Progress of Surface potential measurement using a torsion pendulum

Hang Yincge.yinhang1985@gmail.com

Center for gravitational experiments, Department of PhysicsHuazhong University of Science and Technology, Wuhan, China

LISA Symposium X, 22th May 2014

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Content

1. Introduction

2. Modeling and error analyze

3. Experimental apparatus

4. Measurements• Static mode• Scan mode

5. Summarize

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1.Introduction

The metal is widely used for making test mass in precision measurements.

In the idealized case, the isolated conductor is an equipotential body with the same potential over its surface.

In fact, impurities and microcrystal structure will lead to a nonuniform dipole layer formed on the metal surface. When two metallic surface at finite distance, the force or torque on each of them will produce.

The temporal and spatial variations in surface potential is one of the largest contributors of noise in precision measurements, such as LISA, GP-B, Test of Newtonian Gravitational Square Law and so on.

Investigate the surface potential on test mass carefully is significant.

GP-B

Sensitive axis

Direct effectShear effect

TM

ISL

LISA

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Kelvin probe measurements [1]

[1].N.A.Robertson, J.R.Blackwood, S.Buchman, and R.L,Byer et al, Kelving probe measurements: investigations of the patch effect with applications to ST-7 and LISA, Class. Quantum Grav. 23(2006)2665-2680

1.Introduction

• Kelvin probe is an efficacious way to measure thedistribution of surface potential. It is a non-contact,non-destructive vibrating capacitor device measurespotential difference between a conducting specimenand a vibrating probe tip.

• Kelvin probe measurements is a null measurementtechnique. The potential Vb electrically connects thesample and tip. The surface potential will be found byrecording the output signal as a function of Vb andfitting the data to find the value of Vb where thesignal passes through zero.

•Its sensitivity could achieved 1mV/Hz1/2.

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Measure surface potential by torsion balance [2]

Electrostatic torque

30μV/Hz1/2Resolution

[2]. S.E.Pollack, S.Schlamminger, and J.H.Gundlach, Temporal extent of surface potentials between closely spaced metals, Phys,Rev,Lett. 101(2008)071101

1.Introduction

• The torsion balance is widely used for measuringall kinds of weak force, because of its highsensitivity .

• The average surface potential and its temporalvariations has been measured by University ofWashington base on torsion balance.

• Their result shows that this scheme couldmeasure the value of potential accurately.

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2.Modeling and error analyze

p p 2PE s TM

p

1 ( )2C l

V Vd

Electrostatic torque

Goal:10µV/Hz1/2

pmeasure,min s TM p TM,min

p

14 1/27.1 10) Nm /( HzCV V l V

d

• A scheme has been proposed for measuringdistribution of surface potential base onelectrostatic controlled torsion balance.

• The apparatus consists of a source conductor(5mm×5mm×5mm),pendulum(100mm×40mm×8mm), gravitational compensator, two pair ofelectrodes and a series of translational stages.

•The source conductor with voltage Vs could bemoved relative to surface of pendulum. The voltageof feedback Vf will reflect the value of electrostatictorque between source conductor and sample in theappropriate regions.

2. Design and Error analysisMajor factors effecting the resolution: • Thermal noise of fiber.• Resolution of capacitive sensor.• Fluctuation of voltage applied to pendulum, electrodes and source conductor(SC).

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Thermal noise

Voltage of feedback Vf,nVb,n

Voltage applied to SC

Capacitive sensor

TotalRequirement

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3.Experimental apparatus

Apparatus is made up of a source conductor, pendulum, gravitational compensator,

electrodes, magnetic damping, translational stages and other fixtures.

Pendulum

Translational stage

Electrodes

Source conductor

Gravitational compensator

Positioning device

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3.Experimental apparatus

Thermal noise of free pendulum Resolution of capacitive sensor:6 ×10-7pF/Hz1/2

Noise of electrostatic actuator Torque sensitivity of apparatus is able to achieve our goal

14 1/27 10 Nm / Hz

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Measurement of surface potential with static mode

1.DC voltage VDC applied tos source conductor

2.Record the torque of feedback with different VDC.

3. The surface potential will be found by fitting the data to find the value of VDC,

where the signal equals to extremum.

p 2PE DC TM

1 ( )2CV V

4. Measurements: Static mode

DC 0.05VV

TM 1.6904 0.0018 VV Surface potential

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A measurement of surface potential fluctuations. The spectrum is white at 15μV/Hz1/2 for frequencies above 0.03Hz.

p measure

TMp DC TM p

dV

C V V l

p 2

feedback DC TM 01 ( )2CV V

Resolution of measuring surface potential

4. Measurements: Static mode

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4. Measurements: Scan modeSource conductor

Test mass

z

xy

1V 2V 3V 4V………………

iV nV

1

n

i ij i j is i sj

Q C V V C V V

1

n

s is s ii

Q C V V

Total charge on the ith electrode

Total charge on the source conductor

1 2 2

1 1 1 1

1 12 2

n n ne

e ij i j is i si j i

W C V V C V V

The electrostatic torque ij

ij

CC

isis

CC

DC AC sin( )sV V V t

Modulation voltage applied to source conductor

1 2 2 2

_ 0 DC AC1 1 1

1 1 12 2 2

n n n

e ij i j is ii j i

C V V C V V V

_ DC AC1

n

e is iiC V V V

2

_ 2 AC1

14

n

e isiC V

DC

1ω

2ω

_ AC

tm DC_ 24

n

is iei

ne

isi

C V VV V

C

A weighted average over all potentials on sample.

isn

isi

C

C

Weighting factor

The output could express an average potential over local regions which are face to source conductor.

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4. Measurements: Scan mode

1ω2ω

AC 1.0VV DC 1.5VV DC AC sin( )sV V V t

Modulation voltage applied to source conductor

Power spectrum of torque feedback

The amplitude of τe_1ω and τe_2ω will be obtained by fitting. The fitted equation is expressed as follow.

f e e_1 _a e_1 _b e_2 _a e_2 _b 0 1 1( ) ( ) cos( ) sin( ) cos(2 ) sin(2 ) ...... ( )c c c ct t t t t t d d P t

2 2

e_1 e_1 _a e_1 _b 2 2

e_2 e_2 _a e_2 _b

e _ ACtm DC

e _ 24V

V V

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4. Measurements: Scan mode

The variation of surface potential over time(11 days) is less than 0.5mV.

Measuring distribution of surface potential with scan mode

The result shows that our apparatus could obtain the distribution of surface potential and experimental data had good repeatability.

Scanning with different step

The experimental data with different scanning step reflect more details in distribution of surface potential.

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5. Summarize

Design and install our apparatus for measuring, whose resolution

achieves to our goal.

Measuring the value of surface potential with static mode.

The spatial variations in surface potential could be obtained by

apparatus depend on scanning mode.

Researching for elements which may influence the variations in

surface potential is our focus in the next step.

Investigating the charge management base on our apparatus will be

carried out in the future.

Center for gravitational experiments

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The EndThanks for your attention!