An extended T-A formulation based on potential-chain recursion for electromagnetic modeling of parallel-wound no-insulation HTS coils

Parallel-wound no-insulation (PW-NI) high-temperature superconducting (HTS) coils significantly reduce charging delay while maintaining excellent self-protection capability, demonstrating great potential for high-field applications. Existing models that couple the T-A formulation with equivalent circuits have demonstrated high accuracy in electromagnetic analysis of PW-NI coils. However, eliminating the computational overhead caused by frequent variable mapping and data exchange between electromagnetic and circuit modules is important for improving computational efficiency, particularly in long-duration transient simulations of large-scale magnets. To address this issue, an extended T-A formulation based on potential-chain recursion, termed PCR-TA, is proposed. By directly embedding inter-tape current sharing and radial current bypass behaviors into the finite-element framework, this method computes the transient electromagnetic response of PW-NI coils without requiring an explicit equivalent circuit model. Building upon it, a multi-scale approach is further developed for large-scale PW-NI coils. The validity of the proposed method and its multi-scale extension is verified through comparisons with experimental measurements and field-circuit coupled modeling results. Comparative analyses demonstrate that the PCR-TA method achieves a speedup of approximately 2.4× over the monolithic field-circuit coupled method with explicit circuit interface, whereas its multi-scale extension further increases the speedup to approximately 5.8×. Furthermore, the PCR-TA method is extended to model the continuous transition of PW-NI coils from power-supply charging to closed-loop operation. The results reveal current imbalances with spatially varying characteristics during the free decay. Under an external radial AC magnetic field, asymmetric transient dynamic resistance arises in parallel tapes, driving current redistribution. This work provides an efficient method and tool for the electromagnetic modeling of PW-NI coils under both driven and closed-loop operating conditions.