Interaction of a fluxon with an inductance step in a long Josephson junction

Abstract
Within the framework of the sine‐Gordon model of a long Josephson junction, we have calculated a threshold value of bias current density which admits capture of a fluxon by an effective potential well generated by a step of inductance in the junction. Along with a kinematic approximation, a nontrivial dynamical correction is found. We have also calculated analytically energy emitted by a fast fluxon moving past the step.