Relaxation algorithm in description of superconducting structures

TL;DR

This paper presents a relaxation algorithm for modeling superconducting structures within the Ginzburg-Landau framework, addressing both static and dynamic cases, and applies it to various superconducting devices.

Contribution

It introduces a relaxation method tailored for superconducting structures and discusses its advantages, disadvantages, and artifacts in modeling complex superconducting devices.

Findings

Successfully modeled unconventional Josephson junctions and SQUIDs using the relaxation algorithm.

Identified artifacts and limitations of the relaxation method in superconducting simulations.

Provided a comparative analysis of static and dynamic Ginzburg-Landau equations applications.

Abstract

Relaxation method is described on simple superconducting cases in one and two dimensions in Ginzburg-Landau (GL) formalism. The structure of the algorithm is given for the case time independent and time dependent GL equation. The advantages and disadvantages of the algorithm are specified. Particular cases solved by the relaxation algorithm is unconventional Josephson junction (uJJ), modified uJJ, SQUID built on the base of uJJ and superconduting current limiter. The artifacts of relaxation algorithm are described.