Spherical Harmonics Coefficients of All Magnetic Field Components Generated by Iron Piece

摘要

When a magnet generating highly homogeneous magnetic field is designed, a shimming is required. Usually, the shimming is performed for compensating the magnetic field only in the z-direction by an iron or a coil. Commonly the compensation is achieved for eliminating the coefficients of the spherical harmonics expansion of the magnetic field generated by the magnet. Some papers showed the coefficients of the spherical harmonics expansion in the z- direction for a passive shimming. However, recently, some magnets generate a tilted magnetic field, such as a magic angle rotating field NMR/MRI. Therefore, the coefficients of the spherical harmonics expansion in the x- and y-directions are presented in this paper.