Basic properties of an rf SQUID involving two Josephson junctions connected in series

We have studied the basic characteristics of a radio frequency superconducting quantum interference device (rf SQUID) involving two Josephson junctions connected in series, the case for the widely used grain boundary junction (GBJ) rf SQUID. It is found that the SQUID properties are determined mainly by the weaker junction when the critical current of the weaker junction is much lower than that of the other junction. Otherwise, the effect of the other junction is not negligible. We also find that only when the hysteresis parameter β is less than 1-α, where α is the critical current ratio of the two junctions, will the SQUID operate in the nonhysteretic mode.