Theoretical analysis and calculation of field parameters for magnetic multipole field

Abstract

According to the symmetry, Taylor series expansion formulas were derived for the magnetic multipole fields and field parameters were defined. Theoretical calculation formulas of field parameters of magnetic multipole field were obtained for saddle coils with the Biot_Savart law and the magnitudes of field parameter were analyzed. The rules of calculating field parameters and the high order derivatives of field parameters were also given. Our results may provide a theoretical basis for some applications of the magnetic multipole fields.