Design and performance of the Dual detector with large area capacitive

readout

4rd ILIAS-GW Meeting, October 8th – 9th 2007, Tuebingen

Paolo Falferi for Dual collaboration - IFN - Trento

Goal of the Dual R&D study

to develop a wideband acoustic detector complementary to the advanced interferometric detectors in the high frequency range (>1 kHz), compact, reliable, (relatively) cheap

to detect signals from• Neutron Star binaries merger• Stellar size Black Hole binaries merger• Newborn Magnetars• Neutron Star bar instabilities

Design Evolution

Original main principles of the Dual detector

•avoid small masses

•measure the displacement between two large masses

•select the quadrupolar modes

dual sphere dual cylinder single-mass dual

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

Sensitivity of a Single-mass Dual Detector

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

Quadrupolar FilterX = d1-d2

Noise Matching

Noise matching if K ≈ (SFF/SXX)1/2 = Kn

K mechanical stiffness

Kn readout noise stiffness

Test mass Readout

The optimal noise stiffness for the

single-mass Dual is too high

we have to "soften" the test mass

mechanical amplification

Meq1 meq2 meq3keq1 keq2 keq3

x3x2x1

Measured Displacement

If

Displacement Gain around Resonance

Bandwidth Upper Limit

121 eqeq Mmν≈

31 eqeq mM

23 xx −

321 ννν ==

No Resonant Amplification

No Leverage Amplification

XY

Displacement Gain = Y/X=1/a»1

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)

Shh1/2

(Hz-1/2

)

Frequency (Hz)

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

No Leverage Amplification(back action noise problem)

Hybrid approach: whips on the external surface

x y

L1L2

Whip (transverse wave concentrator)

3/ 4

1

2Min

y L

x L

⎛ ⎞∝ ⎜ ⎟

⎝ ⎠

Minimum Gain (out of resonance)

Resonant and leverage amplification

Displacement readout atthe end of the whips

MolybdenumRext = 50 cmL = 3 mWhip length=32 cmReadout: SQLT/Q: 5x10-9 K

Noise Matching with a Realistic Readout

2D-FEM calculated optimal SQL sensitivity

1 m

1000 2000 3000 4000 5000 60001E-23

1E-22

1E-21

1E-20

Shh1/2

( Hz

-1/2

)

Frequency (Hz)

internal diameter readout K=1.7 1011 N/mwhips and slots K=1.5 108 N/m

( ) ( ) ( )/GWH X hω ω ω≡Response to a GW field h()

• Increased response (mechanical amplification) but also increased number of GW-sensitive (quadrupolar) modes. Mixture of cylinder and whips modes.

•Selective detector (by means of the test mass design, arrangement of the readout and large interrogation area)

Dual is a multimode selective detector

0 1000 2000 3000 4000 5000 60000,1

1

10

100

1000

10000

Hgw (m)

Frequency (Hz)

internal diameter readoutwhips and slots

L=2.1 m (M=7.7 tons)

0 1000 2000 3000 4000 5000 60001x10-23

1x10-21

1x10-19

Frequency (Hz)

Shh1/2

(Hz-1/2

)

0 1000 2000 3000 4000 5000 60001x10-23

1x10-21

1x10-19

Frequency (Hz)

Shh1/2

(Hz-1/2

)

Refined model: 3D FEM

2D plain strain FEM simulation 3D FEM simulation (Ansys)

3D Spurious modes not fully suppressed by selective readout

The number of spurious modes can be reduced by shortening the test mass

Sensitivity of longer-massive version can be recovered by using several short detectors (in the same cryostat) with the same overall mass.

Mo, SQL, T/Q=5x10-9, R=0.35 m

L=1.2 m (M=4.4 tons)

LR

Refined Model: 3D FEM + SQUID Readout

• Complete mechanical 3D FEM simulation

• 4 capacitive wide area transducers in series for a selective quadrupolar readout

• SQUID amplifier with low loss matching transformer

• Electrical LCtot mode tuned to the sensitivity band.

L

C

C

C

C

0 1000 2000 3000 4000 5000 60001x10-23

1x10-21

1x10-19

Frequency (Hz)

Shh1/2

(Hz-1/2

)

Electrical:T=50 mKQ=2x106

Ebias=8x107 V/mC=3 nF

Mechanical:MolibdenumR=0.35 m, L=1.19 m, M=4.4 tons T=50 mKQ=1x107

SQUID noise: 1 h

Realistic Readout

Ideal Noise Matched Readout

Ideal Readout vs Realistic Capacitive SQUID Readout

Achievable sensitivity

4 C/SiC “small” detectors R=0.35 m, L=1.2 m, Total Mass 16.5 tons

T=50 mK, Qm=107, 1 h SQUID, C=3 nF, Ebias=8 107 V/m, Qel=2 106

0 1000 2000 3000 4000 5000 60001x10-23

1x10-22

1x10-21

1x10-20

Shh1/2

(Hz-1/2

)

Frequency (Hz)

Advanced LIGO