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We present theoretical and numerical investigations of vortices driven bystrong dc and ac currents in long Josephson junctions described by a nonlinearintegro-differential equation which takes into account nonlocal electrodynamicsof films, vortex bremsstrahlung and Cherenkov radiation amplified by theattraction of vortices to the edges of the junction. The work focuses on thedynamics of vortices in Josephson junctions in thin films where the effects ofJosephson nonlocality dominate but London screening is negligible. We obtainedan exact solution for a vortex driven by an arbitrary time-dependent current inan overdamped junction where the vortex turns into a phase slip if the lengthof the junction is shorter than a critical length which depends on current. Ouranalytical and numerical results show that the dynamic behavior of vorticesdepends crucially on the ohmic damping parameter. In overdamped junctionsvortices expand as they move faster and turn into phase slips as currentincreases. In underdamped junctions vortices entering from the edges produceCherenkov radiation generating cascades of expanding vortex-antivortex pairs,which ultimately drive the entire junction into a resistive phase slip state.Simulations revealed a variety of complex dynamic states of vortices under dcand ac currents which can manifest themselves in hysteretic current-voltagecharacteristics with jumps and regions with negative differential resistanceresulting from transitions from oscillating to ballistic propagation ofvortices, their interaction with pinning centers and standing nonlinear wavesin the junction.

Dynamic transition of vortices into phase slips and generation of vortex-antivortex pairs in thin film Josephson junctions under dc and ac currents