DEVIATIONS FROM THE FROZEN-IN LAW IN THE PRESENCE OF SMALL (BUT NONZERO) RESISTIVITY

The freezing of magnetic field flux into an electron fluid is examined during fast magnetic field evolution that results from the nonlinear skin effect. First, fast magnetic field evolution, which does not involve flux penetration, is shown to follow naturally from the frozen-in law. Second, fast evolution is analyzed in which large deviations from the frozen-in law (large flux penetration) occur in the presence of small (but nonzero) resistivity. A direct relation is shown between the deviation from the frozen-in law and the energy dissipated per electron along its orbit.