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MHD equilibrium: Difference between revisions
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The force balance equation also implies that the surface ''p'' = constant is a flux surface (assuming flux surfaces exist). | The force balance equation also implies that the surface ''p'' = constant is a flux surface (assuming flux surfaces exist). | ||
In three dimensions, the existence of flux surfaces (nested or not) is not guaranteed. | In three dimensions (as opposed to the ''effectively'' two-dimensional axisymmetric situation), 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 so that the field line covers the surface entirely (ergodically), or rational. | Assuming an initial situation with nested magnetic surfaces, the [[Magnetic shear|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. | ||