  The ultra-fast dynamics of superconducting vortices harbors rich physics
generic to nonequilibrium collective systems. The phenomenon of flux-flow
instability (FFI), however, prevents its exploration and sets practical limits
for the use of vortices in various applications. To suppress the FFI, a
superconductor should exhibit a rarely achieved combination of properties: weak
volume pinning, close-to-depairing critical current, and fast heat removal from
heated electrons. Here, we demonstrate experimentally ultra-fast vortex motion
at velocities of 10-15 km/s in a directly written Nb-C superconductor in which
a close-to-perfect edge barrier orders the vortex motion at large current
values. The spatial evolution of the FFI is described using the edge-controlled
FFI model, implying a chain of FFI nucleation points along the sample edge and
their development into self-organized Josephson-like junctions (vortex rivers).
In addition, our results offer insights into the applicability of widely used
FFI models and suggest Nb-C to be a good candidate material for fast
single-photon detectors.
