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We present analytic cooling and diffusion rates for a simplified model ofcoherent electron cooling (CEC), based on a proton energy kick at each turn.This model also allows to estimate analytically the rms value of electron beamdensity fluctuations in the "kicker" section. Having such analytic expressionsshould allow for better understanding of the CEC mechanism, and for a quickeranalysis and optimization of main system parameters. Our analysis is applicableto any CEC amplification mechanism, as long as the wake (kick) function isavailable.

Cooling and diffusion rates in coherent electron cooling concepts