Kazuhiro Yamamoto Institute for Cosmic Ray Research, the University of Tokyo

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Kazuhiro Yamamoto

Institute for Cosmic Ray Research, the University of Tokyo

Design and expected thermal noise

of the KAGRA sapphire suspensions

23 May 2013Gravitational Wave Advanced Detector Workshop@ Hotel Hermitage, La Biodola, Isola d’Elba, Italy

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0. Abstract

Although there are many topics, but here,I will explain

(1)Main interferometer(2)Vibration isolation(3)Cryogenics

for KAGRA.

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Contents

1.Introduction2.Design 3.Expected thermal noise4.Recent experiments5.Summary

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Room temperature second generation interferometer Fused silica mirror suspended by fused silica fibers

1. Introduction

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KAGRA (Cryogenic second generation) Sapphire mirror suspended by sapphire fibers

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First feasibility study

T. Uchiyama et al., Physics Letters A 242 (1998) 211.

Sapphire fiber : High Q-values and large thermal conductivity

1. Introduction

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StrengthSapphire fibers should support the weight of sapphire mirror.

Mirror : 23 kg Number of fibers : 4

Tensile strength : 400 MPa Safety margin : 7

Fiber diameter must be larger than 1.1 mm.

2. Design

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Thermal conductivity

Fibers should transfer heat (about 1 W).

Crystal (sapphire, silicon, diamond) and pure metal (Al, Cu, Ag) : Thermal conductivity is extremely high (> 1000 W/m/K).

Q-values of pure metal is low. Crystals with high Q-values are candidates (sapphire, silicon).

G. Ventura and L. Risegari, “The art of Cryogenics Low-Temperature Experimental Techniques”, Elsevier (2008) p76.

2. Design

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Sapphire : Thermal conductivity is maximum around 30 K.Temperature of KAGRA mirror will be around 20 K.

Specification sapphire suspensionNumber of fibers : 4

Length of fibers : 0.3 mHeat generated in a mirror : 1 W

Mirror temperature : 23 KTemperature at top end of fiber : 16 K

Thermal conductivity : 5500 (T/20K)3 W/m/K

Fiber diameter must be larger than 1.6 mm.This requirement is severer than that of strength.

2. DesignThermal conductivity

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Assumption : 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.

Design: Number of fiber : 4Fiber length : 0.3 m

Fiber diameter : 1.6 mmQ-values of sapphire fibers : 5*106

3. Expected thermal noiseAssumption and design

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Vertical motion Gradient of interferometer baseline is 1/300. for discharge of water in the mine.

Rotation (Pitch and Yaw) Distance between optical axis and center of gravity of mirror is 1 mm.

Horizontal motion along optical axis Pendulum and violin modes

3. Expected thermal noiseDegrees of freedom

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3. Expected thermal noiseDegrees of freedom

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Resonant frequencies Q-values Pendulum 1 Hz? 1.5*106??

1st violin 220 Hz 8 *106???

Vertical 109 Hz 5*106

Pitch 23.4 Hz 5*106

Yaw 1.4 Hz 2*107

In the cases of Pendulum (and violin) and Yaw, loss dilution factors by gravity were taken into account.

3. Expected thermal noiseResonant frequencies and Q-values

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3. Expected thermal noiseHorizontal and vertical motion

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Between 100 Hz and 200 Hz, there are 1st violin mode and vertical mode. Room temperature interferometer : 1st violin ~ 300 Hz vertical mode ~ 10 Hz

Thick fiber to transfer heat !

Thicker fiber : Lager thermal noise (pendulum mode)

Longer fiber : Lower violin mode, lower vertical mode -> Smaller heat transfer

Shorter fiber : Higher violin mode, higher vertical mode -> Fiber should be longer than mirror radius. Note : These peaks make Signal to Noise Ratio of matched filter for neutrons star coalescence smaller (several per cent).

3. Expected thermal noiseHorizontal and vertical motion

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d

3. Expected thermal noisePitch and yaw rotation

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Yaw rotation does not matter.

Around 20 Hz, there is pitch mode. Room temperature interferometer : pitch mode ~ 3 Hz

Thick fiber to transfer heat !

Pitch mode frequency depends on distance between fibers (d).

This distance must be as small as possible (10 mm~30 mm).

Note : If this mode is lower than 30 Hz, the effect on Signal to Noise Ratio of matched filter for neutrons star coalescence is small.

3. Expected thermal noisePitch and yaw rotation

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T. Uchiyama et al., Physics Letters A 273 (2000) 310.

Our old measurement : Q-values (0.25 mm in diameter) KAGRA fiber : 1.6 mm in diameter

Q-values are 5*106.KAGRA requirement

4. Recent experiments

1818181818T. Tomaru et al., Physics Letters A 301 (2002) 215.

Size effect : Conductivity is proportional to fiber radius.Mean free path of phonon is limited by fiber radius.

Our old measurement : Thermal conductivity

KAGRA fiber : 1.6 mm in diameter


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Test sample (T. Uchiyama)

Sapphire fibers with nail heads are necessary to suspend mirrors.


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Length = 350 mm diameter = 1.8 mm Almost as needed in bKAGRA.Need to check the quality and improvement .

T. Uchiyama asked MolTech GmbH (Germany).Sapphire fibers have already come !


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Ettore Majorana asked IMPEX HighTech GmbH (German company).They made similar fibers (nail heads on the both ends).


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Ettore Majorana asked IMPEX HighTech GmbH (German company).They made similar fibers (nail heads on the both ends).


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Quality check Q-value Measurement in Glasgow and Jena Plan for measurement in Rome and Tokyo (Christian Schwarz and Gerd Hofmann’s visit from Jena to export measurement system) Christian will present poster on Friday morning. Thermal conductivity Measurement in Jena Plan for measurement in Rome and Tokyo Christian will present poster on Friday morning. Strength Discussion with Glasgow (Thanks for E. Hirose)


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Apparatus to measure Q-values in cryostat of Jena

G. Hofmannhttp://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/DocDB/ShowDocument?docid=1638


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Apparatus to measure Q-values in cryostat of Tokyo (ICRR)



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It is comparable with KAGRA requirement !

Preliminary result

Moltech

4. Recent experimentsQ measurement in Jena G. Hofmannhttp://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/DocDB/ShowDocument?docid=1638

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It is slightly larger than KAGRA requirement !

Preliminary result

IMPEXG. Hofmannhttp://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/DocDB/ShowDocument?docid=1638

4. Recent experimentsQ measurement in Jena

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Thermal conductivity measurement in Jena


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It is same as KAGRA requirement (size effect)


Preliminary result

T. Tomaru et al., Phys. Lett. A 301 (2002) 215.

Moltech

C. Schwarz


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It is smaller than KAGRA requirement, but same order of magnitude.

Preliminary result


Moltech

C. Schwarz


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Profile measurement in Glasgow

As grown sampleWe have ground samples.


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Strength test

Discussion with Glasgow (4th of April) Stretch and bend test Some fibers were sent to Glasgow.

Crystal structure

X ray apparatus in Jena


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Bonding between fibers and mirror

Bonding should be investigated. Rebecca Douglas presents a poster in this session.

Other type sapphire suspension

Eric Hennes will report it on Friday morning.


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5. SummaryConstruction of KAGRA interferometer is in progress.

Total length of exavated tunnels is about 2 km. All vacuum tubes has already been manufactured. Cryostat cooling test was finished sucessfully. Test for vibration isolation system (Type-B) will start on this autumn at TAMA site.

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5. SummaryYoung reserachers make their great efforts for KAGRA. Main Interferometer Cotrol with high power light (Yuta Michimura) Vibration Isolation Test for Pre-isolator (Takanori Sekiguchi) Cryogenics Initnial cooling time (Yusuke Sakakibara) Vibration of shield (Dan Chen) Sapphire fiber (Gerd Hofmann) Coating mechanical loss (Kieran Craig) TOBA for low frequency band (Ayaka Shoda)

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Acknowledgement

ELiTES: ET-LCGT interferometric Telescope Exchange of Scientists Grant for collaboration about cryogenic between KAGRA and ET European 7th Framework Programme Marie Curie action (Mar. 2012 - Feb. 2016)

European people can visit Japan for KAGRA.

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Thank you for your attention !

Vielen Dank fuer Ihre Aufmerksamkeit !

Vi ringrazio molto per la vostra attenzione !

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Q measurement in Jena (cool) and Glasgow (300K)

It is slightly smaller than KAGRA requirement !

Preliminary result

4. Sapphire fibers

Y. Sakakibara

Moltech

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4. Sapphire fibersThermal conductivity measurement in Jena

Thermal conductivity of IMPEX fibers will be measured soon.

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Some items for future research (not perfect list)

(a)Investigation material properties (Q, thermal conductivity, strength etc.) of coating, fiber and so on.(b)Sapphire bonding, Sapphire fiber clamp(c)Control and damping scheme Actuators and sensors at cryogenic temperature(d) Mechanical and thermal simulation for payload(e) Vertical spring in cryostat(f) Reduction of initial cooling time Thermal resistance of clamp .... (g) Baffles for scattered light in radiation shield(h) Assembly procedure

7. For future

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8. SummaryCryostat : Assembly is in progress. Cooling test is coming soon.Cryogenic duct : Optimum position of 5 buffles Future work : scattered lightCryocooler unit : Cooling test and vibration measurement : OKCryogenic payload Preparation for 1/4 cryostat to check payload performance is in progress. Current main R&D topics Inital cooling time, Sapphire fiber with nail head, Coating mechanical loss, Vibration of shield

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8. Summary

ELiTES has already started and supports the development of KAGRA cryogenic system.

If you want to join our mission, let us know.

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2. Issues

(1)How to assemble Details of construction, clean room ….

(2)Strength Tensile strength, development of clamp, sapphire bonding …

(3)Control and damping system to reduce fluctuation and instability Actuators (what and where), resonant mode (frequency and Q) and so on

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2. Issues

(4)Cooling

Temperature of mirror (below 20 K), initial cooling time, heat resistance of clamp …

(5)Noise

Thermal noise, vibration via vibration isolation system and heat links …

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After Yusuke left …. Clamp for IMPEX fibers in Jena

4. Sapphire fibers

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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 KAGRAThermal 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.

Horizontal motion along optical axis Pendulum and violin modes Loss dilution by tension (gravity) must be taken into account.

Assumption (2): Number of fiber : 4Fiber length : 0.3 m

Fiber diameter : 0.16 mmQ-values of sapphire fibers : 5*106

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Sensitivity of KAGRAThermal noise

Vertical motion Gradient of interferometer baseline is 1/300. Q-values of stretch is assumed to be 5*106.

Pitch motion Distance between the optical axis and center of gravity of mirror is 1 mm. Q-values of stretch is assumed to be 5*106.Yaw motion Distance between the optical axis and center of gravity of mirror is 1 mm. Q-values of shear is assumed to be 5*106. Loss dilution by tension (gravity) must be taken into account.

Documents

Kazuhiro Yamamoto Institute for Cosmic Ray Research, the University of Tokyo