Calculation errors and applicability of the magnetic dipole model for far-field magnetic fields of HTS magnets and solenoid coils

The magnetic dipole model is of significant value for predicting the far-field distribution of magnetic targets due to its simplicity and computational efficiency. However, its applicable conditions and accuracy boundaries for High-Temperature Superconducting (HTS) magnets and solenoid coils remain poorly defined and lack a systematic quantitative basis. To address this, this paper introduces a weighted second-order moment based on magnetic moments and derives, from electromagnetic field theory, the dimensional characteristics that minimize the dipole approximation error. By combining high-precision numerical experiments incorporating screening current effects and actual measurements, we systematically investigated the calculation accuracy of the dipole model for the external magnetic field of HTS magnets and its variation with distance. The results indicate that the magnet aspect ratio is the key determinant of model accuracy: when the aspect ratio approaches the theoretical optimal value of 0.866, the model achieves the given error threshold within the shortest characteristic distance. For magnets with general aspect ratios, the calculation error at target points beyond 3 times the characteristic dimension can be controlled within 5%; if the aspect ratio is close to the optimal value, this distance can be shortened to approximately twice this dimension. For high-precision scenarios requiring an error ≤ 1%, more than 6 times the characteristic dimension is typically required, which can be reduced to about four times this dimension under optimal geometric conditions. Furthermore, for elongated magnets, the mechanism by which the multi-dipole equivalent model improves accuracy is attributed not only to the reduction of sub-unit size but also to the adjustment of the sub-unit aspect ratio closer to the optimal value. This study provides quantitative guidelines and an engineering basis for the rapid calculation of the far-field magnetic distribution of HTS magnets and solenoid coils.