Cooling and diffusion rates in coherent electron cooling concepts

TL;DR

This paper derives analytic expressions for cooling and diffusion rates in a simplified coherent electron cooling model, aiding understanding and optimization of system parameters across various amplification mechanisms.

Contribution

It provides the first analytic formulas for cooling and diffusion rates in a simplified CEC model, applicable to different amplification mechanisms.

Findings

Analytic expressions for cooling rates.

Analytic expressions for diffusion rates.

Estimation of electron beam density fluctuations.

Abstract

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.