Static vortices in long Josephson junctions of exponentially varying width

TL;DR

This paper investigates static vortex configurations in long Josephson junctions with exponentially varying width using numerical simulations, analyzing stability and critical currents influenced by junction shape parameters.

Contribution

It introduces a detailed numerical analysis of vortex solutions in exponentially varying width Josephson junctions and examines their stability through eigenvalue problems.

Findings

Multiple vortex solutions exist at certain parameter values.

Junction width variation affects magnetic flux and stability.

Critical curves depend on junction shape and flux distribution.

Abstract

A numerical simulation is carried out for static vortices in a long Josephson junction with an exponentially varying width. At specified values of the parameters the corresponding boundary-value problem admits more than one solution. Each solution (distribution of the magnetic flux in the junction) is associated to a Sturm--Liouville problem, the smallest eigenvalue of which can be used, in a first approximation, to assess the stability of the vortex against relatively small spatiotemporal perturbations. The change in width of the junction leads to a renormalization of the magnetic flux in comparison with the case of a linear one-dimensional model. The influence of the model parameters on the stability of the states of the magnetic flux is investigated in detail, particularly that of the shape parameter. The critical curve of the junction is constructed from pieces of the critical curves for the different magnetic flux distributions having the highest critical currents for the given magnetic field.