4,427
edits
MHD equilibrium: Difference between revisions
no edit summary
No edit summary |
No edit summary |
||
| Line 12: | Line 12: | ||
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> | ||
An important concept in this context is the ''flux surface'', which is a surface such that ''B'' is everywhere perpendicular to its normal. | |||
The force balance equation implies that ''p'' is constant along any field line (since grad(''p'') is perpendicular to ''B''); it also implies that the surface ''p'' = constant is a flux surface (assuming flux surfaces exist). | |||
In two dimensions (assuming axisymmetry), the force balance equation reduces to the | In two dimensions (assuming axisymmetry), the force balance equation reduces to the | ||
| Line 18: | Line 21: | ||
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) may break up to form ''magnetic islands'' and ''stochastic regions''. | |||
A large number of codes is available to evaluate MHD equilibria. | A large number of codes is available to evaluate MHD equilibria. | ||