Coherent synchrotron radiation and space charge for a 1-D source on an arbitrary planar orbit

Realistic modeling of coherent synchrotron radiation (CSR) and the space charge force in single-pass systems and rings usually requires at least a two-dimensional (2-D) description of the charge/current density of the bunch. Since that leads to costly computations, one often resorts to a 1-D model of the bunch for first explorations. This paper provides several improvements to previous 1-D theories, eliminating unnecessary approximations and physical restrictions.