Measurement of the thermal conductivity of sapphire fibers

1. Measurement of the thermal conductivity of sapphire fibers TakafumiUshiba, M2 Tsubono Lab., The University of Tokyo

2. Suspension of KAGRA enlarge Hook the mirror on the sapphire fiber with thick edge

3. Sapphire Fiber with Thick Edge Thin part: about 1.8mm in diameter Thick part: 10mm in diameter These fibers are not polished. IMPEX is now manufacturing their fibers. Conceptional drawing of IMPEX fiber Moltech sapphire fibers

4. Theory of the Thermal Conductivity Thermal conductivity : volumetric specific heat → at low temperature : speed of sound → in sapphire (constant) mean free path of a phonon Since is constant at low temperature, the thermal conductivity is proportional to at low temperature.

5. Previous Measurement Physics Letters A 301 (2002) Tomaru et al They use sapphire fibers made by Photoran sapphire fiber is well fitted by 0.0625. Proportional to This result supports that the thermal conductivity is proportional to at low temperature

6. Requirement of Thermal Conductivity For two cryocooler (2W) Thermal resistance of a sapphire fiber : thermal conductivity length of a sapphire fiber cross-section of a sapphire fiber If we require , should be larger than Intermediate mass 16K 4 sapphire fibers Laser Requirement @ 20K ( Test mass absorption 23K

7. Theory of the Thermal Conductivity Thermal conductivity : volumetric specific heat → at low temperature : speed of sound → in sapphire (constant) mean free path of a phonon These are inherent in the material This is the only parameter we can change We should prepare the sapphire fibers which have the long mean free path of a phonon.

8. Thermal Conductivity of Sapphire fibers The side of Moltech and IMPEX sapphire fibers are not polished. 　　→The surface of these sapphire fibers are rough. It makes the thermal conductivity low. (Size effect) Sapphire fiber phonon Highly polished Completely reflected High thermal conductivity Not polished Scattering Low thermal conductivity Even if the size effect limit the thermal conductivity of sapphire fibers, it is not a matter for KAGRA suspension.

9. Thermal Conductivity of Sapphire fibers If the purity of the sapphire fiber is low 　　→The sapphire fibers have defects of phonon and impurities It makes the thermal conductivity low. Sapphire fiber phonon High purity Nothing disturbs phonon High thermal conductivity Defects of phonon or impurities Low purity Scattering Low thermal conductivity We should check the thermal conductivity(purity) of sapphire fiber experimentally!

10. Experimental Setup Heat bath One dimensional approximation heat flux in the sapphire fiber distance between two thermometers cross-section of the sapphire fiber difference of values of two thermometers heater thermometer Sapphire fiber L thermometer Q • First we measure the normal sapphire fiber • Diameter is 1.8mm. • Length is 100mm. • Polished sample. heater

11. Result We could reproduce the result of Tomaru’swork around 80K. 1300 @82K 700 @90K →The method of this measurement might have no serious troubles. However, our result at low temperature is not proportional to . @12K 1100 @17K We do not check the reproducibility of this result because of some troubles. This value might be limited by the impurity This value is much smaller than we expected. We should measure the thermal conductivity of sapphire fiber again.

12. Summary • Requirement of the thermal conductivity • To realize the requirement, the purity of the sapphire fiber has to be very high. • In our result, the thermal conductivity might be limited by the purity of Photoran’s sapphire fiber. • We should measure the thermal conductivity of Photoran’s fiber again. • And, we have to measure the thermal conductivity of Moltech and IMPEX sapphire fibers as soon as possible.

13. Thank you for your attention.