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.

Sketch of a flux tube with magnetic field lines in red

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. 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