The compact STorage ring for Accelerator Research and Technology (cSTART) project aims to store electron bunches of LWFA-like beams in a very large momentum acceptance storage ring. The project will be realized at the Karlsruhe Institute of Technology (KIT, Germany). Initially, the Ferninfrarot Linac- Und Test-Experiment (FLUTE), a source of ultra-short bunches, will serve as an injector for cSTART to benchmark and emulate laser-wakefield accelerator-like beams. In a second stage a laser-plasma accelerator will be used as an injector, which is being developed as part of the ATHENA project in collaboration with DESY and Helmholtz Institute Jena (HIJ). With an energy of 50 MeV and damping times of several seconds, the electron beam does not reach equilibrium emittance. Furthermore, the critical frequency of synchrotron radiation is 50 THz and in the same order as the bunch spectrum, which implies that the entire bunch radiates coherently. We perform longitudinal particle tracking simulations to investigate the evolution of the bunch length and spectrum as well as the emitted coherent synchrotron radiation. Finally, different options for the RF system are discussed.