# Flux tube

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, $ \sigma \to \infty $):

- $ \frac{\partial \vec B}{\partial t} = \vec \nabla \times (\vec v \times \vec B) $

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.
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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