End to End Simulation of LIGO Hiro Yamamoto

End to End Simulation of LIGO Hiro Yamamoto LIGO Lab/CIT l l l Overview of End to End simulation framework Physics in e 2 e Applications => Matt Evans Issues Summary Simulation group l l H. Yamamoto (1 FTE) : Manager, Salesman, Science programmer M. Evans (1 FTE) : Lead Scientist for e 2 e application B. Bhawal (1 FTE), V. Sannibale (1/3 FTE) : Scientist B. Sears (1 FTE), M. Araya (1 FTE) : User Interface programmer Based on talk on Nov. 11, 03 March 15 -19, 2004, Virgo

LIGO End to End simulation what is it l Time domain simulation written in C++ » simulating realistically with non linearity automatically included l l Like MATLAB with Interferometer toolbox Major physics components and tools relevant for LIGO » fields & optics, mechanics, digital and analog electronics, measured noise, STATE SPACE using ABCD, etc l Flexible to design wide varieties of systems » from simple pendulum to full LIGO I to adv. LIGO » from fast prototyping to full design l Easy development and maintenance » use of graphical front end written in JAVA for the system design » object orient design for easy addition of new physics March 15 -19, 2004, Virgo

LIGO End to End Simulation the motivation l l 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 l As easy as back of the envelope March 15 -19, 2004, Virgo

End to End Simulation overview l End to End simulation environment » Simulation programs - program to run – modeler : time series generator – modeler_freq : spectrum analyzer » Description files defining what to simulate - input files – Simple pendulum ~ full LIGO » Graphical Editor to create and edit description files - alfi - editor l LIGO I simulation packages » Han 2 k : used for the lock acquisition design ~ 500 parts » Sim. LIGO : to assist LIGO I commissioning ~ 3000 parts March 15 -19, 2004, Virgo

End to End Simulation perspective l l l e 2 e development started after LIGO 1 design completed (1997 ~ ) LIGO 1 lock acquisition was redesigned successfully using e 2 e by M. Evans (2000 ~ 2001) Major on going efforts (2001 ~ ) » » » l Realistic noise of the locked state interferometer Effect of thermal lensing on the lock acquisition Alignment control system in realistic condition Effect of radiation pressure (for LIGO I and adv. LIGO) e 2 e LIGO I simulation generates linear noise Preparation for adv. LIGO » » Dual recycling cavity code for fast simulation State Space support Better Modal Model class for simulating realistic optics Better Matrix class with expression template for better coding – Efref = t * Ebin + Mref * Efin » more extensive thread support March 15 -19, 2004, Virgo

FUNC X primitive module how to add a new function in OO way l l How to develop a new physics, like locking algorithm? Day 1 » use 100’s of built-in elements in a cumbersome way or write C++ code and recompile and test l Day 2 » use expression parser module, a simplified c like environment. No compilation needed, but limited (no print, no struct …) use and slow simulation. l Day 3 » provide code, and automatically compiled and linked dynamically at run time » like MATLAB mex-file, but automated. Or MATLAB m files are automatically compiled and linked dynamically with matlab » Easy development and fast simulation March 15 -19, 2004, Virgo

e 2 e physics Time domain simulation l Analog process is simulated by a discretized process with a very small time step (10 -7~ 10 -3 s) » single time step in the entire system l Linear system response is handled using digital filter and State Space » » l e 2 e DF = internally the same as the one used at the LIGO site Transfer function -> digital filter Pendulum motion Analog electronics Easy to include non linear effect » Saturation, e. g. l A loop should have a delay » » Strict chronological ordering Need to put explicit delay when needed Simulation time step << time constant of the system Not practical to simulate Core Optics and Mode Cleaner together March 15 -19, 2004, Virgo

e 2 e physics State Space model by ABCD matrix l l l Advanced LIGO Seismic Isolation and Suspension teams have developed their models, available by SS More complex LIGO I model (violin, etc) by SS Runge-Kutta with adoptive time step to achieve given accuracy Can use quad precision internally Input for SS module to simulate x'' + 2 a x' + w 0^2 x = 0 » a and w 0 given as macro » | as row separator » A=2 x 2, B=2 x 1, C=1 x 2, D=appropriate empty matrix A = 0, 1 | -omega 0*omega 0, -2*a B = 0 omega 0*omega 0 C = 1, 0 accuracy March 15 -19, 2004, Virgo = 1 e-12

e 2 e physics Fields and optics l Time domain modal model » field is expanded using Hermite-Gaussian eigen states » number of modes (n+m) <=4 for most of the study l Reflection matrix » » » l tilt vertical shift curvature mismatch Completely modular » Arbitrary planar optics configuration can be constructed by combining mirrors and propagators l l Photo diodes with arbitrary shapes can be attached anywhere Adiabatic calculation for short cavities for faster simulation » Thread is used to calculate multiple sideband evolution at the same time March 15 -19, 2004, Virgo

e 2 e physics optics imperfection l n > n’ Simple lens model » LIGO 1 – lock, mode mixing Thermal lensing l Mode decomposition matrix - tbd Rcurv = R’ curv ITM TEMm’n’ TEMmn » LIGO 1 – actual mirror phase map – more accurate Tmn->m’n’ » Adv. LIGO TEMm’n’ Rmn->m’n’ March 15 -19, 2004, Virgo

Sensing noise Shot noise for an arbitrary input Average number of photons by the input power of arbitrary time dependence Average number of photons Actual number of photons which the detector senses. Simulation option Shot noise can be turned on or off for each photo diode separately. #photons Actual integer number of photons March 15 -19, 2004, Virgo time

Radiation Pressure and noise l l Radiation pressure and torque based on modal model Radiation linear force has noise based on the photon counting » no noise on torque yet l Radiation pressure is applied to the mechanical calculation of the mass in the next time step position Ein Eref pos(RPF, …) optical mass Rad Pressure Force(pos, Ein, Eref) March 15 -19, 2004, Virgo mechanical mass

e 2 e physics Mechanics simulation (1) Seismic motion from measurement 3 » correlations among stacks » fit and use psd or use time series (2) Parameterized HYTEC stack (3) Simple single suspended mirror » 4/5 sensors and actuators » imbalance of sensors and actuator for the length and alignment coupling » violin mode excitation? March 15 -19, 2004, Virgo 4 2 1

MSE : Mechanical Simulation Engine l C++ Library to simulate a fully three dimentional mechanical system, developed by G. Cella » » l modular environments automatic search for working points thermal noise and realistic damping simulation system asymmetries properly propagated Stand alone simulation package, with interface to e 2 e taken into account » frequency and time domain » build and debug a model and integrate to e 2 e by placing wrapper » integration with other mechanical simulation – For adv. LIGO, there are several sub-system level modeling efforts are already doing on, and MSE can interface to those models. March 15 -19, 2004, Virgo

Mechanical noise of one mirror suspended mirror (transfer function or 3 d model) (power spectral density) seismic isolation system (transfer function) seismic & thermal noises seismic motion (power spectral density) March 15 -19, 2004, Virgo

Is double precision enough? will be OK for LIGO I, probably not OK for adv. LIGO Comparision of suspension simulations using double and quad precision internally. March 15 -19, 2004, Virgo

e 2 e Graphical Editor - alfi Laser Photo diode mirror propagator March 15 -19, 2004, Virgo Photo diode

e 2 e example Fabry-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=100 ppm, Lcavity = 4000 m March 15 -19, 2004, Virgo

Inputs and outputs l Description files - box files » what to simulate » use I/O primitives to read and write data l Macro definitions » all numerical values in box files can be written using symbolic names » l % LHO 4 k. mcr % optical path lengths. Leng_ RM 2 BS = 4. 397 [m] "RM-HR to BS-HR Leng_BS 2 ITMx = 4. 965 [m] "BS-HR to ITMx-HR Leng_BS 2 ITMy = 4. 609 [m] "BS-HR to ITMy-HR Leng_Arm. X = 3995. 055 [m] "ITMx-HR to ETMx-HR Leng_Arm. Y = 3995. 055 [m] "ITMy-HR to ETMy-HR Leng_PRC = Leng_RM 2 BS + (Leng_BS 2 ITMx + Leng_BS 2 ITMy) / 2 Snp. Asy = Leng_BS 2 ITMx - Leng_BS 2 ITMy Outputs » » no built in analysis tools time series psd spectrum analyzer March 15 -19, 2004, Virgo

LIGO simulation without programming l Package distributed » Sim. LIGO box files » auxiliary files – macro files, run instructions, support apps » matlab files for easy analysis of e 2 e outputs » modeler < run. in to generate time series and psds » 5 lines in unix terminal to generate the sensitivity curve l Macro files - text file » » » lengths and mirror quantities noise : on-off control : on-off shaking mirrors : length and angle - linear, periodic, random configurations : FP, PRM, full LIGO March 15 -19, 2004, Virgo

Main box of Sim. LIGO two views of alfi and ptimitive menu March 15 -19, 2004, Virgo

COC box suspension, core optics and analog stuff March 15 -19, 2004, Virgo

Optics PRM, arm, radiation pressure, telescope, f-l hack, etc March 15 -19, 2004, Virgo

COC when you want to know what is MMTref, just… March 15 -19, 2004, Virgo

Profile of Sim. LIGO cpu usage point of view Profiler of 3352 action calls per time step << built-in functions +++++++++++++++++++++++++++ Profile of 41 module usage sorted by total times index : frac : total : time/tick : #module : name : (%) : (sec) : (microsec): : -----------------------------0 : 45. 24 : 16. 99 : 2179 : 1 : rec_sum << m+n<=2, 1 thread 1 : 10. 6 : 3. 981 : 510. 4 : 278 : FUNC_2 x 2 2 : 7. 929 : 2. 979 : 381. 9 : 119 : FUNC_16 x 16 3 : 7. 679 : 2. 885 : 369. 8 : 210 : FUNC_1 x 1 4 : 4. 922 : 1. 849 : 237 : 29 : pd_demod 5 : 4. 615 : 1. 733 : 222. 2 : 122 : FUNC_4 x 4 6 : 4. 075 : 1. 531 : 196. 2 : 12 : mirror 2 Profile of 583 box usage sorted by total times << use-defined functions index : frac : total : time/tick : #module : name : (%) : (sec) : (microsec): : -----------------------------0 : 100 : 37. 57 : 4816 : 1 : Detector 1 : 94. 34 : 35. 44 : 4543 : 1 : Detector. COC 2 : 54. 08 : 20. 31 : 2604 : 1 : Detector. COC. Core. Optics 3 : 24. 56 : 9. 224 : 1183 : 1 : Detector. COC. Suspensions 4 : 16. 54 : 6. 215 : 796. 8 : 6 : Controller 5 : 7. 916 : 2. 974 : 381. 2 : 6 : Mech March 15 -19, 2004, Virgo

Summary l l Simulation engine and interface are ready LIGO I simulation is ready » Good playground for length and alignment control design » Sensitivity curve properly simulated - ready to go beyond l LIGO I simulation needs improvements » Michelson cavity is degenerate and badly mode mismatched (better now by thermal compensation) » Better frequency response of cavities » Lock loss study demands more reality » more noise, more reality – scattering noise, acoustic coupling, beam clipping l adv. LIGO simulation demands more » physics (dual recycling cavity) » speed » accuracy, … March 15 -19, 2004, Virgo