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

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.Comment: Presented for M2S, Dresden, July 9-14, 200

Vortex structure 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. Each solution of the corresponding boundary value problem is associated with the Sturm-Liouville problem whose minimal eigenvalue allows to make a conclusion about the stability of the vortex. The change in width of the junction leads to the renormalization of the magnetic flux in comparison to 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.Comment: 8 pages, 10 figures, NATO Advanced Research Workshop on "Vortex dynamics in superconductors and other complex systems" Yalta, Crimea, Ukraine, 13-17 September 200