A Numerical Simulation of Quench Propagation in Nb₃Sn Cables Covered With Protection Heaters

Superconducting magnets are crucial components in various scientific, industrial, and medical applications, offering unparalleled high magnetic fields and energy efficiency. However, the transition from the superconducting to the normal state, known as a quench, can pose significant challenges due to the sudden local release of stored energy and damage to the magnet system. Quench protection strategies have emerged as essential mechanisms to mitigate the adverse effects of quenches. One of the commonly used methods in accelerator magnets is to use strip heaters on coil surfaces. The heater element length and configuration influence the performance of the quench protection. The study of the quench protection by heaters requires the coupled modelling of the Joule heating, normal zone propagation, and transferring heat from the heaters to the cable. In this article, we present a new 2D finite element simulation model to model the increase of the cable resistance under different heater lengths in Nb₃Sn accelerator magnets. The model allows analyzing heaters with several different lengths of heating stations along the cable. This strategy can be used to maximize the cable resistance increase at high operation current while still providing the needed normal zone propagation at lower currents. We demonstrate the model use with a high-field racetrack dipole model.