The IV-characteristic of the long josephson junction at the zero-field step

The influence of Josephson vortices on the formation of the first zero-field step is investigated theoretically by two methods. The first method is based on the numerical solution of the dynamical equations. The spatial distribution of the critical currents along the junction has a small irregularity of 10(-3)% at an arbitrary location, which allows the formation of zero-field steps in the IV-characteristic. The periodic motion of Josephson vortices in the junction is studied in detail using the first method. The IV-curve and the Josephson penetration depths of the magnetic field for different voltage values are determined. According to the second method, described earlier in the literature, the IV-curve can be found analytically from the equality of the input power and the dissipation rate in the junction, and the zero-field step is formed solely by the movement of the Josephson vortices. The comparison of the zero-field steps found by the two methods mentioned above showed that both methods give almost identical results, except for the top of the step, where the second method gives larger values. Thus, it is proven that the first zero-field step in the IV-curve of the long junction is formed by the motion of Josephson vortices.