Some general results on relative magnetic helicity and field line helicity
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Natural Sciences (Astrophysics and Astrononmy)
We present some general considerations on two quantities that are of common use in solar physics: the relative magnetic helicity H and the field line helicity h of a magnetic field B contained in some domain D. 1. We show how these two quantities can be expressed in terms of either the magnetic mapping of B or, when B has a simple topology, the boundary values of two pairs of Euler potentials. The well-known topological invariance of H and h can be immediately seen on the formulae that are presented. 2. We compute how the field line helicity varies in time when the plasma in D has finite resistivity and the footpoints of the magnetic lines on the boundary of D are submitted to shearing motions.
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