Not sure if this is a question for the engineering or physics stack exchange:
The current maximum magnetic field for a nonpulsed magnetic field is around 45 Tesla while pulsed is around 100 Tesla. I'm assuming the primary reason for the limitation is that the coils overheat (from additional current being added) but how come superconductors also seem to have this limitation if they have no resistance and therefore emit no heat? Thanks!
Superconductors stop superconducting when they are in a magnetic field stronger than their critical field or if their current density exceeds their critical current. The 45 Tesla fields you refer to were originally generated with a 31 MW, 33.6 T resistive magnet inside a 11.4 T low-temperature superconductor coil, and more recently with a 14.4 T high-temperature superconductor coil inside a 31.1-tesla resistive magnet. The record field for a pure superconducting magnet, is 32 T for two high-temperature superconducting coils inside an outer low temperature superconducting coil.
At temperatures approaching 0 K, the critical field of a low-temperature superconductor such as Niobium–tin can be as high as 30 T, and can be 140 T or even more in ideal YBCO single crystals, but these are not achievable in practical coils.
The challenges are that superconductors in higher magnetic fields have lower transition temperatures and critical currents, and critical currents can be much lower at grain boundaries than inside a single crystal. If the current density exceeds the critical current density at any point inside the superconducting coil, that point becomes a normal resistive conductor and starts to heat up neighbouring material causing it to also lose superconductivity, causing a cascade known as a "quench". This can destroy the magnetic if not carefully managed.
