Mechanical amplifiers for the DUAL detector: lumped and distributed

element design

3rd ILIAS-GW Meeting, October 26th – 27th 2006, London

Paolo Falferi for DUAL collaboration - IFN - Trento

Goala 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

Pros and Cons

•omnidirectional•arrival direction ID•not selective•complicated (construction and suspension Pbm)

Design Evolution

Pros and Cons

•not omnidirectional•no arrival direction ID•selective •less complicated (suspension Pbm)

Pros and Cons

•not omnidirectional•no arrival direction ID•selective•simple

No Small Masses: DUAL

dual sphere dual cylinder single-mass dual

MolybdenumRext = 0.5mRint = 0.15mL = 3mM = 22 tonT/Q = 10-8 ε0 Kε0=kbTn/

Sensitivity of a Single-mass DUAL Detector

Bonaldi et al. Phys. Rev. D 74 22003 2006

Optimal Transducer Characteristics0=1Sxx= 6x10-46 m2/HzSff= 1.8x10-23 N2/HzNoise stiffness(Sff/Sxx)1/2 = 1.7x1011 N/m

C

Optomechanical and Capacitive Transducers(wide area and selective)

C=30 nFEbias 2x108 V/mQL SQUID amplifier

F106

PinW

Sxx=6x10-44 m2/Hz

Sxx=6x10-44 m2/Hz

Readout Noise Stiffness

mec

n

mecXXFFn

K

K

KSSK

Test Mass Mechanical Stiffness

Noise Matching

REQUIREMENTS

• Broadband amplification up to 5.0 kHz

• Displacement gain factor about 10

• Negligible intrinsic thermal noise

• Lower mechanical stiffness

Leverage type amplifier

H.J. Paik, proceedings First AMALDI Conference

(1995)

Mechanical Amplifier: Lumped Element Design

Displacement Gain = Y/X=1/a»1

X

Y

Limitations for the lumped element mechanical amplifier: bandwidth-gain

limit

Kr Ka

b

r

ra

r

b

rf M

K

KK

K

M

KG

0

f = cut-off frequencyG0 = effective gain

Bandwidth-gain limit

in practicefor a Mo single-mass DUAL with amplifier G0=10 and f=5000 Hzare achievable but...

0 2000 4000 6000 800010-24

10-23

10-22

10-21

10-20

10-19

Single-mass DUAL k = 1.7x1011 (N/m)

Single-mass DUAL with lumped mech. amplifier k = 5x108 (N/m)

Shh

1/2 (

Hz-1

/2)

Frequency (Hz)

Limitations for the lumped element mechanical amplifier: back action noise

problem

The amplifier that permits the requested gain and bandwidth is "too soft": the readout back action noise spoils the detector performance

The lumped element design must be abandoned

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

x y

L1 L2

Gain 6

3/ 4

1

2Min

y L

x L

1

2

30L

L

Minimum Gain (out of resonance)

Whip (transverse wave concentrator)

(D Blair et al, J Phys D: Appl Phys 20, 162 (1987) )

0 2000 4000 6000 800010-24

10-23

10-22

10-21

10-20

10-19

Single-mass DUAL k = 1.7x1011 (N/m)

Shh

1/2 (

Hz-1

/2)

Frequency (Hz)

0 2000 4000 6000 800010-24

10-23

10-22

10-21

10-20

10-19

Single-mass DUAL k = 1.7x1011 (N/m)

Single-mass DUAL with lumped mech. amplifier k = 5x108 (N/m)

Shh

1/2 (

Hz-1

/2)

Frequency (Hz)

0 2000 4000 6000 800010-24

10-23

10-22

10-21

10-20

10-19

Single-mass DUAL with lumped mech. amplifier k = 5x108 (N/m)

Single-mass DUAL with slots k = 1x1010 (N/m)

Single-mass DUAL k = 1.7x1011 (N/m)

Shh

1/2 (

Hz-1

/2)

Frequency (Hz)

0 2000 4000 6000 800010-24

10-23

10-22

10-21

10-20

10-19

Single-mass DUAL k = 1.7x1011 (N/m)

Single-mass DUAL with slots k = 1x1010 (N/m)

Single-mass DUAL with slots and whips k = 6x108 (N/m)

Single-mass DUAL with lumped mech. amplifier k = 5x108 (N/m)

Shh

1/2 (

Hz-1

/2)

Frequency (Hz)

Single-mass DUAL detector, Mo, T=0, M=22 t, R=0.5 m, L=3 m

0 2000 4000 600010-24

10-23

10-22

10-21

10-20S

hh

1/2 (

Hz-1

/2)

Frequency (Hz)

Single-mass DUAL with slots and whips k = 6x108 (N/m) T = 0 K T = 0.05 K T = 4.2 K

Single-mass DUAL detector with slots and whips Mo, M=22 t, R=0.5 m, L=3 m, Quantum Limited Readout, Q=107