Advanced Virgo : cryostat designs Some thermal aspects

Advanced Virgo : cryostat designs Some thermal aspects

Eric Hennes, University of Amsterdam

Gravitational Waves group Amsterdam Nikhef-VU-UvA

Contents

 geometrical overview

 questions to be answered

 thermal properties

 modeling method

results for several design parameters

conclusion

cylinder T

=80 K fixed

L_c D_c

D_m mirror

Simplified geometry

Ambient temperature T

=300K

L_cm

t_m

Mirror:

D

= 0.4 m t

= 0.1 m

A

= p(D

t

+D

/2) R

= D

/2

Cylinder:

D

= 0.65 or 1.0 m L

= 2.5 m

A

= pD

L

Exterior: isolated

cold area viewed by mirrorBaffle ring at T_a transparant area

viewed by mirror

Distance:

L

= 2.5 m

`

To be estimated

P

P

P

•Cryostat power consumption P

due to radiation

•Radiative heat flow P

=P

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)

`

`

Thermal material properties involved

Mirror: Thermal conductivity : k = 1.36 W/Km Thermo-optic coefficient :dn/dT = 0.98 10-5 K

Thermal Expansivity : a = 0.54 mm//Km Emissivity: : e

= 0.89

Cryostate Emissivity: : e

= 0.1 (initial)

= 0.2 (nominal, t< 2 years)

= 0.9 (worst “icing” case)

Baffle “ : e

= 0.12

Ambiance “ : e

= 1.0 (“black”)

Reflection of radiation : diffuse, i.e. non-specular

Mirror temperature distribution : FEM (COMSOL) Domain : DT=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

(equilibrium): P

= P

Modeling method / tools 1





,

ac c ca c

ca

F A E E T T

P  e   

am m ma m

ma

F A E

P  e

) 1

( )

1 )(

1 (

1

mc m mc m c

mc

F F F

E A P F

e e

e e e









 

View factor calculation

general : FEM (COMSOL)

2 simple bodies (A

<<A

) : analytical approximation:

general: A

F

=A

F

with F

: view factor between two circular faces 1 and 2 at distance d:

Modeling method / tools 2

2

1 2 2

1 2

1 2 2

2 1

1 2 ,

2 4 ) 1 , ,

( 



 



 

 

 



 

 















 

 



 



 D

D D

X d D

X D X

d D D F

 ^{( , , ) ( , , )} 

4 1 /

4

c cm

c m cc cm

c m cc m

m mc

ma

F D D L F D D L L

A F D

F    

 p

2 2

1 1

1

c c c

c cc

ca

D

L D

F L

F     



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

 ^D



D

t

m

r T z r dz

t

0

) , ( )

( a

Thermal lensing

change in optical path:

radius of curvature of equivalent isothermal lens (one side flat):

 ^D

 D





D

t

m

T z r dz

dT r dn

t n

r s

0

) , ( )

( )

1 ( ) (

 ^{( ) ( 0 )} 

2

) 1

(

s R

s

R R n

m

m optic

thermo

D  D

 



 T ( t , r ) T ( 0 , r ) 

dT t dn

m

m

D  D



FEM models (thermal & thermo-mechanical)

D_c=1m, 3 baffles,

quadratic hex elements D_c=0.65m, no baffles, linear prism elements

Results small cryostate (e _c =0.2), no baffles

Cryostat power P_ac 180 W

Self-irradiance F_cc 0.87

Mirror

view factor F_mc 0.0123

power P_mc 0.22 W

Av. cooling DT_m 0.23

K

front-back DT_fb 0.10

mid-edge DT_me 0.06

thickness Dt_m(R_m) Dt_m(0) 4 displacement nm

differences

front Dz_f(R_m) Dz_f(0) 13 back Dz_b(R_m) Dz_b(0) 9

Radius of curvature

front surface R_front 1500

back

2200

refractive

120

Temperature profile (299.70 – 299.86 K)

9 nm Front Back

dz=13 nm

Enlargement factor : 2E6

Summary results for e _c =0.2

D

(m) baffles P

(W) P

(W)

R

(km)

0.65 no 180 0.42 0.21 120

1.0

no 370 0.8 0.43 60

b1 320 0.24 0.12 220

b1+b2 340 0.23 0.11 250

b1…..b3 350 0.31 0.16 170

b1…..b4 305 0.40 0.19 100

b1+b4 260 0.44 0.21 120

mirror D_c

Cryostat power for several emissivities e _c

E

: 0.1 0.2 0.9

D

(m) baffles P

(W)

1.0

no 245 370 675

b1 221 320 530

b1+b4 190 260 370

0.65 no 130 180 295

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