ACCURATE CUBIC SPLINE INTERPOLATION OF MAGNETIZATION TABLES

The accurate interpolation of magnetization tables is of paramount importance in the design of high‐precision magnets used for particle accelerators or for magnetic resonance imaging of the human body. Cubic spline interpolation is normally used in combination with the fast converging Newton‐Raphson scheme in the two‐dimensional finite element modelling of such magnets. We compare cubic spline interpolation with experiment, using the magnetization tables as a source of carefully measured experimental data. We show that, in all examined cases, cubic spline interpolation introduces errors large enough to invalidate a design. We also propose a simple solution to the problem, thus combining the best of all worlds: the speed and convergence properties of Newton‐Raphson, the accuracy of a good interpolation scheme, and the convenient mathematical properties of cubic splines. We examine both two‐dimensional and three‐dimensional cases.