Impact of flux jumps on high-precision powering of Nb$_3$Sn superconducting magnets

Nb$_3$Sn superconducting magnets represent a technology enabler for future high-energy particle accelerators. A possible impediment, though, comes from flux jumps that, so far, could not be avoided by design unlike for NbTi technology. However, the impact of flux jumps on the magnet powering has not been properly investigated to date. Flux jumps appear during current ramps at relatively low value of current and tend to disappear towards nominal current. They are usually detected as voltage jumps between different magnet coils but they might also produce overall voltage jumps across the magnet electrical terminals. Such jumps might perturb the power converter feedback control loop and therefore potentially jeopardize its precision performance during energy ramps. This work aims at: (i) presenting preliminary experimental test results on some HL-LHC Nb$_3$Sn model and prototype magnets, and (ii) attempting to build a simplified electrical model of the flux jumps, with focus only at its interaction with the power converter feedback control loop. Such a work is a starting point for outlining possible power converters control strategies able to minimize flux jumps impact on high-precision powering of Nb$_3$Sn superconducting magnets.