The phase transition in superconductors III. Phase propagation below the critical field

Abstract

If a superconducting nucleus is created at one end of a long rod of supercooled tin, it grows down to the other end with a velocity, v , of the order of 10 cm sec -1 . This process has been studied experimentally, by winding search coils round the specimens to record the progressive expulsion of the longitudinal magnetic field; in particular v has been measured as a function of field strength and temperature, for a number of specimens of varying radius, conductivity, and surface condition. It is shown that v is governed by the progress of a thin superconducting filament that shoots out from the nucleus along the surface of the specimen. Subsequently this filament closes up to form a sheath of the superconducting phase, leaving some flux enclosed which takes several seconds to escape, but these later stages of the transition are only briefly discussed. A quantitative theory is developed to account for the rate of advance of the original filament, by considering the conditions for conservation of energy during propagation. It is assumed that the two controlling factors are the interphase surface tension and the electromagnetic damping effect of the eddy currents set up in the normal phase ahead of the filament. The theory is complicated by an interesting phenomenon analogous to the anomalous skin effect, which is observed when the electronic mean free path becomes comparable with the filament thickness; a dimensional analysis of the results reveals that the eddy currents may behave ‘classically’, ‘anomalously’, or somewhat between the two, depending on the conditions of the experiment. Only in the anomalous region is the theory completely successful, but its failure elsewhere can be traced to limitations in the rather simple model which is considered. Values of the interphase tension are deduced from the experimental data; these are in agreement with previous estimates based on intermediate state work, but they are more extensive and probably more reliable. They are briefly compared with the predictions of Ginsburg & Landau (1950) and Pippard (1951, 1953).