Longitudinal stacking of ion beams with pulsed electron beam cooling

Longitudinal ion beam stacking with the combination of barrier rf system and beam cooling has been demonstrated in several experiments. Based on the bunching effect found in the pulsed electron beam cooling experiment at HIRFL-CSRm, we propose a new beam stacking scheme using only pulsed electron beam, in which the barrier voltage and cooling effect can be realized simultaneously. In this paper, we introduce this longitudinal stacking scheme along with the theory of beam dynamics and present a simple analytical model. The simulation demonstrates that this approach could be a useful beam stacking technique without the need for barrier bucket hardware. Moreover, the optimization and limitation of this stacking scheme are discussed, and the effect of the electron beam distribution on the barrier voltage is studied. We expect this stacking method can be applied to accumulate RIBs in low and medium energy storage rings for high-precision experiments, such as the SRing of the HIAF project.

Figure 1

General layout of the e-cooler EC35 in HIRFL-CSRm. 1-electron gun, 2-electrostatic bending plates, 3-toroid, 4-solenoid of the cooling section, 5-magnet system, 6-collector for e-beam, 7-dipole corrector, 8-flange for CSRm.

Figure 2

Schematic view of the EC35 gun. 1-cathode, 2-grid, 3-anode, 4-HV.

Figure 3

Modulated voltage on the grid electrode (dash), pulsed electron beam current (red), and BPM signal (blue) generated by the pulsed electron beam in the experiment. The noise of the current signal comes from the filter.

Figure 4

Schematic view of the barrier bucket generated by a pulsed electron beam, and the particle motion in longitudinal phase space. (Blue: barrier potential in arb. units; magenta: separatrix orbit; orange and green: drift orbit outside the separatrix).

Figure 5

Simulation results of beam distribution in longitudinal phase space during cooling. The boundaries of the ring and the pulsed electron beam are marked with a dashed line. (a) After injection of a short bunched ion beam (uniform); (b–c) The debunching process due to drift motion, no obvious cooling effect is observed yet; (d) Debunching finished and particles start to be bunched into the bucket due to cooling; (e, f) Ion beam is gradually cooled and bunched into the bucket.

Figure 6

Evolution of beam emittance and intensity during stacking with an injection interval of 1.0 s.

Figure 7

Particle distribution in longitudinal phase space at equilibrium compared to the injected beam distribution.

Figure 8

Comparison of the stacking process with different settings in simulation.

Figure 9

Various beam transverse distribution $f(r)$ with beam radius $R_e=2\mathrm{cm}$.

Figure 10

Dependence of the geometric factor on beam radius for various electron beam distributions.