Download GWADW2011Yamamoto

Cryogenic mirrors:
the state of the art
in interferometeric
gravitational wave detectors
Kazuhiro Yamamoto
Institute for Cosmic Ray Research, the University of Tokyo
26 May 2011 Gravitational Waves Advanced Detectors Workshop
@Hotel Hermitage, La Biodola, Isola d’Elba, Italy
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0.Abstract
Advantages of cryogenic interferometers
(LCGT and ET)
(1) Small thermal noise
(2) Small thermal lens
(3) Less serious parametric instability
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0.Abstract
On July, the special articles (in Japanese !) about LCGT will
appear in “Teionkougaku” (Journal of the Cryogenic
Society of Japan).
Kazuhiro Yamamoto wrote the article which has the same
title as that of this talk and will explain outlines of my
article in English. (This is the first Japanese article which
introduces the technical details of Einstein Telescope,
probably.)
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Contents
1. Introduction
2. Thermal noise
3. Thermal lens
4. Parametric instability
5. Einstein Telescope
6. Summary
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1.Introduction
Generation of interferometric gravitational wave detectors
First generation
10 times better sensitivity
Second generation
10 times better sensitivity
Advanced LIGO, Advanced Virgo, GEO-HF, LCGT
Third generation
Einstein Telescope (ET)
Cryogenic interferometers : LCGT and ET
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1.Introduction
Why will cryogenic techniques be adopted ?
(1) Small thermal noise
(2) Small thermal lens
(3) Less serious parametric instability
At first, these advantages in LCGT are explained.
At second, these advantages in ET are summarized.
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2.Thermal noise
Thermal noise : Fundamental noise around 100 Hz
Suspension thermal noise : mirror position fluctuation
(vibration of suspension for mirror)
Mirror thermal noise : mirror surface fluctuation
(elastic vibration of mirror itself)
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2.Thermal noise
Fluctuation-Dissipation Theorem
Relation between thermal noise
and mechanical loss in suspension and mirror
Amplitude of thermal noise is proportional to
1/2
(T/Q) .
In general, Q (inverse number of magnitude of
dissipation) depends on T (temperature).
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2.Thermal noise
Fused silica : mirror substrate material
for room temperature interferometers
Large mechanical loss at cryogenic temperature
Fused silica is not so good in cryogenic interferometers.
Sapphire and Silicon : candidates of substrate material
for cryogenic interferometers
LCGT : Sapphire
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2.Thermal noise
Suspension thermal noise
Sapphire fibers in LCGT
Small mechanical dissipation
T. Uchiyama et al., Physics Letters A 273 (2000) 310.
High thermal conductivity
T. Tomaru et al., Physics Letters A 301 (2002) 215.
Small suspension thermal noise
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2.Thermal noise
Mirror thermal noise
”Cryogenics” (K. Numata and K. Yamamoto)
in ”Optical Coatings and Thermal Noise in Precision measurements”
(Ed. G.M. Harry, T. Bodiya, R. DeSalvo),
Cambridge University Press (it will be published soon !)
Two kinds of mechanical dissipation
Thermoelastic damping
Inhomogeneous strain
Temperature gradient (via thermal expansion)
Heat flow
Dissipation
Structure damping
Unknown mechanism
Almost no frequency dependence
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2.Thermal noise
Mirror consists of not only substrate,
but also reflective coating !
Thermoelastic damping
Heat flow in substrate : Substrate thermoelastic noise
Heat flow between substrate and coating :
Thermo-optic noise
Structure damping
Structure damping in substrate : Substrate Brownian noise
Structure damping in coating : Coating Brownian noise
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2.Thermal noise
History of research of mirror thermal noise
1997 : First feasibility study for cryogenic interferometer
T. Uchiyama et al., Physics Letters A 242 (1998) 211.
Drastic progress of research about mirror thermal noise
Only substrate Brownian noise was recognized before 1997.
It is not trivial that
cryogenic technique can reduce mirror thermal noise. 13
2.Thermal noise
Temperature dependence of mirror thermal noise in LCGT
Below 20 K : Thermal noise is sufficiently small for LCGT.
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2.Thermal noise
Sensitivity of LCGT interferometer
Sensitivity is not limited by thermal noise.
K. Arai et al., Classical and Quantum Gravity 26 (2009) 204020.
K. Kuroda et al., Progress of Theoretical Physics Supplement 163 (2006) 54.
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3.Thermal lens
Thermal lens : Light absorption in mirror
Temperature gradient
Temperature dependent of refractive index
Wave front distortion
Worse sensitivity
Thermal lens is a serious problem
of room temperature interferometers.
Advanced LIGO and Virgo : System to compensate thermal
lens (compensation plate and ring heater) is necessary.
G.M. Harry (for LSC), Classical and Quantum Gravity 27 (2010) 084006.
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3.Thermal lens
Thermal lens in LCGT
T. Tomaru et al., Classical and Quantum Gravity 19 (2002) 2045.
Magnitude of thermal lens : P b / k
Thermal conductivity (k) of sapphire at 20 K
is 10000 times larger than that of fused silica at 300 K.
Temperature coefficient of refractive index (b)
is at least 100 times smaller.
Light absorption (P) is almost same (coating dominant).
Magnitude of thermal lens is at least 106 times smaller.
No system for thermal lens compensation is necessary.
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4. Parametric instability
Parametric instability
Radiation pressure
Optical mode in cavity
(Large amplitude of other
(transverse) optical mode)
Elastic mode in mirror
(Large vibration)
Modulation
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4. Parametric instability
Parametric instability of LCGT is a less serious problem
than that of Advanced LIGO and Advanced Virgo.
K. Yamamoto et al., Journal of Physics: Conference Series 122 (2008) 012015.
(a) Number of unstable modes is 10 times smaller.
(b) Mirror curvature dependence is weaker.
Wider safe curvature region
(c) More effective passive suppression
of instability is possible.
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4. Parametric instability
(a) Number of unstable modes is 10 times smaller.
Number of unstable modes is proportional
to the product of elastic and optical mode densities.
Elastic mode density of sapphire (LCGT)
is 5 times smaller than that of fused silica .
Sound velocity in sapphire is larger.
Optical mode density of LCGT is 2 times smaller.
Larger beam is adopted in Advanced LIGO
and Advanced Virgo in order to reduce
mirror thermal noise.
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4. Parametric instability
(b) Mirror curvature dependence is weaker.
Wider safe curvature region
The reason is that smaller beam radius of LCGT.
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4. Parametric instability
(c) More effective passive suppression
of instability is possible.
Although number of unstable modes of LCGT is smaller, it is
not zero. The tricks to suppress instability is necessary.
One of ideas : loss on barrel surface of mirror
loss on barrel surface
The increase of thermal noise should be taken into account.
Since mirrors of LCGT are cooled, suppression
without sacrificing thermal noise is possible.
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5. Einstein Telescope
Outline of Einstein Telescope
M. Punturo and H. Lueck, General Relativity and Gravitation 43 (2011) 363.
S. Hild et al., Classical and Quantum Gravity 28 (2011) 094013.
Third generation in Europe
10 times better sensitivity than that of LCGT
10 km arm length
Xylophone scheme : Two kinds of interferometers
Low frequency (LF, 10Hz) and High frequency (HF, 100Hz)
LF : Smaller radiation pressure noise, (10 times) smaller light
power (than that of LCGT), cryogenic techniques
HF : Smaller shot noise, larger light power,
without cryogenic techniques 23
5. Einstein
Telescope
S. Hild et al., Classical and Quantum Gravity 28 (2011) 094013.
Only low frequency interferometer (LF) is discussed.
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5. Einstein Telescope
Mirror substrate and suspension wire material :
Sapphire or Silicon
Why is silicon candidate ?
Advantage : Larger substrate (radiation pressure noise)
Disadvantage : Light wavelength is 1550nm, not 1064nm.
Optical properties are not well known.
Temperature of mirror is 10 K (LCGT:20 K).
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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 (Q=109)
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5. Einstein Telescope
(b) Thermal lens
Magnitude of thermal lens : P b / k
Light absorption (P) is 10 times smaller than that of LCGT
(coating dominant) because of smaller light power.
Thermal conductivity (k) at 10 K (ET)
is 10 times smaller than that at 20 K (LCGT).
If ET mirrors are made from sapphire, thermal lens of ET is
comparable with that of LCGT.
No serious problem
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5. Einstein Telescope
(b) Thermal lens
If ET mirrors are made from silicon …
Temperature coefficient of refractive index (b) of silicon
is at least 10 times larger than that of sapphire.
B.J. Frey et al., SPIE Conference Proceedings 6273 (2006) 62732J.
Thermal lens of ET is at least 10 times larger than that of
LCGT.
However, even in this case, this is not serious.
T. Tomaru et al., Classical and Quantum Gravity 19 (2002) 2045.
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5. Einstein Telescope
(c) Parametric instability
Parametric instability : not serious problem
Light power is 10 times smaller than that of LCGT.
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6. Summary
LCGT: Sapphire mirrors (20 K) suspended by sapphire fibers
(1) Small thermal noise
(2) Small thermal lens
(3) Less serious parametric instability
ET-LF: Silicon or sapphire mirrors (10 K) suspended
by silicon or sapphire fibers
(1) Small thermal noise : Cryogenic technique, longer
baseline, larger beam radius, heavier mass, low loss fibers
(2) Small thermal lens
(3) Less serious parametric instability : Smaller light power
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Special thanks to
Dr. Kenji Numata
(University of Maryland/NASA Goddard Space Flight Center)
Dr. Gregory M Harry (Massachusetts Institute of Technology)
Dr. Hiroaki Yamamoto (California Institute of Technology)
Dr. Takayuki Tomaru (High Energy Accelerator Research Organization)
Dr. Harald Lueck (Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut))
Dr. Michele Punturo (Istituto Nazionale di Fisica Nucleare, Sezione di Perugia)
Prof. Fulvio Ricci (Universit`a di Roma La Sapienza)
Dr. Stefan Hild (University of Glasgow)
Dr. Ronny Nawrodt (Friedrich-Schiller-Universitaet Jena)
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Thank you
for your attention !
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