GW detectors optimized for the kHz range

1. GW detectors optimized for the kHz range Francesco MARIN for the DUAL-RD collaboration

2. Motivation …

3. Try to design a detector design devoted to the kHz range. Hopefully • compact • sensitive • cheap… … Back to the beginning

4. Usual detection strategies…

5. z Usual detection strategies…

6. G ·Dw = w0 G Dw Usual detection strategies…

7. lopt=NL • f = 2pdlopt/l = 2phlopt/l … Back to interferometers … dflimited by quantum noise (SQL): (df)2 = hnlaser/2Pin Seems better to get the longest possible lopt. However…

8. lopt = c T/2 df = 2pnlaserh T/2 hmin w … the useful measurement time is just T/2 (T is the g.w. period: T = 2p/w)

9. lopt = c T/2 df = 2pnlaserh T/2 No more dependence on L if we can keep an high N (we just have to keep ‘light on flight’ for a time T/2)

10. N  17 L = 3 km L = 5 cm Ex.: w/2p 3 kHz  lopt 50 km OR… reduce L, increase N. Present limit from mirror losses ( 1 ppm): N  106

11. In favour of long interferometers: less sensitive to ‘local’ noise (effect  1/L) such as • Thermal noise (  go to cryogenic) • Radiation pressure (  go to larger masses) However, present (and future) interferometers are not limited by such effects in the > kHz range.  room for shortening Moreover… For close mirrors, again some (new) useful effects from elastic forces

12. wS wM d L L D For wS << w << wM we have ‘free’, ‘rigid’ masses dd  h/2 D ( >> h/2 d )  ‘Gain’ D/d ( 100)

13. ‘rigid’sphere ‘free moving’sphere dRint h Rint First (??? at least recently) proposed system of this kind: the DUAL SPHERE (2001) M. Cerdonio et al. Phys. Rev. Lett. 87 031101 (2001)

14. Constraints • If L is too large, wM is low  - limit to L - better high sound velocity • Limit to L  limit to the mass M  effect of back-action (radiation pressure) cannot be lowered indefinitely

15. wS  0 wM d F L D Back-action reduction dD = - F/Mw2dL = F/M(wM2 – w2) dd = (F/M) [-1/w2 + 1/ (wM2 – w2)] dd = 0 for w = wM/2

16. 100 1 0,01 From T. Briant, talk given last Sunday 710 712 711 Frequency (kHz) Back-action reduction

17. wS  0 wM d F L D

18. SQL: N = 1 h 1optimized to get a ‘flat’ S/N If Sxx dominates, the best material has the largest vs (allowing the largest L)

19. f(x) 1 Thermal noise Test mass volume wM/W Form factor • Sopt scales as n03 • The best material has the lower r1.5/Y2.5

21. For n0 = 5 kHz: Thermal noise

22. Low freq. suspension wS ( ~ 100 Hz ) Nodal link Either optical (Folded Fabry Perot) or capacitive readout Possible implementation

23. ‘QUAD’ detector X3, F3 X2, F2 X4, F4 X1, F1

27. M. Bonaldi et al. Phys. Rev. D 68 102004 (2003) Mo nested cylinders 16.4 ton height 2.3m 0.94m SiC nested cylinders 62.2 ton height 3.0m 2.9m Q/T=2x108 K-1

28. Example of Thermal and BA noise reduction usingselective readout x1 X1 X = x1+x2-x3-x4 X1 X4 X3 X2

29. Single mass DUAL Detector The DUAL concept which works between two modes of two different bodies can work also between two modes of the SAME body the internal diameter is the length to be measured for the detection An hollow cylinder can work as a DUAL (mode) detector the deformation of the inner surface has “opposite sign” for the first and the second quadrupolar mode M. Bonaldi et al. Phys. Rev. D submitted. Also on gr-qc/0605004

30. + = + = + = The p phase difference concept still holds First quad. mode Second quad. mode Frequency

31. Double channel readout

32. 0.55 0.3 Antenna pattern: like 2 IFO at 45°

33. Complete transfer function Molibdenum Rext = 0.5m Rint = 0.15m L = 3m

34. CONCLUSIONS: we are just beginning • Problems: • SQL readout • availability of large masses (depends on materials) • cosmic rays (underground?) • links between test masses • cryogenic possibilities vs dissipated power • … • Strong R&D necessary (2-3 yrs ?) • Help and ideas welcome