1. Quadruple Suspension Design for Advanced LIGO
Norna A Robertson
LIGO-Caltech & University of Glasgow
for the Advanced LIGO Suspensions Team
aLIGO/aVirgo Workshop
Pisa, Italy
23rd-24th February 2012

2. Outline of Talk Requirements for test mass suspensions in aLIGO
Quadruple suspension design
Mechanical design
Local and global control
Auxiliary features
Prototype work
Current status
Conclusions

3. Requirements for Suspension Design for Test Masses
Support the optics to minimise the effects of
thermal noise in the suspension
seismic noise acting at the support point
Provide damping of low frequency suspension resonances (local control), and provide means to maintain interferometer arm lengths (global control)
while not compromising noise performance
Provide interface with seismic isolation system and core optics
Support optic so that it is constrained against damage from earthquakes
Accommodate a thermal compensation scheme and other systems as needed e.g. vibration absorbers
ERM
End Test Masses (ETM)
Inner Test Masses (ITM)
ERM

4. Suspension Requirements: Test Masses
Top-Level Requirements:
Requirement
Value
Suspension Thermal Noise
10-19 m/ Hz at 10 Hz (longitudinal)
10-16 m/ Hz at 10 Hz (vertical)*#
Residual Seismic Noise
10-19 m/ Hz at 10 Hz
(assumes seismic platform noise
2x10-13 m/rt Hz)
Pitch and Yaw Noise
10-17 rad/ Hz at 10 Hz (assumes beam centering to 1 mm)
Technical Noise Sources
(e.g. electronic noise, thermal noise from bonds)
1/10 of longitudinal thermal noise for each source
(since noise terms add in quadrature, each increases total by 0.5%)
*assumes 10-3 coupling vert. to long.
#except for highest bounce mode peak which can be up to 12 Hz

5. Suspensions and Seismic Isolation – From Initial to Advanced LIGO
active isolation platform (2 stages of isolation)
hydraulic external pre-isolator (HEPI) (one stage of isolation)
4 layer passive isolation stack
coarse & fine actuators
quadruple pendulum (four stages of isolation) with monolithic silica final stage
single pendulum on steel wire

6. Thermal Noise Thermally excited vibrations of
suspension pendulum modes
suspension violin modes
mirror substrates + coatings
Use fluctuation-dissipation theorem to estimate magnitude of motion
To minimise:
use low loss (high quality factor, Q) materials for mirror and final stage of suspension: use silica
use thin, long fibres to reduce effect of losses from bending
use low loss bonding technique: hydroxide-catalysis bonding
reduce thermal noise from upper stages by careful design of break-off/attachment points
low Q, high noise
high Q, low noise

7. Initial LIGO used a single stage wire suspension
Seismic Noise
Seismic noise limits sensitivity at low frequencies - “seismic wall”
Typical seismic noise at quiet site at 10 Hz is ~ few x m/Hz
many orders of magnitude above target noise level
Solution - multiple stages of isolation
Isolation required in vertical direction as well as horizontal due to cross-coupling
Two-stage internal isolation platform has target noise level of 2 x m/rt Hz at 10 Hz.
require 4 more stages, i.e. quadruple pendulum, to meet target of m/rt Hz
Advantage of double over single pendulum, same overall length
Initial LIGO used a single stage wire suspension
Better isolation
Quadruple pendulum transfer function: predicted longitudinal isolation ~ 3 x 10-7 at 10 Hz

8. Suspension Design for Advanced LIGO: Top Level Features
Thermal noise reduction: use monolithic fused silica suspension as final stage
Details in Giles Hammond’s talk
Seismic isolation: use quadruple pendulum + 3 stages of maraging steel blades for vertical isolation
Control noise minimisation: apply damping at top mass (for 6 degrees of freedom) + use quiet reaction pendulum for global control actuation
coil/magnet actuation at top 3 stages
electrostatic drive at test mass
Design is developed from the GEO 600 triple pendulums which have been in operation for more than 10 years.
parallel reaction chain for control actuation
four stages
silica fibres
40 kg silica test mass 8

9. Mechanical Design Starting assumptions
Two chains close to identical: reduces design effort
Approx. equal masses and lengths, modified as needed – e.g. final stage requirement on vertical bounce freq. <12 Hz, violin mode freq. > 400 Hz drives length.
Blades (two at each of three stages) are crossed to reduce footprint
Two wires at top – reduces pitch coupling
Four wires at lower stages – to allow damping and alignment from top mass
Angles, spacing and attachment positions of wires such that all low frequency modes (22 out of 24 total) less than ~5 Hz and visible at top mass.
Build carried out firstly with all-metal masses, then monolithic stage and lowest reaction mass swapped in.
Surrounding welded support structure stiff as practicable
Vertical, Z
yaw
pitch
roll
Transverse, Y
Longitudinal, X

10. Mechanical Modeling and Results
Initial modeling using MATLAB, built up from equations of motion: extension of GEO MATLAB model
Symmetric suspension: longitudinal and pitch coupled, transverse and roll coupled, yaw and vertical uncoupled
Model used to optimise design as parameters were varied (masses, moments of inertia, wire lengths, blade parameters, attachment points). Fast turnaround.
Values of mode frequencies and observability of modes at top mass in all degrees of freedom checked.
Further work using Lagrangian model, firstly in MAPLE and latterly in Mathematica: assumes no symmetry and includes detailed elasticity modelling of wires from beam equation.
Mathematica model includes arbitrary frequency-dependent damping on all sources of elasticity –calculate admittance and use fluctuation dissipation theorem for thermal noise
Can export state-space matrices for use in MATLAB
Example of impulse response in longitudinal with simple (zero-pole) damping controller.
First long. mode and third transverse mode

11. Final Design: Some Key Parameters
Masses (kg)
22, 22, 39.5, 39.5
(main chain)
22, 22, 53, 26
(ETM reaction chain)
22, 22, 59, 20
(ITM reaction chain)
Size of optic
340 mm x 200 mm
Overall length to CofM
1.7 m
Final stage silica fibres
600 mm long
400 micron diam.
Gap between optic and reaction mass
5 mm (ETM)
20 mm (ITM)
Each quad contains approx custom made parts.

12. Final Design: Mode Frequencies
Mode frequencies for main chain (Hz)
Longitudinal: 0.43, 1.00, 2.01, 3.42
Pitch: , 1.24, 1.57, 2.77
Vertical: , 2.22, 3.56, 9.27
Yaw: 0.60, 1.35, 2.39, 3.05
Transverse: 0.46, 1.05, 2.12, 3.31
Roll: , 2.63, 5.06, 13.2
(Identities are approximate – e.g. pitch and roll are also coupled for some modes due to mass distribution)
Highest vertical (9 Hz) and roll (13 Hz) modes are well isolated from external vibrations and undamped by local control.
coupled
coupled
vertical
roll

13. Expected Performance: Residual Seismic Noise
Overall seismic noise performance is product of expected noise on final stage of the internal isolation system x transfer function of the quad pendulum.
sfsdf

14. Local and Global Control
Main (test) Chain
Reaction Chain
Local control: damping at top mass, separately for each chain, using BOSEMs* (next slide) with 10mm x 10mm NdFe magnets
Global control (length and angular) at all four levels
BOSEMs with 10mm x 10mm NdFe magnets at top mass
BOSEMs with 10mm x 10mm SmCo magnets acting between chains at upper intermediate mass
AOSEMs** with 2mm x 6mm SmCo magnets acting between chains at penultimate mass
Electrostatic drive (ESD) using gold pattern on reaction mass/compensator plate at test mass level
*BOSEM = Birmingham Optical Sensor/Electromagnetic Actuator
**AOSEM = ALIGO OSEM = modified initial LIGO OSEM

15. Local Control BOSEM* sensitivity
7 x m/ Hz at 10 Hz
Required longitudinal noise at test mass
10-20 m/ Hz at 10 Hz
Required damping – decay time to 1/e ~ 10 secs
6 BOSEMS on the top mass for 6 degree of freedom (DOF) active damping.
In GEO point-to-point feedback to co-located actuators with same control law
In aLIGO, signals transformed to Euler basis by 6x6 matrix and similar matrix used for the feedback signals: increases design flexibility to achieve required noise performance for each DOF.
coil
flag
IRLED
lens
mask
photodiode
magnet

16. Local Control continued
Two approaches investigated::
Modal damping: convert 24 DOF MIMO into 24 DOF SISO systems. Each system can be damped independently with a relatively simple filter. Since there are sensors only at the top mass, an estimator is needed to fully reconstruct the dynamics. See below for response in X direction.
Multimode damping: extension of the GEO damping scheme. Up to 4 modes per coordinate are damped with a single controller. Gain and phase adjusted for aggressive filtering above the resonances. Method more tolerant of parameter variations.
Likely to use modal damping in X for shorter decay time, multimode for other DOFs.
Eddy current damping was also considered as supplement: full damping by ECD introduces too much thermal noise.
From Strain and Shapiro, submitted to Rev. Sci. Instrum.

17. Example of AOSEM used at penultimate stage
Global Control
Global control signals can be applied at all four stages
Top three stages have coil/magnet actuators
Fourth stage has electrostatic drive (ESD)
Larger forces/lower bandwidth at top, smaller forces/higher bandwidth at bottom
Typical forces per actuator
1.7 N/A at top and upper intermediate stages
0.03 N/A at penultimate stage
4 x N/V2 (+/- 400V) at test mass
Main (test) Chain
Reaction Chain
Example of AOSEM used at penultimate stage

18. Hierarchical Global Control
If each stage’s input is the output of the previous stage, any feedback change is automatically registered by the rest of the loop.
The stability at each stage is independent from the others.
ITM
ETM

19. Other Features of Quad Design
Enhanced gas damping in small gaps (Dolese et al, Phys Rev D 84, 2011)
Led to redesign of compensator plate (CP) for ITM, thinner to give larger gap
ETM to End Reaction Mass (ERM) gap = 5 mm, ITM to CP gap = 20 mm
ETM/ERM gap kept at 5 mm to allow full ESD force: rely on improving gas pressure at end chambers, and possible future redesign of ERM shape
Vibration absorbers added to welded support structure to damp modes
2 kg mass sandwiched between viton O-rings within outer casing
Broadband damping around first few resonances (~ 100 Hz)
Earthquake and bump stops to constrain glass masses have silica tips
Reduce charge build-up and transfer
Thermal Compensation Scheme (TCS) features
Ring heaters surrounding ETM and ITM
Gold-coated barrel on CP
ETM/ITM
CP (purple) ERM (blue)
*ERM = end reaction mass

20. Chain Splitting & Installation Arm
Ability to split both main and reaction chains below top masses for ease of storage, installation and replace/repair scenarios. + + =
Installation arm for replace/repair scenarios

21. Prototype Testing at LASTI
Several prototypes built and tested at LASTI as design matured over past 10 years.
Final “noise” prototype incorporated first full monolithic suspension of 40 kg silica mass, suspended from a BSC-ISI. Investigations included
Understanding and developing the quad model
Mode frequencies and transfer functions
Multi-mode and modal damping
Aspects of hierarchical global control (cavity formed with prototype triple pendulum)
Q values of test mass, pendulum modes and and violin modes
Investigation of use of ESD for acoustic mode damping
Investigation of charge on the optic using the ESD and of discharging using ionized nitrogen
Interactions between ISI and quad
Assembly, installation and alignment procedures

22. Examples of Transfer Functions from LASTI prototype
Example of transfer functions (TF) taken at top mass (drive to response)
Top: measured and modelled TF in X direction with no damping applied
Middle: simulated and measured modal damping of TF in X direction
Bottom: measurements of yaw TF undamped and damped
yaw
Data from Brett Shapiro

23. Current Status Assembly and installation:
2 full quads with monolithic stages assembled at LHO: one (ITM) installed in chamber, the second (ETM) due for installation early March. These will be used for single arm test.
A further 6 assembled and tested in metal form, and sub-assemblies of all the others Total = 12 plus spares.
Next installation due at LLO early summer, two ITMs for short Michelson tests.

24. Testing Results: Transfer Functions Driving and Observing at Top Mass

25. Example of bad transfer function due to chains touching (black trace)
More Testing Results
First two pitch frequencies are most variable, due to strong dependence on setting of “d” values – vertical separation of wire break-off points from CofM. Typical values ~ 1 mm.
Example of bad transfer function due to chains touching (black trace) d1
Centre of mass d2

26. Some Lessons Learned
Two reviews carried out on assembly procedures during Changes included:
Flag redesign for BOSEMs to improve assembly process and relax tolerance on alignment for minimising cross-coupling
Addition of pitch adjustment on upper intermediate mass to help alignment process (masses shown in red)
Reduction of particulates:
Unplated SmCo magnets (used to reduce Barkhausen noise) found to shed particulates: replaced by Ni-plated versions.
Addressed abrasion of bolt heads in high torque locations - use of Nitronic-60 washers
Revised tooling for blade adjustments and other alignments
Improved silica fibre safety after dropped screw broke fibres:
more catch trays and shields, addition to fibre guards, use of captured screws, improved tooling, redesign of shims to be more secure
Attention paid to routing of cabling up reaction chain to minimise effect on dynamics, especially on pitch

27. Conclusions
The assembly and installation of the quadruple suspensions for the test masses in Advanced LIGO are well underway.
The procedures for assembly, including the monolithic elements, alignment, testing and installation are well understood.
The mechanical model of the dynamics of the suspensions is well understood.
The measurements of mode frequencies, transfer functions and damping (local control) fit the model well.
We look forward to the first operation of two quad suspensions in a long cavity which will start soon at LHO.

28. Acknowledgements
The Advanced LIGO Suspensions Team consists of more than sixty scientists, mechanical engineers, electronic engineers, designers, technicians and students from eight institutions.
USA
LIGO Caltech: Jay Copti, Philip Croxton, Todd Etzel, Kate Gushwa, Jay Heefner, Alastair Heptonstall, Kristen Holtz, Tim McDonald, Gary McIntyre, Margot Phelps, Norna Robertson, Calum Torrie
LIGO Hanford Observatory: Jeff Bartlett, Mark Barton, Betsy Bland, Doug Cook, Jeff Garcia, Jesse Garner, Gerardo Moreno, Gerardo Moreno Jnr., Jason Oberling, Andres Ramirez, Travis Sadecki, David Stone, Vern Sandberg
LIGO Livingston Observatory: Carl Adams, Anna Aitken, Joe Betzwiezer, Derek Bridges, Virginia Brocato, Anamaria Effler (LSU) , Robert Giglio, Matt Heintze, Ed Merilh, Mike Meyer, Ralph Moffatt, Bobby Moore, Terry Pitre, Janeen Romie, Danny Sellers, Gary Traylor, Gene Winton
LIGO MIT: Sam Barnum, Michael Hillard, Jeff Kissel, Rich Mittleman, Brett Shapiro UK
University of Glasgow: Angus Bell, Nicola Beveridge, Alan Cumming, Liam Cunningham, Giles Hammond, Jim Hough, Russell Jones, Rahul Kumar, Sheila Rowan, Ken Strain, Marielle Van Veggel
Rutherford Appleton Laboratory (RAL): Justin Greenhalgh, Tim Hayler, Joe O’Dell, Ian Wilmut
University of Birmingham: Stuart Aston (now LLO), Ludovico Carbone, Ron Cutler, Alberto Vecchio
Strathclyde University: Nick Lockerbie, Kirill Tokmakov