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

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, Zendri@lnl.infn.it

Motivations Design of a new detector: • Sensitive at high frequencies GW • Broad band XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

Dual detector: Not Resonant readout Resonant Transducer: M = . ≡ Elast Body Mechanical Amplification G M . Transd Λ ν 1 M = = ≡ Transd Fractional bandwidth ν M G . Elast Body → Broad Band require 1 � � M M G . . trasd Elast Body we are forced to renounce to the resonant transducer

The Dual detector Solution One: Problem if M 2 << M 1 Solution Two: M 2 ≈ M 1 but CM 2 ≠ CM 1 Solution Three: M 2 ≈ M 1 and same CM Dual Detector

Considered geometries Dual Sphere M.Cerdonio et. al., Phys Rev. Let. 87 , 031101 (2001) Dual Torus M.Bonaldi et. al., arXiv:gr-qc/0302012 XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

Mode Expansion r r ρ ∂ r 2 (r, ) r r r u t − = ⋅ [ (r, )] ( ) G(r) Motion Equation L u t F t ∂ 2 t r r r r ∑ = ⋅ (r, ) w (r) ( ) Mode expansion u t q t m m m r r r r ρω = 2 w (r) [w (r)] Spatial solution L n n n ∂ 2 ( ) r r q t ∫ ρ + ρω = ⋅ 2 ( ) ( ) (r) w (r) Time evolution n q t F t G dV ∂ 2 n n n t Measured Amplitude r = ∫ (r) r r P X( ) (r, ) P t u t dV N XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

Dual Torus Thermal and BA noise reduction: Wide area sensing r r r r θ + θ + w (r)= cos( ) sin( ) f a i g a i θ a,n , , a n r a n r r r r × θ + θ w (r)=- cos( ) sin( ) f a i g a i θ a,n , , a n r a n Pos. displ. + Neg. displ. a=3 a=2 sensitive to GW Output Signal a=4 a=30 XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

Dual Torus Thermal and BA noise reduction:selectivity r r r r ( ) r r r P r ∫ = ≡ θ ( , ) ( ) P(r)P( )P(z) X u r t dV P r i . Meas r P N Angular weight = − + − X X X X X 1 2 3 4 meas XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

Dual Torus Thermal and BA noise reduction:selectivity r (r, θ ,z) 1 r P = ∑ ∫ ∫ ∫ = θ θ (r, θ ,z, ) ( ) ( , ) X dVu t f d dzdrg r z , Meas a a n P P , n a N N Mode weight Same for both XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

Dual Torus Thermal and BA noise reduction: Example Selective Strain Noise Power spectrum Not selective = 0.25 Molybdenum: r cm 1 = 0.26 r cm − 2 int = 0.47 r cm − 2 ext XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

Dual detectors:one dimensional analog Transfer Function Transfer function Displacement equivalent force PSD Displacement equivalent input Force PSD ω ( ) X = ω ≡ Transfer Function ( ) i H ω i ( ) F Ext ω − ω ( ) ( ) X X = ω ≡ Dual T.F. ( ) 1 2 H ω D ( ) F Ext XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

Dual detectors:one dimensional analog Back Action reduction Back Action displacement PSD Equivalent B.A. input force PSD B.A. equivalent input force PSD XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

Dual detectors:one dimensional analog Thermal Noise Thermal noise displacement PSD F =F Ext Ther Thermal equivalent input force PSD XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

Dual detectors:one dimension analog XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

Dual torus: Noise figure optimization Quantum limit Calculation 2 ≥ h ω ⋅ ω ( ) ( ) S S FF XX 4 Free parameter for optimization (noise stiffness ) K n = ω ω ( )/ ( ) K S S n FF XX K = 9 10 White band dominated n K = 11 10 B.A. dominated n K = 10 10 Broad Band n XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

Dual Torus: Material ρ ⋅ 4 1. High sound velocity and density v sound 2. High thermal conductivity 3. Reasonable cost and availability 4. High quality factor 5. Max linear dimension 2-3 meters Material used for calculation ρ v [ / ] 3 [ / ] Q m s Kg m s LowTemp SiC N.A. 3200 11200 Mo 7 10300 10 5660 5050 > 8 10 Al 2700 XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

Dual torus Sensitivity Curve (Quantum Limit) = ⋅ = ⋅ 1 1 11 1 .0 1 0 / 1.8 10 / K N m K N m − − n Mo n Si C ≥ ⋅ ≥ ⋅ 8 8 / 2 10 / 2 10 Q T Q T = = = = = = 0.25 0.26 0.47 0.82 0.83 1. 44 r m r m r m r m r m r m − − − − 1 2 int 2 1 2 in t 2 ext ext = = = = 2.35 16. 4 3 6 5 1. h m Tot wei gth t h m Tot weigt h t XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

Dual torus A possible implementation (capacitive readout) To SQUID Amplifier Present Required 1. SQUID at 30 ħ (P. Falferi this congress) 1. SQUID at 1 ħ 2. Electrical bias field 10 MV/m 2. Electrical bias field >200 MV/m ≈ ∝ ⋅ 7 2 3. / 10 N/m 3. Carefully designed matching line S S E C 0 FF XX XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

Dual Torus Optical readout (F.Marin this Conf.) Required 1. Laser Power 10 W 2. Finesse 10 6 Items to be addressed Possible Solution 1. Wide sensing area Folded Fabry-Perot 2. Cryogenics Material with higher Q XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri

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