Josephson current in a finite-size junction interrupting a superconducting ring

We study the behavior of the Josephson current (Formula presented) flowing in a finite-size Josephson junction in a superconducting ring in the presence of an externally applied magnetic field H, taking into account the effect of the shielding currents. The set of self-consistent equations for the system can be solved explicitly for (Formula presented) in the small self-inductance coefficient limit for not negligible effective junction areas. It is found that the resulting (Formula presented) versus H curve presents a Fraunhofer-like prefactor modulating a periodic quasisinusoidal odd function.