Instability of flux flow and production of vortex-antivortex pairs by current-driven Josephson vortices in layered superconductors

We report numerical simulations of the nonlinear dynamics of Josephson vortices driven by strong dc currents in layered superconductors. Dynamic equations for interlayer phase differences in a stack of coupled superconducting layers were solved to calculate a drag coefficient $\eta(J)$ of the vortex as a function of the perpendicular dc current density $J$. It is shown that Cherenkov radiation produced by a moving vortex causes significant radiation drag increasing $\eta(v)$ at high vortex velocities $v$ and striking instabilities of driven Josephson vortices moving faster than a terminal velocity $v_c$. The steady-state flux flow breaks down at $v>v_c$ as the vortex starts producing a cascade of expanding vortex-antivortex pairs evolving into either planar macrovortex structures or branching flux patterns propagating both along and across the layers. The pair production triggered by a rapidly moving vortex is most pronounced in a stack of underdamped planar junctions where it can occur at $J>J_s$ well below the interlayer Josephson critical current density. Both $v_c$ and $J_s$ were calculated as functions of the quasiparticle damping parameter, and the dc magnetic field applied parallel to the layers. The effects of vortex interaction on the Cherenkov instability of moving vortex chains and lattices in annular stacks of Josephson junctions were considered. It is shown that a vortex driven by a current density $J>J_s$ in a multilayer of finite length excites self-sustained large-amplitude standing waves of magnetic flux, resulting in temporal oscillations of the total magnetic moment. We evaluated a contribution of this effect to the power $W$ radiated by the sample and showed that $W$ increases strongly as the number of layers increases.