1 Test Mass Suspensions for AIGO Ben Lee The University of Western Australia.

1

Test Mass Suspensions for AIGO

Ben Lee

The University of Western Australia

Australia-Italy Workshop 3rd-6th Oct 2005

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Introduction

Thermal noise in interferometers.Reducing the thermal noise: what we know so far.

Suspensions for AIGO.Removable modular suspensions.Reducing violin mode Q factors.


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Thermal Noise

10-22

10-20

10-24

10-26

100 101 102 103 104

Thermal Noise

1st Generation Sensitivities

Advanced Sensitivity

The thermal noise must be reduced below the quantum noise limit.

Frequency (Hz)

H(f

) / (

Hz)

1/2


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Suspension Thermal Noise

101

102

103

104

10-28

10-26

10-24

10-22

10-20

10-18

10-16

Quantum NoiseTest Mass Thermal NoiseSusp. Thermal NoiseTotal Noise

H(f

) / (

Hz)

1/2

Frequency (Hz)

Low thermal nose achieved with very high Q modes.

Suspension modes may also affect control systems.


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Low Loss Materials

4nn

222n

2nn

2n

B2 L

Tk4x

From the dissipation dilution theorm:

Thus, materials with low Φ are better. Fused Silica: Φ~3×10-8 [1]Silicon: Φ~2.8×10-8 [2]Sapphire: Φ~3.7×10-9 [3]

There is much more to consider….Thermoelastic loss

(300K)

1. A.M. Gretarsson, G.M. Harry. Rev. Sci. Instrum. 70 (1999) 40812. J. Ferreirinho in: D.G.Blair (Ed), The Detection of Gravitational

Waves, Cambridge Universtiy Press, Cambridge, 1991.3. S. Rowan, et. al. Phys. Lett. A. 5 (2000) 265

References:


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0 1 2 3 4

-7

-6

-5

-4

0 1 2 3 4

-7

-6

-5

-4

Thermoelastic Loss

2th

1

v

2

c

TE

Thermoelastic loss presents a significant frequency dependance to the loss value, Φ.

K

tc2

2v

K32.4

dc 2v

,for fibres

,for ribbons

where

and

1 10 100 1000 10000Frequency (Hz)

10-4

10-5

10-6

10-7

Loss

ang

le,

Φ

Sapphire

Niobium

Fused Silica

Silicon (All 200µm thick)

Thinner ribbon


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Fibers vs Ribbons.

2mgL

EI

2

1

Dissipation dilution factor:•The ratio of restoring force supplied by bending elasticity to the restoring force supplied by tension.

•This phenomena has a significant effect on pendulum mode and violin mode Q factors.

FT

Fb

FT

Fb

The effective loss factor

This value can be lower for ribbons compared to fibres with similar strength.


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AIGO suspension

Sensitivity: 2nm/Hz1/2 (100Hz bandwidth)

Force: 20µN (100Hz bandwidth)

Control mass 30kgTest mass 4.2kg

Removable Modular suspensions.Peg in Hole interface.

Ribbon Suspension


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Peg – Hole Interface

1500.164E+07

.328E+07.492E+07

.656E+07.820E+07

.984E+07.115E+08

.131E+08.150E+08

NODAL SOLUTION

STEP=1SUB =1TIME=1SEQV (AVG)DMX =.752E-05SMN =1472SMX =.350E+08

1500.164E+07

.328E+07.492E+07

.656E+07.820E+07

.984E+07.115E+08

.131E+08.150E+08

NODAL SOLUTION

STEP=1SUB =1TIME=1SEQV (AVG)DMX =.752E-05SMN =1472SMX =.350E+08Test mass

Ribbon

Peg

High pressure contact points

Result:Stress at contact points approaches yield strength of Nb

FEM model of pegs


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Will localised losses at the hole surface significantly affect the thermal noise?

Holes in the test mass

Question…

Model and results courtesy of S. Gras (ACIGA)

FEM model of test mass.Homogeneous structural loss Φs=10-8

Define the extra lossy elements.Apply Φs=10-2 to 10-8

Thermal noise observed by a gaussian beam

Structural losses only

Include non-homogeneous losses Φh=10-2


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Holes in the test mass

Model and results courtesy of S. Gras (ACIGA)

Contour values, Ψ:

Sh+s (spectral density of inhomogeneous model)

Ss (spectral density of homogeneous model)Ψ=

10% increase line

For AIGO interferometer with r0 = 20mm, - Φh cannot exceed 4×10-3


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Reducing Violin Mode Qs

It has been reported by Goßler et. al. [1] the need to reduce the Q factor of the fundamental and first harmonic violin mode.

The purpose is to prevent interference with interferometer length control servo.

This is achieved by adding lossy coatings.

Reference:1. Class. Quantum Grav 21 (2004) S923-S933

Fused silica fibre

Teflon coatings


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Reducing Violin Modes

The Orthogonal Ribbon can reduce violin modes and Q factors.

High Contact Peg

End Flexure

Orthogonal Section

End flexures provide similar pendulum mode Q factors.

Orthogonal ribbon section exhibits fewer, lower Q violin modes in the critical direction.

Pendulum mode freq. and dilution factors

Normal Ribbon

Orthogonal Ribbon

x

y

fpend (Hz) dilu

x

y

0.91

1.12

2.8×10-3

0.27

0.91

0.92

3.1×10-3

3.0×10-3Little difference between normal and orthogonal ribbon.


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Reducing Violin Modes

2

2

4

4

2

2

t

t,zY

z

t,zYEI

z

t,zYT

The violin modes for the orthogonal ribbon can be calculated by solving the beam equation:

Direction of laser field

x direction modes y direction modes

Test Mass


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Reducing Violin Modesm

/Hz1

/2

Expected Suspension Thermal Noise Comparison,

Normal Ribbon and Orthogonal Ribbon

100

101

102

103

10-22

10-20

10-18

10-16

Frequency (Hz)

10-14

10-12

10-10

10-8

Normal RibbonOrthogonal RibbonSimilar low

frequency thermal noise

Lower number, and lower Q factor x direction violin modes.

Small increase in thermal noise, due to lower violin mode Q.


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Conclusion

Removable modular suspension can be achieved with only a slight increase in test mass thermal noise.

Lowering all the violin mode Q factors can be achieved with an orthogonal ribbon.

The orthogonal ribbon has little effect on pendulum mode thermal noise.

AIGO facility can be used to test the practicality of the suspensions presented.

1 Test Mass Suspensions for AIGO Ben Lee The University of Western Australia.

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