NONLINEAR VISCOUS MOTION OF VORTICES IN JOSEPHSON CONTACTS

Nonlinear dynamics of vortices in current-carrying long Josephson contacts is considered for the cases of weak (lambda(J) much greater than lambda) and strong (lambda(J) much greater than lambda) couplings, where lambda(J) and lambda are the Josephson and London penetration depths, respectively. The first case concerns the Josephson vortices described by the sine-Gordon equation, whereas the case lambda(J) much greater than lambda corresponds to Abrikosov-like vortices with highly anisotropic Josephson cores which are described by an integral equation for the phase difference phi within the framework of a nonlocal Josephson electrodynamics. At lambda(J) much less than lambda, an exact solution for the moving vortex in the overdamped regime is obtained, the fluxon velocity v(j) and the voltage-current characteristic V(j) are calculated. It is shown that the lack of the Lorentz invariance of the integral equation for phi in the nonlocal regime leads to specific features of the vortex dynamics as compared to the Josephson vortices. The results obtained are employed for the description of nonlinear viscous motion of magnetic flux along planar crystalline defects in superconductors. It is shown that any percolating network of planar defects can considerably reduce the critical current, change the field dependence of the flux-flow resistivity, and result in a nonlinear V(j) in the flux-flow regime.