Self-Resonant Current Peaks in Josephson Junctions

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Abstract
A finite difference scheme is described which yields solutions of the Josephson phase equation. This simulation technique is used to calculate the self‐resonant current peaks of a Josephson junction for the two cases, R≫ZJ and R≪ZJ, where R is the current drive source resistance and ZJ is the junction impedance. The simulation current peaks are compared with ones derived by a perturbation technique for the same two regimes, and also with experiment. In terms of approximating experimental results, it is found that the perturbation solutions with constant damping, σ, are better than those with constant Q; although at small σ the magnitude and shape of the current peaks do not agree well with observations. However, simulation results at small σ are reasonably consistent with experiment. Simulation results for the case R≪ZJ indicate that self‐limiting will affect the magnetic field dependence of the resonances when L/λJ≥2, where L is the length of the junction and λJ is the Josephson penetration depth.