MHD equilibrium: Difference between revisions

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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).  
Since the field line trajectories are described by Hamiltonian equations, the [[:Wikipedia:Kolmogorov-Arnold-Moser_theorem|KAM theorem]] is relevant; however, it should be noted that the force balance equation does not describe any detail on scales smaller than the gyroradius.
Since the field line trajectories are described by Hamiltonian equations, the [[:Wikipedia:Kolmogorov-Arnold-Moser_theorem|KAM theorem]] is relevant.
 
It should be noted that the force balance equation does not describe any detail on scales smaller than the gyroradius. Therefore, the concept of flux surface is approximate and not exact.
Nevertheless, it is extremely useful for the description and understanding of magnetic confinement.


== Numerical codes ==
== Numerical codes ==

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