suspending the test masses of gravitational wave detectors
TRANSCRIPT
Suspending the Test Masses of Gravitational Wave Detectors
Giles HammondInstitute for Gravitational Research
University of [email protected]
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
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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
)
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• 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
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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
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• Main (test) Chain• Reaction
Chain
•*BOSEM = Birmingham Optical Sensor/Electromagnetic Actuator•*AOSEM = ALIGO OSEM = modified initial LIGO OSEM
Monolithic Suspension Construction
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• 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
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aLIGO Suspensions
Suspension Thermal Noise (Dilution)
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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
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• 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
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( ) ( )( ) ( ) ⎟
⎟
⎠
⎞
⎜⎜
⎝
⎛
−+= 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
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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)
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( ) ( )⎥⎦⎤
⎢⎣
⎡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
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• 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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