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End to End Simulation of LIGO detector

This progress report discusses the end-to-end simulation of the Laser Interferometer Gravitational-Wave Observatory (LIGO) detector. The simulation helps in understanding the complex system, assisting in detector design, commissioning, and data analysis. It covers various aspects of the detector, including optics, mechanics, servo systems, noise sources, and control loops. The simulation framework is a general-purpose tool that enables time-domain simulations and provides a realistic representation of the detector's behavior.

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End to End Simulation of LIGO detector

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

  2. Interferometer forGravitational Wave detection L1 E1 E2 L2 E1- E2∝ L1-L2 h~10-23 L1-L2~10-19m e2e of LIGO - UCLA talk

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

  4. Basic ingredients of LIGO fL fL Thermal noise ~ kT f-2 freq fL-fRF Laser EOM fL Seismic Isolation f-6 PD shot noise ~ 1016 /s Signal to DOF DOF to force fRF e2e of LIGO - UCLA talk Seismic motion ~ 10-6 m

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

  6. 4 km + 2 km 4 km LIGO sites Hanford Observatory (H2K and H4K) • 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 Livingston Observatory (L4K) Both sites are relatively seismically quiet, low human noise - NOT!! e2e of LIGO - UCLA talk

  7. 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. e2e of LIGO - UCLA talk

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

  9. Control Room time frequency Spectrogram e2e of LIGO - UCLA talk

  10. 1.4/1.4 Solar Mass NS/NS Inspiral signal in AS_Q... (Lormand, Adhikari) 103 Frequency (Hz), Df = 16 Hz 102 GPS time (S), DT = 0.062s How does the signal look like e2e of LIGO - UCLA talk

  11. Sensitivities ofLIGO 3 interferometers e2e of LIGO - UCLA talk

  12. Improvements of sensitivities ofHanford 4k interferometer e2e of LIGO - UCLA talk

  13. Different cultures in HEP and GW- my very personal view e2e of LIGO - UCLA talk

  14. LIGO End to End Simulationthe 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 e2e of LIGO - UCLA talk

  15. 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) e2e of LIGO - UCLA talk

  16. 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 e2e of LIGO - UCLA talk

  17. 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 e2e of LIGO - UCLA talk

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

  19. e2e Graphical Editor Laser mirror mirror Photo diode propagator Photo diode e2e of LIGO - UCLA talk

  20. Simulation enginetime loop and independent modules simulation engine matlab, etc construct and init loop data file GUI time evolution loop independent modules derived from module class Mirror laser photo diode 3d mass digital filter math parser M.Evans e2e of LIGO - UCLA talk

  21. e2e example - 1Fabry-Perot cavity dynamics 1 m / s ETMz = -10-8 + 10-6 t Resonant at Reflected Power Transmitted Power X 100 Power = 1 W, TITM=0.03, TETM=100ppm, Lcavity = 4000m e2e of LIGO - UCLA talk

  22. F/m + w2 dz Zmass = S2 + a S + w2 e2e example - 2Suspended mass with control Suspension point Susp. point Pendulum Pendulum res. at 1Hz mixer Force Force = filter * mass position Control on at 10 Mass position e2e of LIGO - UCLA talk

  23. 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); mixer module gain = -5; lockTime = 10; out0 = if ( time_now()<lockTime , in0, in0+gain*in1 ); e2e of LIGO - UCLA talk

  24. e2e physicsTime 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 e2e of LIGO - UCLA talk

  25. 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 e2e of LIGO - UCLA talk

  26. e2e physicsMechanics simulation 3 • 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 2 4 1 e2e of LIGO - UCLA talk

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

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

  29. First LIGO simulationHan2k • 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 e2e of LIGO - UCLA talk

  30. Fabry-Perotideal vs realistic Linear Controllers: Realistic actuationmodeling plays acritical role incontrol design. ideal I 150mA realistic V e2e of LIGO - UCLA talk

  31. Fabry-PerotError signal linearization arbitrary unit arbitrary unit arbitrary unit e2e of LIGO - UCLA talk

  32. 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 e2e of LIGO - UCLA talk

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

  34. 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. e2e of LIGO - UCLA talk

  35. Lock acquisitionreal and simulated observable Not experimentally observable e2e of LIGO - UCLA talk

  36. Second generation LIGO simulationSimLIGO • 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 e2e of LIGO - UCLA talk

  37. SimLIGOA 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 e2e of LIGO - UCLA talk

  38. SimLIGONoise 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 e2e of LIGO - UCLA talk

  39. SimLIGOSystem structure e2e of LIGO - UCLA talk

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

  41. SimLIGONoise components optical lever e2e of LIGO - UCLA talk

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

  43. SimLIGOsensitivity 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 • … e2e of LIGO - UCLA talk

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

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

  46. Dual recycling cavitysimulate 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 (~L2 / L1 ) 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. z3 z1 z2 linear approx. of Ein ,z1 ,z2 for L2 /c Ein L1 L2 e2e of LIGO - UCLA talk

  47. Adv. LIGO MechanicsQuadruple Pendulum structure e2e of LIGO - UCLA talk

  48. Adv. LIGO MechanicsTransfer functions 60cm 60.1cm e2e of LIGO - UCLA talk

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