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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) flute-like instabilities may develop that lead to the formation of ''magnetic islands'' and ''stochastic regions''. In this respect, the [[:Wikipedia:Kolmogorov-Arnold-Moser_theorem|KAM theorem]] for Hamiltonian systems is relevant. | 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) flute-like instabilities may develop that lead to the formation of ''magnetic islands'' and ''stochastic regions''. 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. | ||