Universality of Flux Creep in Superconductors with Arbitrary Shape and Current-Voltage Law

摘要: The nonlinear and nonlocal diffusion equation for the relaxing current density $J(\mathbf{r},t)$ in long superconductors of arbitrary cross section a constant perpendicular magnetic field ${B}_{a}$ is solved exactly by separation variables electric $E(\mathbf{r},t)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}f(\mathbf{r})g(t)$. This solution includes limiting cases longitudinal transverse geometries applies to current-voltage laws $E\ensuremath{\propto}{J}^{n}$ ranging from Ohmic ( $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$) Bean-like $n\ensuremath{\rightarrow}\ensuremath{\infty}$) behavior. profile $f(\mathbf{r})$ weakly depends on $n$ becomes universal exceeding $\ensuremath{\approx}5$. At large times $t$ one finds $E\ensuremath{\propto}1/{t}^{n/(n\ensuremath{-}1)}$ $J\ensuremath{\propto}1/{t}^{1/(n\ensuremath{-}1)}$ $ng1$, $E\ensuremath{\propto}J\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}t/{\ensuremath{\tau}}_{0})$ $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$. contour lines creeping $E(\mathbf{r},t)$ coincide with $\mathbf{B}(\mathbf{r},t)$ remanent state ${B}_{a}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$.