The critical state in hysteretic superconductors

A model description is proposed for the transport properties of type II superconductors. It proceeds from the general concepts of a critical state resulting from thermally activated motion of current vortices (fluxoids) past barriers (pins) due to forces resembling Lorentz forces. A formal description of the variation in strength of the fluxoid-pin interaction is given as a function of local field and temperature. Expressions are derived which describe the variation in sample critical current density with applied field and temperature and which contain two material parameters, the spacing r o and the effectiveness p of pinning sites. Empirical determinations of these parameters, e.g. from the grain size dependence of critical current density, yield plausible values and the values determined in a single experiment (e.g. current density as a function of field) allow successful prediction of the outcome of other experiments (e.g. current density as a function of temperature at constant field).