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[email protected] meeting, GinGin 16-18 July. 2007
PI for Adv.LIGO
FEM Model:No. nodes 95,278No. elements 92,952Element type:solid45 – substratesolid46 – coatingchamfers, wedge and suspension flats included
PARAMETERS:T_ETM = 5ppmT_ITM = 0.5%T_PRM = 6%Wavelength = 1.064e-06 mArm length = 4000 mMirror radius = 0.17 m (coated 0.168m)Optical mode order –> up to the 13th
Total number of optical modes = 59Optical mode family : LGM Axial mode order = 5Total number of acoustic modes = 2500
(range: 9.42kHz – 165.6KHz)RoC step: 0.2m
[email protected] meeting, GinGin 16-18 July. 2007
HOMsmode (n,0) n=1 n=2 n=3
mode (n,n) n=1 n=2
a b a b
[email protected] meeting, GinGin 16-18 July. 2007
Elastic modes
19287 Hz 19476 Hz 20438 Hz 20514 Hz
28943 Hz 28972 Hz 35118 Hz
[email protected] meeting, GinGin 16-18 July. 2007
PI at 2076 m
1197 modes with R>0 and 20 modes with R>1
[email protected] meeting, GinGin 16-18 July. 2007
Overlapping factor
Optical modes – eigenvectorsElastic modes - FEM
[email protected] meeting, GinGin 16-18 July. 2007
Flat top beam
Δf ± f, step 1 Hz, 345 unstable with Rmax =1032
[email protected] meeting, GinGin 16-18 July. 2007
Gauss beam
Δf ± f, step 1 Hz 172 unstable R=1439
Gaussian beam with diffraction losses corresponding to the flat top beam
Ring damper
[email protected] meeting, GinGin 16-18 July. 2007
Optical coatingStrip
Ring damper
mQR ∝
⎟⎟⎠
⎞⎜⎜⎝
⎛Ω×
Δ+Λ
−Ω×Δ+Λ
= aiaiai
aiaii
ii
ii
mj
jmj
QQMcL
PQR 12
121
1112
121
112 /1/1
4δωδωω
[email protected] meeting, GinGin 16-18 July. 2007
Ring damper
1) thermal analysis
-FEM (coating, substrate and side wall strain energy)- optimal configuration (ring width, thickness and loss
angle)
2) modal analysis
- FEM (coating, substrate and side wall strain energy for acoustic modes)
- acoustic mode damping
dvrrrE
fFTkfS B ∫
⎥⎥⎦
⎤
⎢⎢⎣
⎡
+=
1)()()(4)(
220
r
rr
φφ
π
∫
∫
⎥⎥⎦
⎤
⎢⎢⎣
⎡
+
=
dvrrrE
dvrEQ
n
nn
1)()()(
)(
2 r
rr
r
φφ
Null position
beam
side wall
Minimum Strain Energy
0 thickness (m) 0.130
d
eg36
0
-Gaussian pressure profile -ω = 6e-2 m (1/e2)
lossEE ⋅=Δ ωat Emin Δ Emin TNmin
The front face edge has smaller energy concentration than the back face of the test mass
PI meeting, GinGin 16-18 July. 2007
[email protected] meeting, GinGin 16-18 July. 2007
Ring damper
constVring =⋅φ
~ 20 mm (Gaussian,1ppm )~ 10 mm (Messa,1ppm)
21 −= erφ
For the ring at the null position:
[email protected] meeting, GinGin 16-18 July. 2007
Ring damper- FEM model
-part of substrate- the same elastic properties as substrate
solid45
[email protected] meeting, GinGin 16-18 July. 2007
Null position
Secondary minima due to the thickness of the test mass
[email protected] meeting, GinGin 16-18 July. 2007
Thermal noise results
Brownian Noise at 100Hz with RoC = 2076 m (FEM result ): m/√Hz
ITM ETMCoating 5.7031e-21 8.5523e-021Substrate 7.8192e-22 7.8196e-22
Total IFO 1.4621e-20
[email protected] meeting, GinGin 16-18 July. 2007
Ring damper configuration
loss angle, strip width – variables, thickness assumed to be 20μm
[email protected] meeting, GinGin 16-18 July. 2007
Ring damper -models
widths thickness loss angle ΔTN
A 3.0 cm 20μm 1.0e-4 0.1% B 10.0 cm 20μm 1.0e-4 0.5%C 3.0 cm 10μm 1.0e-3 0.5%D 5.0 cm 10μm 1.0e-3 1.0%E 3.0 cm 20μm 1.0e-3 2.0%F 3.0 cm 20μm 5.5e-3 5.0%
[email protected] meeting, GinGin 16-18 July. 2007
Mode suppression
77.012106.7 fsub ⋅⋅= −φ fSiO ⋅⋅+= −− 94 101.1102
φfOTa ⋅⋅+⋅= −− 94 108.1108.3
52φ
Substrate Coating
