Light Baffles and Beam Pipe Design for Gravitational Wave Detectors

1. Light Baffles and Beam Pipe Design for Gravitational Wave Detectors Stefano Selleri1, Riccardo de Salvo2, Giuseppe Pelosi1, Innocenzo M. Pinto3 1 University of Florence, IT, Dept. of Information Engineering; INFN and LVC 2 RicLab LLC, 1650 Casa Grande Street, Pasadena, CA 91104; University of Sannio at Benevento, IT, Dept. of Engineering 3 University of Sannio at Benevento, IT, Dept. of Engineering; Centro Fermi, Rome, IT; INFN; LVC and KSC LIGO-G1900957 Isola d’Elba, May 19-25, 2019

2. OUTLINE • Motivation • Better Pipes • Better Baffles • Simulation Results • Conclusions 2

3. Motivation • The arm length of next generation Gravitational Wave (GW) detectors will extend to tens of kilometers to increase sensitivity. • Vacuum pipes are a very expensive component of the interferometer arms. • There is pressure to use the smallest possible pipe diameter, • To reduce costs; • To allow installation of multiple detectors in a smaller tunnel; • To leave more space for transit. 3

4. Motivation • Large pipe diameters minimize the problem of scattered light. • Scattered light re-illuminate the mirrors and some is scattered back into the stored beam. • Due to vibrations of the vacuum pipe walls scattered light exhibit random phase fluctuations, generating phase noise in the dark fringe, which will limit the sensitivity for GW signals. • More effective pipe baffles are needed to absorb the scattered light if smaller diameter pipes are to be used. 4

5. Better Pipes • Confocal cavities have the minimum beam diameter at the center. • Even moderate pipe diameter-stepping as illustrated below can lead to price reductions exceeding 50%. 5

6. Better Baffles • The baffles currently used have the shape of truncated cones with a half-aperture angle close to 45◦ • Effective truncated conical baffles and beam pipes must both be very dark and have a very low bidirectional reflectance distribution function (BRDF). These two requirements are conflicting or expensive to attain. • Conical baffles inner edge forms a circle centered on the beam, which may originate constructive-interference of diffracted light along the beam/pipe axis. 6

7. Better Baffles • The baffle-edges were given a shark-teeth profile, to prevent constructive interference. • This has its own drawbacks, as the teeth edges produce a glint, which gets worse by electropolish. 7

8. Better Baffles : Helical • Reflections on a helical baffle send light in an infinite helical path along the beam pipe, which is always hidden from the mirrors. • Light is effectively totally absorbed without a chance of scattering towards the mirrors. • This removes the requirement that the pipe surfaces are dark. • Spiral baffles also do not need to be dark. • Shiny hydrophobic surfaces can be implemented • To reduce surface scattering on the baffles themselves • To reduce the vacuum water load in the pipe, the bake-out requirements and its costs. 8

9. BetterBaffles : Helical • Helical baffles do not produce a caustic build-up along the pipe axis. • This property eliminates the need of shark-teeth. • Indeed the presence of shark teeth deteriorates the performances of an helical baffle 9

10. Simulation Results • Lets consider a pipe of 20cm radius, with a 11cm radius clear aperture and a an helical baffle of increasing pitch and one full turn. • A geometrical optics (GO) analysis yields the distance between reflections on the walls p pitch 10

11. Simulation Results • The diffracted field from the baffle is best computed via an integration along the baffle rim according to the Incremental Length Diffraction Coefficients (ILDC) (uniform) formulation of the Geometrical Theory of Diffraction • The theory is suitable as long as the diffracting features are much larger than wavelength, hence also for serrated baffles G. Pelosi, S. Maci, R. Tiberio, and A. Michaeli, “Incre- mental length diffraction coefficients for an impedance wedge,” IEEE Transactions on Antennas and Propagation 40, 1201–1210 (1992). 11

12. Simulation Results • The dyadic diffraction coefficient is relatively simple to implement 12

13. Simulation Results • Conical baffle, 43° half-aperture, midway in a 10km tube. • Incident field on baffle rim is normalized to 1, diffracted field is computed on the far side mirror, on a disk 10cm in diameter. • Serration (teeth are 2cm long and their midline is on the 11cm radius circumference) reduces diffracted field level by about 200 times 13

14. Simulation Results • Helical baffle pitch 40 or 60 cm, halfway in a 10km tube. • Field is reduced by up to 109 with respect to smooth cones and 107 with respect to serrated cones. 14

15. Simulation Results • Helical serrated baffle pitch 40 or 60 cm, halfway in a 10km tube. • Field is reduced by up to 108 with respect to smooth cones and 106 with respect to serrated cones but is WORSE THAN FOR SMOOTH HELICES. 15

16. Simulation Results • Indeed very small pitches, few mm, which anyway are several wavelength, suffices to attain caustic disruption and low field levels. • Field level proves to be periodic with pitch, due to variation in diffracted rays path length and consequent recombination. Yet larger pitches are preferable due to their better behavior for reflected rays 16

17. Conclusions • The use of helical baffles reduce the scattered light problem by many orders of magnitude, even with respect to serrated edges. • Shiny surfaces with low BRDF can be used. • This allows the use of smaller clear aperture and smaller diameter baffles. • Smaller diameter vacuum tubes with helical baffles will dramatically reduce the vacuum costs of future GW detectors. • Smartapplication of the incremental length diffraction coefficients (ILDC) theory (used here for the first time, to the best of our knowledge, in the GW detector modeling Literature) isthe key for efficient (accurate and fast) modeling of light diffraction from pipe baffles. • (paper in preparation…) 17