An amplifier based on a highly-doped Chromium Zinc-Selenide (Cr:ZnSe) crystal
is proposed to increase the pulse energy emitted by an electron bunch after it
passes through an undulator magnet. The primary motivation is a possible use of
the amplified undulator radiation emitted by a beam circulating in a particle
accelerator storage ring to increase the particle beam's phase-space
density---a technique dubbed Optical Stochastic Cooling (OSC). This paper uses
a simple four energy level model to estimate the single-pass gain of Cr:ZnSe
and presents numerical calculations combined with wave-optics simulations of
undulator radiation to estimate the expected properties of the amplified
undulator wave-packet