one arm cavity m0 l1 l2 tm m0 l1 l2 triple quad 16m r = 20m, t=1% r = ∞, t=1% optimally coupled...
TRANSCRIPT
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
1 V
: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)