1. e2e of LIGO - UCLA talk1 End to End Simulation of LIGO detector  LIGO - Laser Interferometer Graviational Wave Observatory  Basics of the Interferometer Detector  Interferometer simulation  Applications of the simulation Hiro Yamamoto LIGO Laboratory / California Institute of Technology LIGO Progress Report : LIGO-G020007 by Alan Weinstein, Caltech

2. e2e of LIGO - UCLA talk2 Interferometer for Gravitational Wave detection L1L1 L2L2 h~10 -23 L 1 -L 2 ~10 -19 m E1E1 E2E2 E 1 - E 2 ∝  L 1 -L 2

3. e2e of LIGO - UCLA talk3 The Fabry-Perot Cavity - the most important dynamics -

4. e2e of LIGO - UCLA talk4 Basic ingredients of LIGO LaserEOM PD fLfL fLfL f L -f RF fLfL f RF freq Signal to DOF to force Seismic motion ~ 10 -6 m Thermal noise ~ kT shot noise ~ 10 16 /s Seismic Isolation f -6 f -2

5. e2e of LIGO - UCLA talk5 Astrophysical sources: Thorne diagrams LIGO I (2002-2005) LIGO II (2007- ) Advanced LIGO seimic thermal quantum

6. e2e of LIGO - UCLA talk6 LIGO sites Hanford Observatory (H2K and H4K) Livingston Observatory (L4K) Hanford, WA (LHO) located on DOE reservation treeless, semi-arid high desert 25 km from Richland, WA Two IFOs: H2K and H4K Livingston, LA (LLO) located in forested, rural area commercial logging, wet climate 50km from Baton Rouge, LA One L4K IFO Both sites are relatively seismically quiet, low human noise - NOT!! 4 km + 2 km 4 km

7. e2e of LIGO - UCLA talk7 Logging at Livingston Less than 3 km a few 100 meters away… Dragging big logs … Remedial measures at LIGO are in progress; this will not be a problem in the future.

8. e2e of LIGO - UCLA talk8 International network LIGO Simultaneously detect signal (within msec)  detection confidence  locate the sources  verify light speed propagation  decompose the polarization of gravitational waves  Open up a new field of astrophysics! GEOVirgo TAMA AIGO

9. e2e of LIGO - UCLA talk9 LIGO Beam Tube  LIGO beam tube under construction in January 1998  65 ft spiral welded sections  girth welded in portable clean room in the field Beam light path must be high vacuum, to minimize “phase noise”

10. e2e of LIGO - UCLA talk10 LIGO vacuum equipment All optical components must be in high vacuum, so mirrors are not “knocked around” by gas pressure

11. e2e of LIGO - UCLA talk11 Seismic isolation stacks

12. e2e of LIGO - UCLA talk12 Suspended Core Optics Optics suspended as simple pendulums Local sensors/actuators for damping and control Coils push/pull on tiny magnets glued to optics Earthquake stops to prevent break-off of tiny magnets

13. e2e of LIGO - UCLA talk13 Control Room Spectrogram time frequency

14. e2e of LIGO - UCLA talk14 How does the signal look like 1.4/1.4 Solar Mass NS/NS Inspiral signal in AS_Q... (Lormand, Adhikari) GPS time (S),  T = 0.062s Frequency (Hz),  f = 16 Hz 10 3 10 2

15. e2e of LIGO - UCLA talk15 Sensitivities of LIGO 3 interferometers

16. e2e of LIGO - UCLA talk16 Improvements of sensitivities of Hanford 4k interferometer

17. e2e of LIGO - UCLA talk17 Different cultures in HEP and GW - my very personal view High Energy PhysicsGravitational Wave Detection group people know of simulationvery few people know of simulation simulation and hardware developments go side-by-side, stimulating each other simulation is used only when there is no other way, and a model is developed only for that problem. fortran, matlab, mathematica, LabView, etc simulation is used to understand the integrated system overall performance is maintained by noise budgets assigned to each subsystem hardware people intend to use simulation to understand problems hardware people try to address problems by dealing with hardware use of simulation for data analysis is a well known procedure simulation for data analysis is non existent

18. e2e of LIGO - UCLA talk18 LIGO End to End Simulation the motivation  Assist detector design, commissioning, and data analysis  To understand a complex system »back of the envelope is not large enough »complex hardware : pre-stabilized laser, input optics, core optics, seismic isolation system on moving ground, suspension, sensors and actuators »feedback loops : length and alignment controls, feedback to laser »non-linearity : cavity dynamics to actuators »field : non-Gaussian field propagation through non perfect mirrors and lenses »noise : mechanical, thermal, sensor, field-induced, laser, etc : amplitude and frequency : creation, coupling and propagation »wide dynamic range : 10 -6 ~ 10 -20 m  As easy as back of the envelope

19. e2e of LIGO - UCLA talk19 E2E perspective  e2e development started after LIGO 1 design completed (1997 ~ )  LIGO 1 lock acquisition was redesigned successfully using e2e by M.Evans (2000 ~ 2001)  Major on going efforts for LIGO I (2001 ~ ) »Realistic noise of the locked state interferometer »Effect of the thermal lensing on the lock acquisition  Efforts for Advanced LIGO (2000 ~ ) »Development of optics and mechanics modules »Trying to expand users who can contribute –A.Weinstein (CIT), J.Betzwieser (MIT), M.Rakmanov (UF), M.Malec (GEO)

20. e2e of LIGO - UCLA talk20 End to End Simulation overview  General purpose GW interferometer simulation framework »Generic tool like matlab or mathematica »Time domain simulation written in C++ »Optics, mechanics, servo,... –time domain modal model, single suspended 3D mass. –analog and digital controller - ADC, DAC, digital filter, etc  End to End simulation environment »Simulation engine - modeler, modeler_freq »Description files defining what to simulate - Simple pendulum, …, full LIGO (constituent files are called “box files” or simply “boxes”) »Graphical Editor to create description files - alfi  LIGO I simulation packages »Han2k : used for the lock acquisition design »SimLIGO : to assist LIGO I commissioning

21. e2e of LIGO - UCLA talk21 GW Interferometer simulation - difficulties -  Simulate chronologically dependent time series »parallelization is difficult  Control systems connect various subsystems very tightly »optimal choice of system time step is hard  Mirror motions may need quad precision »micro seismic peak ~ 10 -6 m »relative mirror motion of interest for LIGO I ~ 10 -20 m »relative mirror motion of interest for LIGO II < 10 -21 m

22. e2e of LIGO - UCLA talk22 End to End Simulation coarse view Optics systemMechanical systemLaser x,  Feedback force Time domain modal model Objects : laser, mirror, photo diode, … Any planar interferometer Fabry-Perot, Mode cleaner,LIGO I, Advanced LIGO,… sensor actuator Transfer function using Digital filter Single Suspended mirror Mechanical Simulation Engine (object-oriented) Control system

23. e2e of LIGO - UCLA talk23 e2e Graphical Editor Laser Photo diode mirror propagator Photo diode

24. e2e of LIGO - UCLA talk24 Mirror digital filter3d mass laser Simulation engine time loop and independent modules GUI data file matlab, etc simulation engine independent modules photo diode time evolution loop math parser derived from module class construct and init loop M.Evans

25. e2e of LIGO - UCLA talk25 e2e example - 1 Fabry-Perot cavity dynamics ETMz = -10 -8 + 10 -6 t Resonant at Power = 1 W, T ITM =0.03, T ETM =100ppm, L cavity = 4000m Reflected Power Transmitted Power X 100 1  / s

26. e2e of LIGO - UCLA talk26 e2e example - 2 Suspended mass with control Force Mass position Suspension point Susp. point Force = filter * mass position Pendulum res. at 1Hz Control on at 10 mixer F/m +  2 dz S 2 + a S +  2 Z mass =

27. e2e of LIGO - UCLA talk27 FUNC primitive module - command liner in GUI -  GUI is not always the best tool  FUNC is an expression parser, based on c-like syntax  all basic c functions, bessel, hermite  special functions : time_now(), white_noise, digital_filter(poles, zeros), fp_guoypahse(L,R1,R2), …  predefined constants : PI, LIGHT_SPEED, …  inline functions : leng(x,y) = sqrt(x*x+y*y); L = leng(2,3); gain = -5; lockTime = 10; out0 = if ( time_now()<lockTime, in0, in0+gain*in1 ); mixer module

28. e2e of LIGO - UCLA talk28 e2e physics Time domain simulation  Analog process is simulated by a discretized process with a very small time step (10 -7 ~ 10 -3 s)  Linear system response is handled using digital filter »e2e DF = PF’s pziir.m (bilinear trans (s->z) + SOS) + CDS filter.c »Transfer function -> digital filter »Pendulum motion »Analog electronics  Easy to include non linear effect »Saturation, e.g.  A loop should have a delay »Need to put explicit delay when needed »Need to choose small enough time step

29. e2e of LIGO - UCLA talk29 e2e physics Fields and optics  Time domain modal model »field is expanded using Hermite-Gaussian eigen states »Perturbation around resonant state  Reflection matrix » tilt »  Completely modular »Arbitrary planar optics configuration can be constructed by combining mirrors and propagators  Photo diodes with arbitrary shapes can be attached anywhere  Adiabatic calculation for short cavities for faster simulation

30. e2e of LIGO - UCLA talk30 e2e physics Mechanics simulation (1) Seismic motion from measurement » correlations among stacks » fit and use psd or use time series (2) Parameterized HYTEC stack »Ed Daw (3) Simple single suspended mirror »M.Rakmanov, V.Sannibale »4/5 sensors and actuators »couple between LSC and ASC (4) Thermal noise added in an ad hoc way »using Sam Finn’s model 1 2 3 4

31. e2e of LIGO - UCLA talk31 Mechanical noise of one mirror seismic & thermal noises seismic motion (power spectral density) seismic isolation system (transfer function) suspended mirror (transfer function or 3d model) (power spectral density)

32. e2e of LIGO - UCLA talk32 Average number of photons Actual integer number of photons Simulation option Sensing noise Shot noise for an arbitrary input Shot noise can be turned on or off for each photo diode separately. Average number of photons by the input power of arbitrary time dependence Actual number of photons which the detector senses. time #photons

33. e2e of LIGO - UCLA talk33 First LIGO simulation Han2k  Matt Evans Thesis  Purpose »design and develop the LHO 2k IFO locking servo »simulate the major characteristics of length degree of freedom under 20 Hz.  Simulation includes »Scalar field approximation »1 DOF, everywhere »saturation of actuators »Simplified seismic motion and correlation »Analog LSC, no ASC »no frequency noise, no shot noise, no sensor/actuator/electronic noise

34. e2e of LIGO - UCLA talk34 Fabry-Perot ideal vs realistic ideal realistic Linear Controllers: Realistic actuation modeling plays a critical role in control design. V I 150mA

35. e2e of LIGO - UCLA talk35 Fabry-Perot Error signal linearization arbitrary unit

36. e2e of LIGO - UCLA talk36 Hanford 2k simulation setup 6 independent suspended mirrors with seismic noise corner station : strong correlation in the low frequency seismic motion Non-linearity of controller

37. e2e of LIGO - UCLA talk37 Automated Control Matrix System LIGO T000105 Matt Evans Same c code used in LIGO servo and in simulation Field signal Actuation of mass

38. e2e of LIGO - UCLA talk38 Multi step locking State 1 : Nothing is controlled. This is the starting point for lock acquisition. State 2 : The power recycling cavity is held on a carrier anti-resonance. In this state the sidebands resonate in the recycling cavity. State 3 : One of the ETMs is controlled and the carrier resonates in the controlled arm. State 4 : The remaining ETM is controlled and the carrier resonates in both arms and the recycling cavity. State 5 : The power in the IFO has stabilized at its operating level. This is the ending point for lock acquisition.

39. e2e of LIGO - UCLA talk39 Lock acquisition real and simulated observable Not experimentally observable

40. e2e of LIGO - UCLA talk40 Second generation LIGO simulation SimLIGO  Assist noise hunting, noise reduction and lock stability study in the commissioning phase  Performance of as-built LIGO »effect of the difference of two arms, etc  Noise study »Non-linearity –cavity dynamics, electronic saturations, digitization, etc »Bilinear coupling  Lock instability  Sophisticated lock acquisition  Upgrade trade study

41. e2e of LIGO - UCLA talk41 SimLIGO A Detailed Model of LIGO IFO  Modal beam representation »alignment, mode matching, thermal lensing  3D mechanics »Correlation of seismic motions in corner station »6x6 stack transfer function »3D optics with 4/5 local sensor/actuator pairs  Complete analog and digital electronics chains with noise »Common mode feedback »Wave Front Sensors »“Noise characterization of the LHO 4km IFO LSC/DSC electronics” by PF and RA, 12-19 March 2002 included

42. e2e of LIGO - UCLA talk42 SimLIGO Noise sources  All major noise sources »seismic, thermal, sensing, laser frequency and intensity, electronics, mechanical  IFO »optical asymmetries (R, T, L, ROC) »non-horizontal geometry (wedge angles, earth's curvature) »phase maps »scattered light  Mechanics »wire resonances, test mass internal modes  Sensor »photo-detector, whitening filters, anti-aliasing  Digital system »ADC, digital TF, DAC  Actuation »anti-imaging, dewhitening, coil drivers

43. e2e of LIGO - UCLA talk43 SimLIGO System structure

44. e2e of LIGO - UCLA talk44 SimLIGO more realistic LIGO simulation Digital ISC COC IOO Suspension Optics ElecOut - analog LSC ASC Diag PutDigital Controller LOS ETM pickoff telescope Env 3D suspended mass w/ OESM

45. e2e of LIGO - UCLA talk45 SimLIGO Noise components optical lever

46. e2e of LIGO - UCLA talk46 LIGO data vs SimLIGO Triple Strain Spectra - Thu Aug 15 2002 Strain (h/rtHz) rana-1029490757.pdf Frequency (Hz) data and simulation out of date

47. e2e of LIGO - UCLA talk47 SimLIGO sensitivity curve  Calculated from a time series of data »Major ingredients of the real LIGO included »Interferometer, Mechanics, Sensor-actuator, Servo electronics »Known noises »Signal to sensitivity conversion  Demonstration of the capability to simulate the major behavior of LIGO »Reliable tool for fine tuning a complex device »Almost any assumptions can be easily tested - at least qualitatively »Trade study »Subsystem design »…

48. e2e of LIGO - UCLA talk48 Power flow in the interferometer Energy loss in substrate Energy loss by mirror ~ 50ppm by Bill Kells

49. e2e of LIGO - UCLA talk49 Advanced R&D: Optics Thermal Compensation Thermal lens Thermoelastic deformation 100 nm “Bump” On HR surface 10 nm “lens” In Beam Splitter In Input Test Mass 100 nm “lens” for Sapphia 1000 nm “lens” for Silika Extend LIGO I “WFS” to spatially resolve phase/ OPD errors Thermal actuation on core optics

50. e2e of LIGO - UCLA talk50 Dual recycling cavity simulate FAST  Can be simulated today, but slow…  simulation time step = cavity length / speed of light  Module based on an approximate calculation of fields in a short cavity runs 500 (~ L 2 / L 1 ) faster than simulation using primitive mirrors.  M.Rakmanov (UF) worked on a dual recycling cavity formulation and did its validation using matlab and e2e primitive optics. Not completed. L1L1 L2L2 z1z1 z2z2 z3z3 E in linear approx. of E in, z 1, z 2 for L 2 /c

51. e2e of LIGO - UCLA talk51 Adv. LIGO Mechanics Quadruple Pendulum structure

52. e2e of LIGO - UCLA talk52 Adv. LIGO Mechanics Transfer functions 60cm60.1cm