Download G020062-00 - DCC

Thermal noise in sapphire - summary and plans
Work carried out at:
Stanford University
University of Glasgow
Caltech
MIT
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Timescales
• Core optics
– Design Requirements Review
– Sapphire silica downselect/Preliminary Design Review
• R & D areas
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Sapphire absorption ( thermal compensation )
Coating absorption
Fabrication issues ( size/quality )
Polishing etc
Thermal noise performance
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June 2002
November 2002
Thermal noise performance
In frequency band of interest:
– “Intrinsic” thermal noise
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Intrinsic dissipation
Attachments
Coatings
Polishing
Electrostatic drive
Others???
– Thermo-elastic thermal noise
To intermediate mass
Sapphire
Mass
Fused silica
ribbons or
fibers
• How accurate is our knowledge
of relevant material properties?
– (J. Camp et al - Caltech)
– (R. Lawrence et al - MIT)
• Scaling with beam size as
expected?
– (E. Black et al - Caltech)
~ 40kg
Fused silica
ears
Expect thermoelastic to be dominant provided intrinsic thermal
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noise is low enough
Intrinsic thermal noise
• Estimated using measurements of Q/loss factors of samples of
sapphire made at high frequencies, assume structural damping
• Original measurements (Braginsky/Mitrofanov et al)
– Q’s > 4 x 108 in samples ~ few cm diam. X 10cm long. Various cuts measured.
– Russian sapphire - varying optical quality
• Recent measurements (Rowan et al, Willems)
– Q ~ 2.7 x 108 in sapphire from Crystal Systems Inc.
– “C-axis cut” (ie c-axis = axis of cylindrical sample)
– Commercial polish (Waveprecison Inc., Insaco)
• Spec. for Adv. LIGO: Q = 3 x108
• Provided this is met - thermo-elastic noise is dominant
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Intrinsic dissipation
C - axis sapphire from Crystal Systems Inc, with visible flaw
Q ~ 108 (Willems et al)
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Intrinsic dissipation
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Stanford/Glasgow : c-axis / m-axis companion sapphire pieces
Both = 12.7cm diameter 5.4cm thick
Nominally Hemex (central 7cm dia.), CSI white grade
Polished by same vendors to same specifications
• Q/loss measurements so far - work in progress
– m-axis piece ~ 5 x 106 (***PRELIMINARY***)
– Companion c-axis sample to be measured
• Measure Q factors for different pieces (“full-size” a-axis piece
ordered by U. Gla - possibility of Q tests)
• Several smaller m-axis, a-axis pieces (3” by 1”) to be measured
• Other samples - masses for TNI to be measured at Caltech???
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Interpretation of results
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Our thermal noise estimates use measured Q (or f(wo)), assume structural
damping
Following Levin and others:
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Estimation of thermal noise in interferometer requires knowledge of response of test mass to
Gaussian force on front face
Energy dissipation through imaginary part of Young’s modulus of test mass
Sapphire has anisotropic material properties (trigonal)
Stress/strain relations described through the elasticity tensor for the material 6 independent elastic constants
In principle: each elastic constant can have imaginary (dissipative) part
Gaussian pressure on front of test mass exercises some set (or all) of these
elastic constants (different set for different cuts of sapphire)
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Interpretation cont.
• Each mode of a test mass also samples a set of the elastic constants
• Each mode samples the constants differently
• In principle by
– (a) measuring the Q of a number of modes of sapphire samples and
– (b) calculating for each mode how much energy was stored in different types of
deformation
One could then back out loss factors associated with each elastic constant
and use to calculate expected thermal noise.
NB: for this type of analysis to have any validity, measured Q’s have to be
some genuine measure of the internal dissipation of the material.
i.e. not limited by suspension losses or any extrinsic mechanism
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Interpretation cont.
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Instead measure Q of c-axis and m, a cuts
However earlier experiments (see Braginsky/Mitrofanov measurements)
expect Q’s of ~ 108 in each case - suggests detailed reverse engineering
of elastic loss coefficients unlikely to prove helpful.
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Nb: requirement is to be less than thermo-elastic noise
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Needs checked - expts underway - see earlier in presentation
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Attachments
Approach: measure Q (loss factor) of the fundamental resonant mode of a suspended
sample before and after the bonding of a silica attachment to the sample.
Estimate loss associated with the bonding
Fused silica fibers
Fused silica
‘cone’
Sapphire rod
~3cm
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Attachments
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Silica/silica bonds
Silica/sapphire bonds
Fused silica attachment
Bond area = 0.5cm2
Bond area = 0.8cm2
Sapphire mass
M = 0.28kg
Fused silica mass
M = 0.5kg
• estimated loss ~ 3 x 10-8
• estimated loss ~ 3 x 10-8
* Preliminary result
• Expect loss scales linearly with bond volume ( or area if thickness held constant)
• LIGO II:
total area = 2 x (3 x 1) = 6 cm2
Expected loss = 7.5 x 10-8
Expected loss = 3.6 x 10-7
• Effect of loss depends on ratio of energy stored in bond to energy stored in mass
For given bond area expect effect to scale with mass supported: 40kg
Expected loss = 1.3 x 10-9
Expected loss = 2.5 x 10-9
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Spec. for intrinsic loss of
fused silica
– 3 x 10-8
Specification for intrinsic loss of
sapphire (ignoring thermo-elasticity)
– 3 x 10-9
Do not expect excess loss introduced by silicate bonding to be a
significant effect in either LIGO-G020062-00-Z
case
Attachments - in progress
• Experimental plans:
– Repeat above measurements on further sapphire samples
– Large a-axis sample on order (U. Gla) for bonding/suspension tests
• Modeling plans:
– Above analyses are based on effect of bonds on Q
– However, clearly loss from bonds is spatially localized
– Work from variety of places (Levin, Nakagawa, Yamamoto et al) points out
this inhomogeneous loss needs different treatment than for modal model
eg: loss located on circumference may be less important than Q
measurements suggest - but no full analytical treatment available
– Work ongoing (Fejer in prep.) on analytical treatment to allow effects of
spatially inhomogeneous loss on thermal noise of test masses to be
calculated.
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Coatings
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Crystal Systems m-axis sample
Dimensions 7.6cm dia x 3cm thick
Q’s of 5 modes measured - sample
then coated by REO (Ta2O5/SiO2)
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7.6cm
HR @1064nm
AR @ 1064nm
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Q’s re-measured for each mode
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nb: Barrel polish “rippled” and coatings run
over on to large portion of barrel
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Coating loss analysed using methods
similar to talk by Sneddon et al:
m-axis sapphire sample, on loan from
LIGO project, through crossed
polarizers.
Dark spots are small amounts of Al,
S. Rowan, P. Sneddon
used as mirrors
• Phi coating =1x10-4 to 10-3
********Preliminary*******
• Further sapphire samples to be studied
as part of coating mechanical loss
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program
Coatings - in progress
• Use FE methods to calculate energy stored in coating vs substrate
• Need to take into account anisotropy of sapphire
• Suitable modifications to current models underway (D.Crooks)
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Other noise sources?
• Excess loss from electrostatic drive?
• Others ????
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Summary
• Q measurements and modeling studies underway allowing
diagnosis of elastic loss at high frequencies from:
– Intrinsic loss
– Loss from attachments
– Coating loss
• As always we make assumptions about frequency dependence
of damping (typically structural)
• In the end, a direct measure of thermal noise will be necessary
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