Scaling and exact solutions for the flux creep problem in a slab superconductor

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, ${U=U}_{0}\mathrm{ln}{(J/J}_{c}),$ with a field dependent ${J}_{c}.$ 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 ${x/t}^{\ensuremath{\beta}}.$ 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 $V\ensuremath{\propto}{I}^{p},$ where $p\ensuremath{\sim}1.$ 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 $V\ensuremath{\propto}{I}^{{U}_{0}/kT}.$