Magnetic diffusion and the motion of field lines

Diffusion of a magnetic field through a plasma is discussed in one-, two- and three-dimensional configurations, together with the possibility of describing such diffusion in terms of a magnetic flux velocity, which, when it exists, is in general non-unique. Physically useful definitions of such a velocity include doing so in terms of the energy flow or in such a way that it vanishes in a steady state. Straight field lines (or plane flux surfaces) diffuse as if flux is disappearing at a neutral sheet, whereas circular field lines (or cylindrical flux surfaces) do so as if flux is disappearing at an 0-type neutral line. In three dimensions it is not always possible to define a flux velocity, for example when the magnetic flux through a closed field line is changing in time. However, in at least some such cases it is possible to describe the behaviour of the magnetic field in terms of a pair of quasi-flux-velocities.