An Extended RSJ-Model Describing AC Josephson Effects of Granular Superconductors

Abstract

A model of a capacitive network of Josephson junctions is developed for the description of granular superconductors in a microwave field. The investigation of the charge of the grains reduces the number of differential equations in comparison to the common calculations for the currents through the Josephson junctions between the grains. The current-voltage characteristics are simulated for simple circuits of identical Josephson junctions and the influence of single junctions with different parameters on the behaviour of the network is demonstrated. The common RSJ-model with finite capacitance is extended taking into account the temperature dependence of the critical current I c and the normal resistance R N from experiments or model calculations. Thus the parameters as the McCumber parameter s C1 the normalized frequency Ω and the microwave amplitude i 1 depend on the temperature. Within this model the inverse ac Josephson effect is simulated over a wide temperature range. Depending on the parameter range, the resulting dc voltage shows values corresponding to the microwave-induced steps or a continuous behaviour caused by unstable or chaotic solutions. The numerical results of the extended RSJ-model are compared to experimental data of different granular superconductors.