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MHD equilibrium: Difference between revisions
→Flux surfaces
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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 | 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 == | ||