1. Pros and cons of cryogenics for Einstein Telescope and Cosmic Explorer
Kazuhiro Yamamoto
Institute for Cosmic Ray Research, the University of Tokyo
I will explain cryogenic payload.
22 May 2014
Gravitational Wave Advanced Detector Workshop
@ Alyeska Resort, Girdwood, Alaska, U.S.A. 1 1

2. 0. Abstract
3rd generation detectors (Einstein Telescope, Cosmic Explorer) have 10 km scale baselines.
Pro and Con of cryogenic for them are summarized here.
I will explain cryogenic payload. 2 2

3. 0.1. Excuses
In official, Cosmic Explorer interferometer is at room temperature.
Kazuhiro Yamamoto assumes some values (especially for Cosmic Explorer).
His calculation is some kinds of order evaluation.
Somebodies who are in charge of it should check.
Kazuhiro welcomes comments and discussions.
I will explain cryogenic payload.

4. Contents Introduction(Pros) Specifications of mirror and fiber
Heat extraction
Issues(Cons)
Summary
I will explain cryogenic payload.

5. Introduction(Pros) 3rd generation interferometer :
10 times better sensitivity than that of 2nd generation
Einstein Telescope (ET) : 10 km baseline in Europe
Low Frequency (LF) and High Frequency (HF)
Cosmic Explorer (CE) : 40 km baseline in U.S.A.
Cryogenic technique is adopted in ET-LF(10K).
(In official, CE interferometer is at room temperature).
Pros and cons of cryogenic in ET-LF and CE (if CE adopts !)are summarized here.
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 5 5 5 5

6. Introduction(Pros) ET-LF Mirror thermal noise : 10 times smaller
Pendulum thermal noise : 300 times smaller
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector.
S. Hild et al., Classical and Quantum Gravity 28 (2011)
R. Nawrodt et al., General Relativity and Gravitation 43 (2011) 363. 6 6 6 6

7. Introduction(Pros) CE Mirror thermal noise : 10 times smaller
Pendulum thermal noise : 10 times smaller
10 times smaller
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector.
10 times smaller
LIGO T v5 7 7 7 7

8. Introduction(Pros)
In principle, at lower temperature, thermal noise is smaller.　
> 50K
Constant
<20K
Enough small
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector.
Sapphire 8 8 8 8 8 8 8 8 8 8 8

9. Introduction(Pros)
In principle, at lower temperature, thermal noise is smaller.　But there is an exception. 　
Silicon
120K
Thermoelastic noise
vanishes.
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector.
Silicon 9 9 9 9 9 9

10. Introduction(Pros) Coating thermal noise
10km scale baselines and cryogenics (20 K)
are excellent remedies.
ET-LF : 10km baseline
10K operation, 9cm beam radius
Drastic improvement of coating loss angle is not necessary.
CE : 40km baseline
Drastic improvement of coating loss angle and enhancement of beam radius are not necessary.
(Beam radius in 40km arms is about 9 cm at least).
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 10 10 10 10 10 10

11. Introduction(Pros) Coating loss angle
Peak around 20K are reported (f = 10-3).
(G. Cagnoli slides on the last Wednesday)
In some papers, there is no peak (f=4*10-4).
(K. Yamamoto et al., Physical Review D 74 (2006)
E. Hirose et al., Physical Review D 90 (2014) )
Even if our coating has loss peak,
thermal noise at lower temperature is smaller and this noise is (at least twice time) smaller than goal sensitivity.
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 11 11 11 11 11 11

12. Introduction(Pros) Coating thermal noise CE : 40km baseline
(120K operation, 12cm radius beam)
Drastic improvement of coating loss is not necessary.
(Beam radius in 40km arms is about 9 cm at least).
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 12 12 12 12 12 12

13. Introduction(Pros)
Why the mirrors and suspension in KAGRA are cooled ?
(1)Smaller thermal noise
(2)Smaller thermal lens
(3)Less serious parametric instability
These items are correct in the case of ET-LE.
K.Yamamoto GWADW2011
Kenji Numata and Kazuhiro Yamamoto,
”Chapter 8. Cryogenics”, in ”Optical Coatings and Thermal Noise in Precision
Measurement” Cambridge University Press (2012).
T. Tomaru et al., Classical and Quantum Gravity 19 (2002) 2045.
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector.
K. Yamamoto et al., Journal of Physics: Conference Series 122 (2008) 13 13 13 13

14. Introduction(Pros) How about CE ? (1)Thermal noise : OK.
(2)Thermal lens (probably OK but) must be checked if silicon at 120K is adopted (temperature coefficient of refractive index is high).
(3)Parametric instability is less serious (than that of room temperature interferometer). Gain at 120K is smaller.
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 14 14 14 14

15. 2. Specification of mirror and fiber
Mirror should be larger in 3rd generation.
(1)Smaller Standard Quantum Limit
(Binary coalescence)
(2)Larger beam radius due to longer baseline
(3)If necessary, beam radius is enhanced
to suppress mirror thermal noise.
KAGRA mirror : 23 kg
(22cm diameter, 15cm thickness)
ET-LF mirror : 211 kg
(>45cm diameter)
CE mirror : 80kg (silicon) , 120kg (sapphire)
[Kazuhiro assumes that size is the same as current one]
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 15 15 15 15

16. 2. Specification of mirror and fiber
Fibers suspending mirror should be thicker
because mirror is heavier.
KAGRA mirror : 23 kg,
(Tensile strength : 400 MPa, Safety margin : 7)
Fiber diameter must be larger than 1.1 mm.
ET-LF mirror : 211 kg,
Fiber diameter is 3.3 mm at least.
CE mirror : 80kg (silicon) , 120kg (sapphire),
Fiber diameter is 2.5 mm at least.
[Kazuhiro assumes that strength is the same as that of sapphire]
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 16 16 16 16

17. 2. Specification of mirror and fiber
Fibers suspending mirror should be longer.
At least, fiber length must be comparable with mirror diameter (about 500 mm).
ET-LF : Length is 2m in length to improve sensitivity at low frequency region.
CE : If 120K operation is selected and upper side of fiber is at room temperature as like Voyager,
2m length is better for thermal insulation.
Otherwise, 0.5m length fiber is better.
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 17 17 17 17

18. 3. Heat extraction Heat absorption in mirror is a crucial issue.
KAGRA : 400 kW in arm, 800 W at beam splitter
(Optimistic) assumption :
0.5 ppm and 20ppm/cm absorption
in coating and substrate
Absorption in coating and substrate:
0.2 W and 0.24W(15 cm thickness) (total : 0.44 W)
[Kazuhiro assumes same absorption and thickness in the cases of ET and CE.]
ET-LF : 18 kW in arm, 63 W at beam splitter
Total heat absorption in mirror : 9 mW and 19 mW
(total : 28 mW)
CE : 800 kW in arm, 125 W input power :
0.4 W and 0.38 W (total : 0.78 W) 18 18 18 18

19. 3. Heat extraction Heat extraction (10K or 20K operation)
Fibers are bottle neck.
Assumption : Fiber thermal conductivity is the same as that of sapphire.
ET-LF : 3.3 mm diameter fibers can transfer 55 mW (10 K operation).
CE : 2.5 mm diameter fibers can transfer 1.5 W (20 K operation).
When fibers can suspend mirror, they could transfer enough heat.
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 19 19 19 19 19

20. 3. Heat extraction Heat extraction (120K operation; CE?) Radiation
Black body radiation can transfer about 7 W.
Black coating on mirror is necessary.
[Kazuhiro explained details on the last Tuesday]
Conduction in fiber
2.5 mm diameter fibers can transfer 0.8 W (Upper end of fiber: 80K).
At least, it does not look impossible.
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 20 20 20 20 20

21. 3. Heat extraction Scattered light by mirror is absorbed
by radiation shield.
KAGRA : Shield at 12K and 20 K
can absorb 2 W and 10 W, respectively.
Assumption : Scattered loss is 10ppm.
ET-LF : 18 kW power in arm. : 0.18W.
CE : 800 kW in arm : 8 W.
They look acceptable.
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 21 21 21 21 21 21

22. 4. Issues(Cons) Initial cooling
KAGRA : 5 weeks, 4 cryocoolers for each cryostat
ET-LF and CE
Several or tens times heavier payload
(1)Short cooling of radiation shield
Powerful heat extraction device with small vibration
(2)Short cooling of payload below 100K
Large heat path without transmission
of external vibration
(or with thermal switch).
If you select 120K operation,
item (2) is not necessary.
[Kazuhiro explained details on the last Tuesday]
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 22 22 22 22 22 22

23. 4. Issues(Cons) Heat extraction
Kazuhiro’s calculation shows that heat absorbed in mirror can be extracted.
But,
assumed absorption is optimistic.
safety margin is not large.
Heat absorption in large mirror should be checked carefully.
“Large” is not a problem but “Large and low absorption” is an issue.
Driving force should provided by ourselves !
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 23 23 23 23 23 23

24. 4. Issues(Cons)
Silicon : Size itself is not a issue. Absorption in large bulk is an issue.
Silicon bulk
450 mm
300 mm
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector.
J. Degallaix slides on the last Tuesday
Harald Lueck(ELiTES meeting 2013)
Source: 24 24 24 24 24 24

25. 4. Issues(Cons)
Sapphire : Some companies can provide large sapphire bulk (As far as Kazuhiro knows, 60kg).
Optical (and mechanical) quality is unknown.
23kg,
23cm diameter,
15 cm thickness
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector.
J. Degallaix slides on the last Tuesday 25 25 25 25 25 25

26. 5. Summary Cryogenics in 3rd generation (10 km scale). Pros
(1)Smaller thermal noise
We do not need drastic improvement
of coating loss angle and
can adopt smaller beam.
(2)Smaller thermal lens
(3)Less serious parametric instability
Even if in the case of 120K operation, these items are correct but gain is smaller.
This is the summary. Design and discussion for ¼ cryostat is in progress. Sapphire fibers with nail head can be provided by Moltech and IMPEX. These R&D items are investigated. Other ideas for mirror suspension were proposed. Collaboration with ELiTES in progress and I hope the collaboration with university of Toyama will established near future.

27. 5. Summary Cryogenics in 3rd generation (10 km scale). Cons
(1)Initial cooling
(a)Shorter cooling of radiation shield
(b)Shorter cooling of payload below 100K
Item (b) is not necessary in 120K operation.
(2)Heat absorption in mirror
Large mirror with low absorption is an issue.
We can purchase larger silicon
with smaller absorption than sapphire bulk.
Driving force must be applied by ourselves.
This is the summary. Design and discussion for ¼ cryostat is in progress. Sapphire fibers with nail head can be provided by Moltech and IMPEX. These R&D items are investigated. Other ideas for mirror suspension were proposed. Collaboration with ELiTES in progress and I hope the collaboration with university of Toyama will established near future.

28. Thank you for your attention !
That’s all. Thank you for your attention.

29. Introduction Heat extraction: Fiber is bottle neck.
Assumption : Fiber thermal conductivity is the same as that of sapphire.
ET-LF : Fiber diameter must 2.0 mm at least (10 K operation).
CE : Fiber diameter must 2.2 mm at least (10 K operation).
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 29 29 29 29 29

30. 5. Einstein Telescope (a) Thermal noise
Mirror thermal noise : 10 times smaller
Suspension thermal noise : 300 times smaller
That’s all. Thank you for your attention.
S. Hild et al., Classical and Quantum Gravity 28 (2011)
R. Nawrodt et al., General Relativity and Gravitation 43 (2011) 363. 30

31. 5. Einstein Telescope (a) Thermal noise
Mirror thermal noise : 10 times smaller
3 times longer arm (10 km)
3 times larger beam radius (9cm)
Suspension thermal noise : 300 times smaller
7 times heavier mirror (200 kg)
5 times longer suspension wire (2 m)
100 times smaller dissipation in wires (Q=109)
That’s all. Thank you for your attention. 31

32. 4. Challenges for cryogenic
1. Issues of cooling : Reduction of heat load
(Absorption in mirror)
In order to keep mirror temperature …
Absorption in mirror : less than 1 W
Coating : 0.4 W (1 ppm)
Substrate : 0.6 W (50 ppm/cm)
Our target of substrate : 20 ppm/cm
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 32 32 32 32

33. Q-values of sapphire fibers : 5*106
Sensitivity of KAGRA
Thermal noise
Assumption (1) : Upper ends of fibers are fixed rigidly.
Resonant frequencies (except for violin modes) are different from the actual system. However, the thermal noise above the resonant frequency is the same.
Assumption (2):
Number of fiber : 4
Fiber length : 0.3 m
Fiber diameter : 0.16 mm
Q-values of sapphire fibers : 5*106
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector.
Horizontal motion along optical axis
Pendulum and violin modes
Loss dilution by tension (gravity) must
be taken into account. 33 33 33 33

34. Introduction
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 34 34 34 34 34

35. Thermal noise (pendulum)
ET-LF : 211 kg mirror, 3.3 mm diameter and 2 m length fiber.
Pendulum Q > 109 Fiber Q > 107
CE : 120 kg mirror, 2.5 mm diameter and 0.5 m length fiber.
20K operation : Pendulum Q > 107 Fiber Q > 5*105
120K operation : Pendulum Q > 2*108 Fiber Q > 3*106
CE : 120 kg mirror, 2.5 mm diameter and 2 m length fiber.
120K operation : Pendulum Q > 6*108 Fiber Q > 2*106
OK, what is cryogenic payload ? This is the cross section of tunnel of LCGT. This tall tower is vibration isolation system. There is cryogenic payload under this vibration isolation. Cryogenic payload is in cryostat. Payload includes mirror, which is the most important part of gravitational wave detector. 35 35 35 35 35 35