Protection Heater Delay Time Optimization for High-Field $\hbox{Nb}_{3}\hbox{Sn}$ Accelerator Magnets

The US LARP collaboration has been pursuing the development of Nb3Sn technology for the interaction region low-beta quadrupole magnets for the future LHC luminosity upgrade. A key component for safe operation of these high-field magnets is the quench protection system. Due to the high stored energy density and the low stabilizer fraction in the conductor, quench propagation in the windings needs to be accelerated to limit the hot spot temperature and coil internal voltages during a quench. For this purpose, quench protection heaters are used to introduce multiple quenches across the windings. Heater delay, i.e. the time delay between heater activation and normal zone initiation under the heater, is a critical design parameter. We present an analysis of the heater delays characteristics for Nb3Sn coil windings based on our recently developed Code for Heater Delay Analysis (CoHDA), and compare with experimental results for various operational currents and temperatures in the LARP HQ and LQ magnets. We demonstrate applicability of our simulation model for heater design optimization of the LHC type low-beta quadrupole coils.