MHD equilibrium: Difference between revisions

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In three dimensions (as opposed to the ''effectively'' two-dimensional axisymmetric situation), 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 [[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 islands'' and ''stochastic regions'' (assuming non-zero resistivity).  

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