Magnetic helicity

The helicity of a smooth vector field defined on a domain in 3D space is the standard measure of the extent to which the field lines wrap and coil around one another. As to magnetic helicity, this 'vector field' is magnetic field. It is a generalization of the topological concept of linking number to the differential quantities required to describe the magnetic field. As with many quantities in electromagnetism, magnetic helicity (which describes magnetic field lines) is closely related to fluid mechanical helicity (which describes fluid flow lines). The helicity of a smooth vector field defined on a domain in 3D space is the standard measure of the extent to which the field lines wrap and coil around one another. As to magnetic helicity, this 'vector field' is magnetic field. It is a generalization of the topological concept of linking number to the differential quantities required to describe the magnetic field. As with many quantities in electromagnetism, magnetic helicity (which describes magnetic field lines) is closely related to fluid mechanical helicity (which describes fluid flow lines). 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.