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It is known that dispersive coupling can be applied to realize three-dimensional cooling in stochastic cooling and laser cooling. In electron cooling, the transverse cooling rate is usually smaller than the longitudinal one, especially for high-energy beams. We find that dispersion can also be introduced into electron cooling (dispersive electron cooling) to redistribute the cooling rate between the longitudinal and transverse planes. In this paper, we present an analytical model to explain and estimate the rate redistribution in dispersive electron cooling, in which both ion dispersion and electron dispersion are included. It demonstrates that a small horizontal dispersion of the ions can enhance the horizontal cooling at the expense of longitudinal cooling, and the electron dispersion is also of benefit to this effect. We also find that this redistribution effect will be more significant when there is a large difference between the horizontal and longitudinal cooling rates, which will be of great significance for high-energy electron cooling in the future.

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.

Coherent electron cooling is a promising technique to cool high-intensity hadron bunches by imprinting the noise in the hadron beam on a beam of electrons, amplifying the electron density modulations, and using them to apply cooling kicks to the hadrons. The typical size for these perturbations can be on theμmscale, allowing us to extend the reach of classical stochastic cooling by several orders of magnitude. However, it is crucial to ensure that the electron and hadron beams are longitudinally aligned within this sameμmscale. In order to provide fast feedback for this process, we discuss the extension of signal suppression to coherent electron cooling and show in both theory and simulation that certain components of the spectral noise in the hadron beam will be predictably modified at the several percent levels, which may be detected by observations of the radiation of the hadron beam.

In previous and existing hadron storage rings, the horizontal and vertical emittances are normally the same or very close. For the Hadron Storage Ring (HSR) of the Electron-Ion Collider (EIC), the design proton transverse emittance ratio is 10:1. To maintain this large emittance ratio, we need to have an online fine decoupling system to prevent transverse emittance exchange. For this purpose, we carried out fine decoupling experiments in the Relativistic Heavy Ion Collider (RHIC) and reviewed its previous operational data. Analytical prediction and numerical simulation are preformed to estimate how small the global coupling coefficient should be to maintain a 10:1 emittance ratio.

The contribution of coherent wiggler radiation (CWR) to the microwave instability threshold in wiggler-dominated storage rings such as damping rings for colliders is discussed in detail. Three different coherent wiggler radiation impedance models are considered: the free-space steady-state model, the parallel-plates shielding steady-state model, and the rectangular-chamber shielding model. The field dynamics of CWR are compared, showing that the broad-band unshielded CWR becomes dominated by resonant structures when chamber shielding is considered. To suppress the narrow-band impedance in damping wigglers with chamber shielding, we propose employing a detuned damping wiggler. A new, simple, analytical method of solving the dispersion relation and detecting the CWR-driven microwave instability threshold is presented. The theory is compared with the numerical simulations of a Vlasov-Fokker-Planck solver for the Electron Ion Collider backup storage ring cooler and confirms that the microwave instability threshold gets higher for negative momentum compaction.

The low energy RHIC electron cooler (LEReC) currently under commissioning at BNL is going to be the first non-magnetized bunched electron cooler (EC). For successful cooling LEReC requires that the electrons in the cooling section (CS) have small angles with respect to co-propagating ions. Since there is no strong magnetic field in the CS, the effects of ions on both the trajectory and focusing of the e-bunches is critical. In this paper we consider the ion beam kick on the electron bunches and derive requirements to the respective alignment of electron and ion beams in non-magnetized coolers.

The Electron-Ion Collider (EIC) uses crab cavities to restore the geometrical luminosity loss associated with the large crossing angle. Due to space limitations, the detector solenoid cannot be compensated locally. This paper presents the lattice design to compensate the detector solenoid effects without interfering with the crab cavities. Skew quadrupoles are employed to avoid additional crab cavities. The correction scheme is checked by beam-beam simulation.

The Low Energy Relativistic Heavy Ion Collider (RHIC) Electron Cooler (LEReC) is the world’s first electron cooler using rf-accelerated electron bunches. Recently, the cooling of gold ion beams in RHIC by 1.6 and 2.0 MeV electrons was successfully achieved. Along with the velocity spread and alignment of the electron beam, the space-charge force between ions and electrons also plays an important role in the cooling process. In order to investigate the cooling dynamics with bunched electron beams and to provide guidance for the LEReC operation, a simulation code was developed, which includes nonmagnetized cooling, intrabeam scattering, and the space-charge effect. In this paper, we present and discuss the simulation results, showing how various effects influence the cooling process as well as provide experimental benchmarking of the simulations.

The Electron-Ion Collider (EIC) presently under construction at Brookhaven National Laboratory will collide polarized high energy electron beams with hadron beams with design luminosities up to 1 × 10 34 cm −2 s −1 in center mass energy range of 20-140 GeV. We studied the planned electron-proton collisions using a Particle-In-Cell (PIC) based Poisson solver in strong-strong beam-beam simulation. We observed a much larger proton emittance growth rate than in weak-strong simulation. To understand the numerical noise and its impact on strong-strong simulation results, we carried out extensive studies to identify all possible causes for artificial emittance growth and quantify their contributions. In this article, we summarize our study activities and findings. This work will help us better understand the simulated emittance growth and the limits of the PIC based strong-strong beam-beam simulation.

The first electron cooling with rf-accelerated electron bunches was recently demonstrated at the low energy RHIC electron cooler (LEReC) at BNL. Successful cooling requires that the electrons in the cooling section have a small angular spread and are well aligned with respect to the copropagating ions. LEReC puts into practice a nonmagnetized cooling of the ions at Lorentz factors ofγ=4.1and 4.9. Hence, unlike in previous coolers, in which the transverse electron dynamics is constrained by longitudinal solenoid fields, the ion-electron focusing and steering strongly contribute to the average angular spread of the electron beam. In this paper we discuss the factors that affect the electron angles and describe the process of tuning the electron beam to maximize the cooling of ion bunches in RHIC.