1. Thermal effects of the small cryotrap on AdVirgo TM
A. Rocchi1, E. Hennes2
1INFN Roma Tor Vergata
2UvA

2. Cryotrap Thermal Effects on AdVirgo TM/1
Simulation performed with ANSYS
2D axysimmetrical model
Key elements:
Cryotrap
Optical baffle: placed 10cm away from the trap
Test mass
2500mm
650mm
2400mm
100mm
600mm
CryoTrap
Baffle TM

3. Cryotrap Thermal Effects on AdVirgo TM/2
Effect on the TM:
Maximum temperature decrease is 0.4K
Gradient in the region of the wires is small (less than 0.1K), differential contraction of the wires is negligible (-1·10-9m for the front wire and -8·10-10m for the back wire)
Appendix
TM depth
Radial coordinate

4. Cryotrap Thermal Effects on AdVirgo TM/3
Effect on the TM is negligible:
Opl increase due to the CryoTrap is very small and the lens is opposite to that due to the YAG (ROCCryoTrapLens=54km)
Coupling losses due to such a lens are of the order of 2800ppm, negligible wrt those due to the YAG (~4.5·105ppm)
TM ROC changes only by 2m (i.e. from 1530m to 1528m)

8. Conclusions Small cryotrap thermal effects on the TMs are small
Lensing effect induced by cooling is negligible wrt that induced by the YAG absorption
Anyway, cryo-lensing is opposite to that of the YAG
The cryotrap is giving a small help to TCS

9. The End

10. Appendix: wires temperature
Temperature along the wires can be analytically calculated.
Heating (cooling) is dominated by radiation for low section wires.
k= thermal conductivity=1.38 for SiO2
e=emissvity=0.9
s=Stephan-Boltzmann constant
r=wire radius
T0=room temperature
Differential equation governing temperature distribution in a thin wire.
Linearized S-B law
Solution is in the form:
B and C are constants defined by the initial conditions
Increase (decrease) of the wire length
a=thermal expansion coefficient=0.55·10-6
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