Ring-based electron cooler for high energy beam cooling

An electron-ion collider (EIC) at Brookhaven National Laboratory is being proposed as a new discovery machine for the nuclear physics and quantum chromodynamics. The hadron beam cooling plays an important role in the EIC machine to achieve its physics goals. The most challenging is cooling of protons at the highest energy in the EIC. In this paper, we present a possible design of a ring-based electron cooler for the high energy hadron beam cooling. In the proposed approach, the electrons will cool the hadrons while being cooled themselves by radiation damping in the storage ring. For the design of the cooler using the storage ring approach several aspects become very important, including electron ring optics design, chromaticity correction, calculating the dynamic aperture, radiation damping, quantum excitation, and intrabeam scattering. In addition, such effects as beam-beam scattering due to interaction of electrons with hadrons becomes of special concern, and we develop a generalized approach to it. In this paper, we take all of the above effects into the design, and discuss the beam lifetime and instabilities in the ring. A special feature of our design is an effective use of dispersion in the cooling section, both for the ions and electrons, to redistribute the cooling rate between the longitudinal and horizontal planes. Finally, the cooling performance is simulated for proton beam at the top energy of the EIC. Our conclusion is that such ring-based cooler could be a feasible approach to provide required parameters of hadron beam at the top energy of 275 GeV for the EIC.

Figure 1

Emittance growth of the 275 GeV proton beam caused by IBS.

Figure 2

Layout of the ring cooler.

Figure 3

Optics of the ring cooler.

Figure 4

Twiss functions in the wiggler and in the transition between wigglers.

Figure 5

Evolution of the electron beam parameters in the ring cooler with two sets of arbitrary initial parameters.

Figure 6

Dynamic aperture tracking result by elegant (black: survived particles; red: lost particles). The dashed line is the rf-momentum aperture (${\epsilon }_{x,\mathrm{rms}}=21\mathrm{nm}$, ${\epsilon }_{y,\mathrm{rms}}=18\mathrm{nm}$, ${\delta }_{p,\mathrm{rms}}=8.9\times {10}^{-4}$).

Figure 7

The dependency of the quantum lifetime on the horizontal and vertical apertures with $A_p=8.8$. (${\lambda }_x/{\lambda }_y/{\lambda }_p=5.2/5.0/5.5{\mathrm{s}}^{-1}$).

Figure 8

CSR impedance of a single wiggler with the shielding gap of 2 and 4 cm.

Figure 9

Dependence of the cooling rate on dispersions.

Figure 10

Evolution of the rms electron beam size and angle spread along the cooling section with and without the space charge effect (${\beta }_i^{*}=100\mathrm{m}$).

Figure 11

The evolution of the hadron beam emittance during cooling (upper plot: $D_i=0m$, $D_e=0\mathrm{m}$; bottom plot: $D_i=2.5\mathrm{m}$, $D_e=2\mathrm{m}$).