Investigation of screening current and SCIS effects on magnetic field uniformity in high-temperature superconducting saddle coils

High field homogeneity in high-temperature superconducting (HTS) saddle coils is critical for accelerator beam extraction. This study proposes a model framework integrating the Frenet-Serret frame of differential geometry and multi-physics field coupling, and innovatively applies coordinate transformations from geometric modeling to electromagnetics and mechanics to enable calcula0tions investigating the influence of screening currents and screening-current-induced stress (SCIS) on magnetic field uniformity. Precise mapping of conductor spatial configurations is achieved through a parametric curvilinear coordinate system constructed using Frenet-Serret frames. Critical currents (Ic) of REBCO tapes are predicted via a deep neural network modeling nonlinear T-B-θ relationships. A transient screening current model based on the T-A formulation reveals field distortion mechanisms induced by current concentration in twisted regions. Electromagnetic-mechanical bidirectional coupling, established through Lorentz forces and deformation gradient tensors, quantifies SCIS effects. Simulations demonstrate that non-uniform screening currents dominate magnetic field uniformity, while SCIS-induced deformation is negligible under self-field conditions but potentially significant in high-precision applications. The study confirms that the interaction among the spatial configuration of the tape, the distribution of screening currents, and SCIS is a key factor restricting the magnetic field quality, providing data support for the regulation of excitation strategies and the optimization of coil structures.