Interferometer Simulations and Lock Acquisition in LIGO
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Video Lecture 45 of 69
Copyright Information: This video is taken from a 2002 Caltech on-line course on "Gravitational Waves", organized and designed by Kip S. Thorne, Mihai Bondarescu and Yanbei Chen. The full course, including this and many other lecture videos, exercises, solutions to exercises, and lists of relevant reading, are available on the web at http://elmer.caltech.edu/ph237/
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### Lecture Description

Interferometer Simulations and Lock Acquisition in LIGO - Week 13, Lecture 24, Part 1  [by Matt Evans]

1. Simulations of all or part of a LIGO interferometer
1. What a simulation is
2. Types of simulations:
1. Frequency domain: fast, but limited to linear systems
2. Time domain: slower, but necessary for nonlinearities

Example of a simulation:  Control system for a Fabry Perot cavity:

1. Laser excites Fabry Perot cavity; returning light tapped off by Faraday isolator, detected to produce electronic signal which drives a magnetic actuator that adjusts a cavity mirror to lock the cavity to the laser.
2. Simulation of the optics, the electronics, the mirror's mechanics, and the electromechanical transducers
3. Linear parts of system treated via transfer functions

In complex system such as LIGO: subsystems (e.g. the above) treated as modules

Uses of simulations:

1. Quantify things that can't be measured experimentally
2. Selectively turn on and off noise sources

LIGO end-to-end (E2E) simulation system

1. Used to develop and implement lock-acquisition method for LIGO-I
2. Being prepared for detailed noise tracking in LIGO-I

Lock acquisition in LIGO-I

1. What is lock acquisition?
2. Locking a single Fabry Perot cavity
1. Pound-Drever-Hall (PDH) error signal ("demod signal")
2. lock acquisition contrasted with maintaining lock once acquired: nonlinear vs. linear
3. Acquisition error signal = (demod signal)/(cavity power) - linear over length changes ~ wavelength
4. Control (actuation) force to lock

B. Locking a LIGO-I interferometer

1. Four degrees of freedom must be locked using five error signals from three readout ports
2. 5 x 4 dimensional sensing matrix (degrees of freedom -> error signals)
1. Invertible in pieces (largest 2x2 piece, then 3x3, then 4x4) -> lock acquisition in stages

c. 5 states of interferometer, from totally unlocked through partial locks to totally locked

d. Examples of evolution through the 5 states: experimental data compared with simulations

### Course Description

Caltech's Physics 237-2002: Gravitational Waves
A Web-Based Course organized and Designed by Kip S. Thorne, Mihai Bondarescu and Yanbei Chen.

This course contains all the materials from a graduate-student-level course on Gravitational Waves taught at the California Institute of Technology, January through May of 2002. The materials include Quicktime videos of the lectures, lists of suggested and supplementary reading, copies of some of the readings, many exercises, and solutions to all exercises. The video files are so large that it may not be possible to stream them from most sites, but they can be downloaded. Alternatively, the course materials on DVD's can be borrowed via Interlibrary Loan from the Caltech Library (click on CLAS, then on Call Number, then enter QC179.T56 2002 ).

Questions and issues about this course and website can be directed to Mihai Bondarescu or Yanbei Chen.