Transcript Slide 1

Mechanical amplifiers for the DUAL detector:
lumped and distributed element design
Paolo Falferi for DUAL collaboration - IFN - Trento
3rd ILIAS-GW Meeting, October 26th – 27th 2006, London
Goal
a wideband acoustic detector complementary to the advanced
interferometric detectors in the high frequency range (1-10 kHz),
compact, reliable, (relatively) cheap
Exploit recent progress
• Improvement of readout sensitivity (SQUID based and optomechanical
devices)
• New materials for the test masses.
• New techniques (FEM) for design optimization of the test masses
and
Give up the classical scheme of the resonant readout
developed to enhance the bar displacement
light transducer mass  narrow bandwidth
No Small Masses: DUAL
Design Evolution
dual sphere
dual cylinder
single-mass dual
Pros and Cons
Pros and Cons
Pros and Cons
•omnidirectional
•arrival direction ID
•not selective
•complicated (construction
and suspension Pbm)
•not omnidirectional
•no arrival direction ID
•selective
•less complicated
(suspension Pbm)
•not omnidirectional
•no arrival direction ID
•selective
•simple
Sensitivity of a Single-mass DUAL Detector
Molybdenum
Rext = 0.5m
Rint = 0.15m
L = 3m
M = 22 ton
T/Q = 10-8 ε0 K
ε0=kbTn/hw
Bonaldi et al. Phys. Rev. D
74 22003 2006
Optimal Transducer
Characteristics
e0=1
Sxx= 6x10-46 m2/Hz
Sff= 1.8x10-23 N2/Hz
Noise stiffness
(Sff/Sxx)1/2 = 1.7x1011 N/m
Optomechanical and Capacitive Transducers
(wide area and selective)
C
C=30 nF
Ebias  2x108 V/m
QL SQUID amplifier
F106
PinW
Sxx=6x10-44 m2/Hz
Sxx=6x10-44 m2/Hz
Noise Matching
K n  S FF S XX  K mec
K n  Readout Noise Stiffness
K mec  Test Mass Mechanical Stiffness
Mechanical Amplifier:
Lumped Element Design
REQUIREMENTS
• Broadband amplification up to 5.0 kHz
• Displacement gain factor about 10
• Negligible intrinsic thermal noise
• Lower mechanical stiffness
Y
Leverage type
amplifier
X
H.J. Paik, proceedings First
AMALDI Conference (1995)
Displacement Gain = Y/X=1/a»1
Limitations for the lumped element
mechanical amplifier: bandwidth-gain limit
Bandwidth-gain limit
Kr
w f G0 
Mb
Kr
Kr

Ka  Kr
Mb
wf = cut-off frequency
G0 = effective gain
in practice
for a Mo single-mass DUAL
with amplifier
G0=10 and nf=5000 Hz
are achievable but...
Kr
Ka
Limitations for the lumped element mechanical
amplifier: back action noise problem
11
Single-mass DUAL k = 1.7x10 (N/m)
8
Single-mass DUAL with lumped mech. amplifier k = 5x10 (N/m)
-19
10
The amplifier that permits
the requested gain and
bandwidth is "too soft": the
readout back action noise
spoils the detector
performance
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10
1/2
-1/2
Shh (Hz )
-21
10
-22
10
-23
10
The lumped element design
must be abandoned
-24
10
0
2000
4000
Frequency (Hz)
6000
8000
mechanical amplifier:
distributed element design
The longitudinal slots
make the tangential
displacements of the
external surface larger
than the internal diameter
changes
The thickness of the slot is
the length to be measured
for the detection
Selection of the quadrupolar modes is still possible
mechanical amplifier:
distributed element design
Whip (transverse wave concentrator)
(D Blair et al, J Phys D: Appl Phys 20, 162 (1987) )
Gain  6
L1
x
Minimum Gain y
(out of resonance) x
y
Min
L2
L 
 1 
 L2 
3/ 4
L1
 30
L2
Single-mass DUAL detector, Mo, T=0, M=22 t, R=0.5 m, L=3 m
-19
-19
10
10-19
11
11
8
11 (N/m)
Single-massDUAL
DUALkkwith
k=
1.7x10
Single-mass
lumped
(N/m)
mech. amplifier k = 5x10 (N/m)
Single-mass
DUAL
==1.7x10
1.7x10
(N/m)
10
Single-mass
k =mech.
1x10 amplifier
(N/m) k = 5x108 (N/m)
Single-mass DUAL
DUAL with
with slots
lumped
11
8
Single-mass DUAL kwith
= 1.7x10
slots and(N/m)
whips k = 6x10 (N/m)
8
Single-mass DUAL with lumped mech. amplifier k = 5x10 (N/m)
-20
-20
10
10-20
-21
-21
1/2
1/2
-1/2
-1/2
1/2 (Hz
-1/2))
SS
(Hz
Shhhh
)
(Hz
hh
10
10-21
-22
-22
10
10-22
-23
-23
10
10-23
-24
-24
10
10-24
00
2000
2000
4000
4000
Frequency
Frequency(Hz)
(Hz)
Frequency
(Hz)
6000
6000
8000
8000
Single-mass DUAL detector with slots and whips
Mo, M=22 t, R=0.5 m, L=3 m, Quantum Limited Readout, Q=107
10
-20
10
-21
10
-22
10
-23
10
-24
Shh
1/2
-1/2
(Hz )
8
Single-mass DUAL with slots and whips k = 6x10 (N/m)
T=0K
T = 0.05 K
T = 4.2 K
0
2000
4000
Frequency (Hz)
6000