Fluids '''10''' (1967) 137]</ref> | ||
Assuming an initial situation with nested magnetic surfaces, the [[Magnetic shear|rotational transform]] of the field line on the surface may either be irrational and cover the surface entirely, or rational. In the latter case, the surface is sensitive to small perturbations and (assuming non-zero resistivity) may break up to form ''magnetic islands'' and ''stochastic regions''. | Assuming an initial situation with nested magnetic surfaces, the [[Magnetic shear|rotational transform]] of the field line on the surface may either be irrational and cover the surface entirely, or rational. In the latter case, the surface is sensitive to small perturbations and (assuming non-zero resistivity) may break up to form ''magnetic islands'' and ''stochastic regions''. In this respect, the [[:Wikipedia:Kolmogorov-Arnold-Moser_theorem]] for Hamiltonian systems is relevant. | ||
A large number of codes is available to evaluate MHD equilibria. | A large number of codes is available to evaluate MHD equilibria. | ||