Numerical investigation of the magnetic flux static distributions in layered josephson junctions

Abstract

Effective numerical algorithms are worked out for solving the nolinearsystem of ODE for finding the static distributions of the magnetic flux inN-stacked JJs, as well as the corresponding matrix Sturm-Liouville problemfor studying their global stability. The particular case of three stacked JJs isinvestigated. A correspondence is made between loss of stability of apossible static distribution of the magnetic flux, obtained by solving thestatic problem, and the switching to dynamic state obtained by solving thedynamic problem. In this work we show by means of numerical simulationthat the transient process of switching from static to dynamic state insymmetric three stacked JJs depends on the way of exceeding theexternal current.