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, d x,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 T K, K. Strain (Feb 2006) F MAX = 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 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 F MAX = 2e-9 * (300)² ~ 180  2.5 times less force available than the Advanced LIGO design  V² = 52  N   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 = *sin(wt): Maximum force available for lock acquisition

ESD Linearization - Code 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 ~ 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 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 used to keep the ITF locked yet, at least a factor 10 less frequency noise needed GOAL: keep the cavity locked using the ESD-quad above 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 (~ 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 Hz. Where do they come from? ( Mechanical resonances of optical components in the region Hz. Acoustic noise coupling)