Using a neural network model to guide protection heater design in Nb₃Sn accelerator magnets

Abstract

A common method for quench protection in accelerator magnets is based on quench protection heaters installed on the coil surfaces. The heaters quickly spread the normal zone across the windings allowing a uniform dissipation of the stored energy. Heater delay is the time required to initiate a normal zone in the coil after heater activation. In high field magnets the heater delays typically range between 5 and 40 ms. Numerical simulations are used for the heater delay prediction while designing the heaters. The simulation models typically include the heater, cable, and insulation layers to compute heat transfer. Challenges arise from numerical stability due to the thin material layers (0.025–0.1 mm) and their temperature-dependent thermal properties. In this study, we created a dataset with heater delay simulations covering a wide range of heater designs and cable parameters relevant for high-field Nb3Sn accelerator magnets. We then analyzed the data and created a machine learning-based surrogate model that can be used as a stand-alone tool to estimate the heater delay in Nb3Sn accelerator magnets with only 7 input parameters. The neural network model provides a fast and user-friendly solution, that is available without investing in numerical model development. The results from the neural network model are very close to the 1D numerical simulations that were used to train the model: the Mean Absolute Error was 0.06305 ms and R-squared was 0.9996319. The neural network simulation time is less than 1 s, making it attractive also for integration with other quench protection design software that typically require tens or hundreds of simulations. We also present design graphs that can be used to estimate the heater delay without any computations at all during the first stages of magnet design. The limitation of the model is that it neglects the heater length.