Measurement of Electrostatic Dissipation on GRS for …beckmann/Talks/Wednesday_parallel/Ninth... · 9 th LISA Symposium, Jun. 21~25, 2012, Paris Measurement of Electrostatic Dissipation

Measurement of Electrostatic Dissipation on GRS for LISA / LPF

F. Antonucci, A. Cavalleri, R. Dolesi, M. Hueller, D. Nicolodi, H. B. Tu, S. Vitale, and W. J. Weber

University of Trento and INFN, Italy

1

Istituto NazionaleDi Fisica Nucleare

9thLISA

Sym

posium

, Jun

. 21~25

, 201

2, Paris

Measurement of Electrostatic Dissipation on GRS Istituto NazionaleDi Fisica Nucleare

/20Hai‐Bo Tu

Content

1. Electrostatic dissipation noise on GRS

2. New measurement challenge with two

techniques

3. Discussion and implication to LISA

2

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1.1 Electrostatic dissipation‐related noise

n vVdCF δ−=

• Two sources to produce electrostatic dissipation: [1, 2]

• Dissipation contributes potential fluctuation Vn :

CTkv B ω

δ4n =

• LISA requires δ < 10‐5 [3]

[1] L. Carbone et al, CQG 22 (2005) S509[2] F. Antonucci et al, 9th Amaldi conference, UK, 10~15/07/2011[3] R. T. Stebbins et al, CQG 21 (2004) S653

vn

δV

3

ωτδ =Ohm

freqlow at dangerous more :ESδ

( ) ⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛×

−

− e 01 Hz10

10 Hz/m/s 103~ 7

2/142/1

5215-2/1 M

aQ

ffS δ

(1) ohmic delay τ arising from sensor circuitry (for instance due to the LPFilter effect)

(2) freq‐independent electrostatic loss arising from conductor surface

mixing with TM potential δV to produce force noise on TM

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1.2 Dissipation model

Actuation / Sensing Circuitry(ohmic losses δohm)

Intrinsic surface losses(model for freq‐ind δΕS) *

Ideal test mass (electrode capacitance C)

( )( ) dC

CCC

MINMAXe

eES

1)ln(2Re

Im∝≈≡

Δ ττπδ

( ) 11221 CRCRR ++≈τ

ωτδ =Ohm

* S. Vitale and C. C. Speake, Proc 2nd Int. LISA Symp., AIP Conf. Proc. 456 (1998)* C. C. Speake, et al, Physics Letters A 263 (1999)

( ) ( )( )

[ ]MAXMINMAXMINMAX

MIN

MAXMINMAX

MINMAX

iC

CCi

iCi

Z

τωτωτπττ

πω

ωτωτωτωτ

ττωδ

<<<<⎟⎠⎞

⎜⎝⎛ +⎥

⎦

⎤⎢⎣

⎡≈

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎦

⎤⎢⎣

⎡

++

+−=

−

Δ

−−

Δ

1

2

211

ln2)ln(2

1

11ln

21tantan

)ln(1

4

MAXiMIN CR τττ <<=<< Δ

δωω ZCiCi e+= 11

21d

Fele ∝

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1.3 Recent measurements on electrode noise (2012)

5

vn

δV⎟⎟⎠

⎞⎜⎜⎝

⎛×⎟⎟

⎠

⎞⎜⎜⎝

⎛×≈

∂∂

= ΔΔ 1/2

2/1

71/22/12/1

V/Hz 100 10fN/Hz 3.1

μx

x

Se

qS

xC

Cq

ST

F

• In general, noisy electrostatic potentials mix with DC voltage differences –such as that caused by TM charging – to create force noise

• Recent experimental upper limit on Dx of 80 mV / Hz1/2 at 1 mHz *

marginally OK for LISA

• δ = 10‐5 would give 20 mV / Hz1/2 at 0.1 mHz

* F. Antonucci et al, PRL 108 181101 (2012)* R. Dolesi, talk on 9th LISA Symp., Paris, 2012

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1.4 Previous measurements on surface loss (2005)

Tech: directly measure transient force due to dissipation by square wave modulation [1, 2]

[1] L. Carbone, PHD thesis, 2005[2] L. Carbone et al, CQG 22 (2005) S509–S519

6

• Results: For 1W2E pair, δ = ( ‐0.3±1.0)*10‐7For 2W1E pair, δ = (10.6±0.6)*10‐7

•Motivation of next step: investigate dielectric loss for LPF

GRS flight model with higher precision

2E

1E

2W

1W

Square mod and Comp voltages

Transient force and loss extraction

‐Vcom

Vcom

Object: A GRS prototype, Au‐coated Mo electrodes, 2 mm capacitive gap

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0 2 4 6 8 10-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

time

ampl

itude

0 1 2 3 4 5 6 7

2

4

6

8

10

12

x 10-8

1/τ

(1/s

)

-ΓES (nN m / rad)

3 free parameter (δ F,δ ES,τv-1)

2 free parameter (δ F = 0,δ ES,τv-1)

2 free parameter (δ F,δ ES=0,τv-1)

2 free parameter (δ F,δ ES,τv-1 measured)

VBIASX

VBIASXY

VBIASno-inj

2.1 Measurement with ringdown tech (2010~2012)

Tech1: measure pendulum amplitude decay as a function of electrode voltages

( )( )ESESFF

ESFvexp

111 δδττ

⋅Γ−⋅Γ⋅Γ+Γ

+=I

Viscousdamping

fiber damping

Electrostaticdamping

Fit condition

δES

(10−7)δF

(10−7 )1/τv

(10−8 /s)χ2 Remark

3 free parameters

7.6(7.5)

-4(12)

1.1(1.6)

1.2 (20 DOF)

Physical

Assuming 1/τv only from gas

4.5(1.3)

8.7(.4) 0.43 1.2

(21 DOF)Physical

AssumingδES =0

-- 16(.03)

-.5(.3)

1.2(21 DOF)

Not physical

7

Result: upper limit of δES 1.5*10−6.

Object: A LPF flight model, Au‐coated electrodes, 4 mm capacitive gap along x

C4

C3

C2

C1

Bias DC voltages

Decay time extraction

V1

V2

V3

V4

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2COMVCNDC ϕ∂

∂≡

( )∑=oddj

MM

MOD tjVV

,

sin4 ωπ

* L. Carbone et al, 6th Amaldi, Japan, 2005

Tech2: Use perfect Square Wave modulation (ideally gives constant torque proportional to V2), delays due to lossy elements cause force transients proportional to delta at every square wave transition *

8

2.2 Measurement with modulation tech (2011~2012)

C4

C3

C2

C1

Square mod and Com voltages

Circuit and surface losses (τ & δES)

‐Vcom

Vcom

Ideal SW to one diagonal pair

Compensation voltages to the other pair

• +/- Vcom and out of phase square wave applied to diagonal pairs, to avoid the change of TM potential• enable to measure circuit loss and surface loss τ & δES together• Huge DC torque (~10-10 N m) cancelled, small transient torque left (~10-17 N m ↔ δES~10-7) for losses extraction

Huge DC torque cancelled Small transient torque left

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2.3 Illustration of measured signalElectrode voltage:

No losses

Ohmic delay

Frequency independent δ

Resulting torque (∝V2):

• 2f signal (+ other even harmonics)• Nearly “Dirac δ-function” for ohmic delay (all cosine)• Longer lived signal for frequency independent δΕS (both sine and cosine)

( )( ) ( ) ( )ttf

jjjj

NN

MMjDC

f ωπ

δωτππ

δ 2sin 41 2cos 8 2

2ln24 2

ESModd ,

2

ES2

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛⋅+

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛+

+⎟⎠⎞

⎜⎝⎛⋅≈

−∑

≈0.681 =1( )

( ) ( ) ( )ttfjj

jjNN

MMjDC

f ωπ

δωτππ

δ 4sin 432 4cos 8

33ln

44ln24 2

ESModd ,

2

ES4

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛⋅+

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛−

++

⎟⎠⎞

⎜⎝⎛⋅≈

−∑

≈0.574 ≈0.67

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2.4 Sensitivity requirements

10

For resolution δES= 10-7

with VM = 8 V need 2f torque resolution 0.02 fNmNoise of current TP ~ 1 fNm/Hz1/2 @ 1mHz10000 s statistical resolution 0.01 fNm @ 1mHz

External torque noise of TP with fused silica fiber

10-3 10-2

10-1

100

101

S N1/2 (f

N m

/ H

z1/2 )

Frequency (Hz)

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2.5 Experimental noises and suppression

11

Challenges and solutions:• Actuation filter gives 400 μs ohmic delay (δ 10-5 at 3 mHz)

Short filter (and also 100 kHz injection, readout transformer circuitry, also responsible for 2f force transients)

• Large DC bias torque signals at odd harmonics (non-linear coupling into 2f/4f/6f signal)

Correct mod electrode potential difference to < 1 bit resolution+/- 150 μV still gives 3 fNm signal

Compensation of mean electrode potential to null translation dependence• AC detector non-linearities, semi-periodic jumps of up to 100 nrad (1 fN m)

Calibrate and correct in data pre-processing• Modulation of electrostatic stiffness at 1f mixes with DC bias signals to give 2f signal

Measure period difference, correct stiffness in time domain torque extraction

• Vm modulates VTM when off-centred, fake delta signal due to switch of VTM (∆x = 50 um ↔ δ = 3e-8)

Calibrate and correct in data post-processing

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2.6 Experimental transient torque

• Tests for both pairs: fM = 1.25 mHz, VM = 8 V, integral time > 80 h;

• Get the averaged transient torque and compare with theoretical prediction ;

• The signal form is as expected for model!

(model works well, δES ~3e‐7)

0 500 1000 1500-0.6

-0.4

-0.2

0

0.2

0.4

0.6

time (s)

torq

ue (f

Nm

)

averaged residual torque (1N/2S pair, 200 modulation cyc)

averaged torqueafter LPFilter (fcut=10mHz)

VMOD (f=1.25mHz,amp=8V)

theroretical Prediction ( δES=3.48e-7)

TMOD

0 500 1000 1500

-0.2

0

0.2

0.4

0.6

0.8

time (s)

torq

ue (f

Nm

)

averaged residual torque (1S/2N pair, 368 modulation cyc)




TMOD

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2.7 Torque demodulation and δ extraction

4.767 4.768 4.769 4.77 4.771x 107

-0.3

-0.2

-0.1

0

0.1

0.2

dem

od to

rque

(fN

m)

Time (s)

3-Nov-2011, run#289, VMOD

= 8 V on 1N/2S, fMOD

= 0.65 m

2f-cos2f-sin

(1) Several tests at different freq in [0.2 2] mHz,

(2) For each run, demod sin/costorque for 2f/4f/6f

(3) Fit to sin torque of one group to get δES and fit to cos torque to get both δES and τ

Data Process:

Result: δES and τ from different harmonics consistent in 2σ

…

2f-cos 2f-sin 4f-cos 4f-sin 6f-cos 6f-sin one-fit0

1

2

3

4

5 x 10-7

δ ES

1N2S: group101

2f-cos 4f-cos 6f-cos one-fit-2

-1

0

1

2

3x 10-5

τ (s

)

1N2S: group101

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dCC

MINMAXES

1)ln(2

∝≈Δ ττ

πδ

2.8 Investigation of dependence of delta on gap

• Purpose for further study:(1) Experimentally study if δES proportional to C, compare with theoretical analysis

→ Rotate housing (or TM) to change capacitance(2) Test δES in different freq to see if δES freq‐ind

→ test at different fMOD as wider as our experimental resolution allows

d1N2S ↓, δ1N2S↑

rotating housing clockwise

For each diagonal pair, test δES at three configurations:

2N

1N

2S

1S

V1S

V2S

V1N

V2N

ϕ

ϕ=0 ϕ=30mrad

d0=4mm∆d≈0.4mm ϕ=‐30 mrad

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Pair τt (μs)* τe (μs)

1N/2S 3.4 ‐1.6(0.7)

2N/1S 3.4 3(1)

2.9 Result of residual τ

* residual ohmic delay from slew rate of mod switch

Result:• residual τ consistent with theoretical expectation in few σ;• δES is freq‐independent in freq range tested• for 1N2S, there still some systematic error

For each pair, fit all data from all three configurations:

⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ⎟⎠⎞

⎜⎝⎛×≈Δ −

μs .43mHz 1102 M8 τδ f

0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

δ ES *

106

fMOD (mHz)

1N2S: group101

τ = 3.3 μs

0.2 0.4 0.6 0.8 1 1.2 1.40

0.1

0.2

0.3

0.4

0.5

0.6

δ ES *

106

fMOD (mHz)

2N1S: group121

τ = -0.8 μs

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0 0.2 0.4 0.6 0.8 1 1.2 1.40

1

2

3

4

capacitance (pF)

freq

-ind

δ ES *

107

2N/1S

slope = 2.52(0.04)e-7 /pFchi2 = 3.4 (2 DOF)

0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.5

1

1.5

2

2.5

3

3.5

capacitance (pF)

freq

-ind

δ ES *

107

1N/2S

slope = 2.44(0.03)e-7 /pFchi2 = 1.1 (2 DOF)

2.10 Result of δES (Xn = 20μm)

1N/2S (69 runs) smaller gap centered Larger gap

δES (1.e‐7) 3.18(0.05) 2.83(0.07) 2.67(0.07)

Chi^2 1.3 (408 DOF)

2N/1S (46 runs) smaller gap centered Larger gap

δES (1.e‐7) 3.49(0.12) 2.95(0.07) 2.68(0.09)

Chi^2 1.1 (270 DOF)

16

(1) Feature proportional‐to‐C verified experimentally, tests in a relative wider capacitance range may be also interesting;

(2) δES from two pairs sensitive in our facility seem uniform!

* After taking into account the translation readout uncertainty 20 μm

1S

2N2S

1N

δ ∝ C

δ ∝ C

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3.1 Discussion: possible sources of δES

Position When TM is centered

2N/1S46 runs

(before venting)8 runs

(after venting)

δES (1.e‐7) 2.95(0.07) 3.16(0.09)

τe (μs) 3(1) ‐8(3)

Chi^2 1.1 (270 DOF) 1.3 (46 DOF)

17

Result:

(1) Tests are basically reproducible, δES before/after venting consistent in 2σ (difference only 5%)

(2) δES should not arise from the surface layers condense quickly from lab atmosphere

* Before venting: GRS kept staying in 3 10‐6 Pa for more than two years* Venting: venting chamber to lab atmosphere for three days by a φ2.5 cm tube of length ~ 30 cm (to absorb dielectric)* After venting: pump chamber to pressure lower than 10‐5 Pa

0.8 1 1.22

2.5

3

3.5

4

capacitance (pF)

freq

-ind

δ ES

2N/1S

Before ventingfit to δ = k*CAfter venting

*10-7

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d

t( )εδεε jrr −= 10�

( )

( )dtdt

tttd

r

r

<<⋅≈

⋅+−

=

ES

εδε

δδ

ε

ε

δES = 2.9e-7, d = 4 mmεr ~ 8, δε ~ 0.01, t ~ 1 μm

0

50

100

0

0.005

0.0110-2

100

102

εr

δES=2.9e-7

δε

thic

knes

s ( μ

m)

Materials * εr δε(10‐4) t (μm)

Fused quartz 3.8 10 (@50Hz) 4.4

Alumina 8.5 20 (@50Hz) 4.9

Air 1 100? 0.12

*http://www.kayelaby.npl.co.uk/general_physics/2_6/2_6_5.html

Assuming some dielectric materials absorbed by conductor surface:

Unlikely that a surface absorbate could be so thick! Need more study …

3.1 Discussion: possible sources of δES

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3.2 Summary

(1) 1N2S pair: δES = (2.83±0.07)×10‐7

2N1S pair: δES = (2.95±0.07)×10‐7

Loss angle from delay: δohm < 2.5×10-8 (at 1 mHz)

For LISA, force noise due to the loss lower than 0.1 fm/s2/Hz1/2 near 1mHz

(2) Torque wave form due to the losses obeys model very well

(3) The tests varying gap: δ ∝ C (match model well)

(4) δ is freq‐independent in freq range tested (match model well)

(5) δ unchanged by venting to air for three days

(6) What causes δ? Need more study …

19

0 500 1000 1500-0.6

-0.4

-0.2

0

0.2

0.4

0.6

time (s)

δ co

ntrib

utio

n to

rque

(fN

m)

averaged residual torque (1N/2S electrodes,from 200 modulation cyc)




TMOD

20

Thank you!Any questions are welcome!

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980 990 1000 1010 1020 1030

-0.1

-0.05

0

0.05

0.1

absolute φ (μrad)

resi

dual

φ ( μ

rad)

Residual err comparison for all runs

run #13 start file #3906run #19 start file #4038run #20 start file #4152run #21 start file #4176

Shift along xmainly caused byground tilt, can befurther correctedby eta output of AC

2.5 Experimental noises and suppression(1) Current actuation filter gives ohmic delay τ~0.4 ms (δ 10-5 at 3 mHz)

Short filters, reduce ohmic delay to τ~4 μs, torque contribution from 1 fNm to 0.01 fNm (also 100 kHz injection, readout transformer circuitry, also responsible to 2f torque transient)

(2) AC detector non-linearities, semi-periodic jumps of up to 100 nrad (1 fN m)

Calibrate and correct in data pre-processing

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4.61 4.612 4.614 4.616x 107

0.35

0.4

0.45

0.5

0.55

δ V 2N

- δ

V 1S (m

V)

Time (s)

16-Oct-2011, run#264, VMOD = 9.132 V on 2N/1S, fMOD = 0.2 mH

Harmonic 1Harmonic 3Harmonic 5

4.61 4.612 4.614 4.616x 107

1040

1050

1060

1070

1080

1090

1100

time (s)

φ AC

( μra

d)

Residual correction with model #22

3.6575 3.658 3.6585 3.659 3.6595 3.66 3.6605 3.661x 107

669

669.5

670

670.5

671

671.5

672

672.5

673

673.5

time (s)

perio

d (s

)

#9 for group15,VMOD=8V,1N/2S,filter

for first half fitfor second half fitmean of T0rising edgetrailing edge

(3) Large DC bias torque signals at odd harmonics (non-linear coupling into 2f/4f/6f signal)

Carefully compensate stray DC bias of electrodes, minimize variable torque at odd harmonics (Correct mod electrode potential difference to < 1 bit resolution +/- 150 μV still gives 3 fNm signal; Compensation of mean electrode potential to null translation dependence)

( ) ( ) ( ) ( )⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂∂

−+⋅−+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+∂∂

−⋅≈0

2

2100

2

2

021 2)(

xCVVVxxCCVVtsqrVtN TMSNSNM ϕ

δδϕ

ϕϕ

δδωω

22

(4) Modulation of electrostatic stiffness at 1f (ΔΓ ~ 2e-11 Nm/rad) mixes with DC bias signals to give 2f signal

Measure period difference, correct stiffness in time domain torque extraction


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• TM translation has another effect: TM potential fluctuation VTM caused by VMOD. The imperfect switch of VTM on transient moment also produces loss mixing with δES.

( ) ( )[ ] 2VT0T0MM

2

VT0 2 xtsqVtsqVxx

CN Δ∝⋅⋅−Δ⋅∂∂

∂= ωω

ϕ

( )tsqxdVV M

0

MT0

4 ω⋅Δ⋅=

-1000 -500 0 500-10

0

10

20

30

η (μrad)

δ sin *

107

δsin Vs. eta

2f4f6f

-1000 -500 0 500-10

0

10

20

30

40

η (μrad)δ co

s * 10

7

δcos Vs. eta

2f4f6f

C4

C3

C2

C1

‐Vcom

Vcom

Δx VT0

→ calibrate tilt-charge effect, correct in data post-processing. (Near centred position: x=50um ↔ 10%δ)


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Summary and discussion

Sources damping Q

Residual gas viscous

(fixed)

dβ/dp = 5.6e‐8 Nm/s

(at p = 3.3e‐6 Pa)3,100,000

Dielectric loss

(fixed)δf = 2.9e‐7 26,700,000

Fiber structural loss δES = 9.0(0.3)e‐7 1,020,000 *

Totally 750,000

Dissipations of 1TM torsion pendulum associated with GRS flight model surrounding (suspending by fused silica fiber, Vinj = 3.5 V)

* The rest damping could also come from other sources like magnetic field

(1) The study focus on the dielectric dissipation of GRS flight model(2) Ringdown tech and square‐wave mod tech employed. Final result of δES is 2.9e‐7, with uncertainty lower than 10%, for all electrodes tested. The value implies its contributed noise for LISA is lower than 0.1 fm/s2/Hz1/2. (3) Features proportional‐to‐C and freq‐ind are experimentally tested, and match model very well(4) Dielectric dissipation on the electrodes studied seem have a good uniformity(5) The physical sources and distributions on electrodes of δESneed more study

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/20Hai‐Bo Tu

3.2 Example of δES and τ extraction

Fitting to all tests from one group to get τ & δES (2N/1S pair, large gap)

Demod even torques for each test (2N/1S pair, large gap, fM = 0.35 mHz)

25

4.525 4.526 4.527 4.528 4.529x 107

-0.2

0

0.2

0.4

0.6

dem

od to

rque

(fN

m)

Time (s)

06-Oct-2011, run#246, VMOD = 7 V on 2N/1S, fMOD = 0.5 mHz

2f-cos2f-sin

4.525 4.526 4.527 4.528 4.529x 107

-0.1

0

0.1

0.2

0.3

dem

od to

rque

(fN

m)

Time (s)


4f-cos4f-sin

4.525 4.526 4.527 4.528 4.529x 107

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

dem

od to

rque

(fN

m)

Time (s)


6f-cos6f-sin

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0.4

0.5

0.6

0.7

0.8

0.9

1

-N2f

-sin

/ N

DC *

106

fMOD (mHz)

torque-demod-analysis

1S / 2N, 7V-Mea. group2031S / 2N, 7V-Fit. group203

0.2 0.4 0.6 0.8 1 1.2 1.4 1.60.2

0.3

0.4

0.5

0.6

0.7

0.8

-N2f

-cos

/ N

DC

* 10

6

fMOD (mHz)

torque-demod-analysis

1S / 2N, 7V-Mea. group2031S / 2N, 7V-Fit. group203

from cos torque: δES & τfrom sin torque: only δESdo the same analysis to

2f/4f/6f torque

9thLISA

Sym

posium

, Jun

. 21~25

, 201

2, Paris


/20Hai‐Bo Tu

3.3 Example of preliminary result: 2N1S pair

C Gap Smaller gap(group203: 6 runs)

Centered (group121: 7 runs)

Larger gap(group191: 8 runs)

2f cosine δES = 3.50(0.71)e‐7τ = 4.2(9.5) μschi^2 = 2.0 (4 DOF)

δES = 3.05(0.36)e‐7τ = ‐2.1(5.3)μschi^2 = 1.0 (5 DOF)

δES = 1.84(0.33)e‐7τ = 18.6(5.0)μschi^2 = 2.1(6 DOF)

2f sine δES = 3.6.(0.17)e‐7chi^2 = 0.5(5 DOF)

δES = 3.14(0.12)e‐7chi^2 = 0.5 (6 DOF)

δES = 2.55 (0.13)e‐7chi^2 = 0.9 (7 DOF)

4f cosine δES = 2.73(0.77)e‐7τ = 13.7(8.7)μschi^2 = 0.8 (4 DOF)

δES = 1.50(0.70)e‐7τ = 16.3(7.1)μschi^2 = 0.2 (5 DOF)

δES = 2.15(0.67)e‐7τ = 12.5(6.6) μschi^2 = 1.2 (6 DOF)

4f sine δES = 3.19(0.24)e‐7chi^2 = 0.5 (5 DOF)

δES = 3.05(0.17)e‐7chi^2 = 1.3(6 DOF)

δES = 2.78(0.17)e‐7chi^2 = 1.4(7 DOF)

6f cosine δES = 3.82(1.49)e‐7τ = ‐8.9(13.8)μschi^2 = 1.4 (4 DOF)

δES = 3.68(1.2)e‐7τ = ‐2.0(11.0)μschi^2 = 1.0 (5 DOF)

δES = 2.14(0.92)e‐7τ = 1.0(8.8) μschi^2 = 2.9 (6 DOF)

6f sine δES = 3.56(0.29)e‐7chi^2 = 1.85 (5 DOF)

δES = 3.34(0.25)e‐7chi^2 = 0.7 (6 DOF)

δES = 2.64(0.22)e‐7chi^2 = 1.1(7 DOF)

One‐fit δES = 3.49(0.12)e‐7τ = 3.1(2.6)μschi^2 = 1.1 (34 DOF)

δES = 3.10(0.09)e‐7τ = ‐0.8(2.0)μschi^2 = 1.1 (40 DOF)

δES = 2.58(0.09)e‐7τ = 6.7(1.9)μschi^2 = 1.6 (46 DOF)

26

(1) δES from 2f/4f/6f components consistent in 2σ(2) τ from 2f/4f/6f components consistent in 2σ and close to zero, as expected(3) these features also found on 1N2S pair (the other sensitive diagonal pair)

1S

2N

1S2N

1S2N

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Measurement of Electrostatic Dissipation on GRS for …beckmann/Talks/Wednesday_parallel/Ninth... · 9 th LISA Symposium, Jun. 21~25, 2012, Paris Measurement of Electrostatic Dissipation