Magnetic helicity

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This page is about helicity in magnetic fields. For fluid mechanical helicity, see helicity

In plasma physics, magnetic helicity is the extent to which a magnetic field "wraps around itself". If magnetic field lines follow the strands of a twisted rope, this configuration would have nonzero magnetic helicity; left handed ropes would have negative values and right handed ropes would have positive values.

Formally,

H=\int {\mathbf A}\cdot{\mathbf B}\,d^3{\mathbf r}

where

{\mathbf B} is the magnetic field strength
{\mathbf B}=\nabla\times{\mathbf A};
\mathbf A is the vector potential of {\mathbf B}

Magnetic helicity is a conserved quantity. It is conserved in electromagnetic fields, even when magnetic reconnection dissipates energy. The concept is useful in solar dynamics and in hydromagnetic dynamo theory.

Magnetic helicity is a gauge-dependent quantity, because A can be redefined by adding a gradient to it (gauge transformation). However, for periodic or perfectly conducting boundaries the magnetic helicity is gauge invariant. If the magnetic field is turbulent and weakly inhomogeneous a magnetic helicity density and its associated flux can be defined in terms of the density of field line linkages.

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