april 24 2004gr fun @ cornell1 a new family of flat-topped beams interesting for future ligo...
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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