Time scales of the flux creep in superconductors

We have studied both theoretically and experimentally flux-creep dynamics in superconductors. A theoretical analysis of nonlinear flux diffusion shows that the relaxation of the electric field proves to be similar for different models of thermally activated flux creep, whereas the long-time decay of the magnetic moment M(t) can be essentially model dependent. A proposed scaling analysis indicates that the short-time decay of M(t) in the subcritical region j${\mathit{j}}_{\mathit{c}}$ is universal and consists of two stages. The initial nonlogarithmic stage is due to a transient redistribution of magnetic flux over the sample cross section, the duration of this stage ${\mathrm{\tau }}_0$ being entirely determined by macroscopic quantities, such as sample sizes, flux creep rate ${\mathit{M}}_1$(T,B)=dM/d lnt, and magnetic ramp rate B${\mathrm{̇}}_{\mathit{e}}$=dB/dt. The second stage corresponds to the approximately logarithmic relaxation M(t)=${\mathit{M}}_{\mathit{c}}$-${\mathit{M}}_1$ln(t/${\mathit{t}}_0$), with ${\mathit{t}}_0$ being a macroscopic time constant that also depends on sample sizes, ${\mathit{M}}_1$(T,B), and the voltage criterion ${\mathit{E}}_{\mathit{c}}$ at which the critical current density ${\mathit{j}}_{\mathit{c}}$ is defined.