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Laser cooling of relativistic heavy ion beams of Li-like C$^{3+}$ andO$^{4+}$ is being in preparation at the experimental Cooler Storage Ring(CSRe). Recently, a preparatory experiment to test important prerequisites forlaser cooling of relativistic $^{12}$C$^{3+}$ ion beams using a pulsed lasersystem has been performed at the CSRe. Unfortunately, the interaction betweenthe ions and the pulsed laser cannot be detected. In order to study the lasercooling process and find the optimized parameters for future laser coolingexperiment, a multi-particle tracking method was developed to simulate thedetailed longitudinal dynamics of laser-cooled ion beams at the CSRe. Thesimulations of laser cooling of the $^{12}$C$^{3+}$ ion beams by scanning thefrequency of RF-buncher or continuous wave (CW) laser wavelength wereperformed. The simulation results indicated that a large momentum spread ionbeams could be laser-cooled by the combination of only one CW laser and theRF-buncher and shown the requirements of a successful laser cooling experiment.The optimized parameters for scanning the RF-buncher frequency or laserfrequency were obtained. Furthermore, the heating effects were estimated forlaser cooling at the CSRe. The Schottky noise spectra of longitudinallymodulated and laser-cooled ion beams was simulated to fully explain andanticipate the experimental results. The combination of Schottky spectra fromthe highly sensitive resonant Schottky pick-up and the simulation methodsdeveloped in this paper will be helpful to investigate the longitudinaldynamics of RF-bunched and ultra-cold ion beams in the upcoming laser coolingexperiments at the CSRe.

Simulation of longitudinal dynamics of laser-cooled and RF-bunched C$^{3+}$ ion beams at heavy ion storage ring CSRe