Download presentation

Presentation is loading. Please wait.

Published byMikel Day Modified over 2 years ago

1
Reciprocity relationships for gravitational-wave interferometers Yuri Levin (Monash University) 1. Example: creep noise 2. Formalism 3. Creep noise again 4. Thermal deformations of mirrors 5. Thermal noise 6. Opto-mechanical displacements 7. Discussion

2
Part 1: creep noise Ageev et al. 97 Cagnoli et al.97 De Salvo et al. 97, 98, 05, 08

3
Quakes in suspension fibers defects Sudden localized stress release: non-Gaussian (probably), statistics not well-understood, intensity and frequency not well-measured. No guarantee that it is unimportant in LIGO II or III Standard lore: couples through random fiber extension and Earth curvature. KAGRA very different b/c of inclined floor Much larger direct coupling exists for LIGO. Top and bottom defects much more important. Levin 2012

4
Part 2: Reciprocity relations If you flick the cow’s nose it will wag its tail. If someone then wags the cow’s tail it will ram you with its nose. Provided that the cow is non-dissipative and follows laws of elastodynamics the coupling in both directions is the same

5
Reciprocity relations Force density Readout variable displacement form-factor

6
Reciprocity relations Force density Readout variable displacement form-factor is invariant with respect to interchange of and

7
stress Part 3: the creep noise again

8
The response to a single event: Location of the creep event Pendulum mode Violin mode

10
Random superposition of creep events parameters, e.g. location, volume, strength of the defect. Fourier transform Probability distribution function Caveat: in many “crackle noise” system the events are not independent

12
Conclusions for creep: Simple method to calculate elasto-dynamic response to creep events Direct coupling to transverse motion Response the strongest for creep events near fibers’ ends => Bonding!

13
Part 4: thermal deformations of mirrors High-temperature region Not an issue for advanced KAGRA. Major issue for LIGO & Virgo Zernike polynomials New coordinates cf. Hello & Vinet 1990 Treat this as a readout variable

14
How to calculate Apply pressure to the mirror face Calculate trace of the induced deformation tensor Have to do it only once! Calculate the thermal deformation Young modulus Thermal expansion Temperature perturbation King, Levin, Ottaway, Veitch in prep.

15
Check: axisymmetric case (prelim) Eleanor King, U. of Adelaide

16
Off-axis case (prelim) Eleanor King, U. of Adelaide

17
Part 5: thermal noise from local dissipation Readout variable Conjugate pressure Uniform temperature Local dissipation Non-uniform temperature. Cf. KAGRA suspension fibers See talk by Kazunori Shibata this afternoon

18
Part 6: opto-mechanics with interfaces Question: how does the mode frequency change when dielectric interface moves? Theorem: Mode energy Interface displacement Optical pressure on the interface Useful for thermal noise calculations from e.g. gratings (cf. Heinert et al. 2013)

19
Part 6: opto-mechanics with interfaces Linear optical readout, e.g. phase measurements Carrier light + Perturbation PhaseForm-factor

20
Part 6: opto-mechanics with interfaces Linear optical readout, e.g. phase measurements Photo-diode PhaseForm-factor

21
Part 6: opto-mechanics with interfaces Photo-diode 1. Generate imaginary beam with oscillating dipoles 2. Calculate induced optical pressure on the interface 3. The phase

22
Conclusions Linear systems (elastic, optomechanical) feature reciprocity relations They give insight and ensure generality They simplify calculations

Similar presentations

OK

Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Brownian thermal noise associated with attachments.

Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Brownian thermal noise associated with attachments.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on db2 architecture overview Ppt on depth first search algorithm examples Ppt on marie curie inventions Ppt on trade fair Ppt on plane table surveying Ppt on lean production system Ppt on science topics for class 9 Ppt on seven ages of life Ppt on interview etiquettes meaning Ppt on hard copy devices