Lecture Description
Thermal Noise in LIGO Interferometers and its Control - Week 12, Lecture 22 [by Phil Willems]
A. Motivation: Brownian motion of a dust grain buffeted by molecules of an ideal gas
- dissipation, mean motion
- Fluctuating force as a random process; its correlation function and spectral density
- Solving for spectral density of particle position
B. Fluctuation-dissipation theorem
C. Damped pendulum: suspension thermal noise derived from fluctuation-dissipation theorem
D. Dissipation in a LIGO test mass or suspension described via imaginary part of generalized elastic modulus, E(f) = (applied force) / (resulting displacement) = Eo (1+i phi)
- Frequency-dependence of loss angle phi: viscous damping, structural damping, damping associated with an internal relaxation process
E. Dissipation/fluctuation processes for a LIGO test mass
- Gas molecules buffeting test mass
- Magnetic forces from actuator (which controls mirror)
- Internal processes inside the test mass itself:
a. Analyzed via sum over normal modes of test-mass oscillation [valid only for homogeneous dissipation]
b. Analyzed via Levin's Direct Method [valid in general]
c. Conventional internal dissipation (due to imperfections, ...)
d. Thermoelastic noise
e. Fused silica vs sapphire for Advanced LIGO (LIGO-II) test masses
f. Measurements of dissipation
4. Dissipation in mirror coatings
5. Dissipation in suspension wires
Course Index
- The Nature of Gravitational Waves
- Gravitational Waves Data Analysis
- Gravitational Wave Sources in Neutron Stars
- Introduction to General Relativity: Tidal Gravity
- Mathematics of General Relativity: Tensor Algebra
- Mathematics of General Relativity: Tensor Differentiation
- Introduction to General Relativity (4/5)
- Introduction to General Relativity (5/5)
- Weak Gravitational Waves in Flat Spacetime (1/6)
- Weak Gravitational Waves in Flat Spacetime (2/6)
- Weak Gravitational Waves in Flat Spacetime (3/6)
- Weak Gravitational Waves in Flat Spacetime (4/6)
- Weak Gravitational Waves in Flat Spacetime (5/6)
- Weak Gravitational Waves in Flat Spacetime (6/6); Propagation of Gravitational Waves Through Curved Spacetime (1/5)
- Propagation of Gravitational Waves Through Curved Spacetime (2/5)
- Propagation of Gravitational Waves Through Curved Spacetime (3/5)
- Propagation of Gravitational Waves Through Curved Spacetime (4/5)
- Propagation of Gravitational Waves Through Curved Spacetime (5/5)
- Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime (1/2)
- Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime (2/2)
- Astrophysical Phenomenology of Binary-Star GW Sources (1/5)
- Astrophysical Phenomenology of Binary-Star GW Sources (2/5)
- Astrophysical Phenomenology of Binary-Star GW Sources (3/5)
- Astrophysical Phenomenology of Binary-Star GW Sources (4/5)
- Astrophysical Phenomenology of Binary-Star GW Sources (5/5); Post-Newtonian G-Waveforms for LIGO & Its Partners (1/2
- Post-Newtonian Gravitational Waveforms for LIGO & Its Partners (2/2)
- Supermassive Black Holes and their Gravitational Waves (1/3)
- Supermassive Black Holes and their Gravitational Waves (2/3)
- Supermassive Black Holes and their Gravitational Waves (3/3); Gravitational Waves from Inflation (1/2)
- Gravitational Waves from Inflation (2/2)
- Gravitational Waves from Neutron-Star Rotation and Pulsation (1/2)
- Gravitational Waves from Neutron-Star Rotation and Pulsation (2/2)
- Numerical Relativity as a Tool for Computing GW Generation (1/2)
- Numerical Relativity as a Tool for Computing GW Generation (2/2)
- The Physics Underlying Earth-Based Gravitational Wave Interferometers (1/4)
- The Physics Underlying Earth-Based Gravitational Wave Interferometers (2/4)
- The Physics Underlying Earth-Based Gravitational Wave Interferometers (3/4)
- The Physics Underlying Earth-Based Gravitational Wave Interferometers (4/4)
- Overview of Real LIGO Interferometers (1/2)
- Overview of Real LIGO Interferometers (2/2)
- Thermal Noise in LIGO Interferometers and its Control (1/2)
- Thermal Noise in LIGO Interferometers and its Control (2/2)
- Control Systems and Laser Frequency Stabilization (1/2)
- Control Systems and Laser Frequency Stabilization (2/2)
- Interferometer Simulations and Lock Acquisition in LIGO
- Seismic Isolation in Earth-Based Interferometers
- Quantum Optical noise in GW Interferometers (1/2)
- Quantum Optical noise in GW Interferometers (2/2)
- LIGO data analysis (1/2)
- LIGO data analysis (2/2)
- The Long-Term Future of LIGO: Facility Limits
- The Long-Term Future of LIGO: Techniques for Improving on LIGO-II
- Large Experimental Science and LIGO as an Example (1/2)
- Large Experimental Science and LIGO as an Example (2/2)
- Resonant-Mass GW Detectors for the HF Band (1/2)
- Resonant-Mass GW Detectors for the HF Band (2/2)
- CAJAGWR talk by W.O. Hamilton on Resonant-Mass GW Detectors
- Doppler tracking of spacecraft for GW detection in the low frequency band
- Pulsar timing for GW detection in the very low frequency band
- LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design (1/2)
- LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design (2/2)
- LISA's Lasers and Optics (1/2)
- LISA's Lasers and Optics (2/2)
- Time-Delay Interferometry [TDI] for LISA (1/2)
- Time-Delay Interferometry [TDI] for LISA (2/2)
- LISA's Distrubance Reduction System (DRS) [Drag-Free System] (1/2)
- LISA's Distrubance Reduction System (DRS) [Drag-Free System] (2/2)
- The Big-Bang Observatory [BBO]: A Possible Follow-On Mission to LISA
- GW's from Inflation and GW Detection in ELF Band via Anisotropy of CMB Polarization
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.
- - Part A - Gravitational-Wave Theory and Sources
- - Part B - Gravitational-Wave Detectors - original outline
- - Part B - Gravitational-Wave Detectors - alternative outline with the lectures reordered more logically
- - Course Materials