Calculation of the wake due to radiation and space charge forces in relativistic beams

Radiation reaction force in a relativistic beam, also known as the CSR wakefield, is often computed using a 1D model of a line charge. While this model can serve as a useful tool for a quick calculation, in many cases its accuracy is not sufficient. In particular, this model misses the so-called compression effects associated with the change of the electromagnetic energy when the beam is compressed longitudinally or transversely. The existing 3D simulation codes that take this effect into account are often slow and are not easy to use. In this work, we propose a new approach to the calculations of radiation and space charge longitudinal forces in free space based on the use of the integrals for the retarded potentials. Our main result expresses the rate of change of particles' energy through 2D (in a 2D model) or 3D integrals along the beam orbit.