Critical-state model for thin superconductors with history dependent Jc( B)

• Published in: Physica. C, Superconductivity Superconductivity, 2003-08, Vol.391 (2), p.178-188
• Main Authors: Kulkarni, D.G., Bhagwat, K.V., Ravikumar, G.
• Format: Article
• Language: English
• ISSN: 0921-4534; 1873-2143
• DOI: 10.1016/S0921-4534(03)00893-1

The peak effect and the accompanying history effects observed in weakly pinned hard type II superconductors have been the focus of attention for the past several years. A phenomenological model that takes into account history dependence in the critical current density was proposed recently to describe these effects. Hall-array measurements of field profiles in the peak region show that they are qualitatively different from those for samples that do not exhibit the peak effect. We present a numerical scheme to calculate the field profiles and dynamic magnetization hysteresis loops for a single crystal platelet sample. We numerically solve time dependent Maxwell’s equations involving curl B and curl E through introduction of an inductance matrix. The E– J relation is assumed as a power law E∼ E c( J/ J c) n , where J c is the critical current density. In this scheme the magnetization loops would be dependent on the sweep rate of the magnetic field as observed in experiments. Further, it also describes the time relaxation of magnetization in a fixed magnetic field. The scheme is first applied to solve the critical state model for the exponential model for J c( B), and samples such as platelets of a single crystal. We then allow history dependence in J c( B) and numerically determine current and field profiles. From the current profiles we obtain the envelope magnetization curves and also the minor loops. We find that the field profiles in the peak region show behavior qualitatively similar to that reported in Hall-array measurements. Our calculations indicate that strong demagnetization effects present in a thin sample do not vitiate the main features of the peak effect observed in a bulk sample.