Nonlinear current diffusion in type-II superconductors

The temporal evolution of flux profiles in superconducting slabs and cylinders is investigated numerically for the situation where the flux-creep activation barrier U depends explicitly on current density j, e.g., U(j) ∞ [(j_c/j)^μ - 1] or U(j) ∞ln(j_c/j). Both field-independent and field-dependent forms of the critical current density j_c are considered. Exact numerical results for the time-dependent magnetization and relaxation time τ are compared to approximate analytical solutions. When the flux-creep activation barriers diverges as j→0, flux- and current-density profiles evolve towards an asymptotic behaviour that is independent of initial conditions. The time-dependent magnetization in the case of full flux penetration is then well described by the appropriate form for the magnetization of the sample in the critical state, but with a time-dependent surface current density replacing the critical current density. The current-dependent flux-creep activation barrier may be obtained from low-temperature experiments using the analysis method of Maley et al. [7], even when j_c depends explicitly on B.