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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 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 flute-like instabilities may develop that lead to the formation of ''magnetic islands'' and ''stochastic regions'' (assuming non-zero resistivity). In this respect, the [[:Wikipedia:Kolmogorov-Arnold-Moser_theorem|KAM theorem]] for Hamiltonian systems is relevant; however, it should be noted that the force balance equation does not describe any detail on scales smaller than the gyroradius. | ||
A large number of codes is available to evaluate MHD equilibria. | A large number of codes is available to evaluate MHD equilibria. | ||