Please ZIP a huge text file like XML before posting. I deleted it.

Post pending from last week.

In order to better make sense of the results we have been obtaining in transfer function measurements, it is suggested to have an analytical model of the system under inspection -- in this case, a model of the suspension system based on the governing laws: Newton's laws.

I have made attempts, over the last couple of weeks, in reproducing transfer functions that we have obtained experimentally. In this elog post, I talk about particular model that I have worked with: one that was built about an year ago (and can be found on LIGOShare Dropbox at LIGOShare/Crackle2Design/SuspensionModel. (Link: https://www.dropbox.com/home/LIGOshare/Crackle2Design/SuspensionModel) I will not go into further details of the model; I will only talk about the results that I have achieved.

The 'suspension_4_2' file is the latest version of the analytical model of Crackle2, and that is the one I worked with. On running the script 'ToMatlab.m', the output is a file that contains, in a format MATLAB can understand, state-space matrices A, B and F. (A represents the dynamics of the system, B is the input coupling matrix and F represents external disturbances.)

In the current case of interest, the state equation can be written as:

In Laplace domain:

Which gives:

This is a 12x12 matrix of transfer functions. (12x12 because the whole system has 12 degrees of freedom in all: 6 of intermediate mass and 6 of lower mass (breadboard setup).) Of interest to me is the last 6, and I have made use of the 6x6 submatrix to compare with experimental data. I have plugged in the required parameters after measuring them. I have attached an excel spreadsheet with the parameters I have used. I have also attached the results I have obtained from this simulation: a comparison of SENS_X/COIL_A transfer functions. Clearly, though the shape is a little similar, the positions of poles and zeros is definitely not matching. I have played around with the parameters as long as they were still sensible values, to try and match with measurements. I was unsuccessful in matching the positions of poles and zeros, and this called for building a better model altogether. I am currently working on building a model of Crackle2 on a simulation platform (also based on Mathematica) built by personnel who have worked at Advanced LIGO and KAGRA. I will talk about that in another elog post.

We're going to swap the two Thorlabs photodiodes currently used with new ones, based on Zach's ISS system.

• The sensors will be 2mm diodes Excelitas InGaAs C30642GH
• The electronic is based on Zach's ISS double transimpedance circuit with some simplification
  • we're going to use one of the PCBs that Zach already got
  • we don't need switchable transimpedance or switchable whitening, so no MAX333 will be stuffed
  • we want to use about 5 mW per diode, which corresponds to about 5 mA (0.95 A/W) on the diode. So a transimpendance of 1k will do the job
• The mechanical support is again based on the ISS design, but the posts are going to be shorter: LIGO-D1500187-v1 &LIGO-D1500188-v1
• The photodiode socket is Digikey part 1437508-7-ND

Status:

• Two diodes are available from the already ordered batch (they're here)
• One PCB is available
• All electronic components have been ordered
• The mechanical mounts are being machined at the campus shop 

[Xiaoyue, Gabriele]

We easily realigned the Michelson interferometer, getting a visiblity of 98% (probably our best ever). Maximum signal on the two PDs was at about 7.22 V, minimum at 0.14 V. The optical gain has been updated to the new value of 4.58e-8 m/mW.

Here is the sequence to lock the Michelson, automation will come in the future:

1. All suspension and block damping loops must be on
2. engage FM1+FM3+FM4+FM5 in the LOCK_SERV filter bank. Gain is presently at 0.8, but we didn't check carefully the loop UGF
3. switch on output, then input
4. switch off all dampings
5. engage boost (FM2) and resonant gain (FM6)

We could then switch from the standard signal to the whitened ones. It works, but it's less robust since the whitened signals almost saturates the ADC, due to a lot of noise at about 300 Hz (this will be lower under the bell jar and hopefully even lower in vacuum).

A first stretch of data with the Michelson locked on the whitened signals and without bell jar is the following period:
    Wed Jul  8 14:22:41 PDT 2015
    Wed Jul  8 14:31:00 PDT 2015

We measured the ratio of the two photodiode signals where they are dominated by displacement noise, and it turned out ot be basically the same as the non whitened ones.

At frequencies above 3-4 kHz we are dominated by lasr intensity noise. We changed the intensity noise monitor filter banks to have a band pass between 3 and 4 kHz and a low pass of 2 Hz. We tried to change the relative PD gains, but it was difficult to see any change. This is likely due to the intermittent saturation of the ADC.

Another stretch of data locked on the whitened signals:​
    Wed Jul  8 15:08:49 PDT 2015
    Wed Jul  8 15:13:50 PDT 2015

[Kla, Xiaoyue] We fabricated more ~ 500 nm Cu pillars and did DMA tests. This time we decided to extend our load sweep to post yield so we have retrospect of the real yielding strength for each pillar. Also we make sure of a good contact and alignement that can induce dislocation avalanches post yielding. In future study we will further increase the static load resolution (step numbers).

In the analysis I calibrated the storage and loss modulus based the average phase shift ~ 5 deg in MG, FQ data (elog 955). The calibrated data gives mostly positive loss modulus all the way up to yield. However my analysis so far is still not convincing because of the emergent negative loss modulus. I plan to "clean up" the raw data by passing it through a low pass filter and look into single cycles instead of the overall demodulation at 1 Hz to see the time evolution of hysteresis behavior.

Lock lasted for more than 10 hours last night. The residual RMS of the error signal reduced slightly over the night time, as expected. Finally the Michelson unlocked for the same reason as the last time, a misalignment. Unfortunately we forgot to save the calibration line amplitude monitor, so we don't have a continuous measurement of the optical gain variation.

The bad news is that we had a lot of low frequency (<100 Hz) glitches, all night long. Some periods were more quiet, but never very good. The second attachment show a comparison of the spectrum averaged over the whole 10 hours and over the best 5 minutes I could find. It's clear that the low frequency noise is much lower without glitches. And very close to my guess for frequency noise. So we need to work on removing all those glitches.

This week we are going to improve the optical setup. The main goals are:

• Equalize the Michelson arm lengths to reduce frequency noise coupling
• Install the black glass baffles and beam dump
• Recenter all mirrors

Here is the planning for the activities:

1. Lock again the Michelson (if working) and measure the macroscopic arm asymmetry using frequency noise injection
2. Remove the bell jar
3. Install new block safety stops (if possible)
4. Measure all optics positions and approximate position of beams on mirrors. In particular, find online a drawing of the mount used with picomotors.
5. Report dimensions to the Optocad drawing and check if the length asymmetry is consistent with measurement
6. Decide the new positions of all optics in the Optocad drawing
7. Invent and install a temporary system to finely adjust the BS angular position
8. Move all optical elements to the nominal positions
9. Install black glass baffles and beam dumps in nominal positions
10. Weight all mounts, posts and clamps, to properly reconstruct center of mass position and Saikanth's matrices
11. Re-balance breadboard
12. Center all the OSEMs and turn damping on (breadboard and suspension)
13. Align the Michelson interferometer, taking care that the beams are centered on the end mirrors. We might have to move the baffles a bit to center them on the beams.
14. Check the beam clearance everywhere, and check for scattered light off edges
15. Clean all mirrors
16. Lock again the Michelson interferometer and check the sensitivity
17. Measure the coupling of frequency noise and estimate difference in Michelson arm lengths. If necessary adjust with translation stage and realign
18. Put back the bell jar
19. Check again the Michelson sensitivity

Other things to do after all those are successfull (not necessarily this week)

• Measure the DAC and coil driver noise (including non-linear noise when a low frequency signal is present) and add it to the noise budget
• Test the autolocker script
• Test the noise injection properties of Saikanth's damping loops
• Interface the picomotor driver with the cymac and write an alignment script

If everything goes according to schedule, we should finally receive the feedthrough on Friday. At that point we will 

1. connect all the cables using the feedthrough
2. move the electronic boxes to the rack and use flat ribbon cables to connect them to the chamber feedthrough
3. clean up the BNC connections
4. test all signal paths

The following stuff is well known, so feel free to skip it. However, I don't remember if I ever wrote it properly in the elog, so here it is.

Let's consider a Michelson interferometer with balanced beam splitter and arms with length L1 and L2. The fields at the symmetric and antisymmetric ports are given by:

We can rewrite these in terms of the sum and difference of the two arm lengths

Our Michelson error signal is given by the difference of the two powers:

Now, the lengths can be splitted in the microscopic and macroscopic parts:

The locking loop takes care to keep the error signal around zero, so any static offset is removed by it. This effectively turns the cosine into a sine.

We now consider small fluctuations around the operating point. We can have a change in the microscopic length difference or in the laser frequency:

Keeping only the first order terms in the small quantities, we get a final expression for the Michelson error signal at mid fringe:

From this we find the two important and well known results:

1. The optical gain of the Michelson error signal, for small deviation from mid fringe, is given by
   
   
    
2. Laser frequency noise is equivalent to displacement noise via the following relation
   
   

In the process of literature search, we read an interesting paper “Dynamic Hysteresis in Cyclic Deformation of Crystalline Solids”. It's a simulation work demonstrating possible intermittent viscoplasticity through elastic coupling of dislocations under cyclic loading. When trying to replicate the simulation but plug in real materials parameters, we got confused with the physical meaning of the driving frequency:

If we take single crystalline copper as the example, and take all the materials parameters from literature in order of magnitude: the drag coefficient B ~ 1e-5 Pa*s, burger vector b ~ 1e-10 m, and D ~ 1e10 Pa, then the normalized frequency should be in order of \ki_d D b = (1 / B b) D b = D/B = 1e15 Hz.

Even though the frequency of interest \omega = 0.00025, at which we starts to see the intermittent disloaction dynamics is 3 ~ 4 orders lower, we are still surprised to find it far away from any meaningful mechanical oscillations. 

Hence I emailed and asked the author Lasse Laurson. He suggested that the problem lies in the length with which the drag coefficient of units Pa*s needs to be multiplied. In my case I multiplied burger vector b according to the Peach-Koehler formular F_glide = \tao b, where \tao is the resolved shear stress; but Lasse thinks that a more natural length for collective dislocation dynamics is the average spacing of dislocations, 1/\sqrt(\rho), where \rho is the dislocation density \rho = 10^12 m^-2. By using that instead of b, the unit frequency becomes (\sqrt{1/\rho} D b ) / B = 1e11 Hz, and the frequency of interest would be ultrasonic 10 ~ 100 MHz.

We should replace the cymac HDD as soon as is feasible. Last week I had finished correcting all of the bad blocks on the disk, but now the SMART status reports that there are two new blocks that have gone bad. I think a disk failure is imminent. 

I've started the disk scan that will allow me to fix the newly failing blocks, which seems to be neccesary to clone the disk contents to a new drive. 

I edited /opt/rtcds/tst/x1/target/fb/master to record the default set of EPICS channels for the KR2 model, and added a file where arbitrary EPICS records can be specified to be added to the frame files (such as autolocker status). Specifically, these two lines were added to the list of .ini files for daqd to search:

autoburt was installed on the cymac. For future reference, it lives on the LIGO "projects" svn repository (Link). Every hour, at five minutes past the hour, the script attempts to take a BURT snapshot of all the models found in x1/target. 

The command burttoday was aliased to cd /opt/rtcds/tst/x1/burt/autoburt/today, which is a symbolic link to the most recent snapshots. The program burtgooey can be used to manually restore from the snapshot files. 

Gabriele mentioned having trouble accessing the trend data, but as far as I can tell, x1/target/fb/daqdrc is set up properly to save trend data, and looking in /frames/trend, it looks like trend files are being written out with nonzero filesize. Maybe this is an nds/data access issue rather than a daqd/data saving issue. 

A. Hardware activities

1. Finish soldering new photodiode electronics, build the photodiodes and test them
2. Test for vacuum leak on long periods
3. When opening the chamber, install the nylon screws to clamp the OSEMs
4. Finalize the design of the new electronic boards
5. Finalize the design of the magnet clamps and the new test blade wire clamps, and place to the order

B. Software and operation

1. Test autolocker
2. Test the optical gain monitoring 
3. Measure the plant transfer function up to higher frequency. There seems to be a lot of resonances above few hundreds Hz, which creates "ripples" in the closed loop transfer function, since they get too close to unity gain. 
4. Compute the requeirement for the Michelson error signal residual fluctuation, based on coupling of intensity noise.
5. Based on 3 and 4, design a better shape for the locking loop, with the right amount of low frequency gain and enough roll-off to avoid that the high frequency resonances influence the closed loop transfer function 
6. Implement automatic alignment using picomotors
7. Prepare infrastructure for crackling noise runs
8. In all cases, leave the system locked as long as possible!
9. If stable overnight, start taking modulated data for crackling noise

C. Noise hunting

In brief, understand and reduce all noises. All measured noises should go in the noise budget, that must be kept up to date with the understanding of the sensitivity.

1. Understand and fix intensity noise issue
   1. compute a projection of intensity noise for the last sensitivity
      1. based on coherence
      2. based on the measurement we performed with injection of intensity noise
   2. try to reconstruct response of the two whitened diodes using the measured transfer functions
   3. measure directly the response of the photodiodes with a single beam (no Michelson interference). We need to break the vacuum and block one Michelson arm to do this
   4. if needed, re-measure and fit whitening filters
2. Measure coupling of seismic and acoustic noise, looking at the coherence with microphone and accelerometer as before
   1. Using seismic noise, estimate the transfer function from table motion to Michelson displacement, and check if it is comparable with the expectations (maybe perform some noise injections using a shaker)
3. Compute an estimate of frequency noise, using the measure coupling and
   1. the sensitivity at low frequency that we measured with large asymmetry as an upper limit
   2. the nominal frequency noise of a Nd:Yag laser
4. Measure the coil driver and DAC noises, without any input signal and with a low frequency signal that mimics the normal operation. It’s important to check for increase of noise when there is input. 
   1. Another complementary approach is to bypass the whitening and see if there is any increase of noise. And use the result to infere the coil driver / DAC noise in normal operations. Additionally, we should be able to lock using an increased resistor, which would reduce the contribution of coil driver or DAC noise. This is worth a try, to see if the noise gets better anywhere
5. Measure the resonance frequency of the two blades. How similar are they?
6. Measure the ADC noise when there is an input signal, similar in amplitude to the one we have during lock. Check for an increase of noise when there is signal
7. Check the photodiode calibrations in mW and compute shot noise
8. Compute the noise due to residual vacuum fluctuations (see P940008 and G.Cella's computation)
9. Study the origin of the peaks at few hundreds hertz. Are they resonances of the test blades? Or excess motion due to resonances of the suspension, like wire bounce modes?
10. Check how the noise changes with small motions of the input beam (maybe due to different local responses of the diodes, small beams, defects on the mirrors, etc…). Diodes usually have a sweet spot where the coupling from beam jitter to intensity noise is minimum (surface inhomogeneities) 
11. Check if the noise changs withe the beam size on the diodes
12. Study noise stationarity and dependence of seismic environment

The Michelson remained locked for about 9 hours after I left yesterday night. The attached pictures show a trend of the locking error point and of the calibration line amplitude. For some reasons I don't understand right now it seems that the good signal to estimate the optical gain variation is Q, not I. Optical gain reduced during the night, as confirmed by the fringes I saw this morning which were about half of the normal.

The pressure at 8:30 AM was 2.59 Tor. I restarted the pump at 8:45 AM

Pending update from a couple of weeks ago.

As I mentioned in the first update on Analytical Modeling of Crackle2, I had worked on the Mathematica model built by Gabriele to generate analytical results for the suspension transfer functions. The model could not reproduce the experimentally observed results, and so I had to shift to a different model. I had started using the Mathematica-based SUspension Model CONstructor (SUMCON) built by folks at KAGRA. What one can do with the interface, in brief, is as follows:

• Define bodies/stages and associate one of them as attached to ground: In our case, the cage is attached to ground, and there's an intermediate suspension stage and the payload (optics breadboard).
• Give shape information, mass, moment of inertia, initial position values for each of the bodies.
• Setup wires for suspending one stage from another, and also input properties such as thickness, length, material.
• Define springs (in our case blade springs) and their properties (Q, spring constant, etc.)
• Setup other things, which are not relevant to our setup, such as inverted pendulum, heat links, dampers etc.

It is pretty intuitive to use; it can be found here.

Results for Crackle2:

The attachments below show the transfer function predictions for our suspension setup. Unfortunately, even after spending a lot of time, I couldn't recover data points of these plots to plot them on the same axis as experimentally obtained ones. There are a couple of channels available for one to extract data points, but somehow none of them seem to be working for me... Still, one can easily compare the frequency positions of each of these peaks with experimental results and observe the close matching.

The goal is to start crackling noise data taking before the end of the week.

Activities to do

1. Summarize the findings concerning the seismic coupling investigations (Xiaoyue, Yingtao)
2. Complete the test and assembly of the new photodiode (Xiaoyue, Yingtao)
3. Install the new photodiode (all)
4. Investigate the origin of the bad sensitivity we have right now (Gabriele)
5. Finish DAC noise measurements, including effect of dithering lines (Gabriele)
6. Laser intensity noise projection (Gabriele)
7. Automation of alignment using picomotors (Gabriele)
8. Move electronic rack far from optical table (Gabriele)

Since have already spent much effort on characterizing seismic noise, and we aim to start crackling noise measurement this week, I am writing to summarize the work and the conclusions we can draw so far:

• The TF from excitation to shadow sensor approximation is almost flat, we mount accelerometer B&K 4138 to directly monitor table motion (output to SR560, LPF3kHz 6dB, gain100, ADC TEST2 channel) (Elog 1142, 1143) 
• We first applied 1/f^2 calibration directly to accelerometer output and we suffered from spectral leakage problem (Elog 1144) 
• Since we lost lock, we opened the chamber. We mounted a another accelerometer (output to SR560, LPF3kHz 6dB, gain10000, ADC TEST2 channel) onto the post (Elog 1156) and measured the TF from table to the suspended board motion (Elog 1159) The attenuation turned out to be orders of magnitude weaker than the model prediction (seismic attenuation z2/z0) (Elog 1165)

• We suspected acoustic noise coupling so we put back the bell jar, re-measured TF from table to board or Mich, and measured the seismic spectrum (Elog 1169) (note accelerometer output gain changed to1000). We also used the result to project seismic noise -- in frequency from 20 ~ 200 Hz it's two times of the total noise in Mich (Elog 1170).

The result suggested we cannot trust our seismic propagation measurements using B&K 4318:

• We are reaching the accelerometer sensitivity limit for frequency below 100 - 200 Hz when measuring the seismic spectrum without excitation: when there's no excitation, the accel1 (table) and 2 (post) measured the same spectrum for frequency below 100 - 200 Hz. The table accelerometer is sensing more high frequency acoustic noise in open air.
• There can be some signal coupling at the level of cabling: there always appeared a noise lump between 10 to 200 Hz when photodiodes detect fringes. After exchanging the ADC inputs we, the coupling is trandferred to test1, so it happens before ADC! Note that I made the wrong inference in (Elog 1169). 

Plan for the next step

• I will borrow the accelerometer/ from Dmass to do the same characterization again. Actually Dmass asked me if I also want to have his wonderful accelerometer when I was taking away the shaker, I turned down because I think we have several "good" ones in our lab...
  • Wilcoxon accelerometer(s) + mounting blocks
  • Cable (from wilcoxon to amp)
  • multi channel amplifier
  • power (24-30V unit - attached to amplifier last I checked)

Lessons to take away

• Never have imaginary trust in any piece of equipment just because we /other people used it before. Always check the basic properties i.e. sensitivity/noise floor, give some known input to see if the output is making sense (better in a real experimental condition), to make sure it's reliable before going into measurements. 
• Don't turn down gift from other people!!

We left the setup (almost) undisturbed for the weekend. The suspension shadow sensor signals all show a continuos drift, with so sign of slowing down. I guess this means that the legs aren't settling down to a stable condition after all, even after two days.

The block shadow sensors show stable Y and Z signals, but the X signals are drifting too. It seems that, as already observed on Friday, we mostly have a tilt of the table around the front-back axis.

Bell jar back in position at 3pm.

Started pumping at 3:03pm.

Pump stopped at about 5:05pm LT.

At 5:45pm LT the pressure is 590 mTorr

Friday September 18th from 19:00 LT: frequency 0.4 Hz, drive gain 1.0

Saturday September 19th from 10:00 LT: frequency 0.4 Hz, drive gain 0.7

Saturday September 19th from 21:25 LT: frequency 0.4 Hz, drive gain 0.3

Sunday September 20th from 8:45 LT: frequency 0.4, drive gain 0.15

Sunday September 20th from 21:42 LT: gain 0

Yesterday we installed a low pass filter after the coil driver, to check if this is the origin of the increase of noise when we are driving the blade. In brief, now with the low pass filter we don't see any broadening of the microphone signal histogram when we are driving the blade.

The following plot shows that the histograms of the two microphone are the same with and without drive

The following plot compares this result with what we got in the past, without low pass. The broadening of the histograms was clearly visible when there was no low pass filter:

We see that the distributions of both microphones are different with respect to the past. So just to be sure we are running a new test with the same amplitude of motion, but without low pass

I placed order of high carbon steel and brass blades for further AE tests use. 

The materials were chosen based on former investigation of potentially high crackling-noisy materials candidates, based on referable AE and hysteresis properties. Details were noted in LIGO-T1500225-v1.

The materials were ordered from McMaster:

General Purpose 1074/1075 Spring Steel
Spring-Tempered Strips—Unpolished (Cold Rolled)
Yield Strength: Not rated but can be inferred from rockwell hardness C44 ~ 1.4 GPa (refer attached chart)
Modulus of Elasticity: 190-210 GPa 
Thickness: 0.093''
Benchmark load: 16 kg ~ 55% ys, 22 kg ~ 67% ys, 27 kg ~ 83 % ys, 32 kg ~ 98 % ys

Easy-to-Form 260 Brass
Sheet—Unpolished
Yield Strength: 52,000 psi ~ 360 MPa
Modulus of Elasticity: 16000 psi ~ 110 GPa
Thickness: 0.094''
Benchmark load: 4 kg ~ 48%, 6 kg ~ 73% 7.8 kg ~ 94% ys

After reviewing my notes carefully for writing this elog I found I made a stupid mistake ordering 260 Brass because the right material for Cu-Al alloy should be 2024 Aluminum. This is a bloody lesson: always write elog at the time of actions; it did help thinking and self-checking. Although brass is not our best candidate based on AE and hysteresis review, there are many hysteresis /cyclic deformation results for brass, and it's much softer than steel. I will do a detailed investigation to estimate how good/bad the brass can be regarding its crackling noise properties in this case. I will also order 2024 Aluminum and schedule the machining for both AE and Crakle2 testing blades.

For convenience here I am also including the nominal mechanical properties for aLIGO maraging steel:
Yield Strength: 1.9 GPa [2000 Braccini]
Modulus of Elasticity: 186 GPa (T040116-00-K) 
Thickness: 0.0755''
Benchmark load: 16 kg ~ 57%, 21 kg ~ 75% 26 kg ~ 93% ys

Pressure was up to 3 Tor, so at 4:30pm LT I switched on the pump.

Pump stopped at 5:15pm LT. Pressure at 300 mTorr

So far, we got three full crackling noise runs. Data have been archived in /frames/archive/Crackle2

• Between 1127888764 and 1127981074, amplitude 3000 uN (calibration gain servo on, UGF servo on)
• Between 1128369557 and 1128524607, amplitude 6000 uN (calibration gain servo on, UGF servo on)
• Between 1128819564 and 1128985182, amplitude 3000 uN (calibration gain servo off, UGF servo off)

Log files are attached.

Using two of the latest runs of the Crackle2 experiment (1314, 1326) I could get some upper limits for crackling noise in Advanced LIGO, based also on the geometrical scaling laws described in T1400427.

The two runs gave upper limits for modulated noise in the region between 60-200 Hz, and detected some noise modulated by the drive in the region below 50 Hz. However, this is due to DAC non-linearities, so that's not a measurement of crackling noise.

In the following plot, beside the obvious LHO sensitivity and design sensitivity of full aLIGO, there are blue and red bars. Blue and red refers to the two data taking runs (respectively at 3mN/5um and 6mN/10um drive). Solid lines are measured modulated noise. Dashed lines are upper limits.

The colored bands give some extrapolations:

• the green one assumes tha we believe in the measured modulated noise at low frequency, and extrapolate down to 10 Hz like f^-5. However, we know this is DAC noise, not crackling noise.
• the cyan, red and blue curves ues the upper limits at frequencies above ~50 Hz and scale down like f^-1, f^2 and f^-3. In the worst case scenario (f^-3) our limit is touching the aLIGO design sensitivity at 10 Hz.

Jamie helped me debug our hard disk problems with the cymac. Only one SATA cable was installed by the manufacturer, despite the eight drive bays... We scavenged the DVD drive cable for a new 1TB disk, since we never use it. 

I had to clean up some old frame files because the hard drive had filled up before doing this. The presence of the /frames/archive directory messes with the calculations of the wiper script, so it wasn't working properly. 

Anyways, I'm copying over all of the frame files to the new disk, and then I will set it up to mount at /frames. I've set it up under a LVM so we can easily extend the capacity of /frames with even more new disks, if we want. 

All frames have been copied over, and the new disk is now mounted at /frames.

Here is a tentative list of actions to get Crackle 2.1 operative. (Almost) all parts have arrived.

Electronics

1. Finish populating and cabling the second OSEM box
2. Test the second OSEM box, measure and fit all transfer functions
3. Cabling from ADC/DAC to optical table (OSEM boxes)
4. Cabling from OSEM boxes to vacuum chamber feed-through
5. Install and test new KR2 realtime model

Mechanics and optics

1. Install all optical components on the breadboard, rough alignment
2. Fine tune test blade length and resonance frequency
3. Cable all OSEMs, photodiodes and motors to the back of the board
4. Measure OSEM spectrums
5. Suspend the breadboard, with the roll-decoupling stage, from a test setup, balance
6. Measure roll and pitch resonances, tune, measure isolation
7. Measure the OSEM spectrum, compare with breadboard on table
8. Align the Michelson and get fringes, lock it if possible
9. If locked, measure and adjust Michelson arm asymmetry
10. Integrate the breadboard into the full suspension
11. Install and cable all suspension OSEMs
12. Cable the suspension
13. Integrate the system into the vacuum chamber, final cabling
14. Test all damping loops, measure again isolations
15. Lock the Michelson in air
16. Measure and adjust Michelson arm asymmetry
17. Pump down
18. Lock the Michelson in vacuum

I modified the SumCon model to include the roll decoupling stage. The masses and moment of inertia are close to the correct ones, while the wire lengths and spring constants are not tuned. So the following is still a qualitative more than quantitative simulation. I found a bug in my previous simulations (the breadboard wasn't well balanced, so it was not vertical). With the new simulation, the result is that the roll decoupling gets worse when the breadbaord suspension point is moved up farther away from the center of mass, as I was expecting.

However, it looks that the decoupling at 10 Hz only gets worse by a factor 2 or so by moving the suspension point from 40mm to 150mm above the c.m. At 20 Hz the worsenng is larger, but we have more margin there. So it looks safe to move up the suspension point, since this should ease a lot the balacing of the beadboard. In the attached figure, the mismatch number for the old suspension model refers to the difference in stiffness of the last two suspension blades.

Here is how the OSEMs are cable to the breakout board on the back of the suspended breadboard:

D1/C1 = Z1 (left looking at the front of the bread board)

D2/C2 = Z2 (right looking at the front of the bread board)

D3/C3 = X1

D4/C4 = X2

D5/C5 = Y1

D6/C6 = Y2

My previous fits for the coil driver whitening filters of the second box were not very good, so here is a revision:

Looking again into the measured transfer functions, I noticed that CH1 and CH2 are much more noisier than the others. Those two channels are in a different board (the one that allows double DAC input to a signle coil, a feature not used here. I should check why those two channels are noisier: it might be due to the fact that the low passed driving cricuit is not stuffed. To be investigated

For future reference, the QPD is a Centronic QD100 quadrant diode. As descibed in Koji's elog entry, the transimpedance is D980325-B, and the QPD matrix circuit is described in the elog entry

After fixing the matrix problem, I could implement succesfully the common mode damping loop for the two Z OSEMs. Z1+Z2 is used as error signal for a damping loop (CTRL_COMM) that feeds back the correction signal to +Z1 and +Z2. It works fine with a gain of 0.1 and I doesn't seem to introduce noise in MICH, altough the sensitivity wasn't very good this morning.

Looking at past data, I noticed that the locking control signal is ghighly coherent, at low frequency, with the differential mode of X1 and X2:

So I used AUX2 to implement a damping loop that uses X1-X2 and feeds back to +X1 and -X2. It still need to be tuned, but it's working well:

The action of both common Z and differential X dampings could reduce the low frequency LOCK control signal:

Maybe there is some noise reintroduced by the X damping, I still need to do some fine tuning. 

Nothing of all reported here is automated yet. 

* one leg got an air leak - ask Steve V to repair or send back to Newport for exchange

* Xiaoyue will check weights for new carbon steel blades

* may start new blade run in 10 days

* RSI paper to be resubmitted this week

A summary table of crackling noise measurements on maraging steel blades

Attached are the summary results of the analysis of last week Crackle 2.1 run, with both frequency dependence f=[0.125, 0.250, 0.500] Hz at amplitude ~6 mN, and amplitude dependence A = [8, 6, 4, 2] mN at frequency 0.125 Hz.

For 0.5 Hz driving, the automatic segment quailty evaluation didn't exclude the last few segments that have noisy spectrum. I manually put aside the noisy segments, and reanalyzed the data. Here is a summary for the tests with driving frequency variance: f_drive = [0.125, 0.25, 0.5] Hz. It looks like the demodulated noise spectrum are skewed toward lower frequency range with an increasing driving frequency...

I gave a presentation on the recent progress on micromechanical investigations for crackling noise: 

I applied AC load perturbation (DMA) to quasi-static compressive loading on single crystalline Cu nano-pillars with diameters of 500 nm and demodulate for dynamic moduli at frequencies from 0.1 to 10 Hz under the progressively higher static loads. By tracking the collective aspects of the oscillatory stress-strain time series, we observe an evolving dissipative component of the dislocation network response that signifies a smooth transition from perfect elasticity to avalanche yielding. 

We postulate that the rate-dependent dissipation is due to microplasticity associated to dislocation avalanche combined with slow viscoplastic relaxations, based on which we perform mesoscopic simulations and obtain response in well agreement with experiment. By analyzing the noise-free simulation results, we can predict for the statistics of microplasticity events before avalanche yielding.

The slides are uploaded to LIGO document G1601391-v1.

We have four sets of measurements carried out with maraging steel blades and different amplitudes and frequencies. From 1543

I analyzed those measurements, using the scaling formulas described in T1600246-v2. The first step is to extract the crackling noise coefficients C_i that characterize the crackling noise properties of the material. From the document, for the small test blades the noise spectrum is given by eq. 67:

From the measurements, I extractes the measurements or upper limits of the C2, C4 and C5 coefficients. Since we don't know the frequency dependence of the craklling noise, I absorbed the into a frequency dependence of the C coefficients. I used a least square method to extract the best estimates of the coefficients from the different modulation of the noise. The following plots summarize the results:

 In each plot, the linestyle corresponds to the measurement set, while the color determine if the noise modulation was detected with a positive coefficient, a negative coefficient, or there was no detection and we only got an upper limit. The blue band is what i take at an estimate of the cracling noise upper limit at low frequency. There is no smart way to extract this band form the data, just a "fit" by eye. Also, I'm still saying we have upper limits on crackling noise, since we haven't ruled out all other possible sources of noise modulation.

Using those estimates of the crackling noise coefficients and eq. 68 from the document, I can project the upper limits into the Advanced LIGO sensitivity.

One point to be noted: I assumed a one to one transfer function from vertical motion of the blade tips to vertical motion of the test mass, and 1/1000 coupling of vertical to horizontal at the test mass level. Both assumptions are somehow flawed: for the coupling from blade tip to test mass vertical we should consider the dynamics of the vertical bounce modes; for the coupling of vertical to horizontal, the QUAD model doesn't include any term, but we should consider the coupling through pitch and yaw. See section 9 of the document for more discussion on this topic.

Here's the money plot:

Each band correspond to one term in equation 68 above. We see that two terms are above the Advanced LIGO sensitivity. Those corresponds to terms that were neglected in the previous analysis, since we excluded them with "physical" arguments, although based on shaky grounds. They are terms in the noise modulation that are linear in the external drive. All other terms are well below the sensitivity: as expected the new scaling law computation further reduced them with respect to the old computation. However, the two new terms are worrysome. I'll have to review all my computations to be sure there aren't any mistakes. It's going to take a while, since there's a lot of math hidden behind the lines.

I can also assume a more optimist coupling of vertical blade to vertical test mass, as discussed in section 9 of the document. Basically I'm computing the elevant TF by first converting the blade tip motion to a force and the applying this force to the PUM. This provides some low pass, as it should be in the real system:

This plots gives a better picture of the situation. However the truth might be somewhere in the middle. I'm planning on addint the full dynamics of the suspension stages below the blades in the crackling noise model, to get the right answer once for all. But this will take some more math and time.

A summary table of crackling noise measurements on highC steel blades loaded at 90% of norminal yielding.

I recently recomputed the entire model that I used to scale crackling noise from the results of the Crackle2 experiment to advanced LIGO. The computation now includes a simplified (but realistic) model of the quadruple suspension. Details and MATLAB codes are available in the DCC: T1700076-v2.

Since we don't have new data yet with maraging steel blades, I still used old data from May 2016. At that time we had a bug in the calibration of the Michelson displacement, due to a flipped sign in the actuation transfer function (see SUS_Lab/1621). Luckily we saved both the SERV_IN and SERV_OUT data, and I could recover the actuation transfer function from the X1KR2 filter archive. I could then recalibrate properly the low frequency part of the MICH signal and run again the crackling noise analysis.

The final result is summarized in the plot below. The assumptions are that crackling noise indeed scales as derived in my note, and that the coupling from test mass vertical motion to test mass horizontal motion is of the order of 1e-3. I used O2 seismic motion data from Hanford to estimate the motion of the UIM. The three curves correspond to the three possible (and unknown) dependencies of crackling noise on the local stress and stress rate. Refer to my note for more details.

I think it would be useful to add this final step where you compute the aLIGO noise estimates, into the DCC document.

I also used to use 0.001 for the vertical to horizontal coupling, but recently someone was telling me that the factor is a bit larger; I think Brett or Dennis would know.

I agree. I'm waiting for new data with maragig steel before writng that up.

pk2pk:  cexit count=32000,  Z1=30um, Z2=40um

pk2pk reference:  cexit count=32000,  Z1=30um, Z2=40um

** Measurement ran with current monitors functioning

I applied the demodulation analysis on both simulated and experiment crackling noise data. I will summarize the analysis up-to-date in mainly three sections categorized in terms of the object of study (writing in progress):

I. Simulated, controlled modulated noise  (a, b, c)

II. Simulated noise based on micromchanical model (a, b, c)

III. Crackle Experiment data (a, b, c)

Each main section will be written to answer the three questions: (a) how do we generate/collect the data, (b) how do we analyze the noises, and (c) what are the results, conclusion/discussion.

On Xiaoyue's request, I'm starting a bunch of crackling noise measurement runs

** On June 2nd morning (probably at 10:19am) there was some kind of power failure in the sub basement labs. All computers (including the cymac) went down. The laser was off too. At 11:35am I started restoring the normal working condition. At 11:46am I restarted the crackling measurement

At the same time I'm copying the frame files to the external disk for the runs that are already completed

• transferring 2017_05_25 to /media/Crackle (GPS 1179796778 to 1180214603). Done
• transferring 2017_05_30 to /media/Crackle (GPS 1180217853 to 1180382458). Done
• transferring 2017_06_01 to /media/Crackle (GPS 1180382537 to 1180560837). Done
• transferring 2017_06_03 to /media/Crackle (GPS 1180560951 to 1180723674). Done

I am taking on the crackling noise measurement runs

* On June 2nd morning (probably at 10:19am) there was some kind of power failure in the sub basement labs. All computers (including the cymac) went down. The laser was off too. At 11:35am I started restoring the normal working condition. At 11:46am I restarted the crackling measurement

Note that after the power down event, the cts2uN filters in currmon channel were switched off. I didn't notice this until 2017-06-12. All current monitor data in the time period 2017-06-01 to 2017-06-12 needs proper conversion.

** Check on June 7th we completely lost the alignment (optgain = 0.7, UGF = 48 Hz). coil HF channels are not properly notched (0.0633 Hz instead of 0.095 Hz). The autocalibration channel output is off too (AUTOCALIB_OUT = 0.2 rather than 1). I realigned the michelson with updated optical gain back to normal ~ 0.56. I adjust the autocalibration gain to output 1. I started another crackling measurement with same parameters as 06-05 on 06-07.

July 5th: cannot engage boost, will open the chamber tomorrow for a check.

At the same time I'm continuing copying the frame files to the external disk for the runs that are already completed:

• transferring 2017_05_25 to /media/Crackle (GPS 1179796778 to 1180214603). Done
• transferring 2017_05_30 to /media/Crackle (GPS 1180217853 to 1180382458). Done
• transferring 2017_06_01 to /media/Crackle (GPS 1180382537 to 1180560837). Done
• transferring 2017_06_03 to /media/Crackle (GPS 1180560951 to 1180723674). Done
• transferring 2017_06_05 to /media/Crackle (GPS 1180724001 to 1180903119). Done

We have analyzed and summarized all the May (Elog 1707) and June (Elog 1726) measurements. We now have four different driving amplitude A = [16000, 24000, 28000, 32000] cts + three different driving frequency F = [0.0317, 0.0633, 0.095] Hz demodulation (mich - currmon) results for comparison. maraging_k_3.pdf shows the the demodulation results with electronic noise subtraction for all measurement runs. 

We fit the demodulated noises vs. spectrum frequency using a power law model:

n = G f^(-k)

where G = exp(b) is the gain we are fitting as a measure of the noise power. Note we use k = 3 because the demodulation results from the simulated crackling strain rate gives no spectral frequency dependency. The integration gives 1f multiplication, and the cantilever spring damping gives additional 2f. We used weighted non-linear regression to fit the data and obtained parametric estimation on the grain. 

power_fit_gain_k_3.pdf plots G vs. driving frequency as well as driving amplitude. The fitting error is huge so we don't see any significant dependency of the noise power on driving frequency. There is a weak amplitude dependency: we don't have demodulated noise for the smallest driving amplitude (A = 16000 cts) test runs.

After two months of measurement run without much maintaining, the setup has drifted enough and the table leveling and michelson alignement reference no longer works. We opened the chamber to try to recover the setup. Hopefully we can improve the sensitivity with a careful noise study and re-run more large amplitude driving measurements, to reduce measurement/statistical errors of the fitting demodulation results.

Below is a table summarizing the second round of crackling noise measurements

I combined all the good demodulation results from the tests with driving amplitude A=320000, driving frequency F =

0.0317 Hz (2017_05_16, 2017_08_10, 2017_08_13),

0.0633 Hz (2017_05_18, 2017_08_16),

0.095 Hz (2017_05_30, 2017_08_18).

using the analysis method described in previous elog (Elog 1753), and then do the power-law n = G f^(-k) fitting with exponent k = 3 on the demodulated noises for each driving frequency components as described in Elog 1737, as a way to quantify and compare the noise levels for different driving frequencies. The fitting results are shown in the figure below to the left. The fitted gain G (in logarithm scale) vs. the driving frequency G is plotted in the figure below to the right. We see very consistent demodulated noises at 1FI, 2FI, 2FQ components as before. However, within the error bar, no frequency dependency is discernible.

Based on the test results posted, I did the following analysis:

1. Compared measured transfer function to the LISO calculations. Attachment 4 and 6. The transfer functions match well with LISO.

2. Compared measured noise at the output to the LISO calculations. Attachment 1 and 3. The noise is more than LISO calculations by roughly a factor of 2, but I think it is expected - there is coil driver noises (amplified more than 300 times). Also, LISO uses ideal resistors, considering that the noise here is dominated by resistor noise. We also have plots of the noise spectrum with DAC noises injected. In this case, the noise in the passband (20 - 100Hz) is much more, suggesting that the board noise is dominated by the DAC noise.

3. Compared input-referenced measured noise to DAC noise. Attachment 2 and 5. We divided the noise by the transfer function and compare it directly with the DAC noise model. We can see that, in the passband, the board noise is about a factor of 10 less than the DAC noise (channel 2 and 4 has more noise; the signal is polluted by the ADC). 

4. A simple calculation based on the transfer function comparing the ADC noise and the amplified DAC noise. 

DAC noise > 300nV/rtHz. Passband amplification > 50dB > 300. Amplified DAC noise in the passband > 90uV/rtHz, compared to ADC noise 4uV/rtHz.

FYI: 1. I cannot attachment PDF plots directly since it will stuck the elog server. I put some PNG plots, but PDF plots can still be found in the compressed files.

2. Also, channel 2 is more noisey. It comes from ADC not the noisemon.

When we connect the voltage monitor channel of the noisemon board to a long cable (100ft), the op amp (LT1792) oscillates. Usually putting a 50 ohm resistor at the end will fix it. In this post, I studied how the oscillation happens and why putting a 50 ohm resistor will fix it.

We know 1) op amp has a dominant pole, giving a phase shift of 90 degrees 2) op amp oscillates when the loop gain is unity and the phase shift is 180 degrees. 3) Op amp has some non-zero output resistance.

Based on 3), we can see that when the output is capacitively loaded, there will be another pole in the transfer function due to the RC configuration. Since both R and C are small, it will be at high frequency (as op amp oscillations usually are). Thus, beyond the dominant pole, the phase will keep shifting to 180 degree based on 1). When this happens before the loop gain drops to unity, there will be oscillation based on 2).

Fix: insert a resistor at the output. This fixes the problem since it adds a zero with frequency a bit higher than the parasitic pole. This zero pulls the phase up so that when the loop gain reaches unity, the phase is around 90, at least far from 180, preventing oscillation from happening. The transfer function of this is simulated in LISO. From the plot, we can see the effect of the output resistance pulling the phase up to zero (90 in the case of an opamp because of the dominant pole).