A broad band acoustic detector of GW: The dual torus J.P.Zendri* - - PowerPoint PPT Presentation

A broad band acoustic detector

• f GW: The dual torus

J.P.Zendri* For the Auriga collaboration

* I.N.F.N. Padova Section, Via Marzolo 8, 35010 Padova, Italy, Zendri@lnl.infn.it

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

M Mechanical Amplification G M = ≡

.

1

Transd Elast Body

M Fractional bandwidth M G ν ν Λ = = ≡

Broad Band require

. .

1

trasd Elast Body

M 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

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

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 m m

u t q t = ⋅

∑

r r r r

2 2 2

( ) ( ) ( ) (r) w (r)

n n n n

q t q t F t G dV t ρ ρω ∂ + = ⋅ ∂

∫

r r

2 2

(r, ) [ (r, )] ( ) G(r) u t L u t F t t ρ ∂ − = ⋅ ∂ r r r r r r

2w (r)

[w (r)]

n n n

L ρω = r r r r

Measured Amplitude

N

(r) X( ) (r, ) P P t u t dV = ∫ r r r

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

Motion Equation Mode expansion Spatial solution Time evolution

Dual Torus

Thermal 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 i

θ θ

θ θ θ θ

×

+ + r r r r r r r r

a=2 sensitive to GW a=4 a=30 a=3 Output Signal

• Pos. displ.
• Neg. displ.

+

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

Dual Torus

Thermal and BA noise reduction:selectivity

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

.

( ) ( , ) ( ) P(r)P( )P(z)

Meas r N

P r X u r t dV P r i P θ = ≡

∫

r r r r r r r

Angular weight

1 2 3 4 meas

X X X X X = − + −

Dual Torus

Thermal and BA noise reduction:selectivity

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

, ,

(r,θ,z) 1 (r,θ,z, ) ( ) ( , )

Meas a a n n a N N

P X dVu t f d dzdrg r z P P θ θ = =∑

∫ ∫ ∫

r r

Same for both Mode weight

Dual Torus

Thermal and BA noise reduction: Example Selective Not selective Strain Noise Power spectrum

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

1 2 int 2

0.25 0.26 0.47

ext

r cm r cm r cm

− −

= = =

Molybdenum:

Dual detectors:one dimensional analog Transfer Function

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

( ) Transfer Function ( ) ( )

i i Ext

X H F ω ω ω = ≡

Displacement equivalent force PSD Transfer function

1 2

( ) ( ) Dual T.F. ( ) ( )

D Ext

X X H F ω ω ω ω − = ≡

Displacement equivalent input Force PSD

Dual detectors:one dimensional analog Back Action reduction

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

Back Action displacement PSD Equivalent B.A. input force PSD B.A. equivalent input force PSD

Dual detectors:one dimensional analog Thermal Noise

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

Thermal noise displacement PSD Thermal equivalent input force PSD

Ext Ther

F =F

Dual detectors:one dimension analog

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

Dual torus: Noise figure optimization

Quantum limit Calculation

XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri 2

( ) ( ) 4

FF XX

S S ω ω ⋅ ≥ h

Free parameter for optimization (noise stiffness )

n

K ( )/ ( )

n FF XX

K S S ω ω = Broad Band White band dominated B.A. dominated

9

10

n

K =

11

10

n

K =

10

10

n

K =

Dual Torus: Material

• 1. 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

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

sound

4

v ρ ⋅

SiC Mo Al Material used for calculation

3

[ / ] Kg m ρ

LowTemp

Q

3200 N.A.

s

v [ / ] m s 10300 2700 11200 5660 5050

8

10 >

7

10

Dual torus

Sensitivity Curve (Quantum Limit)

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

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

− − −

≥ ⋅ = = = = = = ⋅

Dual torus

A possible implementation (capacitive readout)

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

Present 1. SQUID at 30 ħ (P. Falferi this congress) 2. Electrical bias field 10 MV/m

7 2

3. / 10 N/m

FF XX

S 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 Torus

Optical readout (F.Marin this Conf.)

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

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

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

• 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 the

noise 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)