A new family of flat-topped beams
interesting for future
LIGO interferometers
Mihai Bondarescu
California Institute of Technology
April 24 2004
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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
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April 24 2004
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International Network of Interferometric Detectors
• Network
Required for:
» Detection
Confidence
» Waveform
Extraction
» Direction by
Triangulation
TAMA300
Tokyo
LIGO
Hanford, WA
LIGO
Livingston, LA
April 24 2004
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GEO600
Hanover Germany
VIRGO
Pisa, Italy
4
Slide adapted from a talk by Kip
LIGO
Collaboration of ~350 scientists at ~30 institutions
Hanford Washington
4 km
April 24 2004
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2 km
5
Slide adapted from a talk by Kip
Livingston,
Louisiana
4 km
April 24 2004
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Slide adapted from a talk by Kip
LIGO’s International Partners
GEO600, Hanover Germany [UK,
Germany]
VIRGO: Pisa, Italy [Italy/France]
AIGO, Jin-Jin West Australia
April 24 2004
TAMA300, Tokyo [Japan]
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Slide adapted from a talk by Kip
How a LIGO Interferometer Works
Fabry-Perot
Cavity
Beam
Splitter
April 24 2004
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Fabry-Perot
Cavity
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Slide adapted from a talk by Kip
April 24 2004
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Slide adapted from Rejean J Dupuis talk
from
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http://www.ligo.org/results/
Noise in LIGO
Adopted from Kip’s Talk
(LIGO-G030137-00-Z)
April 24 2004
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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
April 24 2004
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Slide from a talk prepared by Pavlin Savov for PCGM
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
April 24 2004
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Mesa Beam
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Slide from a talk prepared by Pavlin Savov for PCGM
Building a MESA beam
Minimal Gaussian
April 24 2004
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Building a MESA beam
Minimal Gaussian
April 24 2004
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Building a MESA beam
Minimal Gaussian
2
e
April 24 2004
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x  i ( z corrrections )
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Building a MESA beam
Minimal Gaussians
April 24 2004
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Building a MESA beam
Mesa
April 24 2004
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Flat and Concentric Configurations
(O’Shaugnessy, Thorne)
April 24 2004
(Bondarescu, Kazarian,Savov)
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Flat and Concentric Configurations
(O’Shaugnessy, Thorne)
April 24 2004
(Bondarescu, Kazarian,Savov)
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My proposal
Mirror
April 24 2004
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Overlap
minimal
Gaussians
centered on
these lines
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Mimimal Gausian’s axis
What’s different?
Surfaces of
constant phase
April 24 2004
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What’s different?
D
Flat Mirrors
April 24 2004
Confocal Mirros
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Mesa Beams Comparison
April 24 2004
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Mexican-Hat Mirrors’ Corrections
April 24 2004
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Tilt Instability
• Reduce Thermoelastic
Noise
• Evaluate Tilt Instability
for New Mirrors’
Shapes
• Compare to
Conventional
Spherical Mirrors
April 24 2004
Fabry-Perot Cavity
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The Eigenvalue Problem
ikL
 e   G L / 2 G 2T
April 24 2004
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G
L/2

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Mesa Beam Profiles
April 24 2004
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Flat-Concentric MB Comparison
Eigenstates Comparison
Eigenvalues Comparison

April 24 2004
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c

(  1) 
m
28
*
f
Again Flat-Concentric
Configurations Relation
 
  ( r )( 1  g )


e

e
U
( r )( 1  g *( r ))
U
G=1-L/R


c
 (  1)
m 1

*
f
 F ( f )
*
c
(Yanbei Chen)
April 24 2004
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Results and Conclusions
• Thermoelastic Noise
(O,Shaughnessy, Strigin, Vyatchanin)
S
• Tilt Instability
T
(Mode Mixing)
MH
h
MH
G
/ S h  0 . 34
/T
G
 5 . 29
• Nearly Flat Concentric
Duality (in Progress)
April 24 2004
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Inspiral Group Report: S1 Preliminary Report