Computing transfer functions of multipole devices directly from magnetic field data, including fringe field effects and higher order aberrations

Abstract

The scalar and vector potentials of a magnetic multipole device are described in terms of magnetic field measurements gathered on either a cylindrical surface or a median plane [1]. Fringe field effects and multipole contributions of arbitrary order, as well as the discrete nature of the field measurements, are taken into account. This description has been used to calculate the transfer function of the device, directly in terms of the field measurements. The method as described in this paper can be applied to single beam guiding elements as well as to clusters of elements, and can be extended to calculate the transfer function for a complete beam line setup or a storage ring. The accuracy of the results is only limited by the accuracy of the field measurements.