  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.
