Coherent synchrotron radiation transient effects in the energy-dependent region

Coherent synchrotron radiation (CSR) is a well known phenomenon that originates from coherent superposition of electromagnetic waves by ultrarelativistic electrons. CSR longitudinal effects during the passage of a Gaussian beam from a straight to a circular path have often been studied in a regime in which they are energy independent. Nevertheless, the approximations used in such a regime may fail in several practical situations, as in the case of low-energy injectors or for small-wavelength structures within the bunch distribution in CSR-related instability problems. These situations demand a deeper investigation of longitudinal transient effects in the region where the approximations above are no longer valid: a strong gamma dependence is found, and described in this paper, in the rate of energy change induced by CSR during the transient of a Gaussian bunch between a straight and a circular path, which was studied with the help of the authors' previous work. Results show that the overall CSR longitudinal effects, in this case, are reduced. One of the outcomes of previous work by Saldin et al. was extended to this situation and very good agreement between the two studies was found.