Self-similar magnetic structures and magnetic flux “Giant” creep

Abstract

The penetration of a magnetic flux into a type-II high-Tc superconductor occupying the half-space x > 0 is considered. At the superconductor surface, the magnetic field amplitude increases in accordance with the law b(0, t) = b0(1 + t)m (in dimensionless coordinates), where m > 0. The velocity of penetration of vortices is determined in the regime of thermally activated magnetic flux flow: v = v0exp⨑ub;−(U0/T)(1-b∂b/∂x)⫂ub;, where U0 is the effective pinning energy and T is the thermal energy of excited vortex filaments (or their bundles). magnetic flux “Giant” creep (for which U0/T≪ 1) is considered. The model Navier-Stokes equation is derived with nonlinear “viscosity” v ∝ U0/T and convection velocity vf ∝ (1 − U0/T). It is shown that motion of vortices is of the diffusion type for j → 0 (j is the current density). For finite current densities 0 0.