Exploring solutions for Type-II superconductors in critical state

Abstract

An analytical solution is found for magnetic induction in a type-II superconducting plate in parallel geometry. In this study, critical current density is modeled following the Ming Xu et al., approach which requires the adjusting parameters $n$ and $B^*$. A symmetry relation between the generating equations of the $H>0$ and $H<0$ cases is presented, as well as an equivalence between vertical and power laws for a superconductor in steady state. We present a systematic procedure for identifying magnetic induction profiles and we analyze the physical characteristics of the superconducting plate when $n$ and $B^*$ vary. Specifically, we present flat surface plots of the penetration field, double penetration field, critical current density and, finally, an application of our results to calculate the shielding field, which prevents the occurrence flux jumps.