Effect of external magnetic field on fluxon dynamics and current voltage characteristics of long Josephson junctions

The presence of zero field steps (ZFS) on the volt-ampere characteristics of long Josephson junctions has been generally accepted as a manifestation of fluxon propagation. Each step represents an equal number of fluxons and antifluxons resonating in the junction in a period fixed by the junction length. However, extra steps have been experimentally observed which appear to correspond to non-integral numbers of fluxons traversing the junction in one period. We use a computer simulation of the sine-Gordon equation and a separate mechanical model to demonstrate that it is feasible to maintain a different number of fluxons and antifluxons in the junction within one period. With the appropriate choice of asymmetric boundary conditions corresponding to an applied magnetic field, one end of the junction, upon arrival of an antifluxon, may release one or more extra fluxons, while the opposite end is capable of absorbing these extra fluxons. Thus, the number of fluxons passing through a given point in the junction is not equal to the number of antifluxons passing the same point within a period. If the difference between the number of fluxons and antifluxons is an odd number, steps in addition to ZFS appear on the volt-ampere characteristic. We demonstrate that a variety of complex step behavior in magnetic fields can be explained by using the concept of creation and annihilation of fluxons at the boundaries.