Scaling and exact solutions for the flux creep problem in a slab superconductor
D. V. Shantsev, Y. M. Galperin, T. H. Johansen
DOI 10.1103/PhysRevB.65.184512 · Physical Review B
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Abstract
The flux creep problem for a superconductor slab placed in a constant or time-dependent magnetic field is considered. Logarithmic dependence of the activation energy on the current density is assumed, U=U0ln(J/Jc), with a field dependent Jc. The density B of the magnetic flux penetrating into the superconductor is shown to obey a scaling law, i.e., the profiles B(x) at different times t can be scaled to a function of a single variable x/tβ. We found exact solution for the scaling function in some specific cases, and an approximate solution for a general case. The scaling also holds for a slab carrying transport current I resulting in a voltage V∝Ip, where p∼1. When the flux fronts moving from two sides of the slab collapse at the center, the scaling is broken and V(I) crosses over to V∝IU0/kT.
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