The term "critical current" is often used for the current that generates the maximum magnetic field a superconductor of a given size/geometry can sustain. In practice the actual maximum current before quench is much lower (orders of magnitudes in some cases, I've heard) due to imperfections in metallic lattices.

This [1] is worth a few listens.

1. https://omegataupodcast.net/285-superconductivity/