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Register a new userCooling and diffusion rates in coherent electron cooling concepts
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We present analytic cooling and diffusion rates for a simplified model of coherent electron cooling (CEC), based on a proton energy kick at each turn. This model also allows to estimate analytically the rms value of electron beam density fluctuations in the kicker section. Having such analytic expressions should allow for better understanding of the CEC mechanism, and for a quicker analysis and optimization of main system parameters. Our analysis is applicable to any CEC amplification mechanism, as long as the wake (kick) function is available.
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We compare the method of Coherent Electron Cooling with Enhanced Optical Cooling. According to our estimations the Enhanced Optical Cooling method demonstrates some advantage for parameters of LHC.
The Microbunched Electron Cooling (MBEC) proposed by D. Ratner is a promising cooling technique that can find applications in future hadron and electron-ion colliders. In this paper, we develop a new framework for the study of MBEC which is based on the analysis of the dynamics of microscopic 1D fluctuations in the electron and hadron beams during their interaction and propagation through the system. Within this framework, we derive an analytical formula for the cooling rate and benchmark it against 1D computer simulations with a agreement between the analytical and numerical results. We then calculate the expecting cooling time for a set of parameters of the proposed electron-ion collider eRHIC in a simple cooling system with one chicane in the electron channel. While the cooling rate in this system turns out to be insufficient to counteract the intra-beam scattering in the proton beam, we discuss how the electron signal can be amplified by two orders of magnitude through the use of plasma effects in the beam.
Increasing the luminosity of relativistic hadron beams is critical for the advancement of nuclear physics. Coherent electron cooling (CEC) promises to cool such beams significantly faster than alternative methods. We present simulations of 40 GeV/nucleon Au+79 ions through the first (modulator) section of a coherent electron cooler. In the modulator, the electron beam copropagates with the ion beam, which perturbs the electron beam density and velocity via anisotropic Debye shielding. In contrast to previous simulations, where the electron density was constant in time and space, here the electron beam has a finite transverse extent, and undergoes focusing by quadrupoles as it passes through the modulator. The peak density in the modulator increases by a factor of 3, as specified by the beam Twiss parameters. The inherently 3D particle and field dynamics is modeled with the parallel VSim framework using a $delta$f PIC algorithm. Physical parameters are taken from the CEC proof-of-principle experiment under development at Brookhaven National Lab.
The Microbunched Electron Cooling (MBEC) is a promising cooling technique that can find applications in future hadron and electron-ion colliders to counteract intrabeam scattering that limits the maximum achievable luminosity of the collider. To minimize the cooling time, one would use amplification cascades consisting of a drift section followed by a magnetic chicane. In this paper, we first derive and optimize the gain factor in an amplification section for a simplified one-dimensional model of the beam. We then deduce the cooling rate of a system with one and two amplification cascades. We also analyze the noise effects that counteract the cooling process through the energy diffusion in the hadron beam. Our analytical formulas are confirmed by numerical simulations for a set of model parameters.
The initial modulation in the scheme for Coherent electron Cooling (CeC) rests on the screening of the ion charge by electrons. However, in a CeC system with a bunched electron beam, inevitably, a long-range longitudinal space charge force is introduced. For a relatively dense electron beam, its force can be comparable to, or even greater than the attractive force from the ions. Hence, the influence of the space charge field on the modulation process could be important. If the 3-D Debye lengths are much smaller than the extension of the electron bunch, the modulation induced by the ion happens locally. Then, in that case, we can approximate the long-range longitudinal space charge field as a uniform electric field across the region. As detailed in this paper, we developed an analytical model to study the dynamics of ion shielding in the presence of a uniform electric field. We solved the coupled Vlasov-Poisson equation system for an infinite anisotropic electron plasma, and estimated the influences of the longitudinal space charge field to the modulation process for the experimental proof of the CeC principle at RHIC.
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