  A theoretical model for laser cooled continuous-wave fiber amplifier is
presented. The amplification process takes place in the Tm3+-doped core of the
fluoride ZBLAN (ZrF4-BaF2-LaF3-AlF3-NaF) glass fiber. The cooling process takes
place in the Yb3+:ZBLAN fiber cladding. It is shown that for each value of the
pump power and the amplified signal there is a distribution of the
concentration of the Tm3+ along the length of the fiber amplifier, which
provides its athermal operation. The influence of a small deviation in the
value of the amplified signal on the temperature of the fiber with the fixed
distribution of the Tm3+ions in the fiber cladding is investigated.
