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 (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 [[axisymmetry|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 [[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.  
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.  
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== Numerical codes ==
== Numerical codes ==


In two dimensions (assuming [[Toroidal coordinates|axisymmetry]]), the force balance equation reduces to the  
In two dimensions (assuming [[axisymmetry]]), the force balance equation reduces to the  
[[:Wikipedia:Grad-Shafranov equation|Grad-Shafranov equation]].
[[:Wikipedia:Grad-Shafranov equation|Grad-Shafranov equation]].
A large number of codes is available to evaluate MHD equilibria.
A large number of codes is available to evaluate MHD equilibria.