Calculation of critical currents in Josephson Junctions

We were able for the first time to calculate the critical current in a Josephson junction, under the influence of a magnetic field. This was accomplished for the general case and without any preliminary assumptions on the self-induced field. Based on these calculations, we were also able to retrieve the spatial distribution of the critical current in the junction, given its magnetic field dependence. The junction size can be large compared to the global penetration depth γJ, and the self induced field does not have to be neglected. The calculation of the critical current as a function of the external magnetic field, Ic(H), is based on the DC Josephson effect. Here the phase difference across the junction is related to the magnetic field. If the spatial distribution of the critical current, jc(x), is known, then Ic(H) = ∫-∞∞dx jc(x) exp{2πi F[jc(x)]} We can now calculate numerically a sample of critical currents for simulated distributions. Results can be compared very favourably with calculations made by others [2] under the assumption of a global penetration depth γJ. In addition, we use the spatial dependence of the penetration depth to yield more accurate results