Coordinate transformation in the model of long Josephson junctions: geometrically equivalent Josephson junctions

TL;DR

This paper demonstrates a coordinate transformation linking variable width Josephson junctions to equivalent models with coordinate-dependent properties, revealing how inhomogeneities affect magnetic flux behavior and critical current characteristics.

Contribution

It introduces a coordinate transformation method to relate variable width junctions to quasi-one-dimensional models with inhomogeneities, enabling simplified analysis and potential technological advantages.

Findings

Exponential width variation leads to distributed resistive inhomogeneity acting as flux vortex attractor.

Numerical simulations of critical current vs. magnetic field curves.

Replacing distributed inhomogeneity with a local one at the junction end is feasible.

Abstract

The transition from the model of a long Josephson junction of variable width to the model of a junction with a coordinate-dependent Josephson current amplitude is effected through a coordinate transformation. This establishes the correspondence between the classes of Josephson junctions of variable width and quasi-one-dimensional junctions with a variable thickness of the barrier layer. It is shown that for a junction of exponentially varying width the barrier layer of the equivalent quasi-one-dimensional junction has a distributed resistive inhomogeneity that acts as an attractor for magnetic flux vortices. The curve of the critical current versus magnetic field for a Josephson junction with a resistive microinhomogeneity is constructed with the aid of a numerical simulation, and a comparison is made with the critical curve of a junction of exponentially varying width. The possibility of replacing a distributed inhomogeneity in a Josephson junction by a local inhomogeneity at the end of the junction is thereby demonstrated; this can have certain advantages from a technological point of view.