Suspending the Test Masses of Gravitational Wave Detectors

Giles HammondInstitute for Gravitational Research

University of Glasgowgiles.hammond@glasgow.ac.uk

SUSSP 73, St Andrews, August 2017

2

Overview

• aLIGO suspensions and requirements

• Seismic noise & thermal noise

• Suspension construction

• Dissipation dilution

• Noise model of suspensions

• Warm and cold upgrades to aLIGO

• Summary

About Myself

3

• Suspension for Advanced gravitational wave detectors; silica, silicon, sapphire (now) • MEMS gravimeters for

gravity imaging (now)

• Precision measurements ofgravity; axion searches andCasimir force (PhD, postdoc)

• aLIGO ISI(postdoc)

End Test Masses (ETM)

Input Test Masses (ITM)

Suspensions in aLIGO

aLIGO Layout and Core Optics

4

5

Suspensions in aLIGO

LIGO-G1100434-v2

6

Suspension Inventory

• Two Input Test Mass (ITM) suspensions• Two End Test Mass (ETM) suspensions• One Beamsplitter (BS) suspension• Seven HAM Small Triple Suspensions (HSTS)• Two HAM Large Triple Suspensions (HLTS)• One, Output Mode Cleaner (OMC) Suspension• SUS electronics racks• Spare suspension components/parts• Spare SUS electronics

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Suspension System Functions

• Support the optics to minimise the effects of– thermal noise in the suspension– seismic noise acting at the support point

• Provide damping of low frequency suspension resonances (local control),and

• Provide means to maintain interferometer arm lengths (global control)– while not compromising low thermal noise of mirror– and not introducing noise through control loops

• Provide interface with seismic isolation system and core optics system• Support optic so that it is constrained against damage from earthquakes• Accommodate a thermal compensation scheme and other systems as

required e.g. acoustic mode dampers, baffles, alignment fiducials, ancilliarytooling, vibration absorbers

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Requirements:Test Masses

• Top-Level Requirements:

Requirement Value Suspension Thermal Noise 10-19 m/√ Hz at 10 Hz (longitudinal)

10-16 m/√ Hz at 10 Hz (vertical)*#

Residual Seismic Noise 10-19 m/√ Hz at 10 Hz(assumes seismic platform noise2x10-13 m/√ Hz)

Pitch and Yaw Noise 10-17 rad/√ Hz at 10 Hz (assumes beam centering to 1 mm)

Technical Noise Sources(e.g. electronic noise, thermal

noise from bonds)

1/10 of longitudinal thermal noise for each source

(since noise terms add in quadrature, each increases total by 0.5%)

*assumes 10-3 coupling vert. to long.#except for highest bounce mode peak

Initial LIGO and aLIGO

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• active isolation platform (2 stages of isolation)

• quadruple pendulum (four stages of isolation) with monolithic silica final stage

• 4 layer passive isolation stack

• single pendulum on steel wire

• coarse & fine actuators

• hydraulic external pre-isolator (HEPI) (one stage of isolation)

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Initial LIGO and aLIGO

Penultimate silica mass, 40 kg

Silica test mass, 40 kg

Catcher structure

Ear

Ear

Silica fibres welded

between the ears

Steel suspension

wires leading to upper

metal suspension

stages

Silica test mass 10.7kg

310 μm diameter steel piano wire

Wire clamps

Catcher and suspensions structure

(some components omitted for clarity)

LIGO Advanced LIGO

ASD and RMS

fupper (Hz)flower (Hz)

A (m

/√H

z) spectral density=A m/√Hz

RMS= [ ]lowerupper

f

f

ffAdfAupper

lower

−=∫ 22 mwhite noise

faLIGO

Time series : Random noise

FFT: Random noise

A (m

/√H

z)A(

m)

Time (s)

Frequency (Hz)

• There are two characteristic features that cause large motions over smallfrequency bands.• Earth tides at ≈10-5Hz (diurnal and semi-diurnal variation)• Microseismic peak at ≈0.16 Hz• These are below the operating bandwidth for Advanced LIGO=> why theproblem?• Root Mean Square (RMS) motion of the test masses is important (mrms) aswell as the noise, or spectral density, at a particular frequency (m/√Hz)

Seismic Noise in aLIGO

fupper (Hz)flower (Hz)

A (m

/√H

z) spectral density=A m/√Hz

RMS= [ ]lowerupper

f

f

ffAdfAupper

lower

−=∫ 22 mwhite noisefaLIGO

• Seismic noise limits sensitivity at low frequencies - “seismic wall”

• Typical seismic noise at quiet site at 10 Hz is ~ few x 10-10

m/√Hz – many orders of magnitude

above target noise level • Isolation required in vertical

direction as well as horizontal due to cross-coupling

• Two-stage internal isolation platform has target noise level of 2 x 10-13 m/√Hz at 10 Hz.

• require 4 more stages, i.e. quadruple pendulum, to meet target of 10-19 m/√ Hz

better isolation

• Advantage of adouble over singlependulum, sameoverall length

• Quad pendulum transfer function: predicted isolation ≈3 x 10-7 at 10 Hz

Seismic Noise

n

ground

mass

ff

xx

2

0

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

Active Seismic Isolation• Sense motion with seismometers and actuate to drive their

output to zero

• Advanced LIGO: Passive isolation above 10Hz, Active isolationfrom 100mHz-10Hz

M

x0

Filter

Sensor

Actuate

Feedback: velocity damping, integral controlFeedback loop

Filter

Feedforward: measure ground and predict motion

BSC Seismic Isolation

Thermal Noise

0.0000010.00001

0.00010.001

0.010.1

110

1001000

10000100000

0.1 1 10 100frequency (Hz)

ther

mal

noi

se (a

rbitr

ary

units

)

16

• Thermally excited vibrations of– suspension pendulum modes– suspension violin modes– mirror substrates + coatings

• Use fluctuation-dissipation theorem toestimate magnitude of motion

• To minimise:– use low loss (high quality factor)

materials for mirror and finalstage of suspension (fused silica)

– use thin, long fibres to reduceeffect of losses from bending

– use low loss bonding technique:hydroxide-catalysis bonding

– reduce thermal noise from upperstages by careful design of break-off/attachment points

low Q, high noise

high Q, low noise

Origin of Thermal Noise

• Thermal noise is the statistical movement of particles driven by thermalenergy

• The most common example is Brownian motion with energy per degreeof freedom distributed equally over the kinetic and potential energy

Brownian motion observed infat droplets suspended in milk

• A general theoretical description of fluctuations wasdeveloped by Callen, Welton & Greene (1950)

• A strong correlation between the loss in a system(dissipation) and its thermal noise was shown:Fluctuation-Dissipation theorem

• Both thermal energy and the dissipation in a systemdetermine its thermal noise.

• example: Johnson Voltage noise

TkB

fTRkV

V

B Δ=

=

4

02

V=0

[ ])(4)( ωω ZTkS B ℜ=

The Fluctuation-Dissipation Theorem

( ) ( )xikxmF )(1 ωφω ++= &&

( ) ( )xikF )(1 ωφω +−=

( ) ( )vikimviF )(1 ωφω

ωω +−=

( )v

FZ )(ωω =

( ))(1 ωφω

ω ikimi +−=

Homework: go through this derivation

The Fluctuation-Dissipation Theorem

( ) ( )xikxmF )(1 ωφω ++= &&

( ) ( )xikF )(1 ωφω +−=

( ) ( )vikimviF )(1 ωφω

ωω +−=

( )v

FZ )(ωω =

( ))(1 ωφω

ω ikimi +−=

The Fluctuation-Dissipation Theorem

ωωφ

ωωω kkmiZ )()( +⎟

⎠⎞

⎜⎝⎛ −=

( ) kkmiY

)()( 2 ωφω

ωω+−

=

( )( ) ( )222

2

)()()(

kkmkmikY

ωφωωωωωφω

+−−−=

The Fluctuation-Dissipation Theorem

[ ] [ ])(4)(4)( 21

2 ωω

ωω

ω YkTZkTSx ℜ=ℜ= −

( ) ( ) ⎥⎥⎦

⎤

⎢⎢⎣

⎡

+−=

222 )()(4)(

kkmkkTSx

ωφωωφ

ωω

( ) ⎥⎥⎦

⎤

⎢⎢⎣

⎡

+−=

40

2220

2

20

)()(4)(

ωωφωωωωφ

ωω

mkTSx

Origin of Thermal Noise

• Thermal noise of the optical materials and suspension elements manifests asstatistical fluctuations of the front surface which is sensed by the laser beam:– coatings and suspensions are important areas of R&D.

• The fluctuation of the surface can be produced by two possible mechanisms:

– Brownian motion of the surface – Brownian thermal noise– statistical temperature fluctuations within the test mass cause local

changes of the surface position (thermal expansion) – Thermoelastic noise

• The origin is the thermal energy that is stored in the atoms of the system soimprovements require:

– ultra pure materials with low mechanical loss– lower temperature

• Thermal energy ( ) drives resonantmodes

• Width of resonance related tomechanical loss of material, φ:

• Mechanical loss is energy dissipation byinternal friction in material

• Lower loss material → lower off -resonance thermal noise

• Use of fused silica (φ <10-7) mirrorsubstrates and suspension fibres in roomtemperature GWDs

Mechanical Loss

Q1

0

==Δ φω

ω

pendulum mode

internal mode of mirror

detection band

lower loss

Frequency (Hz)

Ther

mal

dis

plac

emen

t (m

Hz-

1/2 )

TkB

aLIGO Quadruple Suspension

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• The input test masses (ITM) and end testmasses (ETM) of Advanced LIGO will besuspended via a quadruple pendulum system

• Seismic isolation: use quadruple pendulumwith 3 stages of maraging steel blades forhorizontal/vertical isolation

• Thermal noise reduction: monolithic fusedsilica suspension as final stage

• Control noise minimisation: use quietreaction pendulum for global control of testmass position

• Actuation: Coil/magnet actuation at top 3stages, electrostatic drive at test mass

aLIGO Quadruple Suspension

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40kg silica test mass

parallel reaction chain for control

four stages

• The input test masses (ITM) and end testmasses (ETM) of Advanced LIGO will besuspended via a quadruple pendulum system

• Seismic isolation: use quadruple pendulumwith 3 stages of maraging steel blades forhorizontal/vertical isolation

• Thermal noise reduction: monolithic fusedsilica suspension as final stage

• Control noise minimisation: use quietreaction pendulum for global control of testmass position

• Actuation: Coil/magnet actuation at top 3stages, electrostatic drive at test mass

aLIGO Monolithic Stage

26

Steel wires

Penultimate mass (PUM)

Ear

Steel wire break-off prism

Silica fibres

End/input test mass

Ear

Ear

FibreNeck

Stock WeldHorn

Local and Global Control• Local control: damping at top mass, separately for

each chain, using BOSEMs (next slide) with 10mm x 10mm NdFe magnets

• Global control (length and angular) at all four levels– BOSEMs with 10mm x 10mm NdFe magnets

at top mass

– BOSEMs with 10mm x 10mm SmCo magnets acting between chains at upper intermediate mass

– AOSEMs** with 2mm x 6mm SmCo magnets acting between chains at penultimate mass

– Electrostatic drive (ESD) using gold pattern on reaction mass/compensator plate at test mass level

27

• Main (test) Chain• Reaction

Chain

•*BOSEM = Birmingham Optical Sensor/Electromagnetic Actuator•*AOSEM = ALIGO OSEM = modified initial LIGO OSEM

Monolithic Suspension Construction

28

• Hydroxide catalysis bonding of the ears

• Fibre pulling with CO2 laser

• Fibre profiling forimporting intoFinite ElementAnalysis

Laser Pulling

800µm diameter at bending point (200MPa for 10kg mass per fibre)

400µm diameter (800MPa for 10kg mass per fibre)for the remainder of the fibre to lower bounce mode(<10Hz) and increase violin modes (>500Hz)

• Monolithic suspensions & signal recycling pioneered in GEO-600 →upscaled to aLIGO

Monolithic Suspensions

32

aLIGO Suspensions

Suspension Thermal Noise (Dilution)

33

YITL

kk

EED

ξ2

fibre

gravity

elastic

total ≈≈=

• Profile fused silica fibre• Extract elastic strain energy andmodal frequencies from ANSYS

• Loaded suspension fibres themajority of energy in gravity ⇒ diluteloss due to elastic energy

• ξ=2 (bending top/bottom)

Fibre Strength

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Fused Silica

• Fused silica is a remarkable material: high strength, low mechanical loss,can be welded and drawn into fibres

• With 10kg on a 400 μm diameter, 60 cm long fibre:

• and the extension is

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εσ=Y

( ) MPa78010400/81.910 26 =×××= −πσ

mmLY

LL 66.0107210780

9

6

=×⎥⎦

⎤⎢⎣

⎡××=×⎥⎦

⎤⎢⎣⎡=×= σεΔ

• The strain is 1% at this load !!!

Fused Silica

36

• Explosive fracture at 4 GPa (strain of 6%, extension of 11mm for a20cm long fibre )

• aLIGO fibres operate with a safety factor of ≈7

Fibre Geometry

37

• The fibre geometry defines the dilution of the suspension and canbe approximated analytically as

• Fibres are not infinitely stiff attachments and thus the analyticaldilution values are modified with FE analysis (Dcyl=75)

12/

4/3

4

wtI

RI

rec

cyl

=

= π

Geometry D (Analytic) D (FEA) Dimensions

Cylindrical 112 75 φ 0.8mm

Rectangular 480 - 0.1mm×1mm

YITLD ξ

2≈

Fibre Profile

0 10 20 30 40 50 60Distance along fibre (mm)

400800

120016002000240028003200

fibre

cro

ss-s

ectio

n di

amet

er (m

icro

ns)

200

400

800

1200

1600

fibre

cro

ss-s

ectio

n di

amet

er (m

icro

ns)

00 100 200 300 400 500 600

Distance along fibre (mm)

• Fibre stock is 3 mm diameter– Ease of welding and handling, stiff connection

• Short 800 μm diameter section– Bending takes place close to the attachment point (modal frequencies)– Reduces thermoelastic noise

• 400 μm diameter over the majority of the fibre length– Violin mode ≈510Hz, vertical mode ≈9Hz

Suspension Thermal Noise

39

( ) ( )( ) ( ) ⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

−+= 22224

24ωωωφω

ωφωω

ωototalo

totaloBx m

TkS

( ) ( ) ( ) ( ) ( )( )ωφωφωφωφωφ iweld,isurface,iTE,ibulk, +++=i

• Use the following loss terms to model the welds, ear horns and fibres

( ) ( ) ( ) ( )⎥⎦

⎤⎢⎣

⎡+++= ωφωφωφωφ n

elastic

n2

elastic

21

elastic

11E

EE

EE

EDtotal K

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

+⎟⎠⎞

⎜⎝⎛ −= 2

2

TE 1 ωτωτβσα

ρωφ

YCYT

o

dh sφφ 8

surface ≈

77.011bulk 102.1 f−×=φ

( ) 7weld 108.5 −×=ωφ

A.M. Gretarsson et al., Phys. Rev. A, 2000 G. Cagnoli and P.A. Willems, Phys. Rev. B, 2002P.A. Willems, T020003-00M.Barton et al., T080091-00-KA. Heptonstall et al., Phys. Lett. A, 354, 2006A. Heptonstall et al., Class. Quant. Grav, 035013, 2010

• Surface loss: dislocations, un-terminated danglingbonds and micro-cracks on the pristine silica surface• Thermoelastic loss: heat flow across the fibre due toexpansion/contraction leads to dissipation.• Bulk loss: strained Si-O-Si bonds have two stableminima which can redistribute under thermalfluctuations.

Suspension Thermal Noise• aLIGO utilises thermoelastic cancellation to meet the noise requirement of

10-19 m/√Hz at 10Hz.• Fused silica has a Young’s modulus which increases with temperature

dTdY

Y1=β

Expa

nsio

n at

low

stre

ssC

ontra

ctio

n at

hig

h st

ress

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

+⎟⎠⎞

⎜⎝⎛ −= 2

2

TE 1 ωτωτβσα

ρωφ

YCYT

o

aLIGO Suspension Thermal Noise

41

test mass (φ34cm)

Hydroxide catalysis bonding

CO2 laser welding

• ANSYS predictions of violin mode quality factors are in good agreement (≈15%)with ringdown measurements at the LIGO Advanced Systems Test Interferometer(LASTI) at MIT where the first monolithic suspension was installed.

Ringdown Time to 1/e

42

• Violin frequency with tension T and mass per unit length μμTc =

( ) mkgr /000277.0220210200 262 =×××=××= −πρπμ

NmgT 1.984/ ==

smc /595000277.0

1.98 ==

HzLccf 496

6.02595

2=

×===

λ

ee NNQ /18

/1 106.3 ππ =×⇒=88

/1 101.1106.3 ×=×=eN daysfe 7.2

496101.1101.1 88

/1 =×=×=τ

Useful Equations

Thermal displacement noise

Fluctuation Dissipation theorem

Quality factor

Dissipation dilution (in horizontal direction)

43

( ) ( )⎥⎦⎤

⎢⎣

⎡ℜ=ωω

ωZ

TkSx14

2B

( ) ( )( )220

2220

202 4

φωωωωφω+−

=m

Tkx Bthermal

Q1

0

==Δ φω

ω

YITL

kk

EED 2

fibre

gravity

elastic

total ≈≈=

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

+⎟⎠⎞

⎜⎝⎛ −= 2

2

TE 1 ωτωτβσα

ρωφ

YCYT

o

dh sφφ 8

surface ≈

( ) 7weld 108.5 −×=ωφ

Dominant fibre loss terms (thermoelastic is minimised with appropriate fibre stress)

Other useful equations

m=mass on 1 fibre

Lgf pendulum π2

1=

mLYAfbounce π2

1=

bouncemasstestfree ff 2__ =

2/4RI π=

εσ=Y

LY

L ⎥⎦⎤

⎢⎣⎡= σΔ

πκρτ32.4

2Cdcircular =

A Simple Model

44

• Using the previous equations

A Simple Model

45

• Using the previous equations

aLIGO Sensitivity

46

47

• Light suspensions (1g-100g) are being developed around the world for radiationpressure/SQL experiments (ICRR, MIT, Glasgow, AEI Hannover, Italy)

• Glasgow has developed triple suspensions for AEI

Ears- fibre weld

Lower stage spring

Welding

Thin Fibre Work

48

Heavy Suspensions• We have already built up 2 single fibre 40kg tests (using 1200MPa fibre stress)

• Latest system been hanging since Dec 9th 2016

• 4 fibre (160kg) planned for late 2017

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Cryogenic Suspensions• Cryogenic suspensions operating at

120K/20K offer significant gains insensitivity

• Silicon has a zero in its thermalexpansion at these temperatures

• At 120K, use radiative cooling toremove heat

• At T<50K, need to use conductionthrough fibres

KAGRA 23kg sapphire payload (R. Kumar)

Crystal growth machine

(Glasgow)

Summary

• Suspensions are a key component to provide:

– Seismic isolation of the test masses

– Low thermal noise operation

• aLIGO fused silica installation is a mature technology. This represents a wellengineered robust design which is optimised for low thermal noiseperformance

• Good understanding of loss terms => high Q factors for violin modes

• Thin fibre work underway for suspending 100g/1g optics

• Further lowering thermal noise requires lower mechanical loss and/or lowtemperature operation

– Heavy test masses and/or higher fibre stress

– Cryogenic operation

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