Critical state magnetization of hard type-II superconductors with rectangular and cylindrical cross-sections

Abstract

Magnetization loops in the critical state for the critical current density$J_c = J_1 + J_2 e^{ - |B|/B_0 }$ and$J_c = J_1 + J_2 /(1 + |B|/B_0 )$ are calculated. The geometry considered is an infinitely long superconductor with a finite cross-section in the shape of a rectangle or circle. Explicit formulas are derived for the various branches of the complete high-field hysteresis loop. In the discussion emphasis is put on the behavior of the width, δM, of the hysteresis loop, and a simple graphical method to fit model parameters to experimental data is outlined.