A more efficient computational procedure for calculating the critical current of a multi-junction superconducting interferometer

The textbook procedure for the solution of the critical current of an N-junction superconducting interferometer is a 2N-1 dimensional steepest descent problem. A solution by this procedure is complicated by the existence of multiple local minima. The equations are reformulated to reduce the problem to a three-dimensional steepest descent problem. From this reduced equation set, a non-steepest-descent procedure is developed. This technique produces a solution by adjusting a trial critical current value until tangency between a straight line and a special error function is achieved. For a 10-junction test case, an 80-to-1 reduction in computer time was achieved.