Solutions of a Nonlinear Equation of a Resistively Shunted Model of Josephson Junctions

Abstract

Approximate solutions of the nonlinear equation that describes the behavior of microwave-irradiated superconducting weak links are obtained. The method of the solution is based on the fact that the phase of Josephson oscillation is locked to an externally applied coherent radiation under a bias current of a microwave-induced step. It can be concluded that the approximate solutions have three internal variables which are functions of d.c. bias current and microwave current. The d.c. voltage-current relation when d.c. current is biased to a current step is found to follow Ohm’s law when the step vanishes. This result has been confirmed experimentally. The height of a current step as a function of the incident microwave current has been numerically calculated. The calculated values agree well with those obtained by an analog computer. The internal three variables have been also calculated numerically.