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MHD equilibrium: Difference between revisions
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The static, single-fluid, ideal Magneto- | The static, single-fluid, [[Ideal Magneto-Hydrodynamics|ideal Magneto-Hydrodynamic]] (MHD) equilibrium of a near-Maxwellian magnetically confined plasma is obtained by solving the force balance equation | ||
<ref>J.P. Freidberg, ''Plasma physics and fusion energy'', Cambridge University Press (2007) ISBN 0521851076</ref> | <ref>J.P. Freidberg, ''Plasma physics and fusion energy'', Cambridge University Press (2007) {{ISBN|0521851076}}</ref> | ||
:<math>\vec \nabla p = \vec j \times \vec B</math> | :<math>\vec \nabla p = \vec j \times \vec B</math> | ||
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Here, the pressure ''p'' is assumed to be isotropic, but a generalization | Here, the pressure ''p'' is assumed to be isotropic, but a generalization | ||
for non-isotropic pressure is possible. | for non-isotropic pressure is possible. | ||
<ref>R.D. Hazeltine, J.D. Meiss, ''Plasma Confinement'', Courier Dover Publications (2003) ISBN 0486432424</ref> | <ref>R.D. Hazeltine, J.D. Meiss, ''Plasma Confinement'', Courier Dover Publications (2003) {{ISBN|0486432424}}</ref> | ||
== Flux surfaces == | == Flux surfaces == | ||
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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 [[ | 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. | ||