a broad band acoustic detector of gw: the dual torus · 2003. 3. 29. · a broad band acoustic...
TRANSCRIPT
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
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 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
XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri
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.
+
XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri
Dual TorusThermal and BA noise reduction:selectivity
XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri
.( )( , ) ( ) 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
XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri
,,
(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
XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri
1
2 int
2
0.250.260.47ext
r cmr cmr cm
−
−
===
Molybdenum:
Dual detectors:one dimensional analog Transfer Function
XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri
( )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
XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri
Back Action displacement PSD
Equivalent B.A. input force PSDB.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 TherF =F
Dual detectors:one dimension analog
XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri
Dual torus: Noise figure optimizationQuantum limit Calculation
XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri
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
XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri
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)
XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri
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)
XXXVIIIth Rencontre de Moriond, 2003, J.-P.Zendri
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.)
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 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)