1. Acoustic properties of a prototype for a hollow spherical gravitational antenna (^) Laboratori Nazionali del Gran Sasso dell’INFN (*) Laboratori Nazionali di Frascati dell’INFN M. Bassan, S. Giannì, Y. Minenkov ^, R. Simonetti Dip. Di Fisica, Università di Tor Vergata e INFN, sezione Roma Tor Vergata With crucial help from L. Quintieri *, A. Rocchi, ILIAS - London Oct 27th 2006

2. Summary Shperical Antenna Bulk Sphere Discussion Hollow Sphere Advantages Comparison bulk- hollow General features Suspensions Experimental results Realization of a cavity Bonding methods Fabrication of a hollow sphere Experimental results Comparison of results: bulk-hollow Conclusions

3. People interested in making high Q resonators of VERY large size will have to deal with the issue of bonding. We have addressed here the problem of preserving mode shapes and Q factors in brazed metallic resonators. Who cares about these tests ?

4. Advantages it is omnidirectional it can determine the direction of incoming g.w. it can determine the polarization state of the g.w. it has a larger cross section of a bar at the same frequency it has a wider bandwidth Bulk Sphere it has the largest mass its cross section for the 1st spheroidal quadrupole mode is larger it is difficult to construct and cool its bandwidth is still too narrow wrt interferometers Hollow Sphere its cross section for 1st spheroidal quadrupole mode is somewhat smaller than the bulk sphere it is an easier object to fabricate and cool using both 1st and 2nd mode we can recover both bandwidth and overall cross section Why a Spherical Antenna ?

5. Why a hollow sphere ?

6. The cross section is smaller wrt bulk, but it can make up at the n=2 mode bulk shell Cross section for the 1st and 2nd modes Why a hollow sphere ? Choice of thickness can be used for centering two bandwidths Larger surface/ volume => easier cooling

7. Why a hollow sphere ? Larger surface/ volume => easier cooling The cross section is smaller wrt bulk, but we can make up at the n=2 mode Choice of thickness can be used for centering two bandwidths

8. (C) Effects of bonding on modes and Qs ? (A) How do we produce it ? casting fabricating from plates welding two half-spheres Will elastic continuity be retained across the welding interface ? Will the bonding affect Q ? Need to practice and investigate on a small size sample (B) How do we suspend it ? Can’t suspend it from center of mass Would surface suspension affect Qs ? Problems with a Hollow Sphere

9. Bulk Sphere in CuAl 6% (kindly provided by Minigrail) General Features Density  = 8145 kg/m 3 Diameter  = 0.15 m Mass M = 14.4 kg Young Modulus Y = 121x10 9 N/m 2 Poisson Ratio σ = 0.33 Sound Velocity v s = 3854 m/s Expected Resonant frequency (n=1 l=2) f = 13313 Hz Our Benchmark:

10. Effect of suspension on the Q of the quadrupolar modes of the bulk sphere (A)Testing suspension : surface vs center of mass

11. T=300 K T=300 K ÷ 4.2 K Excitation : PZT or mag. hammer ReadOut : PZT or accelerometer Measuring Apparatus

12. Frequencies Quality factors Q Tests: T=4.2 K, T=77.4 K, T=300 K Bulk Sphere in CuAl 6% Experimental results

13. Machining 22 mm “Hollowing” the sphere

14. Electron Beam Welding Diffusion Furnace Brazing Tested by Minigrail people. Really bad results: poor beam penetration cracks Uneven welding Test on a hollow cylinder CuAl6%: m=4.261Kg, L=0.228m, Φ=56mm, thick. 22mm, f o sp =8312Hz, τ < 1s Results: OK at T=300K Degraded after thermal shock at T=77K Satisfactory results: OK a T=300K OK thermal shock a T=77K (B) Bonding methods:

15. General features Density  = 8145 kg/m 3 Inner diameter(thick.= 22 mm)  = 0.106 m Mass M = 9.3 kg Young Modulus Y = 121x10 9 N/m 2 Poisson Ratio σ = 0.33 Speed of sound v s = 3854 m/s Expected resonant frequency: (n=1 l=2) f = 7537 Hz Hollow sphere in CuAl 6%

16. T=300 K T=300 K ÷ 4.2 K Same experimental set-up as for the bulk sphere Hollow sphere in CuAl 6%

17. Frequencies Quality Factors Q Tests: T=4.2 K, T=77.4 K, T=300 KQ vs Temperature T= 4.2 K ÷ 300 K (C ) Hollow sphere in CuAl 6% Experimental results

18. BULK SPHERE Frequenza (Hz) f1= 12637.7  0.1 f2= 13126.5  0.1 f3= 13429.4  0.1 f4= 13943.1  0.1 f5= 14040.0  0.1 Frequenza (Hz) f1= 7074.2  0.1 f2= 7456.9  0.1 f3= 7479.6  0.1 f4= 7542.4  0.1 f5= 7604.5  0.1 HOLLOW SPHERE T=300 K Frequencies Mode location and splitting

19. f (Hz) 13313 7537 5025 Good Agreement with theory ! f piena =13313 Hz f cava =7537 Hz Det (A p )=0 Validating Lobo’s Calculations

20. Q Bulk 300 K Q Hollow 300 K Q Bulk 77.4 K Q Hollow 77.4 K Q Bulk 4.2 K Q Hollow 4.2 K Comparing Hollow vs Bulk Sphere

21. Good agreement with elastic theory:  potential gravitational antenna Good results from furnace brazing: homogeneity is mantained and Q degradation is small For the future: additional tests on different brazing techniques and procedures. Investigation of alternate bonding methods: diffusion welding and electron beam welding. CONCLUSIONS