Measurement of thermal conductivity of sapphire rods II

1. Measurement of thermal conductivity of sapphire rodsII TakafumiUshiba The university of Tokyo at Hongo Tsubono Laboratory KAGRA Cryogenic Payload Meeting

2. Contents • Purpose of the measurement • How to measure • Result • Discussion • Summary KAGRA Cryogenic Payload Meeting

3. Purpose of the measurement • Final goal measure the thermal conductivity of Moltech and INPEX sapphire rods with nail head. • Near goal measure thermal conductivity of polished Photoran’s sapphire rods near peak temperature to confirm the purity of sapphire rods is well or not. KAGRA Cryogenic Payload Meeting

4. How to measure Heat bath • Sample size diameter : sample length : 100mm • One dimensional approximation. :thermal conductivity L :length between two temperature sensors, Q:heat flow,A :sample cross section, :difference of values of two temperature sensors temperature sensor L Q temperature sensor heater KAGRA Cryogenic Payload Meeting

5. How to measure • Sample size diameter : sample length : 100mm • One dimensional approximation. :thermal conductivity L :length between two temperature sensor, Q:heat flow,A :sample cross section, :difference of values of two temperature sensor heat bath temperature sensor heater KAGRA Cryogenic Payload Meeting

6. Result This time, I take three data near 30K. KAGRA Cryogenic Payload Meeting

7. Discussion • Error bars uncertainty of offset voltage of thermometer • Peak’s shape If the offset voltage of thermometer does not depend on temperature, the shape of peak of thermal conductivity is same as the real peak. KAGRA Cryogenic Payload Meeting

8. Summary • I measure thermal conductivity near 30K • The result has too large error bars because of the offset voltage of the temperature sensor. • In this measurement, I do not confirm the purity of sapphire rod is well or not. • So, I need to measure thermal conductivity of sapphire rod again near 30K. KAGRA Cryogenic Payload Meeting