1. Feb 3, 2009Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA1 Advanced Virgo : cryostat designs Some thermal aspects Eric Hennes, University of Amsterdam Gravitational Waves group Amsterdam Nikhef-VU-UvA Cascina, Februari 3, 2009 Contents  geometrical overview  questions to be answered  thermal properties  modeling method  results for several design parameters  conclusion

2. Feb 3, 2009Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA2 cylinder T c =80 K fixed LcLc DcDc DmDm mirror Simplified geometry Ambient temperature T a =300K L cm tmtm Mirror: D m = 0.4 m t m = 0.1 m A m =  (D m t m +D m 2 /2) R m = D m /2 Cylinder: D c = 0.65 or 1.0 m L vc = 2.5 m A c =  D c L c Exterior: isolated cold area viewed by mirror Baffle ring at T a transparant area viewed by mirror Distance: L cm = 2.5 m `

3. Feb 3, 2009Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA3 To be estimated P am P mc P ac Cryostat power consumption P ac due to radiation Radiative heat flow P mc =P am from and to mirror (in equilibrium) Mirror temperature distribution, without or with baffle(s) Effect T-distribution on mirror optics (optical path) (Design of baffle heating) ` `

4. Feb 3, 2009Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA4 Thermal material properties involved Mirror:Thermal conductivity: k = 1.36 W/Km Thermo-optic coefficient:dn/dT = 0.98 10-5 K -1 Thermal Expansivity:  = 0.54  m//Km Emissivity::  m = 0.89 Cryostate Emissivity: :  c = 0.1 (initial) = 0.2 (nominal, t< 2 years) = 0.9 (worst “icing” case) Baffle “:  b = 0.12 Ambiance “:  amb = 1.0 (“black”) Reflection of radiation: diffuse, i.e. non-specular

5. Feb 3, 2009Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA5 Mirror temperature distribution: FEM (COMSOL) Domain:  T=0 Boundary: .n=J (outward conducted power flux) Radiation heat exchange general: FEM Isothermal mirror equilibrium : analytical approximation cooling power: ambiance to mirror: mirror to cryostat: solving T m (equilibrium): P mc = P am Modeling method / tools 1

6. Feb 3, 2009Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA6 View factor calculation general: FEM (COMSOL) 2 simple bodies ( A m <<A c ): analytical approximation: general: A 1 F 12 =A 2 F 21 with F cc : view factor between two circular faces 1 and 2 at distance d : Modeling method / tools 2

7. Feb 3, 2009Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA7 Mirror geometrical properties change (mirror initially flat) mirror thickness change due to thermal expansion: mirror surface radii of curvature: FEM mechanical analysis Modeling method / tools 3 Thermal lensing change in optical path: radius of curvature of equivalent isothermal lens (one side flat):

8. Feb 3, 2009Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA8 FEM models (thermal & thermo-mechanical) D c =1m, 3 baffles, quadratic hex elements D c =0.65m, no baffles, linear prism elements

9. Feb 3, 2009Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA9 Results small cryostate (  c =0.2), no baffles Cryostat power P ac 180W Self-irradiance F cc 0.87 Mirror view factor F mc 0.0123 power P mc 0.22W Av. cooling TmTm 0.23 K front-back  T fb 0.10 mid-edge  T me 0.06 thickness  t m (R m )   t m (0) 4 nm displacement differences front  z f (R m )   z f (0) 13 back  z b (R m )   z b (0) 9 Radius of curvature front surface R front 1500 km back surface R back 2200 refractive R thermo-optic 120 Temperature profile (299.70 – 299.86 K) 9 nm Front Back dz=13 nm Enlargement factor : 2E6

10. Feb 3, 2009Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA10 Summary results for  c =0.2 D c (m)bafflesP c (W)P m (W)  T m (K) R thermo-optic (km) 0.65no1800.420.21120 1.0 no3700.80.4360 b13200.240.12220 b1+b23400.230.11250 b1…..b33500.310.16170 b1…..b43050.400.19100 b1+b42600.440.21120 b4 b3 b2 b1 mirror DcDc

11. Feb 3, 2009Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA11 Cryostat power for several emissivities  c Ec:Ec:0.10.2 0.9 D c (m)bafflesP c (W) 1.0 no245370675 b1221320530 b1+b4190260370 0.65no130180295

12. Feb 3, 2009Thermal aspects of Advanced Virgo cryostat design, Eric Hennes, UvA12 Final remarks & conclusion All radii of curvature are larger than 100 km and exceed by far those predicted for beam power absorption (see van Putten et al.) Conclusion: no mirror optics problems expected for any proposed design Lowest cryostat power is obtained using (only) 2 baffles on either side Including the recoil mass into the models will result into a smaller radial temperature gradient, and consequently, into even larger radii of curvature