Intrinsic Fluctuations in a Superconducting Ring Closed with a Josephson Junction

The distribution in the external flux at which a superconducting ring closed with a weak link admits a quantum of flux is determined assuming that the weak link can be treated as a Josephson junction. We find that this transition occurs at an appreciable fraction of the flux quantum from the theoretical critical external flux. To a first approximation the width of the distribution is proportional to the inductance of the ring and varies as T2/3ic^-1/3, where T is the temperature and ic the critical current.