Maximum heat transfer along a sapphire suspension fiber for a cryogenic interferometric gravitational wave detector

We have shown experimentally that the thermal conductivity of a sapphire fiber, which is used as a suspension and thermal conductor of mirrors in a cryogenic interferometric gravitational wave detector, is limited by boundary scattering of phonons in the temperature range below 40 K, and that maximum heat transfer along the fiber is proportional not to the square of the diameter of the fiber, but to the cubic. For the design of a sapphire suspension fiber for the LCGT project (1 mm in diameter, 25 cm in length and two loops), the maximum heat transfer along the fiber from the mirror at 20 K to the medium mass at 10 K is 340 mW.