*Article* **Magnetic Field Saturation of Non-Insulation High-Temperature Superconducting Coils during Overcurrent**

**Wei Wu \*, Yusong Gao and Zhijian Jin**

School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China; yusongao@sjtu.edu.cn (Y.G.); zjjin@sjtu.edu.cn (Z.J.)

**\*** Correspondence: wei.wu@sjtu.edu.cn

**Abstract:** Non-insulation high-temperature superconducting coils provide a much lower risk of burnout in fault/abnormal conditions, such as hot-spot quench and overcurrent. This study employs an equivalent circuit grid model, coupled with magnetic field calculation and the *E*–*J* power law of superconductors, to deeply and systematically investigate the overcurrent charging process in a double-pancake non-insulation coil. An evident saturation of the magnetic field in the axial direction of the coil was observed and verified by experiments. Experimentally, the entire process, including the behavior of the magnetic field, was consistent with the numerical results. Based on the verified model, two main points were addressed: (1) Transient current distribution inside the coil during overcurrent charging was studied. Potential quenching risks were found to be at the innermost and outermost turn near the electrodes, as well as the pancake-to-pancake connection part. (2) Magnetic field saturation, which is a unique phenomenon in non-insulation superconducting coils during overcurrent charging, was studied in detail and first quantitatively defined by a new concept "converged load factor". Its relationship with turn-to-turn resistivity was revealed.

**Keywords:** high-temperature superconductor; non-insulation coil; overcurrent; numerical modeling; magnetic field saturation
