Minimizing the Resonant Frequency of MGAS Springs for Seismic Attenuation System in Low Frequency Gravitational

Waves Interferometers

Maddalena Mantovani, Juri Agresti, Erika D’Ambrosio, Riccardo De Salvo, Barbara Simoni

Motivations

Ground Based Interferometer are Limited by Newtonian Noise under 10 Hz

Recent Calculations Show the Possibility of Suppression of Newtonian Noise by Suspending the Test Masses in Deep Caves

Seismic Attenuation was Designed to Match that Limit

Suppression of NN by a Factor of 10-6 in Amplitude, 30 in Frequency Seismic Attenuation Must be Redesigned to Match the New Limit

Giancarlo Cella Draft

Horizontal Achievable with Longer Wires in WellsVertical Attenuation Requires New Development

Cella Suppression of Newtonian Noise

*1/100 Underground Seismic Amplitude

Horizontal Attenuation

Filter

Inverted Pendula

Existing MGAS Spring

Control LVDT

Magnet

Coil

Practical Limit 200mHz

LIGO-T010006-00-R

Frequency Tuning

Method to Lower the Resonant Frequency below the Mechanical Limitations

Apparatus Schematics

Load

Blade

Control CircuitLVDT Driver

Signal 1

Signal 3

Spectrum Analyzer

Control LVDT

Signal 2

Source

Filter to ground LVDT

Mechanical Actuator

Ground to Payload LVDT

Actuator

Simulated Noise

Control CircuitLVDT Driver

Source

Ground to Payload LVDT

Mechanical Shaking Actuator

Spectrum Analyzer

Filter Actuator

Control LVDT

Load

Filter to ground LVDT

Signal 3

Signal 2

Signal 1

Mechanical Setup

Blades

Variable Gain

Control Circuit

MGAS already neutralize > 90% of cantilever spring stiffness

Circuit corrects the last few per cent of stiffness and stabilizes performance

Actuator

MGAS Blade

Control LVDTThermal

Compensation

• LVDT

• Variable Gain

• Amplificator-Voice Coil

Tunable spring in parallel with MGAS spring

100÷300 sec

Set Point Integrator Thermal Drift Correction( )

Payload

Characterization Work

• Determination of the Working Point

• Circuit Calibration

• Frequency behavior as a function of the Gain

• Q Factor Analysis

Impulse Response

Frequency Response

After fixing the vertical height to the minimum frequency point we change the Gain to find the frequency behavior vs.

gain

0

0.1

0.2

0.3

0.4

0.5

-10 -5 0 5 10

Gain

Frequency [Hz]fit

gain [turns]

y = m2*(m0-m1)^0.5

ErrorValue

0.016428-8.8043m1

0.000261590.11096m2

NA0.00035801Chisq

NA0.9997R

326

0

mHz

G

8.8043

0

G

Hz

Q Factor Analysis; Two Methods

Fitting the Damped Exponential in Free Oscillations

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

-5 0 5 10 15 20

Waveform G=2.5

Voltage [V]

time [sec]

Q

Fitting the Resonant Width in the Transfer Function

0fQf

-50

0

50

0.01 0.1 1 10

Transfer Function

Frequency [Hz]

y = 20*log(m1*m2 ̂2/((m2 ̂2-...

ErrorValue

0.0249861.8764m1

0.00112860.43352m2

20.1362.096m3

NA6362.2Chisq

NA0.97913R

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

-5 0 5 10 15 20

Waveform G=9

Voltage [V]

time [sec]

-0.6

-0.55

-0.5

-0.45

-0.4

-0.35

-0.3

-5 0 5 10 15 20

Waveform G=-3.5

Voltage [V]

time [sec]

-0.65

-0.6

-0.55

-0.5

-0.45

-0.4

-0.35

-0.3

0 5 10 15 20

Waveform G=-8.3

Voltage [V]

time [sec]

/0 1 cos 2 ty c c t e

0

50

100

150

200

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

Q Factor

Frequency [Hz]

y = m1*m0^m2

ErrorValue

59.684585.74m1

0.107461.8393m2

NA3132.9Chisq

NA0.97901R

factorQ

Impulse Response

-50

-40

-30

-20

-10

0

10

20

30

0.01 0.1 1

Frequency [Hz]

y = 20*log(1*m2^ 2/((m2 ̂2-m...

ErrorValue

0.0028150.47752m2

4.000516.259m3

NA1897.6Chisq

NA0.98421R

Transfer Function Measurement

(filter body to payload)

20 0

2 222 2 0

0 2

20logH

f

Q

Lowering the system stiffness

As the Transfer Function is shifted to lower frequencies,

The Q factor decreases

-30

-20

-10

0

10

20

30

40

0.04 0.06 0.08 0.1 0.3 0.5

dB (G=1)dB (G=5)dB (G=4)dB (G=3)dB (G=2)dB (G=8.5)dB (G=-1)dB (G=-2)dB (G=-2.5)dB (G=-2.8)dB (G=-3)

Frequency [Hz]

Transfer Function with Different Gain values

0

5

10

15

20

25

30

35

40

0.06 0.08 0.1 0.3 0.5

Transfer Function G=8.5

Frequency [Hz]

y = 20*log(m1*m2 ̂2/((m2 ̂2-...

ErrorValue

0.0136671.7675m1

0.000274620.36361m2

3.443945.173m3

NA40.974Chisq

NA0.99659R

-10

0

10

20

30

40

0.2 0.3 0.4 0.5 0.6

Transfer Function G=3

Frequency [Hz]

y = 20*log(m1*m2 ̂2/((m2 ̂2-...

ErrorValue

0.023071.8548m1

0.000450120.27612m2

1.972124.354m3

NA51.879Chisq

NA0.99664R

-25

-20

-15

-10

-5

0

5

10

15

0.01 0.1 1

Transfer Function G=-3

Frequency [Hz]

y = 20*log(m1*m2 ̂2/((m2 ̂2-...

ErrorValue

0.986063.5196m1

0.0103940.079989m2

0.158850.80982m3

NA298.29Chisq

NA0.97027R

1

2

3

1

2

3

0

10

20

30

40

50

0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4

Resonant Frequency [Hz]

y = m1*m0^m2

ErrorValue

41.092358.81m1

0.0933592.0882m2

NA24.881Chisq

NA0.99413R

Q Factor Analysis

0

50

100

150

200

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

Q Factor

Frequency [Hz]

y = m1*m0^m2

ErrorValue

59.684585.74m1

0.107461.8393m2

NA3132.9Chisq

NA0.97901R

0

10

20

30

40

50

0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4

Resonant Frequency [Hz]

y = m1*m0^m2

ErrorValue

41.092358.81m1

0.0933592.0882m2

NA24.881Chisq

NA0.99413R

Impulse Response Frequency Response

Both methods show a quadratic behavior for the Q factor

Implies structural, non viscous, damping

Need for Thermal Compensation

The large thermal dependence of the blade working point with temperature, at low stiffness, makes it practically

impossible to obtain very low resonant frequencies

2 Ey

dY g

dT L

Where is the thermal expansion coefficient given

by the Young’s modulus

E

Virginio Sannibale et al.

y

Y

Thermal Compensation Circuit

100÷300sec

Overnight Blade Tip Position stability Integrated on 10 Period

0

2

4

6

8

10

12

14

-615.6 -613.1 -610.6

Blade Position averaged on 10 Period

Range

Blade Position [micron] averaged 100 sec and decimated

-612.4834Mean

1.1317328Std Deviation

1.2808192Variance

0.08042875Std Error

-0.51884154Skewness

-0.25288313Kurtosis

0

2000

4000

6000

8000

1 104

-687 -667 -647 -627 -607 -587 -567 -547

LVDT Readout Histogram

LVDT Signal [micron]

Blade Position [micron]

LVDT Signal [micron]

351079Points

-611.72936Mean

17.369398Std Deviation

0.029314489Std Error

0.017346127Skewness

0.023316299Kurtosis

These residuals are mainly the r.m.s. 100 mHz oscillator resonance excited by the seismic activity

Power Considerations

The Power consumption is of the order of 10mW

-50

-40

-30

-20

-10

0

10

0.1 1

Frequency [Hz]

Two Anomalies at Low Frequency are Discovered

1/f

1/f 2-50

-40

-30

-20

-10

0

10

20

30

0.01 0.1 1

dB

Frequency [Hz]

Right 1/f2 Behavior

1/f 2

1. Slower Slope in the Lower Frequency Transfer Function Measurements

Transfer Function Measurements with different Excitation Amplitude

-60

-50

-40

-30

-20

-10

0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Transfer Functions with Different Excitation Amplitude

dB (25mV)dB (10mV)dB (5mV)dB (70mV)

Frequency [Hz]

The slope does not change

-50

-40

-30

-20

-10

0

10

20

30

0.1 1

Transfer Function with Different Integration Times

dB (t=200sec)dB (t=100sec)dB (t=300sec)

Frequency [Hz]

Transfer Function Slope for Different Integration Times

The Slope does not depends on the integration time

Need for more investigations

-45

-40

-35

-30

-25

-20

-15

-10

-5

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Transfer Function measurements for different vertical positions

dB (-.850V) nomrdB (-1.14V) normdB (-0.696V) normdB (-0.350V) normdB (-1.46V) normdB (0.003V) normdB (0.497V) normdB (1.25V) norm

Frequency [Hz]

Slope for Different Vertical Positions

-2.2 100

-2.1 100

-2 100

-1.9 100

-1.8 100

-1.7 100

-1.6 100

-1.5 100

50 100 150

y = -1.1119 - 0.0072851x R= 0.98337

Resonant Frequency [mHz]

Second anomaly founded

50

100

150

200

250

300

350

400

450

-4 -3 -2 -1 0 1 2 3 4

Vertical Position [V]

• So far the working point to frequency dependence has always been observed to be hyperbolic, getting narrower at lower frequency

• At lower frequency we find a departure from the hyperbolic behavior (the fit in the bottom data set is a fourth power polynomial)

• We suppose that higher order effect may be taking over when the anti-spring gets close to fully neutralize the spring constant

• The newly observed behavior is coincidental with the departure from 1/f2 of the attenuation transfer function

• We do not know yet if the two anomalous effects are correlated.

Is this useful for LIGO??

the LIGO Deep Fall Back solution prototype for one-pier preattenuators

Vertical Attenuation

Horizontal Attenuation

Bellow equivalent springs

Cantilevers

350 Kg Payload

DFBS prototype

Real time

DFBS Prototype

So far driven down to 120mHz despite the additional springs (4/3 of the equivalent bellow stiffness) in

fully passive configuration

Expect ≤ 30mHz if tuned with electromagnetic anti-spring

attenuation plateau at 10-3 proven on preceding prototypes (expect similar performance)

• This development of Electromagnetic Correction Springs was designed to boost the Low Frequency attenuation performance of Geometric Anti Springs for future Underground Low Frequency Gravitational Wave Interferometric Detectors (Horizontal Attenuation was always easily available)

• This development allows for further depression of seismic perturbations, beyond the performance of the Superattenuators, reaching down to 1 Hz and even below.

Conclusions

-50

-40

-30

-20

-10

0

10

0.1 1

Frequency [Hz]

• The retrofitting of this technology on existing system like the LIGO deep fall back pre-isolator solution may allow the introduction of attenuation factors as large as one thousand for frequencies above 1 Hertz

• Sizeable attenuation at the micro seismic peak at 150 mHz can be obtained as well

Conclusions

-50

-40

-30

-20

-10

0

10

0.1 1

Frequency [Hz]

• Find the source of the less then 1/f2 behavior

• Repeat the Measurements with Accelerometers

• Study and Reduce the Control Circuit Noise Improving some of its Performances (Yanyi Chen)

• Make a Mechanical Thermal Compensation

• Use this Seismic Attenuation System on the Mexican Hat Interferometer (Barbara Simoni)

Next Steps