Power-Law Critical-State Model for Magnetization of Type-II Superconductors

Abstract

The magnetization of a type-II superconductor obeying the power-law critical state model J c = KB-n is discussed for the case of an infinitely long rectangular bar placed in a parallel field. Explicit formulas are derived for all branches of the high-field hysteresis loop. Both the infinite slab and circular cylinder geometries are included as special cases. It is shown that the vertical width of the hysteresis loop has the asymptotic high-field behavior ΔM(B a) ∼J c(B a), with a prefactor given by the geometrical aspect ratio. Also, two more terms in the functional expansion of ΔM { J c} are derived. These terms are shown to vanish rapidly when the applied field exceeds the full penetration value. This allows for a new way of extracting J c(B) from magnetization data.