Flux tube
A flux tube is a generally tube-like (cylindrical) region of space containing a magnetic field, B, such that the cylindrical sides of the tube are everywhere parallel to the magnetic field lines.
As used in astrophysics, a flux tube generally means an area of space through which a strong magnetic field passes, in which the behavior of matter (usually ionized gas or plasma) is strongly influenced by the field.
They are commonly found around stars, including the Sun, which has many flux tubes from tens to hundreds of kilometers in diameter.
A well-known example is the flux tube between Jupiter and its moon Io.
A flux tube can be defined passing through any closed, orientable surface
The tube follows the field lines, possibly turning, twisting, and changing its cross sectional size and shape as the field lines converge or diverge.
Since no field lines pass through the tube walls there is no flux through the walls of the tube, so all the field lines enter and leave through the end surfaces.
The strength (magnitude) of the vector field, and the cross sectional area of the tube varies along its length, but the surface integral of the field over any surface spanning the tube is equal.
The flux tube model is important in explaining the so-called color confinement mechanism, why quarks are never seen separately in particle experiments.
In 1861, James Clerk Maxwell gave rise to the concept of a flux tube inspired by Michael Faraday's work in electrical and magnetic behavior in his paper titled "On Physical Lines of Force".
intersecting the tube, equal to the surface integral of the magnetic field
, of the flux tube is small enough that the magnetic field is approximately constant,
In magnetohydrodynamics, Alfvén's theorem states that the magnetic flux through a surface, such as the surface of a flux tube, moving along with a perfectly conducting fluid is conserved.
This can be shown mathematically for a flux tube using the induction equation of a perfectly conducting fluid
which can be rewritten using Stokes' theorem and an elementary vector identity on the first and second term, respectively, to give[6]
Reducing the length of the tubes results in a decrease of the magnetic field's strength.
[4] In magnetohydrostatic equilibrium, the following condition is met for the equation of motion of the plasma confined to the flux tube:[4]
where With the magnetohydrostatic equilibrium condition met, a cylindrical flux tube's plasma pressure of
[4] The field line's twist around the axis from one end of the tube of length
Examples of solar flux tubes include sunspots and intense magnetic tubes in the photosphere and the field around the solar prominence and coronal loops in the corona.
[1] The large flux tube of the sunspot has a field intensity of around 3 kG with a diameter of typically 4000 km.
[1] The magnetic field within the flux tube can be compressed by decreasing the gas pressure inside and therefore the internal temperature of the tube while maintaining a constant pressure outside.
[4] These flux tubes are concentrated strong magnetic fields that are found between solar granules.
[7] Plasma that is trapped within magnetic flux tubes that are attached to the photosphere, referred to as footpoints, create a loop-like structure known as a coronal loop.
[8] These coronal loops get their characteristic high luminosity and ranges of shapes from the behavior of the magnetic flux tube.
The confined magnetic field strength varies from 0.1 to 10 G with diameters ranging from 200 to 300 km.
[8][9] The result of emerging twisted flux tubes from the interior of the Sun cause twisted magnetic structures in the corona, which then lead to solar prominences.
[12] The extension of the magnetosphere away from the sun known as a magnetotail is modeled as magnetic flux tubes.
[12] Mars and Venus both have strong magnetic fields resulting in flux tubes from the solar wind gathering at high altitudes of the ionosphere on the sun side of the planets and causing the flux tubes to distort along the magnetic field lines creating flux ropes.
[12] Particles from the solar wind magnetic field lines can transfer to the magnetic field lines of a planet's magnetosphere through the processes of magnetic reconnection that occurs when a flux tube from the solar wind and a flux tube from the magnetosphere in opposite field directions get close to one another.
