Modelling and Testing of Cryogenic Suspensions Giles Hammond Institute for Gravitational Research SUPA University of Glasgow on behalf of the KAGRA suspensions team, ELiTES R&D WP1-WP2 2 nd Elites Meeting, Tokyo 4 th -5 th December

2 Motivation for cold suspensions KAGRA suspension –Modelling of suspensions –Blade spring tests –Fibre tests –Weld tests Direction of future R&D Silicon strength tests Summary Overview

3 Stages of Suspension Development Bonding – type of bonding for KAGRA (indium, hydroxide-catalysis, combination of both) Spring/fibre production and characterisation – strength, thermal conductivity, mechanical loss, surface treatment Construction and repair – manufacture, installation, repair scenarios, prototypes Modeling/Characterisation – manufacture, installation, repair scenarios aLIGO suspension

Upper springMaraging steel Upper wireMaraging steel Intermediate mass60.9kg copper Recoil wireTungsten Recoil mass:37.2kg copper Test mass fibre1.8mm sapphire Test mass:23kg sapphire spring Motivation for Cold Suspensions R&D for cold suspensions is a generic activity which is well aligned with both aLIGO upgrades (e.g. silicon) and the KAGRA detector The final stage of the KAGRA suspension K) has been modelled with aLIGO Mathematica model (LIGO DCC T ) Assess the benefit of springs in the final sapphire stage: – to provide lower vertical eigenfrequency – to account for length variation of sapphire fibres 4

5 Cryogenic sapphire is the baseline for implementation in KAGRA and offers equivalent thermal noise performance to the Advanced detectors Sapphire springs in final suspension stage: – Reduce vertical thermal noise from recoil mass wires – Lower vertical bounce mode to ≈50 Hz – Provide compliance for variations in fibre length Modeling of Cold Suspensions aLIGO: m/  Hz at 10 Hz KAGRA K 5 see talk by Takanori Sekiguchi (horizontal and vertical contribution: no violin modes)

Lower Stage Thermal Noise For low temperature operation any heat input by the detector laser beam is extracted via conduction up the suspension fibres. Model loss terms in a similar way to the fused silica but with suitable parameters for crystalline materials, which vary with temperature ( , , C, Y ) A.M. Gretarsson et al., Phys. Rev. A, 2000 G. Cagnoli and P.A. Willems, Phys. Rev. B, 2002 A.V. Cumming, et al., CQG, , 2009 : small for thin fibres Dissipation dilution 6

Cold Suspensions for KAGRA KAGRA baseline: sapphire fibres, 1.6 mm diameter 300 mm long 23 kg sapphire test mass 20 K test mass temperature Due to the stiffness of sapphire and thickness of fibres (for heat extraction) the static stretch in fibres is small (  20 µm) the vertical mode frequency of the suspension is high  150 Hz => Motivation for cryogenic springs Sapphire fibre test sample (IMPEX, KAGRA) Prototype geometry for sapphire blade spring 7

FEA model of a single IMPEX fibre with a prototype sapphire blade spring 1.6 mm diameter sapphire fibre 5.75 kg (25% KAGRA mass) Sapphire blade (width: 100 mm thickness: 4 mm length: 200 mm) Blade clamps (assumed steel) 10 mm 1.6 mm Sapphire Suspension FEA Modelling Modef no spring (Hz)f spring (Hz) Pendulum0.89 Vertical bounce Violin MPa Spring deflection ≈1 mm 8

Loss terms to consider: Fibre – surface loss, thermoelastic Blade thermal noise – surface loss, thermoelastic Thermal noise associated with the joints (bonds/clamps) Recent measurements on Moltech fibres have shown measured losses of  6x10 -7 at 20 K – if assume this is all surface loss then h  s ~1x Thermoelastic loss curves Sapphire Suspension FEA Modelling 9 Mechanical loss of Moltech fibre see talk by Dan Chen

Both indium (as used in high Q measurement systems by our Russian colleagues) and hydroxide catalysis bonding are plausible techniques for making low mechanical loss attachments between the spring/fibre and fibre/test mass ear Both were evaluated for use by GEO in the 1990’s Recent Glasgow measurements of the mechanical loss of K show a value of  5.0E-4 For more details of both indium bonding and hydroxide-catalysis bonding see talk by Rebecca Douglas in the afternoon session Bonding of Suspension Elements 10

Consider fundamental horizontal mode of suspension at 20 K and analyse the stored energy ComponentEnergy ratio %Loss of componentLoss contribution to total Fibre main section E-074.3E-07 Fibre ends1.48.0E-081.1E-09 Blade1.25.2E-106.4E-12 Blade clamps E-043.6E-09 Connection - Bond E-04*6.5E-09 Total loss4.4E-07 Dissipation dilution6.75 Pendulum mode loss6.6E-8 Sapphire Suspension FEA Modelling * see talk by R. Douglas in the afternoon session 11

12 Sapphire Suspension FEA Modelling From the thermal noise model the important loss terms are: (i) Bonding interface. Address via: – connection geometry designs to reduce energy contained in bond – bond R&D to reduce loss and thickness (e.g. testing Indium and Hydroxide catalysis bonds) (ii) Surface loss in fibre. Address via: – higher quality surface preparation during manufacture – heat treatment (polishing) of surfaces post manufacture – manufacture techniques such as laser heated pedestal growth

Blade Strength Tests In Glasgow we have performed cantilever beam breaking tests on sapphire samples from IMPEX (mechanically polished and thermo-polished samples) Sample has the load applied at the end of the cantilever Breaking occurs at clamping point and stress in cantilever can be found from: Sapphire spring test samples (IMPEX, KAGRA) 122 mm 16 mm 1 mm Motor drive Test cantilever Applied force 13

14 UndeflectedDeflected Blade Strength Tests

Measured a total of 26 sapphire samples (8  mechanically polished 1 mm thick, 10  thermo-polished 1.5 mm thick and 8  thermo-polished 2 mm thick) Mechanical polish has average breaking stress of 233 MPa Thermo-polish has an average breaking stress of 466 MPa The springs to need to support  40 MPa so a comfortable safety factor is present (>5) Strength likely to depend on surface quality of samples and clamping quality Similar tests will be undertaken on fused silica (warm aLIGO) / silicon (cold aLIGO, ET) Blade Strength Tests did not break 15

It is important to understand details of the thermo-polish procedure and how this correlates with increased strength No obvious stress was observed through crossed polarisers in the mechanically polished samples The thermo-polish samples are rougher (1500 nm rms) than the mechanically polished samples (75 nm rms) Blade Strength Tests Mechanically polished Thermo-polished 16

17 Moltech fibre has successfully hung 4 kg, 10 kg, 15 kg test weights and survived 3 break attempts in the strength testing machine (24.5 kg, 40.2 kg, 60.3 kg: pulling out of clamps) 60.3 kg is over 10x load of KAGRA suspension (232 MPa) During the test hangs the mass was translated by  0.5 mm (equivalent to 3 mm for a 30 cm KAGRA fibre) Moltech Fibre Strength Tests 15kg test hang 60.3 kg strength test

IMPEX fibres with monolithic nail end and jointed nail end have also been tested Weakest nail end appears to be the jointed end The IMPEX fibre hung the 15 kg mass (73 MPa) in a static test (safety factor of 3) Failed after a few minutes of translation by  0.5 mm (equivalent to 3 mm for a 30 cm KAGRA fibre) IMPEX Fibre Strength Tests IMPEX fibre Broken jointed end 15kg test hang Monolithic end Jointed end 18

19 The remaining monolithic nail end was then tested again with 4 kg, 10 kg, 15 kg masses The mass was also translated by  0.5 mm (equivalent to 3 mm for a 30 cm KAGRA fibre) IMPEX Fibre Strength Tests Pendulum tests with 15 kg test weight Waxed IMPEX fibre with monolithic end still attached

20 The remaining monolithic nail end was then strength tested One nail end broke at 82.1 kg (400 MPa) while the other broke at 50.3 kg (245 MPa) Monolithic nail ends have significant safety factor (>10) IMPEX Fibre Strength Tests 50.3kg strength test Waxed IMPEX fibre with monolithic end still attached

21 The remaining central section was further tested The sample finally broke at 94.7 kg (462 MPa) IMPEX Fibre Strength Tests Video frame showing the break Waxed IMPEX fibre (no ends)

To assess the ease of jointing sapphire some simple weld tests have been performed on the Moltech fibres Ends were butted against each other, but no pressure applied Material joined easily on application of heat with CO 2 laser Slow polishing was used to heat a region a few cm each side of the weld with reducing laser power to lower thermal stress Weld Tests Weld Laser heating 22

Weld Polished fibre Weld Tests Moltech fibre (as provided) Weld 23 Polishing changes the surface quality => will be interesting to test how this changes the thermo-mechanical properties.

Significant progress has been made on R&D which is focussed on the sapphire suspension production. Future areas of R&D may include: (i) Jointing techniques –Mechanical loss and strength tests of indium bonds, hydroxide catalysis bonds, or a combination of both (ii) Heat treatment (polishing) of sapphire fibres to lower surface loss –Mechanical loss and thermal conductivity of polished surfaces (iii) Fibre strength tests –Monolithic IMPEX fibres (iv) Weld tests to assess repair scenarios –Mechanical loss, thermal conductivity, strength and reproducibility of welds (v) Tests with prototype suspensions including single spring/fibre/mass and four fibre systems –Cooling tests, suspension fabrication and repair scenarios (e.g. welding and re- attaching fibres) Future R&D 24 see talk by Aleksandr Khalaidovski

Strength of Silicon Strength testing is a generic activity for cryogenic suspensions Tensile strength tests have recently undertaken on silicon samples with different surface treatments – polished, etched, Si 3 N 4, wet oxidised A.V Cumming, Class. Quant. Grav., accepted 2013 Etched samples are ~50% stronger than those with mechanically polished edges – likely due to higher quality surfaces, with less polishing damage see talk by Alessandro Bertolini 25

26 Summary The addition of sapphire springs in the final suspension stage is important to provide vertical compliance and also lower the suspension vertical mode Robust thermal noise estimates using measured data (surface loss, bond loss of Indium) show that the suspension performance is close to the KAGRA baseline There is a clear path for future R&D which is focussed on providing the final article suspensions Strength tests are very encouraging Initial tests to weld sapphire fibres show positive results ComponentSafety factor Springs  5 (mechanical polish),  10 (Thermo-polish) Moltech, IMPEXcentral section  8,  16 IMPEX jointed end 33 IMPEX monolithic end  10