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)=${\mathit{B}}_{\mathrm{dc}}$+${\mathit{B}}_{\mathrm{ac}}$ cos\ensuremath{\omega}t. 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 ${\mathit{J}}_{\mathit{c}}$(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 (${\mathit{M}}_{\mathit{n}}$) are numerically obtained for various forms of ${\mathit{J}}_{\mathit{c}}$(B). Our results bring out the importance of the sample shape used in the calculation and also point out the features in ${\mathit{M}}_{\mathit{n}}$ vs ${\mathit{B}}_{\mathrm{dc}}$ that clearly reflect the details of the field dependence in ${\mathit{J}}_{\mathit{c}}$(B).