Data-driven modeling of quenches in superconducting accelerator magnets

Abstract

A superconductor transitions to the normal-conducting state above certain limits on temperature, current density, and magnetic flux density. This process is known as a resistive transition or quench. Superconducting accelerator magnets usually operate close to their quench limits for economic reasons and because the application requires the highest achievable field. The magnet protection after a quench in the main dipole and quadrupole magnets of the Large Hadron Collider (LHC) is based on a combination of heating elements, known as quench heaters (QH), extraction resistors, and bypass diodes. Magnet protection is achieved by safely reducing the current through the magnet to zero in a very short time, so that the hot-spot temperature in the coils does not exceed a critical value, typically around 250–300 kelvin. Additional measures for the LHC upgrade include a current-pulse protection system, in which a short pulse of current from a capacitor is fed to the windings of a superconducting coil. This method, known as Coupling-Loss-Induced Quench (CLIQ) protection, will be implemented in the Nb${}_3$Sn quadrupole magnets of the high-luminosity upgrade of the Large Hadron Collider (HL-LHC). While the efficiency of quench heater and CLIQ systems can indeed be estimated by multiphysics simulations (thermal, electric, and magnetic), significant uncertainties remain in the nonlinear material parameters and system responses, as long as cryogenic testing and magnetic measurements are unavailable to gauge these material parameters, which are used in the numerical simulations.

In this paper, we explore a hybrid, data-driven numerical model implemented in CERN’s field calculation program ROXIE to study the efficiency of magnet protection with both quench heaters and CLIQ. This is achieved by combining statistical analysis of test data from magnets protected with quench heaters and/or CLIQ with multiphysics simulations of magnet protection using quench heaters alone. As an example of mitigating ignorance (defined in the sense of unrecognized physical effects such as superconducting filament degradation, hydraulic effects, or stress-dependent material parameters), we augment simulations without CLIQ circuits by testing data of the HL-LHC dispersion-suppressor dipole (MBH) and the inner-triplet quadrupole (MQXF) protected with both quench heaters and CLIQ. We first train the hybrid model with data from the MBH dipole and MQXF quadrupole magnets, validate the results with selected data from specific MBH magnet tests, and then estimate the hot-spot temperature of a Nb${}_3$Sn 12-T dipole magnet (12-T Valued Engineering, 12-T VE) that is still in the design and prototyping phase.

This data-driven, hybrid modeling of quenching superconducting accelerator magnets can be viewed as an example of Model-Based System Engineering, a recently established approach for post-processing magnetic measurements. And although the CLIQ circuit response can well be simulated, we take this as an example of a delta model in which an ignored or unknown physical effect is substituted by tests and measurements.