Computation of Charged-particle Transfer Maps for General Fields and Geometries Using Electromagnetic Boundary-value Data

The passage of a charged particle through a region of nonvanishing electromagnetic fields (e.g., a bending magnet, multipole magnet, spectrometer, electrostatic lens, electromagnetic velocity separator, etc.) can be described by a transfer map [1]. In the magnetic case, computation of this map in canonical coordinates requires a knowledge of the vector potential and its multiple derivatives within the region. This information is shown to be calculable from boundary data with the aid of Helmholtz’s theorem and a novel application of the Dirac monopole vector potential. This can be done without solving Laplace’s equation within the region, a generally formidable problem. Using the methods to be described, modules could be added to existing electromagnetic codes that would produce reliably, when requested, associated transfer maps to any desired order for arbitrary static charged-particle beamline elements.