pi for adv - university of western · pdf filepi for adv.ligo fem model: no. nodes 95,278 no....

sgras@cyllene.uwa.edu.auPI 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

sgras@cyllene.uwa.edu.auPI 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

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Diffraction losses

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Diffraction losses

TEMb01

TEMa01

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

HOMs

TEM01

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Ring damper

TEM16

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Adv.LIGO HOMs

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Elastic modes

19287 Hz 19476 Hz 20438 Hz 20514 Hz

28943 Hz 28972 Hz 35118 Hz

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

PI at 2076 m

1197 modes with R>0 and 20 modes with R>1

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

PI for Adv.LIGO

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

LCGT

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

LCGT

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

LCGT

Including diffraction losses

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Flat top beam

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Flat top beam losses

L = 4km

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Overlapping factor

Optical modes – eigenvectorsElastic modes - FEM

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Flat top beam

Δf ± f, step 1 Hz, 345 unstable with Rmax =1032

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Flat top beam

sgras@cyllene.uwa.edu.auPI 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

sgras@cyllene.uwa.edu.auPI 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

sgras@cyllene.uwa.edu.auPI 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

sgras@cyllene.uwa.edu.au

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

sgras@cyllene.uwa.edu.auPI 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:

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Ring damper- FEM model

-part of substrate- the same elastic properties as substrate

solid45

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Ring damper- sapphire

assumed isotropy C-axis

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Ring damper- sapphire

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Ring damper- f.silica

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Null position

Secondary minima due to the thickness of the test mass

sgras@cyllene.uwa.edu.auPI 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

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Ring damper configuration

loss angle, strip width – variables, thickness assumed to be 20μm

sgras@cyllene.uwa.edu.auPI 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%

sgras@cyllene.uwa.edu.auPI 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

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

F model

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

PI for Adv.LIGO

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

Mode suppression

sgras@cyllene.uwa.edu.auPI meeting, GinGin 16-18 July. 2007

AIGO 5km Ring damper