Thermal noise limit to the Virgosensitivity

Virgo Perugia Group:

L.Gammaitoni, F.Marchesoni, M.Punturo, P.Amico,C.Cattuto, H.Vocca, L.Carbone, R.Mischianti, F.Travasso

1 1 0 100 1000 100001 0

-24

1 0-23

1 0-22

1 0-21

1 0-20

1 0-19

1 0-18

1 0-17

h~∆L/L

T o t

Seism

Thermal

Shot

RadPres

Creep

ThPend

ThMirror

h(f)

[1/

sqrt

(Hz)

]

Frequency [Hz]

The Virgo Sensitivity Curve• The current

suspension forthe Virgo laststage is madeby a doubleloop of C85steel wires

• C85 shows thebest thermalnoise value formetal wiresuspension

• The pendulumthermal noise isdominantbetween 3 and50 hz

Sb

matgB CTLm

E

mN

gE

L

gTkX

φθ

πωω

+≈ 2

252

41

4)(

• Material internalloss angle

3 Contributions to the thermal noise

Pendulum Thermal Noise

• Clamping losses– Can be reduced

by using specialclamps withhigh clampingpressure

– “Spacers” onthe wire-mirrorcontact point

• Ideal solution:– Monolithic

wires

20)(1

0

0

ff

ff

w +∆+=φφ

• Geometricaldilution factor

En

gM

r

LQ

wpend πφ 2

21=

Breaking strength

Clamps & SpacersTop View

Bottom View

Tool Steel insert

• High pressureClamps andSpacers areused to reducethe friction(stick and slipprocess)between wireand clampingdevices ormirror

• Monolithicsolution willeradicate theproblem!

• Silicatebonding will beused to connectthe wires to themirror

1 10 100 100010

-7

10-6

10-5

10-4

10-3

Fused Silica

Fused S i l i ca

S Q 2

Supras i l

C u B e

T i t a n i u m

Tungs ten

M a r v a l

C 8 5 s t e e l

N i o b i u m

I n v a r

Sapph i re

S iC

A l u c h r o m

C h r o m a l l o y

φw(f)

frequency (Hz)

Measured Losses of Materials• All metals (and sapphire) have a similar loss

φ≈10-4

φ≈10-6

Afactor

10on“h”

sensi-tivity

Ref. Phys. Lett. A 255 (1999) 230-235

Fused Silica Vs C85 Breaking Strength: Production facility• Fused Silica breaking strengh is strongly dependent on the production

and handling procedures

– Impurities inserted in the production procedure can decrease thebreaking strength down to few hundreds of MPa.

• For this reason we abandoned the induction oven wire production facility

• A new facility to produce fused silica wires has been realized using a H2-O2 flame (*)

(*)With the collaboration of the G

lasgow G

eo600 Group

Fused Silica Vs C85 Breaking Strength: Handling

• Fused silica fibers are very sensitive to surface scratchs caused bycontact with metal or other hard materials.

• In this case the Griffith’s law relate the scratch size to the breakingstrength

• In literature humidity plays a role in the aging of the fiber, but for themoment we haven’t conclusive data.– A 200 µm diameter fused silica fiber has been loaded for more than one year with

5.5 kg in a very humid environment.

– Failure has occurred after the last strong earthquake in Perugia.

Fused Silica Vs C85 Breaking Strength: Results• The C85 steel shows an high breaking strength (Tb~2.74GPa) and a good “confidence factor” (Cs~0.65). For

this reason C85 has been selected as reference solution for the Virgo mirror suspension wires

• Synthetic Fused Silica shows a similar breaking strength if well produced and carefully handled, but the“confidence factor Cs” is still lower because of a large dispersion of the measured breaking strength valuesand handling problems.

140 160 180 200 220 240 260 280

2000

3000

4000

5000

6000

Bre

akin

g St

reng

th (

Kg/

mm2 )

Ethilic Alcool

Bre

akin

g St

reng

th (

MPa

)

Wire diameter (µm )

200

250

300

350

400

450

500

550

600

650

Acid Solution

2000250030003500

40004500500055006000

0

1

2

3

4

5

6

7

Alchool

AcidSolution

Breaking Strength (MPa)

C85 Steel (Mpa) F.S. Alchoolcleaning (Mpa)

F.S. Acid solutioncleaning (Mpa)

2743±64 3577±827 4031±711

Fused silica fibers plasticity

• Fused silica fibers are brittle and don’t show any plasticity behaviour

0 ,00 1,55x10 -3 3,09x10 -3 4,64x10 -3 6,18x10 -3 7,73x10 -3 9,27x10 -3 1,08x10 -2 1,24x10 -2 1,39x10 -2 1,55x10 -2

0 ,00

3,27x10 8

6,54x10 8

9,81x108

1,31x109

1,64x109

1,96x109

2,29x109

2,62x109

2,94x1090 ,00 1 ,50 3 ,00 4 ,50 6 ,00 7 ,50 9 ,00 10,50 12,00 13,50 15,00

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

9,0

∆LC

EC=1.9 x 101 1 N/m2

CleanDirty

Mm

∆LD

Lw=700+πRM /2 [mm]

ED=2.0 x 101 1 N/m2

VIRGO mirror T=5.2 Kg

∆L [mm]

Loa

d [K

g]

stre

ss [N

/m2]

strain ∆ε 0,00 2,58x10-3

5,15x10-3

7,73x10-3

1,03x10-2

1,29x10-2

1,55x10-2

1,80x10-2

2,06x10-2

2,32x10-2

2,58x10-2

2,83x10-2

0,00

7,70x108

1,54x109

2,31x109

3,08x109

3,85x109

4,62x109

5,39x109

6,16x109

6,93x109

0,00 2,50 5,00 7,50 10,00 12,50 15,00 17,50 20,00 22,50 25,00 27,50

0,0

2,0

4,0

6,0

8,0

10,0

12,0

14,0

16,0

18,0

6.7 x 10 9 PascalBreaking point

∆Lw

Mm

Lw=700 [mm]

Ew=(2.40 ± 0.04) x 1011

N/m2

VIRGO mirror T=5.2 Kg

∆L [mm]

Loa

d [K

g]

stre

ss [N

/m2 ]

strain ∆ε

C85 Steel Fused Silica

Phase modulation@ 12 MHz Pockels

Cell

λ/2

Laser

100mW @ 1.06 µm

Spring loadedC85 steel wire

PZT

Vacuum Chamber

Creep noise: the problem• C85 steel wires under load show anelastic elongation

– DC elongation of the wire

– Shot noise (filtered by the suspension wire) in the interferometer because of thehorizontal-to vertical coupling (see Marchesoni et al., Phys. Lett. A 237 (1997) 21-27)

– A spring loaded C85 wire has been used as support for a mirror in a Mach Zenderinterferometer

( )( ) 2

22 112)(

0 Qf

qfx

ff +−

=π

λ

• The mechanical transfer function is measuredby shaking the structure

• q λ and qλ½ are measured independently

770 775 780 785 790

10 -14

10 -13

disp

lace

men

t in

m/H

z1/2

frequency in Hz

q step sizeλ rate

( )( )( ) smq

s

mq

/102.01.2

101.08.1

101.02.1

10

15

15

−

−

−

⋅±=

⋅±=

⋅±=

λ

λ

Creep noise: the solution• C85 steel wire creep is strongly reduced by low temperature annealing

(stress relaxation):– suspension wires are kept under tension with a load larger than the Virgo mirror

for a week at 150°C in N2 atmosphere

– the final creep rate is qλ≈2·10-14m/s and the noise contribution is reported in thesensitivity curve.

5 10 15 20 251.20x10

-5

1.25x10-5

1.30x10-5

1.35x10-5

1.40x10-5

time in daysIn

crea

sing

leng

th

Len

gth

in m

• And for fused silicasuspension wires?– no conclusive data are

available.

– preliminary results show thatthe creep phenomenon shouldbe negligible

2µm

kgm

CT

cml

mr

load

wire

wire

5.5

5.34

60

100

=°=

== µ

1 10 100 100010

-23

10-22

10-21

10-20

10-19

10-18

C85 steel wire (total) Fused Silica wire (total) FS pendulum thermal noise Mirror thermal noise

h [1

/sqr

t(Hz)

]

Frequency [Hz]

The expected Virgo sensitivity with fused silica fibers