Modeling the fields of magneto-optical devices, including fringe field effects and higher order multipole contributions, with application to charged particle optics

A new method for the calculation of the magnetic field of beam guiding elements is presented. The method relates the calculation to measurement data of the magnetic field in a direct way. It can be applied to single beam guiding elements as well as to clusters of elements. The presented description of the magnetic field differs from the classical approach in that it does not rely on power series approximations. It is also both divergence free and curl free, and takes fringe field effects up to any desired order into account. In the field description, pseudodifferential operators described by Bessel functions are used to obtain the various multipole contributions. Magnetic field data on a two-dimensional surface, e.g., a cylindrical surface or median plane, serve as input for the calculation of the three-dimensional magnetic field. A boundary element method is presented to fit the fields to a discrete set of field data, obtained, for instance, from field measurements, on the two-dimensional surface. Relative errors in the field approximation do not exceed the maximal relative errors in the input data. Methods for incorporating the obtained field in both analytical and numerical computation of transfer functions are outlined. Applications include easy calculation of the transfer functions of clusters of beam guiding elements and of generalized field gradients for any multipole contribution up to any order.