Kazuhiro Yamamoto

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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 _at_ Alyeska Resort, Girdwood, Alaska,
U.S.A.
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0. Abstract
3rd generation detectors (Einstein Telescope,
Cosmic Explorer) have 10 km scale baselines. Pro
and Con of cryogenic for them are summarized
here.
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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.
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• Contents
• Introduction(Pros)
• Specifications of mirror and fiber
• Heat extraction
• Issues(Cons)
• Summary

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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.
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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.
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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
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1. Introduction(Pros)

In principle, at lower temperature, thermal noise
is smaller.
gt 50K Constant lt20K Enough small
Sapphire
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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).
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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 (f410-4). (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 (2)Smaller
thermal lens (3)Less serious parametric
instability These items are correct in the case
of ET-LE. K.Yamamoto GWADW2011 https//agenda.infn
.it/contributionDisplay.py?sessionId17contribId
69confId3351
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.
K. Yamamoto et al., Journal of Physics
Conference Series 122 (2008) 012015.
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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)Smal
ler 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
(gt45cm 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)
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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. Kazuhiro explained details on the
last Tuesday
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4. Issues(Cons)

• Heat extraction
• Kazuhiros 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 !

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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
J. Degallaix slides on the last Tuesday
Harald Lueck(ELiTES meeting 2013) https//events.e
go-gw.it/indico/conferenceOtherViews.py?viewstand
ardconfId7
Source http//www.iisb.fraunhofer.de/content/dam/
iisb/de/images/geschaeftsfelder/halbleiterfertigun
gsgeraete_und_methoden/gadest_2011/
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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.
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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
(Q109)
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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 5106
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

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Thermal noise (pendulum) ET-LF 211 kg mirror,
3.3 mm diameter and 2 m length fiber. Pendulum
Q gt 109 Fiber Q gt 107 CE 120 kg mirror, 2.5 mm
diameter and 0.5 m length fiber. 20K operation
Pendulum Q gt 107 Fiber Q gt 5105 120K operation
Pendulum Q gt 2108 Fiber Q gt 3106 CE 120 kg
mirror, 2.5 mm diameter and 2 m length fiber.
120K operation Pendulum Q gt 6108 Fiber Q gt
2106
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