An alternating direction implicit method applied to the calculation of a magnetic field from a measured boundary

Abstract An alternating direction implicit (ADI) method is applied to the problem of calculating the components of a magnetic field in a grid, when values of the components are given on the boundary. The calculations are here applied to the axially symmetric case of a long lens spectrometer. The procedure may be extended to a multidimensional case. The ADI method is shown to give more accurate magnetic fields compared to measured fields all over the region, both in regard of systematic and random errors in the measurement. The ADI-method thus turns out to be useful as soon as an accurate determination of a magnetic field in a region is of interest e.g. for cyclotron calculations and investigations of different types of magnetic lenses.