  Non-linear electrical transport studies at high-pulsed magnetic fields, above
the range accessible by DC magnets, are of direct fundamental relevance to the
physics of superconductors, domain-wall, charge-density waves, and topological
semi-metal. All-superconducting very-high field magnets also make it
technologically relevant to study vortex matter in this regime. However, pulsed
magnetic fields reaching 100 T in milliseconds impose technical and fundamental
challenges that have prevented the realization of these studies. Here, we
present a technique for sub-microsecond, smart, current-voltage measurements,
which enables determining the superconducting critical current in pulsed
magnetic fields, beyond the reach of any DC magnet. We demonstrate the
excellent agreement of this technique with low DC field measurements on
Y$_{0.77}$Gd$_{0.23}$Ba$_2$Cu$_3$O$_7$ coated conductors with and without
BaHfO$_3$ nanoparticles. Exploring the uncharted high magnetic field region, we
discover a characteristic influence of the magnetic field rate of change
($dH/dt$) on the current-voltage curves in a superconductor. We fully capture
this unexplored vortex physics through a theoretical model based on the
asymmetry of the vortex velocity profile produced by the applied current.
