Simulations of the early period of flux entry into a single-Josephson-junction superconducting loop using the Werthamer theory

The behavior of a superconducting quantum interference device (SQUID) during the period up to the entry of the first flux quantum has been studied by numerical simulation. The theory of Josephson tunneling due to Werthamer, which includes the time-dependent aspects of the Bardeen--Cooper--Schieffer (BCS) theory, was used. Several interesting qualitative features were observed. One is the discovery of an approximate effective RC time constant (tau/sub g/+theta), where tau/sub g/ is the RC time constant in units of the gap time and theta is a constant. With this as a scaling factor, the results become approximately independent of RC for the early period of flux entry. A second, related, feature of the results is that the time required for the entry of the first flux quantum accurately follows a simple empirical formula for a wide range of the values of the various parameters of the experiment. In addition, some of the results were compared with those obtained with approximate versions of Josephson's tunneling equation. In general, these approximations gave poor results