Abstract
Within the construct of the complete Kim-Anderson model for the critical-current density, we have calculated the initial magnetization curves and full hysteresis loops of type-II superconductors immersed in an external field H=+cos(ωt), where (≥0) is a dc bias field and (>0) is an ac field amplitude. We denote the maximum and minimum values of H by (=+) and (=-). According to the Kim-Anderson model, the critical-current density is assumed to be a function of the local internal magnetic-flux density , ()=k/(+‖‖), where k and are constants. We consider an infinitely long cylinder with radius a, and the applied field along the cylinder axis. The field for full penetration is =[(+2ka-]/. A related parameter is =[(-4ka-]/. Magnetization equations for full hysteresis loops are derived for three different ranges of : 0<≤, ≤≤, and ≤. Each of these three cases is further classified for several ranges of . To describe completely the descending and ascending branches of the full hysteresis loops for all cases, 58 stages of H are considered and the appropriate magnetization equations are derived. In addition to these equations for a cylinder, the corresponding equations for a slab are presented. Comparison with previous work by Ji et al. and by Chen and Goldfarb in the appropriate limits supports the validity of the present derivation.
- Received 4 May 1992
DOI:https://doi.org/10.1103/PhysRevB.47.915
©1993 American Physical Society