Abstract
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.
Highlights
When the trajectory of a relativistic beam is bent by magnetic field, the beam radiates electromagnetic field and experiences a radiation reaction force
It has later been generalized in Refs. [4,5] for a bending magnet of finite length and is currently implemented in several computer codes routinely used for simulations of beam dynamics in accelerators
In this paper we propose a different approach to the calculation of the 3D coherent synchrotron radiation (CSR) wake when the beam propagates in free space
Summary
When the trajectory of a relativistic beam is bent by magnetic field, the beam radiates electromagnetic field and experiences a radiation reaction force. In this paper we propose a different approach to the calculation of the 3D CSR wake when the beam propagates in free space (that is neglecting the effects of metal boundaries). While the method developed in those papers is adequate for studies of such problems as microbunching instability, where the self-consistent nature of the particlefield interaction is crucial, here we aim at the applications of the CSR wake in situations when it is relatively small and can be treated as a perturbation These situations appear in the design of bunch compressors with a high peak current where even a relatively small CSR wake can lead to a large transverse emittance growth of the beam. We use the CGS system of units throughout this paper
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