4,427
edits
MHD equilibrium: Difference between revisions
→Flux surfaces
| Line 27: | Line 27: | ||
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. In combination with the existence of stochastic field regions this means that the concept of flux surface can only be approximate and not exact. | It should be noted that the force balance equation does not describe any detail on scales smaller than the [[Larmor radius|gyroradius]]. In combination with the existence of stochastic field regions this means that the concept of flux surface can only be approximate and not exact. | ||
Furthermore, the force balance equation depends on a number of assumptions, such as that of static equilibrium, whereas fusion-grade plasmas are clearly strongly driven systems far from equilibrium. | Furthermore, the force balance equation depends on a number of assumptions, such as that of static equilibrium, whereas fusion-grade plasmas are clearly strongly driven systems far from equilibrium. | ||
Nevertheless, ideal MHD equilibrium is extremely useful for the description and understanding of magnetically confined plasmas. | Nevertheless, ideal MHD equilibrium is extremely useful for the description and understanding of magnetically confined plasmas. | ||