The covariant transport of electromagnetic fields and its relation to magnetohydrodynamics

Ohm's law in ideal magnetohydrodynamics (MHD) leads to an induction equation which can be interpreted in terms of magnetic flux being transported by the plasma flow. It is shown that this frozen-in condition is the non-relativistic limit of a corresponding relativistic condition for the electromagnetic field tenser. Several invariants for this type of transport are analyzed. The relativistic formulation also includes a broader class of transporting flows, which may differ from the plasma Bow. A classification and interpretation of these transporting flows is given and it is shown that the corresponding evolutions of the electromagnetic field also includes cases of non-ideal MHD evolution. Thus it is possible to find invariants in non-ideal MHD similar to the magnetic flux far ideal plasma flows. (C) 1997 American Institute of Physics.