# Trapped Flux in Superconductors

A. B. Pippard

## Abstract

When a magnetic field is applied to a superconductor the normal state may be restored, and on removing the field the superconducting state is re-established, usually with a proportion of the field trapped in normal channels. The amount of flux trapped has been studied systematically as a function of temperature in rods of pure tin and of tin alloyed with indium up to 3%. In order to obtain significant results the specimens must be single crystals, homogenized by prolonged annealing, and having well-polished surfaces. The proportion of flux trapped is very small ($\sim$0$\cdot$1%) in pure tin, increasing steadily as the indium concentration is increased. For indium concentrations less than about 2$\cdot$3% the proportion trapped tends to zero as the temperature tends to the transition temperature. For greater indium concentrations there is a sharp rise in trapping to a very high value ($\sim$50%) at the transition temperature. The trapped flux is rather firmly bound. In order to account for these results a model of the superconducting state is developed, based on the theories of London & London and of Gorter & Casimir, and incorporating the idea of coherence. Typical processes such as spontaneous nucleation of the superconducting phase are analyzed and used to discuss the factors influencing the coalescence of adjacent superconducting domains, which is an essential part of the trapping mechanism. It is concluded that for not too great indium concentrations coalescence is achieved only through the presence of flaws, and that the sudden change in behaviour at 2$\cdot$3% indium marks the beginning of spontaneous coalescence. The model appears to be capable of accounting qualitatively for most of the details of the observed behaviour.