Solving the Hysteresis Loop Calculation Problem for Josephson Junction Stacks

A detailed investigation of the IVC breakpoint and the breakpoint region width gives important information concerning the peculiarities of stacks with a finite number of intrinsic Josephson junctions. The current-voltage characteristics for a stack of n Josephson junctions is defined from solving the system of n nonlinear differential equations. The current voltage characteristic has the shape of a hysteresis loop. On the back branch of the Hysteresis loop, near the breakpoint Ib, voltage V(I) decreases to zero rapidly. The goal of this work is to accelerate the computation of IVC based on numerical solution of the system. A numerical-analytical method was proposed in. This method showed perfect results in IVC calculations for a stack of 9 and 19 intrinsic Josephson junctions and the computation time reduced by five times approximately. The question of choosing a change-over point from “analytical” to numerical calculation was open. In testing computations the change-over point was taken equal to 2Ib. In the case of periodic boundary conditions an equation, determining the approximate location of Ib, was obtained. This moment we succeeded to develop an algorithm determining the approximate value Ib in more complicated technically case of non-periodic boundary conditions with g = 1. All calculations were performed using the REDUCE 3.8 system.

система джозефсоновских переходов, вычисление вольт-амперных характеристик, петля гистерезиса, задача Коши для систем нелинейных дифференциальных уравнений, метод Рунге-Кутта четвёртого порядка точности, асимптотические формулы решения задачи Коши при больших t, численно-аналитический метод вычисления ВАХ, вывод асимптотических формул, используя систему REDUCE 3.8