Analytic calculation of the magnetic field created by Halbach permanent magnets array

The magnetic field created by Halbach permanent magnets array was studied in the paper. First, according to Ampere's hypothesis of molecular current, the magnetic field created by a rectangular permanent magnet was equivalent to that excited by surface current, so the field formula for it was derived. Then, on the basis of superposition principle and coordinate transformation, the expression of Halbach magnetic field is acquired. Finally, compared with 2D and 3D FEM, the analytic formula is proved to accurately simulate the field distribution of Halbach array including the end, and be more precise than that of the Sine method.