Nawrodt 05/2010

Thermal noise in the monolithic final stage

Ronny NawrodtMatt Abernathy, Nicola Beveridge, Alan Cumming, Liam Cunningham, Giles

Hammond, Daniel Heinert, Jim Hough, Iain Martin, Peter Murray, Stuart Reid, Sheila Rowan, Christian Schwarz, Paul Seidel, Marielle van Veggel

GWADW2010 Meeting, Kyoto 19/05/2010

Institut für Festkörperphysik, Friedrich-Schiller-Universität JenaSonderforschungsbereich Transregio 7 „Gravitationswellenastronomie“

Institute for Gravitational Research, University of GlasgowEinstein Telescope Design Study, WP2 „Suspension“

Nawrodt 05/2010

Overview

• Motivation and demands

• Thermal noise in suspension elements

• 3rd generation detectors

– Cooling issues– Material selection– Thermal noise

• Summary

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Nawrodt 05/2010 GWADW2010 Kyoto/Japan

Introduction

• sensitivity enhancement by a factor of 10 between 1 Hz and 10 kHz

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frequency [Hz]

h [1

/ H

z]1st generation2nd generation3rd generation

seismicsuspensionradiation pressure

photon shot noise

thermal noise (test masses)

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ww

.et-g

w.e

u]

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Demands

• support the test mass (proper breaking strength)

• ability to produce (quasi-)monolithic suspension

• „proper“ dynamics (mode frequencies, mode separation, etc.)

• low thermal noise– low mechanical loss– „good“ thermal properties (thermo-elastic noise)

• high thermal conductivity to transport thermal load from test masses into the thermal bath

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Material selection

• possible materials are dependent on the test mass material:

– fused silica

– sapphire– silicon

• important „boundary condition“:

– fabrication of suspension elements (cutting, polish, …)– design and shaping of suspension fibre/ribbons

– keep crystalline structure in order to obtain a high thermal conductivity

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can be bonded by means of catalysis-hydroxide bonding[e.g. van Veggel 2009, Dari 2010]

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Thermal noise in suspension elements

• pendulum mode

• violin mode

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24

0

2220

20B4

M

TkS pendulum

n nnn

nnnBvioline

LTkS42222

22

)()()(4

2222 12)(

nMLLn

2

2

22 n

LMg

n with and

[e.g. Saulson 1992]

M

, L, n

Lg

20with

Adding internal stiffness of fibre or ribbon leads to more realistic models. [e.g. Gonzalez 2000]

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Mechanical loss in suspension elements -1-

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[Gretarsson, Harry 1999]

[Cagnoli, Willems 2002]

• mechanical loss of suspension material is a key parameter and can be assumed to consist of 3 contributions:

– bulk loss ,

– surface loss ,

– thermoelastic loss unstressed fibre

fibre under tension • with a proper choice of it is possible to cancel TE loss in

suspension elements

Nawrodt 05/2010

Dilution factor

• The mechanical loss within a fibre contributes inhomogeneously into the thermal noise calculation.

• for pendulum energy is stored in grav. potential (loss free) and the elastic potential of the fibre material (bending!)

• only energy stored in bending is dissipated to a fraction

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Most of the bending occurs at the suspension point

 

[e.g. Saulson 1992]

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Mechanical loss in suspension elements -2-

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mec

hani

cal l

oss

Fused Silica Sapphire Silicon

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hani

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oss

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hani

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oss

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thermoelastic(unstressed)

bulk Brownian surface total

300 K 300 K 300 K

20 K 20 K 20 K

all dia. 1 mm

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Surface loss in silicon suspension elements

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as = 0.5 pmLow surface loss in silicon (surface lossparameter ~1 order of magnitude lower than fused silica).[see talk by C. Schwarz]

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Cancelation of TE loss in silicon

• cancellation of TE noise due to proper strength in fibre not needed (although possible) for crystalline fibres at low temperatures (TE peak shifts towards high frequencies while cooling – reason: large thermal conductivity)

• dY/dT < 0 for silicon compensation

possible for a<0 (18-125 K)

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0 50 100 150 200 250 300-0.5

0

0.5

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3x 10

-6

temperature [K]

ther

mal

exp

ansi

on c

oeffi

cien

t [1/

K]

a < 0

 

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Cooling issues

• residual optical absorption causes heating of the test masses• heat capacity is very low at cryogenic temperatures (Debye T3

law) small absorption causes large temperature change• suspension will provide the operational temperature which will

also be defined by the mirror material (in case of silicon: <22K)

• suspension will operate in Casimir regime (phonon mean free path is limited by geometry) thinner elements will have smaller thermal conductivity

• thinner elements will have their peak in TE loss at higher frequencies tradeoff between thermal noise and conductivity

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Multi-stage design -1-

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Thermal bath

„Universe“

TM

5 m, 300 Kj = 10-4

j = 10-3

1 m, 300 Kj = 10-6

[Majorana, Ogawa 1997, VIR-0015E-09]

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Multi-stage design -1-

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Thermal bath

„Universe“

TM

5 m 300 K, 20 Kj = 10-4

1 m300 K, 20 Kj = 10-6

[Majorana, Ogawa 1997, VIR-0015E-09]

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Multi-stage design -3-

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Thermal bath

„Universe“

TM

5 m j = 10-4

1 mj = 10-6

300 K

5 K

20 K

[Majorana, Ogawa 1997, VIR-0015E-09]

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300K, 5K, 20K20K, 20K, 20K

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Towards a monolithic design using silicon -1-

• fabrication:

– fabrication of (poly-)crystalline fibres was shown [Pisa group, µ-PD technique]

– possible fabrication of ribbon-like structures (thin flexures for measuring coating thermal noise), limitted to wafer diameter (approx. substrate diameter, ~ dia. 500 mm)

– possible fabrication of long ribbons/fibres from thinner but long single crystal ingots (fabrication + surface quality currently unclear), length up to several meters possible

– use of ribbons might be justified by bonding method to be used for jointing the different parts (natural flat surface for ribbons)

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Towards a monolithic design using silicon -2-

• bonding + thermal conductivity:– silicate bonding possible with promising mechanical properties

[talk by S. Reid]– initial measurements of the thermal conductivity of the bond by

colleagues at Florence show a high thermal conductivity

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[M. Lorenzini, WP2,3 workshop Jena 03/2010]

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Shaping the suspension elements

• Willems et al. 1999 -> TN in non-uniform fibres (neck region)• shaping allows a further decrease of thermal noise +

tayloring the different mode types (pendulum, suspension, bounce, etc.)

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[Cumming et al. CQG 26 2009]

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Conclusion

• Summary– suspension design algorithm developed for AdvDetectors can be

applied to 3rd generation as well– new material properties (cryogenic regime) do not cause problems– multi-stage suspension weak coupling from upper to lower

stages close to resonance– application to possible ET design: see talk tomorrow

• open questions:

– monolithic suspension will be operated in non-thermal equilibrium impact on thermal noise?

– thermal conductivity through bonds needs detailed study– Investigation of direct bonding and lattice mismatch onto thermal

conductivity

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