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

Ernst Helmut Brandt

doi:10.1103/PhysRevLett.76.4030

← Back to search

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

Ernst Helmut Brandt

DOI 10.1103/PhysRevLett.76.4030 · Physical Review Letters

T1

Active bibliographic source — not scientific approval

Bibliographic access preserves source history; it does not approve extracted materials or validate reported claims. Review warnings on each occurrence separately.

Abstract

The nonlinear and nonlocal diffusion equation for the relaxing current density J(r,t) in long superconductors of arbitrary cross section in a constant perpendicular magnetic field Ba is solved exactly by separation of variables in the electric field E(r,t)=f(r)g(t). This solution includes the limiting cases of longitudinal and transverse geometries and applies to the current-voltage laws E∝Jn ranging from Ohmic ( n=1) to Bean-like ( n→∞) behavior. The electric field profile f(r) weakly depends on n and becomes universal for n exceeding ≈5. At large times t one finds E∝1/tn/(n−1) and J∝1/t1/(n−1) for n>1, and E∝J∝exp(−t/τ0) for n=1. The contour lines of the creeping E(r,t) coincide with the field lines of B(r,t) in the remanent state Ba=0.