Minor hysteresis loops and harmonic generation calculations in a generalized critical-state model

Abstract

We present analytic calculations of minor hysteresis loops obtained when a sample is subjected to a time-varying field B(t)=B_dc+B_ac cosωt. We enumerate eight classes of minor hysteresis loops, and calculations are done within the critical-state model but for an arbitrary field dependence of the critical current density J_c(B). The sample shapes considered are the zero-demagnetization factor cases of a circular cylinder, and of a slab, in a longitudinal field. Harmonic components of the magnetization (M_n) are numerically obtained for various forms of J_c(B). Our results bring out the importance of the sample shape used in the calculation and also point out the features in M_n vs B_dc that clearly reflect the details of the field dependence in J_c(B).