Download - GW detectors optimized for the kHz range
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GW detectors optimized for the kHz range
Francesco MARIN for the DUAL-RD collaboration
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Motivation …
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Try to design a detector design devoted to the kHz
range. Hopefully
compact
sensitive
cheap…
… Back to the beginning
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Usual detection strategies…
Lh
L2
L
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Usual detection strategies…
Lh
L2
L
L zh
F 2
2
z )(2 2
0
22
0
2
iLh
L
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Usual detection strategies…
L zh
F 2
2
)(2 2
0
22
0
2
iLh
L
G
G · =
0.0 0.5 1.0 1.51
10
100
1000
10000
L (
m)
0
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… Back to interferometers …
lopt/ hlopt/
lopt=NLL
Seems better to get the longest possible lopt. However…
limited by quantum noise (SQL):
()2 = hlaser/2Pin
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… the useful measurement time is just T/2
(T is the g.w. period: T = 2/)
lopt = c T/2
laser h T/2
hmin
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lopt = c T/2
laser h T/2
No more dependence on L if we can keep an high N
(we just have to keep ‘light on flight’ for a time T/2)
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Ex.: 3 kHz lopt 50 km
L = 3 km
N 17
OR… reduce L, increase N. Present limit from mirror losses ( 1 ppm): N 106
L = 5 cm
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In favour of long interferometers: less sensitive to ‘local’ noise
(effect 1/L) such as
• Thermal noise ( go to cryogenic)
• Radiation pressure ( go to larger masses)
However, present (and future) interferometers are not limited
by such effects in the > kHz range.
room for shortening
Moreover…
For close mirrors, again some (new) useful effects
from elastic forces
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D
LLd
S
M
For SM we have ‘free’, ‘rigid’ masses
d h/2 D ( >> h/2 d ) ‘Gain’ D/d ( 100)
0.0 0.5 1.0 1.51
10
100
1000
10000
L (
m)
0
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First (??? at least recently) proposed system of this kind:
the DUAL SPHERE (2001)
‘free moving’ sphereRint h Rint
‘rigid’ sphere
M. Cerdonio et al. Phys. Rev. Lett. 87 031101 (2001)
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Constraints
If L is too large, M is low
- limit to L
- better high sound velocity
Limit to L limit to the mass M effect of back-action
(radiation pressure) cannot be lowered indefinitely
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Back-action reduction
S 0 M
F
D
L
d
D = - F/M2 L = F/M(M2 – 2)
d = (F/M) [-1/2 + 1/ (M2 – 2)]
d = 0 for = M/2
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Back-action reduction
710
Frequency (kHz)
711 712
1
100
0,01
From T. Briant, talk given last Sunday
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S 0 M
F
D
L
d
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SQL: N = 1
1 optimized to get a ‘flat’ S/N
If Sxx dominates, the best material has the largest vs
(allowing the largest L)
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Thermal noise f(x) 1
Test mass volume
M/Form factor
Sopt scales as 03
The best material has the lower 1.5/Y2.5
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Mo Si SiC
Density 10.3 2.3 3.2
Young (GPa) 330 150 450
1.5/Y2.5 1.7 E-23 1.3 E-23 1.3 E-24
Sound velocity (m/s) 5600 8000 11900
Diameter (m) for M = 4 kHz
0.6 1.0 1.5
Sopt (cylinder 3 m) 1.9 E-23 2.0 E-23 7.6 E-24
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Thermal noise
For 0 = 5 kHz:
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Low freq. suspension
Possible implementation
S ( ~ 100 Hz )
Nodal link
Either optical (Folded Fabry Perot) or capacitive readout
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‘QUAD’ detector
X1, F1
X3, F3
X4, F4X2, F2
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0 1000 2000 3000 4000 5000 6000 7000 80001E-24
1E-23
1E-22
1E-21GEOLIGO
VIRGO+
LIGO Adv.
Frequency (Hz)
Mo QUAD (3m SQL) Mo QUAD (3m Sxx = 10^-44 m^2/Hz)
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0 2000 4000 6000 8000 10000 120001E-23
1E-22
1E-21
1E-20
GEOLIGO
VIRGO+
LIGO Adv.
Frequency (Hz)
Si QUAD (dia 45cm)
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0 1000 2000 3000 4000 5000 6000 7000 80001E-24
1E-23
1E-22
1E-21
SiC QUAD (3m SQL)
GEOLIGO
VIRGO+
LIGO Adv.
Frequency (Hz)
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Mo nested cylinders 16.4 ton height 2.3m 0.94m
SiC nested cylinders 62.2 ton height 3.0m 2.9m
Q/T=2x108 K-1
M. Bonaldi et al. Phys. Rev. D 68 102004 (2003)
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X1
X4
X3
X2
X = x1+x2-x3-x4
X1
x1
Example of Thermal and BA noise reduction using selective readout
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Single mass DUAL Detector
The DUAL concept which works between two modes of two different bodies can work also between two modes of the SAME body
the deformation of the inner surface has “opposite sign” for the first and the second quadrupolar mode
An hollow cylinder can work as a DUAL
(mode) detector
the internal diameter is the length to be measured for the detection
M. Bonaldi et al. Phys. Rev. D submitted. Also on gr-qc/0605004
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+ =
+ =
+ =
First quad
. mod
e
Second
quad. mode
Frequency
The phase difference concept still holds
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Double channel readout
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0.3
0.55
1 1 2 2
2 2 2 2, , , ,{ , }T og T og x T og T og xMAX X X X X
Antenna pattern: like 2 IFO at 45°
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Complete transfer function
MolibdenumRext = 0.5mRint = 0.15mL = 3m
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CONCLUSIONS: we are just beginning
Problems:- SQL readout- availability of large masses (depends on materials)-cosmic rays (underground?)- links between test masses- cryogenic possibilities vs dissipated power- …
Strong R&D necessary (2-3 yrs ?) Help and ideas welcome