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Flux tube: Difference between revisions
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[[File:Flux tube.png|300px|thumb|right|Sketch of a flux tube with magnetic field lines in red]] | |||
A flux tube is a region of space bounded by a [[Flux surface|flux surface]], i.e., a surface such that the magnetic field is everywhere perpendicular to the surface normal. | A flux tube is a region of space bounded by a [[Flux surface|flux surface]], i.e., a surface such that the magnetic field is everywhere perpendicular to the surface normal. | ||
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Contrary to [[Magnetic island|magnetic islands]], that are bounded by a [[Separatrix|separatrix]], there is not necessarily any essential dynamical difference between the regions inside and outside of a flux tube. | Contrary to [[Magnetic island|magnetic islands]], that are bounded by a [[Separatrix|separatrix]], there is not necessarily any essential dynamical difference between the regions inside and outside of a flux tube. | ||
== Flux conservation == | |||
In the framework of [[Ideal Magneto-Hydrodynamics]], the MHD kinematic equation reads (in the perfectly conducting limit, <math>\sigma \to \infty</math>): | |||
:<math> | |||
\frac{\partial \vec B}{\partial t} = \vec \nabla \times (\vec v \times \vec B) | |||
</math> | |||
This has the important consequence that a given volume of plasma contained within a flux tube ''remains'' inside the flux tube as it is advected, twisted, and stretched by the fluid flow. | |||
<ref>A. Dinklage, ''Plasma physics: confinement, transport and collective effects'', Vol. 670 of Lecture notes in physics, Springer (2005) {{ISBN|3540252746}}</ref> | |||
<ref>W.D. D'haeseleer et al, ''Flux coordinates and Magnetic Field Structure'', Springer-Verlag {{ISBN|3-540-52419-3}}</ref> | |||
This implies that the topology of the flux tube cannot change due to the fluid flow. | |||
Stated differently, the magnetic flux contained in a volume element of the plasma is carried along unchanged as the element moves. | |||
Also, two plasma elements connected by a field line will always remain connected by that same field line as the plasma flows. | |||
This is sometimes known as the ''Frozen Flux Hypothesis''. | |||
== See also == | |||
* [[:Wikipedia:Flux tube]] | |||
== References == | |||
<references /> | |||