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Design and performance of the Dual detector with large area capacitive readout 4 rd ILIAS-GW Meeting, October 8 th – 9 th 2007, Tuebingen Paolo Falferi for Dual collaboration - IFN - Trento

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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

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Design Evolution Original main principles of the Dual detector avoid small masses measure the displacement between two large masses select the quadrupolar modes dual spheredual cylindersingle-mass dual

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Molybdenum R ext = 0.5m R int = 0.15m L = 3m M = 22 ton T/Q = 10 -8 ε 0 K ε 0 =k b T n / Sensitivity of a Single-mass Dual Detector Optimal Transducer Characteristics 0 =1 S xx = 6x10 -46 m 2 /Hz S ff = 1.8x10 -23 N 2 /Hz Noise stiffness (S ff /S xx ) 1/2 = 1.7x10 11 N/m Quadrupolar Filter X = d 1 -d 2

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Noise Matching Noise matching if K ≈ (S FF /S XX ) 1/2 = K n K mechanical stiffness K n readout noise stiffness Test massReadout The optimal noise stiffness for the single-mass Dual is too high we have to "soften" the test mass mechanical amplification

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M eq1 m eq2 m eq3 k eq1 k eq2 k eq3 x3x3 x2x2 x1x1 Measured Displacement If Displacement Gain around Resonance Bandwidth Upper Limit No Resonant Amplification

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No Leverage Amplification X Y Displacement Gain = Y/X=1/a»1

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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)

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Hybrid approach: whips on the external surface x y L1L1 L2L2 Whip (transverse wave concentrator) Minimum Gain (out of resonance) Resonant and leverage amplification Displacement readout at the end of the whips

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Molybdenum R ext = 50 cm L = 3 m Whip length=32 cm Readout: SQL T/Q: 5x10 -9 K Noise Matching with a Realistic Readout 2D-FEM calculated optimal SQL sensitivity 1 m internal diameter readout K=1.7 10 11 N/m whips and slots K=1.5 10 8 N/m

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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 internal diameter readout whips and slots

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L=2.1 m (M=7.7 tons) 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) L R

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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 LC tot mode tuned to the sensitivity band. L C C C C

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Electrical: T=50 mK Q=2x10 6 E bias =8x10 7 V/m C=3 nF Mechanical: Molibdenum R=0.35 m, L=1.19 m, M=4.4 tons T=50 mK Q=1x10 7 SQUID noise: 1 Realistic Readout Ideal Noise Matched Readout Ideal Readout vs Realistic Capacitive SQUID Readout

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Achievable sensitivity 4 C/SiC “small” detectors R=0.35 m, L=1.2 m, Total Mass 16.5 tons T=50 mK, Q m =10 7, 1 SQUID, C=3 nF, E bias =8 10 7 V/m, Q el =2 10 6 Advanced LIGO

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