We present a comprehensive investigation of the temperature distribution in laser-cooled cylindrical solid-state samples doped with rare-earth ions. We consider Yb~(3+)-doped fluorozirconate samples pumped at a wavelength of 1015 nm with Gaussian and "Top-Hat" pump beams. The influence of the parameters of a beam on the temperature distribution is investigated in detail for optimizing the sample design for the all-optical cryocooler.
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