April 24 2004 GR fun @ Cornell 1

A new family of flat-topped beams interesting for future LIGO interferometers

Mihai Bondarescu California Institute of Technology

April 24 2004 GR fun @ Cornell 2

Collaborators and Consultants

• K. Thorne (Caltech)• Pavlin Savov (Caltech)• Erika D’Ambrosio (Caltech)• S. Vyatchanin (MSU, Moscow)• S. Strigin (MSU, Moscow)• R. O’Shaughnessy (NWU, Chicago)• P. Kazarian (GCC)

April 24 2004 GR fun @ Cornell 3

April 24 2004 GR fun @ Cornell 4

International Network of Interferometric Detectors

• Network Required for:» Detection

Confidence

» Waveform Extraction

» Direction by Triangulation

LIGO Hanford, WA

LIGO Livingston, LA

GEO600Hanover Germany

TAMA300Tokyo

VIRGOPisa, Italy

Slide adapted from a talk by Kip

April 24 2004 GR fun @ Cornell 5

LIGO Collaboration of ~350 scientists at ~30 institutions

Hanford Washington

4 km

2 km Slide adapted from a talk by Kip

April 24 2004 GR fun @ Cornell 6

Livingston, Louisiana

4 km

Slide adapted from a talk by Kip

April 24 2004 GR fun @ Cornell 7

LIGO’s International Partners

VIRGO: Pisa, Italy [Italy/France]GEO600, Hanover Germany [UK, Germany]

TAMA300, Tokyo [Japan]

AIGO, Jin-Jin West Australia

Slide adapted from a talk by Kip

April 24 2004 GR fun @ Cornell 8

How a LIGO Interferometer WorksFabry-Perot

Cavity Fabry-PerotCavityBeam

Splitter

Slide adapted from a talk by Kip

April 24 2004 GR fun @ Cornell 9Slide adapted from Rejean J Dupuis talk from http://www.ligo.org/results/

April 24 2004 GR fun @ Cornell 10

Noise in LIGO

Adopted from Kip’s Talk(LIGO-G030137-00-Z)

April 24 2004 GR fun @ Cornell 11

What is Thermoelastic Noise and How to Reduce It?

• Random Thermal Fluctuations (~0.5 mm)

• Hot Regions Expand; Cold Contract

• Beam Intensity Averages Over Mirror Surface

• Imperfect Averaging = Thermoelastic Noise

Gaussian Beam

Slide from a talk prepared by Pavlin Savov for PCGM

April 24 2004 GR fun @ Cornell 12

What is Thermoelastic Noise and How to Reduce It?

• Random Thermal Fluctuations (~0.5 mm)

• Hot Regions Expand; Cold Contract

• Beam Intensity Averages Over Mirror Surface

• Imperfect Averaging = Thermoelastic Noise

Mesa Beam

Slide from a talk prepared by Pavlin Savov for PCGM

April 24 2004 GR fun @ Cornell 13

Building a MESA beam

Minimal Gaussian

April 24 2004 GR fun @ Cornell 14

Building a MESA beam

Minimal Gaussian

April 24 2004 GR fun @ Cornell 15

Building a MESA beam

Minimal Gaussian

€

e−x 2+ i (z+ corrrections)

April 24 2004 GR fun @ Cornell 16

Building a MESA beam

Minimal Gaussians

April 24 2004 GR fun @ Cornell 17

Building a MESA beam

Mesa

April 24 2004 GR fun @ Cornell 18

Flat and Concentric Configurations

(O’Shaugnessy, Thorne) (Bondarescu, Kazarian,Savov)

April 24 2004 GR fun @ Cornell 19

Flat and Concentric Configurations

(O’Shaugnessy, Thorne) (Bondarescu, Kazarian,Savov)

April 24 2004 GR fun @ Cornell 20

My proposal

MirrorOverlap minimal

Gaussians centered on these lines

April 24 2004 GR fun @ Cornell 21

What’s different?

Surfaces of constant phase

Mimimal Gausian’s axis

April 24 2004 GR fun @ Cornell 22

What’s different?

Flat Mirrors Confocal Mirros

D

April 24 2004 GR fun @ Cornell 23

Mesa Beams Comparison

April 24 2004 GR fun @ Cornell 24

Mexican-Hat Mirrors’ Corrections

April 24 2004 GR fun @ Cornell 25

Tilt Instability

• Reduce Thermoelastic Noise

• Evaluate Tilt Instability for New Mirrors’ Shapes

• Compare to Conventional Spherical Mirrors

Fabry-Perot Cavity

April 24 2004 GR fun @ Cornell 26

The Eigenvalue Problem

ψψλ GTGGe LL

ikL

2/222/=

April 24 2004 GR fun @ Cornell 27

Mesa Beam Profiles

April 24 2004 GR fun @ Cornell 28

Flat-Concentric MB Comparison

λλ *)1( f

m

c −=

Eigenstates Comparison Eigenvalues Comparison

April 24 2004 GR fun @ Cornell 29

Again Flat-Concentric Configurations Relation

)(

)1(

*

*1

))*(1)((

)1)((

fc

f

m

c

rgr

gr

F

U

U

ee

ψ

η

ψλψ

ψλλ

α

α

=

−=

Φ=Φ

=

+

−−

−−

(Yanbei Chen)

G=1-L/R

April 24 2004 GR fun @ Cornell 30

Results and Conclusions

• Thermoelastic Noise (O,Shaughnessy, Strigin, Vyatchanin)

• Tilt Instability (Mode Mixing)

• Nearly Flat Concentric Duality (in Progress)

34.0/ =SS G

h

MH

h

29.5/ =TT GMH