Two Methods for the Calculation of CSR Fields

Two methods for the calculation of fields of three dimensional charge distributions on general trajectories are described. Although the source functions are three dimensional, the numerical field calculation is reduced to one-dimensional integrals that have to be evaluated numerically. The first method determines the longitudinal electric field of charge densities that can be factorized into arbitrary longitudinal and transverse distributions. The field is split into a ‘linear-motion-part’ that is independent of the shape of the general trajectory and a second part, that is under certain conditions, independent on the transverse density function. A special case of this method is the ‘small-angle-approach’ described in [1]. The second method allows the complete field calculation (electromagnetic fields and potentials) of spherical Gaussian distributions without further restrictions. A generalization for general Gaussian distributions is proposed. A couple of examples demonstrate the applicability of these approaches.