a broad band acoustic detector of gw: the dual torus · 2003. 3. 29. · a broad band acoustic...

A broad band acoustic detector of GW: The dual torus

J.P.Zendri*For the Auriga collaboration

* I.N.F.N. Padova Section, Via Marzolo 8, 35010 Padova, Italy, [email protected]

Motivations

XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

� Sensitive at high frequencies GW

� Broad band

Design of a new detector:

Dual detector: Not Resonant readout

Resonant Transducer:

.

.

Elast Body

Transd

MMechanical Amplification G

M= ≡

.

1Transd

Elast Body

MFractional bandwidthM G

ννΛ= = ≡

Broad Band require . . 1trasd Elast BodyM M G→! !

we are forced to renounce to the resonant transducer

Solution One:

Problem if M2<< M1

Solution Two:

M2≈M1 but CM2≠CM1

Solution Three:

M2≈M1 and same CM

Dual Detector

The Dual detector

Considered geometries


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

M.Bonaldi et. al., arXiv:gr-qc/0302012

Dual Sphere

Dual Torus

Mode Expansion

(r, ) w (r) ( )m mm

u t q t= ⋅∑r rrr

22

2

( ) ( ) ( ) (r) w (r)nn n n

q t q t F t G dVt

ρ ρω∂ + = ⋅∂ ∫

r r

2

2

(r, ) [ (r, )] ( ) G(r)u t L u t F tt

ρ ∂ − = ⋅∂

rr rr rr

2w (r) [w (r)]n n nLρω =r rr r

Measured Amplitude

N

(r)X( ) (r, )P

Pt u t dV= ∫r

rr


Motion Equation

Mode expansion

Spatial solution

Time evolution

Dual TorusThermal and BA noise reduction: Wide area sensing

+a,n , ,

a,n , ,

w (r)= cos( ) sin( )

w (r)=- cos( ) sin( )a n r a n

a n r a n

f a i g a i

f a i g a iθ

θ

θ θ

θ θ×

+

+

r rrr

r rrr

a=2 sensitive to GW

a=4 a=30

a=3Output Signal

Pos. displ.

Neg. displ.

+


Dual TorusThermal and BA noise reduction:selectivity


.( )( , ) ( ) P(r)P( )P(z)Meas rN

P rX u r t dV P r iP

θ= ≡∫r r r rr r r

Angular weight

1 2 3 4measX X X X X= − + −

Dual TorusThermal and BA noise reduction:selectivity


,,

(r,θ,z) 1(r,θ,z, ) ( ) ( , )Meas a a nn aN N

PX dVu t f d dzdrg r zP P

θ θ= =∑∫ ∫ ∫r

r

Same for bothMode weight

Dual TorusThermal and BA noise reduction: Example

Selective

Not selective

Strain Noise Power spectrum


1

2 int

2

0.250.260.47ext

r cmr cmr cm

−

−

===

Molybdenum:

Dual detectors:one dimensional analog Transfer Function


( )Transfer Function ( )( )

ii

Ext

XHF

ωωω

= ≡

Displacement equivalent force PSD

Transfer function

1 2( ) ( )Dual T.F. ( )( )D

Ext

X XHFω ωω

ω−= ≡

Displacement equivalent input Force PSD

Dual detectors:one dimensional analog Back Action reduction


Back Action displacement PSD

Equivalent B.A. input force PSDB.A. equivalent input force PSD

Dual detectors:one dimensional analog Thermal Noise


Thermal noise displacement PSD

Thermal equivalent input force PSD

Ext TherF =F

Dual detectors:one dimension analog


Dual torus: Noise figure optimizationQuantum limit Calculation


2

( ) ( )4FF XXS Sω ω⋅ ≥ h

Free parameter for optimization (noise stiffness ) nK

( ) / ( )n FF XXK S Sω ω=

Broad Band

White band dominated

B.A. dominated

910nK =

1110nK =

1010nK =

Dual Torus: Material1. High sound velocity and density

2. High thermal conductivity

3. Reasonable cost and availability

4. High quality factor

5. Max linear dimension 2-3 meters


sound4vρ ⋅

SiC

Mo

Al

Material used for calculation3[ / ]Kg mρ LowTempQ

3200 N.A.sv [ / ]m s

10300

2700

11200

5660

5050 810>

710

Dual torusSensitivity Curve (Quantum Limit)


8

1 2 int

1

2

1

/ 2 100.25 0.26 0.472.35 16.

1 0

4

.0 1 /n Mo

ext

K

Q Tr m r m

N

r mh m Tot wei

m

gth t−

−

−

≥ ⋅= = == =

= ⋅8

1 2 in

11

t 2

/ 2 100.82 0.83 1.

1.8 10

1.

/

443 6 5

n Si

ext

C

Q Tr m r m r mh m Tot weigt t

N m

h

K

− −

−

≥ ⋅= = == =

= ⋅

Dual torus A possible implementation

(capacitive readout)


Present

1. SQUID at 30 ħ (P. Falferi this congress)

2. Electrical bias field 10 MV/m7 2

03. / 10 N/mFF XXS S E C≈ ∝ ⋅

Required

1. SQUID at 1 ħ

2. Electrical bias field >200 MV/m

3. Carefully designed matching line

To SQUID

Amplifier

Dual TorusOptical readout (F.Marin this Conf.)


Required

1. Laser Power 10 W

2. Finesse 106

Items to be addressed Possible Solution

1. Wide sensing area Folded Fabry-Perot

2. Cryogenics Material with higher Q

Conclusions


� The SQL sensitivity of a new kind of broad band GW detector has been studied.

� On the relevant frequency range the calculated sensitivity is comparable with the predicted sensitivity of the next IFO generation with the further advantage of the detector compactness.

� A crucial point to reach the sensitivity goal is to increase thenoise stiffness of the present transducer generation.

� R&D on electromechanical and optomechanical transducers is starting

� More theoretical studies are required (sources, calculate the sensitivity using different real read-out, cosmic rays effect)

a broad band acoustic detector of gw: the dual torus · 2003. 3. 29. · a broad band acoustic...

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