Solving the critical state using flux line properties

Abstract

A method of solving the critical state in superconductors using the vector potential and commercial software (FlexPDE) is described. It avoids both time dependence and power law resistivity. It uses a material parameter which describes how far flux lines move before most become unpinned. This allows small oscillations and minor hysteresis loops to be modelled. The theory is applied to the problem of demagnetisation in bulks due to crossed fields. It may explain why experimental results do not agree with theory. The theory can be extended to coils, and two and three dimensions. This requires the introduction of a scalar potential Vo. This is not the usual scalar potential, which is due to electrostatic charges as the field is run up, but the integral of this value at the final field after charges have dissipated.