Ground testing of the LISA Pathfinder Gravitational Reference Sensor by means

of torsion pendulum F.Antonucci1,2,A. Cavalleri1,3,R. De Rosa4,5,L. Di Fiore4,R. Dolesi1,2,F. Garufi4,5,A. Grado4,6,Tu HaiBo1,2,M. Hueller2,L. Milano4,5,

G. Russano1,2, S. Vitale1,2,W. J.Weber1,2 and S. Wen2

1INFN Gruppo Collegato di Trento, Povo (TN), Italy, I-38123, 2 University of Trento, Dipartimento di Fisica, Povo (TN), Italy, I-38123 , 3Istituto di Fotonica e nano tecnologie CNR-FBK, Povo (TN), Italy, 4INFN Sez. Napoli, Via Cintia, Napoli, Italy, I-80126, 5University of Napoli “Federico II” - Dept. of Physical Science, Napoli, Italy, I-80126, 6INAF – OACN, Salita Moiariello 16, Napoli, Italy, I-80131

The GRS is a capacitive sensor used to measure test mass (TM) position and actuate it in 6-degrees-of-freedom. At the moment we are testing the LPF flight

model replica GRS, characterized by 4mm gap between TM and the electrodes.

Test mass

x

y

z

x sensing electrodes

y sensing electrodes

z sensing electrodes

y injection electrodes

z injection electrodes

Testing GRS performances on ground: 4-mass facility

Force acting on the TM produce a torque 𝑁𝑦:

N y =bFx +N y,TM

TEST MASS: gold coated Al with same surface finishing

(at nm level), gold coating procedure and caging features of

flight model.

GRS

STC

MRORO

UV fiber support

FM Heaters and

thermoters

• Low frequency : pendulum resonance frequency of 0.8 mHz, with a

50µm Tungsten fiber .

• Indipendent Optical Redaout: autocollimator, MRORO system..

• Integrated with flight-like UV discharge setup.

• Front end electronics: ELM-Light electronics.

• Vacuum system: typical pressure value ~ 10-4 Pa.

• Temperature sensors

• Bakeout heaters (6→110°C) .

• Magnetometers.

• Stiffness compensator STC: auxiliary capacitive readout.

Temperature gradient induced force The aim is to do a detailed study of a specific class of force noise induced by

temperature gradients. When there is a temperature difference on opposite sides

of the TM sensor surface, a force gradient is induced through three main

mechanisms (PHYSICAL REVIEW D 76, 102003 (2007)):

• Radiometric effect is due to the differential momentum transfer to the TM

surfaces from impacting residual gas molecules. 𝑑𝐹𝑅𝐸𝑑∆𝑇𝑥

≈ 𝐴𝑘𝑅𝐸𝑃04𝑇0

=18𝑝𝑁

𝑘× 𝑘𝑅𝐸

𝑃

105𝑃𝑎

293𝐾

𝑇0

Where A is the area of a TM surface, 𝑘𝑅𝐸 is a radiometric correction factor for

the modification to the simple infinite parallel plates model and the temperature

distribution inside the sensor.

• Thermal radiation pressure is due to the momentum transfer from the

thermal photons emitted from the surfaces.

𝑑𝐹𝑅𝑃𝑑∆𝑇𝑥

≈ 𝑘𝑅𝑃8

3

𝜎𝐴𝑇03

𝑐=27𝑝𝑁

𝑘× 𝑘𝑅𝑃

𝑇0293𝐾

3

Where σ is the Stefan-Boltzaman constant and 𝑘𝑅𝑃 is a correction factor to the

simple infinite parallel plates model.

• Asymmetric out-gassing of the molecules absorbed by the internal walls of

the sensor. An asymmetry, temperature-dependent out-gassing, can result in a

differential pressure. This asymmetric out-gassing also depends on the

amount and type of impurities on the surfaces.

𝑑𝐹𝑂𝐺𝑑∆𝑇𝑥

≈ 𝐴𝑄 𝑇0𝐶𝑒𝑓𝑓

Θ

𝑇2= 4

𝑝𝑁

𝐾

𝑄(𝑇0)

1.4 𝑛𝐽 𝑠

Θ

3 ∙ 104𝐾

293𝐾

𝑇0

2

Where Q is a flow factor and Θ is the activation temperature of the molecular species.

Measurement technique

Four independent heaters (2 flight model heaters on each of the x-surfaces) were

used to apply oscillating temperature gradients along the x-axis of the sensor.

Pressure in the vacuum chamber was varied by changing the turbo pumping

speed.

The slope of the straight-line (dFRE

/dΔTx) vs. pressure is a direct measurement of

the radiometric effect at a certain temperature. Extrapolating the line to zero

pressure gives the pressure-independent, thermal-gradient related force due to the

combination of radiation pressure and differential out-gassing. Also force is

measured as a function of thermal gradient at a fixed pressure to check the

linearity of the behavior.

T

x

MRORO (Multiple Reflection Optical Readout) An optical device based on optical levers. It is an auxiliary sensor for the 4TM facility with the goal of improving the

angular sensitivity. This should in turn improve the performances in term of force measurements, allowing to put better

upper limit to the GRS force noise. Such a device, based on multiple reflections, was designed, developed and tested in

Napoli, with LISA group collaboration, and then integrated in the Trento 4TM facility. Two measurement runs has been

performed: one with the current MRORO TM (Dec 2011) and the other with a lower reflectivity TM surface. The results

confirming the increased sensitivity in acceleration noise. MRORO is better than GRS level above 2 mHz and consistent to

LISA PF requirements above 20 mHz.

𝜙 𝜔 = 𝐻 𝜔 𝑁(𝜔)

dF/dΔx = 𝟕𝟐. 𝟑 ± 𝟎. 𝟓 𝒑𝑵/𝑲

Intercept −𝟎. 𝟏𝟏 ± 𝟎. 𝟎𝟐 𝒑𝑵/𝑲

T0

≈ 293K

Pressure ≈ 𝟏. 𝟒𝟐 ∙ 𝟏𝟎−𝟕𝒎𝒃𝒂𝒓

Brownian Force Noise

To calculate Brownian noise we measured the

torsional damping coefficient in the pressure

range of 10-5-10-3 Pa by direct measurement

of the amplitude decay time 𝜏:

I and N is respectively the torsion pendulum

moment of inertia and torque.

𝛽 = −𝜕𝑁

𝜕Φ=2𝐼

𝜏

TM

Light beam (5 reflections)

L =

2

Fiber collimator

DC motors

QPD

Y

X x translation

)sin(2 ndx

dVQPD

𝑉𝑄𝑃𝐷 Vertical displacement, 𝜑 rotation

𝐻𝑄𝑃𝐷 Horizontal displacement, 𝜂 rotation

)cos()cos(2)cos(

2 2

n

LDLn

d

dVQPD

)cos(2

)cos(2 2

n

LDLn

d

dHQPD

To reduce temperature

fluctuation, the experiment is

conducted inside an insulated

housing whose temperature is

feedback-controlled by a simple

simple PID loop, consist of the

system, thermometers, and

heaters. The long-term (~1 day)

temperature stability at the GRS

is ~20mK.

The experiment conducted at T = 303K and P = 1.67e-6mbar.

Top: applied oscillating temperature gradient of 200mK across the TM

every 500s.

Middle: modulated torsion pendulum signal.

Bottom: derived force.

Knowledge of the concentration of different gas species is needed to more

accurately calculate the pressure in the vacuum chamber. Residual gas analysis

reveals that the dominant gas species are H2, H

2O, N

2, O

2, Ar, CO

2, and their

isotopic compounds. Data shown here corresponds to when the pressure was

2.6e-7 mbar.

Results from experiments conducted at three different temperatures closely

follow the theoretical estimation:

The requirement for LPF is 3x10-4N/K/mbar + 100pN/K at 303K.

dF x

d (ΔTx)≈ 2. 3× 10

− 4 N

K mbar+50

pN

K

T(K) Slope (µN/K/mbar) Slope stat. Error (µN/K/mbar) Intercept(pN/K) Intercept stat. error (pN/K)

289,2 247 2 26 3

295,5 239 3 36 1

304,3 275 4 53 4

𝜑

𝜂

sm±=P

β/100.49.8 36

Gas damping of the motion of a macroscopic test

body is a source of Brownian noise in experiments

that are sensitive to very small forces. For our

pendulum it is characterized by a viscous damping

coefficient dβ/dv (v is TM velocity).

If the TM is enclosed in a nearby housing, the

residual gas damping coefficient is larger than in an

infinite gas volume. Simulations, that has been

performed as a function of gap size, show that β

increase significantly when the distance between

TM and surrounding walls is smaller than the TM

itself. For 4TM pendulum configuration, the

simulation gives: sm=

P

βsimul 36107.87

The power spectrum of Brownian force noise,

associated with the molecular impacts, is

related to the damping coefficient via the

fluctuation-dissipation theorem by:

β=ωSF 4KT

Measurement technique

We measured decay time for different value of pressure in order to

extract, from the fit β vs. pressure, 𝜕𝛽 𝜕𝑃 .

For this measurements run we have a ring-down times in the limit of

zero pressure about 6.5 day (Q ≈ 2.8x103) and the pressure calibration

uncertainties is 15%.

The residual zero pressure intercept β0, from other dissipation

mechanism, has been removed from dataset.

Using 𝜕𝛽 𝜕𝑃 of GRS we can estimate the acceleration noise on a

mass M along x-direction at 10-5 Pa.

𝜕𝛽 𝜕𝑃 for GRS is obtained as difference between the measured value

(4TM with GRS) and the simulated one for 4TM without GRS:

sm=P

β 364TM 103.27

2/12

2/1

5

152/1

10104.9

4kT

Hzms

Pa

P=

P

βP

M=S GRS

a

Gas species ArConcentration (%) 3 29 34 32 1 0.4

H2 H2O N2 O2 CO2

H(ω) is the pendulum transfer function with resonance frequency at 0.8mHz

(considering 50µm Tungsten fiber).

Measuring angular motion, it is thus possible, through the knowledge of

pendulum parameters, to estimate the external torque exciting the pendulum .

The relation between the Fourier transform of applied torque and angle

displacement is:

Ref: PhysRevLett 103 104061 2009

STC

GRS

b

𝐹𝑥

MRORO

x

y

z

The Trento group has developed a 4 TM torsion pendulum facility for testing on ground the GRS.

The pendulum is sensitive to all surface-related forces exerted on the test mass by the sensor and

allows us to detect and measure noise sources that can limit GRS performance.

𝑁𝑦,𝑇𝑀 is y component with respect to the TM center.