BabyIAXO, a 20 m-long twin-bore helioscope aiming for search of axion like particles, is currently in the engineering design phase and its construction is to be completed within the next 4 years. In addition to X-ray detectors and focusing optics, the system is equipped with a 50 MJ magnet with a common coil layout, containing two 10 m-long NbTi flat racetrack coils cooled by a group of cryocoolers. It has to operate at 10 kA, preferably in persistent mode with disconnected power supply, allowing to simplify the sun-tracking rotation system of BabyIAXO. A direct current mode is possible as well. Hence, quench protection is a high priority. Here, we present the electrical circuit of the BabyIAXO magnet and its protection layout when operated in persistent mode. The quench process is calculated using a 3-D thermo-electrical model of the coil windings, also accounting for the presence of the coil casing and the quench-back effect. Impact of the operating current, conductor properties, voltage detection threshold and location of hot-spot on the peak temperature is discussed. Quench protection aspects of the HTS busbars and persistent mode switch are also addressed.
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