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Concept# Magnetic helicity

Summary

In plasma physics, magnetic helicity is a measure of the linkage, twist, and writhe of a magnetic field. In ideal magnetohydrodynamics, magnetic helicity is conserved. When a magnetic field contains magnetic helicity, it tends to form large-scale structures from small-scale ones. This process can be referred to as an inverse transfer in Fourier space.
This second property makes magnetic helicity special: three-dimensional turbulent flows tend to "destroy" structure, in the sense that large-scale vortices break up into smaller and smaller ones (a process called "direct energy cascade", described by Lewis Fry Richardson and Andrey Nikolaevich Kolmogorov). At the smallest scales, the vortices are dissipated in heat through viscous effects. Through a sort of "inverse cascade of magnetic helicity", the opposite happens: small helical structures (with a non-zero magnetic helicity) lead to the formation of large-scale magnetic fields. This is for example visible in the heliospheric current sheet, a large magnetic structure in the Solar System.
Magnetic helicity is of great relevance in several astrophysical systems, where the resistivity is typically very low so that magnetic helicity is conserved to a very good approximation. For example: magnetic helicity dynamics are important in solar flares and coronal mass ejections. Magnetic helicity is present in the solar wind. Its conservation is significant in dynamo processes. It also plays a role in fusion research, for example in reversed field pinch experiments.
Generally, the helicity of a smooth vector field confined to a volume is the standard measure of the extent to which the field lines wrap and coil around one another. It is defined as the volume integral over of the scalar product of and its curl, :
Magnetic helicity is the helicity of a magnetic vector potential where is the associated magnetic field confined to a volume . Magnetic helicity can then be expressed as
Since the magnetic vector potential is not gauge invariant, the magnetic helicity is also not gauge invariant in general.

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