  The influence of low temperatures on the performance of a high-power
single-frequency fiber laser amplifier is evaluated with a numerical
simulation. Cooling the fiber can allow to take advantage of both higher
damping of the acoustic waves in the silica glass, and higher laser efficiency.
We first report on the measurement of the stimulated Brillouin scattering (SBS)
threshold in a silica fiber as a function of the temperature from 300~K down to
77~K. We then present the measurements of small-signal absorption and gain
spectra of an erbium doped alumino-phosphosilicate fiber, at room temperature
and liquid nitrogen temperature. Based on these data, we derive a numerical
study of the combined effects of cooling on the SBS threshold and the amplifier
efficiency, and conclude on the interest of this technique for SBS limited high
power Er doped fiber amplifiers (EDFA). The temperature increase caused by the
pump laser in the fiber core is also addressed.
