Common features of vortex structure in long exponentially shaped Josephson junctions and Josephson junctions with inhomogeneities

TL;DR

This paper compares vortex structures in three models of long Josephson junctions, revealing their similarities and differences through numerical analysis of flux distributions and critical curves.

Contribution

It introduces an equivalence between exponentially shaped Josephson junctions and rectangular junctions with distributed inhomogeneities, supported by numerical evidence.

Findings

Critical curves for different models are very similar under certain parameters.

Numerical calculations of flux distributions and bifurcation curves were performed.

An equivalence between exponentially shaped and inhomogeneous rectangular junctions is demonstrated.

Abstract

We study vortex structure in three different models of long Josephson junctions: exponentially shaped Josephson junction and Josephson junctions with resistor and shunt inhomogeneities in barrier layer. Numerical calculations of the possible magnetic flux distributions and corresponding bifurcation curves have done. For these three models the critical curves ``critical current-magnetic field'' are constructed. We develop an idea of the equivalence of exponentially shaped Josephson junction and rectangular junction with distributed inhomogeneity and demonstrate that at some parameters of shunt and resistor inhomogeneities at the ends of the junction the corresponding critical curves are very close to the exponentially shaped one.