Mechanical amplifiers for the DUAL detector: lumped and distributed element design 3 rd ILIAS-GW Meeting, October 26 th – 27 th 2006, London Paolo Falferi for DUAL collaboration - IFN - Trento

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

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 spheredual cylindersingle-mass dual

Molybdenum R ext = 0.5m R int = 0.15m L = 3m M = 22 ton T/Q = ε 0 K ε 0 =k b T n /   Sensitivity of a Single-mass DUAL Detector Bonaldi et al. Phys. Rev. D Optimal Transducer Characteristics  0 =1 S xx = 6x m 2 /Hz S ff = 1.8x N 2 /Hz Noise stiffness (S ff /S xx ) 1/2 = 1.7x10 11 N/m

C Optomechanical and Capacitive Transducers (wide area and selective) C=30 nF E bias  2x10 8 V/m QL SQUID amplifier F  10 6 Pin  W S xx =6x m 2 /Hz Readout Noise Stiffness 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 KrKr KaKa  f = cut-off frequency G 0 = effective gain Bandwidth-gain limit in practice for a Mo single-mass DUAL with amplifier G 0 =10 and f =5000 Hz are achievable but...

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 L1L1 L2L2 Gain  6 Minimum Gain (out of resonance) Whip (transverse wave concentrator) (D Blair et al, J Phys D: Appl Phys 20, 162 (1987) )

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

Single-mass DUAL detector with slots and whips Mo, M=22 t, R=0.5 m, L=3 m, Quantum Limited Readout, Q=10 7