One Arm Cavity

M0

L1

L2

TM

M0

L1

L2

TRIPLE

QUAD

16m

R = 20m, T=1% R = ∞, T=1%

Optimally coupled cavity (no mode matched light reflected back)

Finesse ~ 625

Goals

QUAD TESTING:

• Electrostatic Drive (ESD)

• Hierarchical Control

• Lock Acquisition

ESDs

4 pairs of gold electrodes, coated onto the reaction mass

Each pair of electrodes forms a capacitor, which attracts the mirror surface (dielectric) placed in front of it

F = (r, dx,a)V²

distance between test mass and reaction mass

Constant geometry factor depending on the electrode pattern design

The attractive force F is proportional to the square of the applied voltage V

LASTI

Q1

Q4

Q2

Q3

Bias, Control

Design for Advanced LIGO - I

= 7e-10 N/V²

* Measured in GEO (4.9e-10 N/V²), for Advanced Ligo estimate of 35% more force produced for a given voltage thanks to a different electrode pattern

Electrostatic drive (ESD) results from GEO and application in Advanced LIGO T060015-00-K, K. Strain (Feb 2006)

FMAX = 7e-10 * (800)² = 450

Coupling coefficient a [N/V²] expected* to be:

Maximum force available for lock acquisition (with a difference of 800 V between the two channels):

LASTI Measurement - I

t)sin(αV2t)(sinαVαVF

t)Vsin(V

VV

VαV2αVαVF )Vα(VF

2222

CON

BIAS

CONBIAS22

BIAS2

CONBIAS CON

BIAS driven with an offset and CONTROL with a sine wave having same amplitude as the offset

With a 7Hz line, taking into account the controller and the 1/f² F -> POS transfer function, we expect the component (7Hz) to be twice as big as the 2(14 Hz)….

…but component not measured at all!!

2 component component

LASTI Measurement - II

SINE on controls + OFFSET on BIAS SINE + OFFSET on a single electrode

By driving a single electrode with an OFFSET plus a SINE, we get what we expect (similar results for all of the 8 electrodes):

What’s the problem?

the metallic part standing in for the QUAD mirror changes the behavior of the electric field between the ESD electrodes and the test mass, ( fringe field is not dominant anymore)

TEST MASS

It looks like each electrode driven by itself gives the expected response, but it doesn’t “see” its pair..

Possible explanation:

LASTI Numbers

FMAX = 2e-9 * (300)² ~ 180

2.5 times less force available than the Advanced LIGO design

V² = 52N 2.15e-9 N/V² Measured coupling coefficient about a factor 3 bigger than the

expected one for Advanced LIGO, but maximum voltage difference available about 2.5 smaller (300V instead of 800V)

Cavity error signal calibration: 2e6 counts/ mm 610 V/mm

Coupling coefficient a measured by driving ALL the electrodes with V = 110 +110*sin(wt):

Maximum force available for lock acquisition

ESD Linearization - Code

N90F that so 300V,V :caseour In

2/VV 0,Ffor :particularIn

/2αV/2FF

:range force theof middle in the be toso F choose I where,FFα

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:is force F required theproduce apply to toneed I that voltageThe

OFF MAX

MAX

2MAXMAXOFF

OFFOFF

FORCE

VOLTAGE

ESD Drive - I

The corrections which we need to send to the ESD are too high:

When the cavity is kept locked acting on the triple, the pk-pk correction sent to the OSEM is about 4000 counts, which is equivalent to:

Normalized Error Signal

Correction Signal

* NPRO Laser frequency noise specifications not available, expected about 100 times less

~100 Hz/sqrt(Hz) @ 100 Hz

Frequency Noise Reduction

Frequency noise reduced

by about a factor 10

Phase-lock loop: NPRO frequency stabilized to the PSL (via-fiber)

ESD Linearization - Efficiency

ESD driven @ 7 Hz

Reduction by about a factor 10 of the first

harmonic

Better evaluation of the efficiency of the linearization code

ESD Drive - II

Not more than 25% change in the open loop

TF of the longitudinal loop (both OSM-triple and ESD-quad drive)

measured with the “right” (blue) and “wrong” (red)

sign of the ESD loop

The ESD can’t be usedto keep the ITF locked

yet, at least afactor 10 less frequency

noise needed

GOAL: keep the cavity locked using the ESD-quad above 20-30 Hz and the OSM-triple below

QUAD “Hierachical Control”

QUAD - L2 below 10 Hz, Triple above

Correction Signal

Error Signal

QUAD “Hierachical Control”

Test Mass Charge: ESDs as Sensor

Top Mass of the QUAD (M0) driven at 2.5 Hz

4 electrodes of the ESDs used as sensors, connected as input signal to an SR560

BSC ground connected to the SR560 ground

Test Mass Charge: ESDs as Sensor

What seen by the L2 sensors

Summary

ESD: not behaving according to the design frequency noise too big to used them for keeping the cavity

locked

linearization code tested, works properly

Cavity controlled below 10 Hz acting on the QUAD-L2 (“Hierarchical Control”)

Plans

Improve frequency stabilization (get rid of the fiber?) Technical problems to be discussed: space for a new input bench, …

Tests on QUAD Noise Prototype (ESD, Hierarchical control, Lock Acquisition)

Measurement - III

All of the 8 electrodes driven with an OFFSET plus a SINE

No significant difference measured in the amplitude of the component by inverting the sign of the drive on the BIAS

OFFSET+SINE on controls –(OFFSET+SINE) on BIAS

HARMONIC COEFFICIENTS

OFFSET+SINE on all the electrodes

ESD Drive - I

When the cavity is kept locked acting on the triple, the pk-pk correction sent to the OSEM is about 4000 counts, which is equivalent to:

The impact of the ESD is of the order of 5% (maximum gain applicable without saturating the actuators):

Open loop TF of the longitudinal loop (both OSM-triple and ESD-quad drive) measured with the “right” and “wrong” sign of the

ESD loop

The ESD can’t be used even to keep the ITF locked

BLU: right sign

RED: wrong sign

ESD Drive - II

Difference between the drive configurations not even

noticeble in the power spectra..

..except for a resonance which gets excited when driving the ESD (with the right sign).

Problems

With the current optical set-up, the frequency noise is still too high (~10 Hz/sqrt(Hz) @ 100 Hz), at least a factor 10 times less noise needed

PSL should provide ~ 0.05 Hz/sqrt(Hz) above 500 Hz (Any Measurement available?) and with the phase lock loop on we should get the same performance as with the PSL. Are we limited by the fiber (acoustic noise, ..)?

The RMS of the cavity error signal is dominated by structures around 100-300 Hz. Where do they come from? ( Mechanical resonances of optical components in the region 400-700 Hz. Acoustic noise coupling)