Cooling rate for microbunched electron cooling without amplification

Abstract

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 longitudinal cooling rate and benchmark it against 1D computer simulations. 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.

Transverse dynamics considerations for microbunched electron cooling

“…which is identical to the result of the one-dimensional analysis [5]. Another important quantity is the Fourier spectrum of δnðzÞ, which is given by…”

“…In our previous work [5,6], we studied one-dimensional (1D) shot noise effects in a particle beam by examining the fluctuations in the beam distribution function. Here, we extend this technique by also considering the transverse motion of the beam, which was neglected in our earlier treatment.…”

“…This transformation results in a new hadron distribution function after the kicker, i.e., f 2 → f 3 , where η. As far as the specific expression for the hadron energy change Δη ðhÞ ðzÞ is concerned, we can reuse the result derived in our 1D analysis [5], namely…”

“…In our previous work [5,6], we presented a onedimensional (1D) theory for MBEC that described the cooling of the hadron energy spread. Our analysis, which only considered the longitudinal portion of the motion, was based on a kinetic theory approach that tracks the evolution of fluctuations in the hadron and electron beams as they move through the cooling lattice.…”

Evolution of ion bunch profile in the presence of longitudinal coherent electron cooling

“…The future electron-ion collider demands a strong hadron cooling technique to reach the luminosity level where all the relevant physics can be fully covered. As a potential candidate to provide such a cooling technique, the concept of Coherent electron Cooling (CeC) and its variants have been extensively investigated [1][2][3][4][5]. Both analytical and simulation tools have been developed to predict the ion bunch evolution in the presence of CeC, which is essential for diagnosing as well as optimizing the cooling system [6,7].…”