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 == | == See also == | ||
* [[:Wikipedia:Flux tube]] | * [[:Wikipedia:Flux tube]] | ||
== References == | |||
<references /> | |||
Latest revision as of 12:29, 26 January 2023
A flux tube is a region of space bounded by a flux surface, i.e., a surface such that the magnetic field is everywhere perpendicular to the surface normal.
In flux coordinates, such a surface has cylindrical topology. In a closed magnetic field region, the topology is toroidal.
The magnetic flux traversing any cross sectional area of a flux tube is invariant.
Contrary to magnetic islands, that are bounded by a 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, ):
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. [1] [2] 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
References
- ↑ A. Dinklage, Plasma physics: confinement, transport and collective effects, Vol. 670 of Lecture notes in physics, Springer (2005) ISBN 3540252746
- ↑ W.D. D'haeseleer et al, Flux coordinates and Magnetic Field Structure, Springer-Verlag ISBN 3-540-52419-3