  Coherent electron cooling is an ultra-high-bandwidth form of stochastic
cooling which utilizes the charge perturbation from Debye screening as a seed
for a free-electron laser. The amplified and frequency-modulated signal that
results from the free-electron laser process is then used to give an
energy-dependent kick on the hadrons in a bunch. In this paper, we present a
theoretical description of a high-gain free-electron laser with applications to
a complete theoretical description of coherent electron cooling.
