The geometry of ytterbium-doped active media in diode-pumped lasers can be calculated with the help of numerical
modeling for the optimization of high-energy and repetitively pulse amplifiers. In the first step the optimum thickness
of the longitudinally pumped gain medium of Yb:YAG is obtained with a theory of quasi-three level laser ions. For the
parameters of the amplifier which will deliver a 100 J, 10 Hz, 10 ns pulse, the optimum thicknesses is 5.5mm with a
doping concentration of 3.92*1020 cm-3 taking the amplified spontaneous emission (ASE) into account. In the second
step, we analyze the laser performance of the amplifiers by using various cooling configurations. The cooling
configurations investigated here include those both by forced convection cooling in a narrow passage. In every case
we determine the temperature rise, the longitudinal and radial temperature gradient, and the resulting energy storage
and extraction efficiency. The simulation results show that, with a pumping intensity of 20 kW/cm2 at 10 Hz and a
doping concentration of 3.92*1020 cm-3 at a thickness of 5.5 mm thick piece Yb:YAG, for a laser injection fluence of
0.2 J/cm2 (10 ns) ,the output laser fluence and optical-to-optical efficiency are expected to be 7.2 J/cm2 and 35%,
respectively, at a heat exchange coefficient of 1 W/cm2/K of water and 250 W/m2/K of gas.
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