Models of force-free magnetic fields in resistive media

Review of some of the basic properties of force-free fields under circumstances where the conductivity of the medium is finite and the electric current density is related not only to the magnetic field but also, by Ohm's law, to the electric field and the plasma velocity. It is pointed out that the natural constraint that the electric field and plasma velocity should be finite everywhere is not fulfilled in some previously used models. Models with a constant ratio alpha of the electric current density and magnetic field intensity have been used extensively in the past. They are of some importance, since solutions with the plasma at rest are possible only if alpha is constant. However, it is shown that solutions of constant alpha cannot be matched to an external current-free region of finite conductivity, since alpha can have no discontinuity in a medium where the conductivity varies continuously. Hence, for most applications models with a varying alpha and a moving plasma must be used.