Electron cooling of a bunched ion beam in a storage ring

A combination of electron cooling and rf system is an effective method to compress the beam bunch length in storage rings. A simulation code based on multiparticle tracking was developed to calculate the bunched ion beam cooling process, in which the electron cooling, intrabeam scattering (IBS), ion beam space-charge field, transverse and synchrotron motion are considered. Meanwhile, bunched ion beam cooling experiments have been carried out in the main cooling storage ring (CSRm) of the Heavy Ion Research Facility in Lanzhou, to investigate the minimum bunch length obtained by the cooling method, and study the dependence of the minimum bunch length on beam and machine parameters. The experiments show comparable results to those from simulation. Based on these simulations and experiments, we established an analytical model to describe the limitation of the bunch length of the cooled ion beam. It is observed that the IBS effect is dominant for low intensity beams, and the space-charge effect is much more important for high intensity beams. Moreover, the particles will not be bunched for much higher intensity beam. The experimental results in CSRm show a good agreement with the analytical model in the IBS dominated regime. The simulation work offers us comparable results to those from the analytical model both in IBS dominated and space-charge dominated regimes.

Figure 1

Layout of the HIRFL-CSR accelerator complex.

Figure 2

Evolution of beam emittance (rms), distribution of momentum spread and bunch length in the procedure of cooling combined with rf field ($V_{rf}=1.0\mathrm{kV}$) for $6.9\mathrm{MeV}/u$ ${{}^{12}\mathrm{C}}^{6+}$ beam.

Figure 3

Evolution of the model particles distribution in longitudinal phase space (red dot), the space-charge potential (blue line) and the particles distribution in the longitudinal for one bunch of ${{}^{12}\mathrm{C}}^{6+}$ beam in CSRm. The black dashed line is the rf bucket with $V_{rf}=1.0\mathrm{kV}$ and the green line is the fitting result by the Fokker-Plank equation. The fitting result of bunch length and momentum spread is given.

Figure 4

The measured BPM signal (black) of the bunched beam, the beam linear charge density (red) calculated from the BPM signal and the Fokker-Plank fitting result (blue) in the experiment of $3.7\mathrm{MeV}/\mathrm{u}$ ${{}^{112}\mathrm{Sn}}^{36+}$. The rms bunch length is about $28\pm 0.2\mathrm{ns}$ ($I=17.7\mu \mathrm{A}$, $V_{rf}=1.4\mathrm{kV}$, $g=3.7$, $\sigma =2.3\times {10}^{-4}$).

Figure 5

Dependency of the rms bunch length on the stored particle number for different rf amplitude for $3.7\mathrm{MeV}/\mathrm{u}$ ${{}^{112}\mathrm{Sn}}^{36+}$ and $6.9\mathrm{MeV}/\mathrm{u}$ ${{}^{12}\mathrm{C}}^{6+}$ ion beams.

Figure 6

The dependence of the beam emittance on particle number for the beam ${{}^{112}\mathrm{Sn}}^{36+}$ and ${{}^{12}\mathrm{C}}^{6+}$ in the simulation.

Figure 7

Comparison of the bunch length between simulation and experiment. The dashed lines are fitted to the simulation results.

Figure 8

The bunch length versus particle number in the simulation (colored) and experiment (black) for $6.9\mathrm{MeV}/\mathrm{u}$ ${{}^{12}\mathrm{C}}^{6+}$ ion beam. In the simulation, the bunch length is estimated by considering the effects of IBS and space charge independently. The dashed lines are fitted to the simulation results.