Broad band acoustic detectors J.P. Zendri* on behalf of the AURIGA - - PowerPoint PPT Presentation

J.P. Zendri*

• n behalf of the AURIGA collaboration

www.auriga.lnl.infn.it

Broad band acoustic detectors

5th International LISA Symposium 12-15 July 2004

5th International LISA Symposium 12-15 July 2004

Acoustic detector noise budget:one dimensional lumped model

2 2 2 2

( ) ( ) 4

B n FF XX

k T S S ω ω ω ≡ ⋅ ≥ h ( )/ ( )

n FF XX

K S S ω ω =

Quantum mechanics constrain Tn The noise stiffness Kn is unconstrained

5th International LISA Symposium 12-15 July 2004 ( ) ( ) ( ) ( )

FF X V X n V II

T S S S S ω ω ω ω ∝ ⋅ ⋅ ฀

2

( )/ ( ) ( )/ ( )

n VV II II FF

S S K S S ω ω α ω ω = ฀ I X Transducer Efficency α ≡ =

2 2

( ) ( ) ( ) ( )

FF VV XX II

S S S S ω ω ω α α ω

−

= × ≈ ×

General result:

5th International LISA Symposium 12-15 July 2004

Practical limits to the Kn Passive transducers Active transducers

2 2

( )/ ( ) 10 / 10

n bias VV II

K E S S MV m Breakdown ω ω

−

↓ ∝ Ω ↓ ฀

For instance capacitive For instance optical

5 6

10 10

n

K Finesse LaserPower Watt ∝ × ≥ ↓ ÷ ↓

Kn OK but problems for cryogenics

5th International LISA Symposium 12-15 July 2004

Methods to increase the efficiency: resonant transducers

Mechanical signal amplified before the transduction One mode transducer Two mode transducer Velocity transformer

bar Tr

ω ω = /

BAR TR

M M = /

bar TR BAR

M M ν = Required Increment of a around resonance Bandwidth upper limit

bar First Last

ω ω ω = = /

BAR LAST

M M = /

bar First BAR

M M ν = Required Increment of a around resonance Bandwidth upper limit Broad Band amplification but still a complete thermal noise analysis is missing

J.P. Richard, Phys. Rev. Let. 52, 165 (1984) H.J. Paik, Jour. Appl. Phys. 47, 1168 (1976)

• D. Blair et al, Appl. Phys. 20, 162 (1987)

5th International LISA Symposium 12-15 July 2004

Auriga method: Resonating matching line

( ) ( ) ( )

2 2

I 1 x ( ) /

Bias s in eff el el el

i ME L L L i Q ω ω α ω ω ω ω ωω = = + − +

2

1 ( ) 1

eff P P in S el eff el eff el

M L L L L L L C L Q R ω ω   ≡ −   +   ≡ ≡

Enhancement of the transducer efficiency around the mechanical modes

el mech

ω ω ⇒

5th International LISA Symposium 12-15 July 2004

This because the equivalent electric mode mass is light Auriga operate with a Q factor of ~ 500.000

2 2

20 .

Tr Bias el el

C E M gr ω = ฀

Tuning the electrical mode to the mechanical modes require a very high electrical Q quality factor

Tr

C = Transducer capacitance

800 850 900 950 1000 1050 1100 1E-6 1E-5 1E-4 1E-3 Wide Band Noise Level Spurious HV Plate Resonances 3 Main Modes

Auriga Output PSD at 4.5 K

SΦΦ

1/2 [Φ0/Hz 1/2]

Frequency [Hz]

5th International LISA Symposium 12-15 July 2004

Around the sensitivity bandwidth Auriga noise is dominated by LC thermal noise

5th International LISA Symposium 12-15 July 2004

Auriga readout

1.5 2.0 2.5 3.0 3.5 4.0 4.5

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

N

Double SQUID white band noise

PSD [µΦo

2/Hz]

Temperature [K]

150 200 250 300 350 400 450

5000

Auriga Old

N

−

=

h B n

k T N ω =

h

h

5th International LISA Symposium 12-15 July 2004

AURIGA present Sensitivity

800 820 840 860 880 900 920 940 960 980 1000 1E-21 1E-20 1E-19

Noise curve prediction at 4.5K Auriga Now T=4.5 K Auriga Old T=0.1 K

Shh

1/2 [Hz

• 1/2]

Frequency [Hz]

5th International LISA Symposium 12-15 July 2004

Solution One: Wrong! Dominated by thermal and BA of the reference mass Solution Two: M2~ M1 but CM2CM1 Solution Three: M2 ~ M1 and same CM Dual Detector

Increase the bandwidth: The Dual detector

5th International LISA Symposium 12-15 July 2004

Considered geometries for Dual

Dual Sphere

M.Cerdonio et. al., Phys. Rev. Let. 87, 031101 (2001)

Dual Torus

M.Bonaldi et. al., Phys Rev. D62, 102004 (2003)

5th International LISA Symposium 12-15 July 2004

Quantum Limited sensitivity curve (dual torus)

8 1 2 int 1 2 1

/ 2 10 0.25 0.26 0.47 2.35 16. 1 4 .0 1 /

n Mo ext

K Q T r m r m N r m h m Tot wei m gth t

− − −

≥ ⋅ = = = = = = ⋅

8 1 2 in 11 t 2

/ 2 10 0.82 0.83 1. 1.8 10 1. / 44 3 6 5

n Si ext C

Q T r m r m r m h m Tot weigt t N m h K

− − −

≥ ⋅ = = = = = = ⋅

In order to get Kn ~1011 N/m a lever geometrical amplification of at least 10 is required

5th International LISA Symposium 12-15 July 2004

Broad band lever amplification Hinges X Y Mirror

Mechanical amplification=Y/X=1/a>>1

H.J. Paik et al, Proc. Of the first Amaldi Meeting, edited by E. Coccia et al, World scientific Singapore, p201 (1995)

Auriga design:

Prototype under test:Amplification

5th International LISA Symposium 12-15 July 2004

Mode Domain Lever Domain

Material Al7075

• T=300 K
• Gaussian Beam waste 0.375 mm
• Mirrors Fused silica

Geometrical gain factor=10

Parameters for simulation

5th International LISA Symposium 12-15 July 2004

Prototype test:assembling procedure

Harmonic oscillator Amplifier

250 500 750 1000 1250 1500 1750 2000 2250 1E-18 1E-17 1E-16 1E-15 S

1/2 xx(f) [m/Hz 1/2]

Frequency[Hz]

5th International LISA Symposium 12-15 July 2004

Prototype thermal noise estimation The amplifier thermal noise contribution is negligable

Resonator Therm Therm xx Amplifier out xx

S Gain S

− − −

≈ ×

Resonator alone

Room Temperature Thermal Noises Measurement: 10 µK Stabilized Thermal Box!

NTC Thermistors Technology ｱ5μK Active ｱ1mK Thermal Box 1 μ Yag LASER

5th International LISA Symposium 12-15 July 2004

Prototype thermal noise measurement set-up

5th International LISA Symposium 12-15 July 2004

A possible implementation in Dual-Torus

5th International LISA Symposium 12-15 July 2004

Dual Torus Therm. and BA noise reduction: Wide area sensing

GW sensitive (quadrupolar) mode: Some GW not sensitive mode which provide only noise: High order modes are averaged out

Signal=mean displacement over the readout area=Green surf.+Yellow surf.

Some of the low order modes are averaged out

Unperturbed torus Mode Shape Rejected Not Rejected

5th International LISA Symposium 12-15 July 2004

Dual Torus Therm. and BA noise reduction: Selective readout

Meas-Selective 1 2 3 4

X X X X X = − + −

meas-Standard

X X =

Meas-Selective

Maximized X →

Meas-Selective

X → Quradrupolar mode (Signal) Octupolar (Noise)

5th International LISA Symposium 12-15 July 2004

1 2 int 2

0.25 0.26 0.47

ext

r cm r cm r cm

− −

= = =

Material:Molybdenum: Dimensions: Red:Selective readout

Strain Noise Power spectrum

Blue: Not Selective readout

Example of Thermal and BA noise reduction using selective readout

5th International LISA Symposium 12-15 July 2004

Conclusions

• Well designed impedance matching lines between the

main resonator and the amplifier has been used to widen the useful band of the Auriga detector more than one order

• f magnitude
• Broad band detectors should be obtained using lever
• transducers. In particular the proposed detector “dual”

promises a sensitivity of the order of 10-23 Hz-1/2 in the frequency range between 1kHz to 5 kHz.