Download 3. Heat extraction

Pros and cons of cryogenics
for Einstein Telescope and
Cosmic Explorer
Kazuhiro Yamamoto
Institute for Cosmic Ray Research, the University of Tokyo
22 May 2014
Gravitational Wave Advanced Detector Workshop
@ Alyeska Resort, Girdwood, Alaska, U.S.A.
1
0. Abstract
3rd generation detectors (Einstein Telescope,
Cosmic Explorer) have 10 km scale baselines.
Pro and Con of cryogenic for them are summarized
here.
2
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.
3
Contents
1. Introduction(Pros)
2. Specifications of mirror and
fiber
3. Heat extraction
4. Issues(Cons)
5. Summary
4
1. 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.
5
1. Introduction(Pros)
ET-LF
Mirror thermal noise : 10 times smaller
Pendulum thermal noise : 300 times smaller
S. Hild et al., Classical and Quantum Gravity 28 (2011) 094013.
R. Nawrodt et al., General Relativity and Gravitation 43 (2011) 363.
6
1. Introduction(Pros)
CE
Mirror thermal noise : 10 times smaller
Pendulum thermal noise : 10 times smaller
10 times smaller
10 times smaller
LIGO T1400316-v5
7
1. Introduction(Pros)
In principle, at lower temperature, thermal noise is
smaller.
> 50K
Constant
<20K
Enough
small
Sapphire
8
1. Introduction(Pros)
In principle, at lower temperature, thermal noise is
smaller. But there is an exception.
Silicon
120K
Thermoelastic
noise
vanishes.
Silicon
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1. 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).
10
1. 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) 022002.
E. Hirose et al., Physical Review D 90 (2014) 102004.)
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.
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1. 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).
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1. Introduction(Pros)
Why the mirrors and suspension in KAGRA are
cooled ?
(1)Smaller thermal noise
Kenji Numata and Kazuhiro Yamamoto,
”Chapter 8. Cryogenics”, in ”Optical Coatings and Thermal Noise in Precision
Measurement” Cambridge University Press (2012).
(2)Smaller thermal lens
T. Tomaru et al., Classical and Quantum Gravity 19 (2002) 2045.
(3)Less serious parametric instability
K. Yamamoto et al., Journal of Physics: Conference Series 122 (2008) 012015.
These items are correct in the case of ET-LE.
K.Yamamoto GWADW2011
https://agenda.infn.it/contributionDisplay.py?sessionId=17&contribId=69&confId=3351
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1. 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.
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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]
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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]
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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.
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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
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.
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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.
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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.
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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.
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4. Issues(Cons)
Heat extraction
Kazuhiro’s calculation shows that heat absorbed in
mirror can be extracted.
But,
(1) assumed absorption is optimistic.
(2) 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 !
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4. Issues(Cons)
Silicon : Size itself is not a issue. Absorption in large
bulk is an issue.
Silicon bulk
450 mm
300 mm
Harald Lueck(ELiTES meeting 2013)
https://events.egogw.it/indico/conferenceOtherViews.py?view=
standard&confId=7
Source:
http://www.iisb.fraunhofer.de/content/dam/iisb/de/im
ages/geschaeftsfelder/halbleiterfertigungsgeraete_u
nd_methoden/gadest_2011/
J. Degallaix slides on the
last Tuesday
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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
J. Degallaix slides on the last
Tuesday
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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.
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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.
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Thank you for your attention !
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1. 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).
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5. Einstein Telescope
(a) Thermal noise
Mirror thermal noise : 10 times smaller
Suspension thermal noise : 300 times smaller
S. Hild et al., Classical and Quantum Gravity 28 (2011) 094013.
R. Nawrodt et al., General Relativity and Gravitation 43 (2011) 363.
30
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
3 times longer arm (10 km)
7 times heavier mirror (200 kg)
5 times longer suspension wire (2 m)
100 times smaller dissipation in wires (Q=109)
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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
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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
Horizontal motion along optical axis
Pendulum and violin modes
Loss dilution by tension (gravity) must
be taken into account.
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1. Introduction
34
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*10635