Self-similar distribution in “giant” magnetic flux creep

Abstract

The problem of magnetic field penetration into the half-space is considered in parallel geometry in an external magnetic field increasing with time in accordance with the law B(0, t, τ0 = B c 1 (1 + t/τ0) m , m ≥ 0, t ≥ 0 (τ 0 is the time of magnetic flux redistribution and B c 1 is the lower critical field). It is assumed that the flow of vortices is thermally activated in the “giant” creep mode (i.e., for weak pinning creep and high temperatures). A model equation is derived for describing the magnetic flux evolution. Analytic formulas are obtained for the depth and velocity of magnetic field penetration. It is shown that the giant creep regime is stable for 0 ≤ m ≤ 1/2.