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

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