Vortex Structures in Exponentially Shaped Josephson Junctions

We report the numerical calculations of the static vortex structure and critical curves in exponentially shaped long Josephson junctions for in-line and overlap geometries. Stability of the static solutions is investigated by checking the sign of the smallest eigenvalue of the associated Sturm-Liouville problem. The change in the junction width leads to the renormalization of the magnetic flux in comparison with the case of a linear one-dimensional model. We study the influence of the model's parameters, and particularly, the shape parameter on the stability of the states of the magnetic flux. We compare the vortex structure and critical curves for the in-line and overlap geometries. Our numerically constructed critical curve of the Josephson junction matches well with the experimental one.