I repeated this on a lock stretch from 2015-06-07 00:00:00Z to 02:00:00Z, but the result is pretty much the same. The best constraint we can put on coating noise right now from the residual is about a factor of 2.2 higher than the GWINC prediction. I also think the residual is not yet clean enough in this frequency band to make an inference about its spectral shape.

I tried increasing the CARM gain by 3 dB to see if the residual would decrease, but it does not (except maybe round 6 kHz; see the attached dtt pdf). So this broadband excess in the sum may not be frequency noise.

There is an error in the above plots.

Only the DCPD sum should be corrected by the DARM OLTF to get the equivalent freerunning noise. The DCPD null should not be corrected. To refer to noise to DARM displacement, however, all these quantities must be corrected by the DARM cavity pole.

This time I've included the DCPD dark noise (sum of A and B), also not corrected by the loop gain.

A few more corrections and additions:

• These plots use median averaging. As is widely known, this biases the estimate of the ASD downward by a factor of sqrt(ln(4)). This is now corrected in the new attachment.
• I looked at the 540 Hz pcal line in order to get a tighter value for the optical gain; it is 3.85 mA/pm. I am still assuming a DARM pole of 355 Hz, which is what is currently installed in the DARM calibration.
• The shot noise as predicted by GWINC lines up fairly well with the DCPD null stream, with minimal additional tuning of the of the parameters required. Input power is 24.2 W, with 88% transmission efficiency of the IMC. SRM transmissivity is 37%, DCPD quantum efficiency is 85%. The round-trip arm losses are set at 84 ppm, which is what I found previously was required to achieve a recycling gain of 40 W/W. Loss at the beamsplitter is 500 ppm, excess SRC loss (the "TCS loss") is 0, and SRC modematching is perfect, which are the defaults in IFOModel. Of course, we should get a better handle on these numbers and then actually verify that the GWINC shot noise estimate still agrees with the null. For now, it is just a weak indicator that we roughly understand the shot noise level.
• The apparent low-frequency excess in the null stream (<30 Hz) seems roughly consistent with the expected contribution from dark noise that Dan and I measured a few months ago. Since Koji has retuned by hand the digital compensation of the DCPDs, ideally we should measure this again.
• Some extra plots (cross spectrum and coherence of DCPDs A and B) and parameters file attached in zip.

We've also made timeseries plots of the glitches in the noisemons before, just after, and several hours after the auocalibration. The glitches seem to come back most strongly in the LL DAC. The first three slides have a 10,100 Hz bandpass so the glitches can be seen clearly. The last two slide have just one second of data, so a single glitch can be seen in the raw data.

Gabriele: I was wondering whether you see any significant differences in coherences between the data pre 2015/6/6 7:32 UTC (pick a good time where we saw about 70Mpc range) and the data after 2015/6/6 8:32 UTC. alog 18931 suggest there was an alignment shift of the signal recycling cavity between them. (I attached the summary page range plot.)

Here are some plots of the AS_A_RF36 and AS_B_RF36 signals around the time of the SRC cavity shift (2015/06/06 07:55 UTC).

PITCH:
AS_B_RF36_I and AS_B_RF36_Q are servoed to zero - the don't see any jump.
AS_A_RF36_I and AS_A_RF36_Q both show a clear jump at that time, so there is a good chance to find a better PIT error signal.

YAW:
The jump does show up in the two I sensors in YAW as well. While the current YAW input matri seems to work for stability (18h locks), I am still not sure about its lock-point. More work needed.

As for the EX ESD, during each lock we ramp down the bias on EX from 380 V to 0 V, after we've transitioned control of darm to EY.

We have not verified that this is in fact the optimal bias for minimizing the effect of the charge on EX; i.e., DAC noise and driver noise may still produce motion of the optic even if the applied bias voltage is 0 V.

Therefore, I spent 10 minutes tonight investigating this by trying a few different negative bias voltages with the IFO at 15 W. This didn't seem to really have an effect. However, inactivating the ESD driver did (see attachment).

At 24 W, the improvement is more noticeable. The attached png shows the comparison between tonight's spectrum and our previous best. The previous best was taken with the old EY ESD configuration, but we've seen over the past week that the new driver and the recalibration have not changed the shape or magnitude of the control noise, so the comparison is fair.

Also attached are some coherences with the new DARM spectrtum. We can see that SRCL has high coherence between 15 and 70 Hz (and also between 2 and 6 kHz... strange), and there is nonnegligible coherence with intensity from 100 to 400 Hz (this will probably be improved once Robert and Kiwamu continue their IMC WFS offset tuning).

If the EX driver does not come back on after lockloss and you cannot reset it using the EX ESD screen, then you toggle H1:ISC-EXTRA_X_BO_4 between 0 and 1 using caget.

66 Mpc!!!  You guys caught L1!  Very nice.

Here is also a DARM spectrum and time series, as well as the summary page range graph. The glitches occur in the short science segment just before 18h.

We need to do some more thorough follow-up, but I can give some quick feedback that might give some hints. The initial signs seem to suggest that the problem might be due to input pointing glitches or alignment fluctuations in the PRC.

The loudest glitches in that short science segments were coincident with ASC-REFL_A_RF9_I_PIT_OUT_DQ, which looks like it was being used as the error signal for INP1 and PRC2 loops, feeding back onto IM4 and PR2. The corresponding YAW channel was also significant, but not quite as much so. We also saw ASC-REFL_B_RF9_I_PIT_OUT_DQ as somewhat significant, which looks like it was being used in both the INP1, INP2, and PRC2 loops and feeding back on IM4 and PR2.

So, we now start believing that these loud glitches were related to the cleaning activity on the X arm vacuum tube (alog 18992). Here I show glitch wave forms in time series from three glitch events (out of many) that were observed in this past Friday, 5th of June.

Typically the glitches were very fast and I am guessing that the glitch itself happens on a time scale of 10 ms or maybe less. Usually the OMC DC signals or the DARM error follows with a relatively slow oscillation with a period of roughly 100 msec which I believe is an impulse response of the DARM control. All the three events showed a power drop in the carrier light everywhere ( TRX, TRY and POP) indicating that the power recycling gain dropped simultaneously. For some reason POP_A_LF showed slower power drop which I do not understand. Also, in all three events that I looked at, the OMC DCPDs showed small fluctuation roughly 20 ms before the big transient happens.

1. 2015-06-05 17:49 UTC

(This one contains two glitch events apart only by roughly 200 msec)

2. 2015-06-05 15:51 UTC

3. 015-06-05 17:55 UTC

4. High passed version of glitch event 1

(all the time series are high-passed with zpk([0], [40], 1) ). You can see a glitchy behavior in REFL WFS (as reported by TJ) as well as TRX QPD  (and a little bit in TRY QPD).

Looking at the initial power up, we can see that an increase of a factor of ~10 causes ~0.7 µrad of pitch misalignment. During the accelerated drift in the last 3-5 minutes before the lock loss another 0.4 µrad of pitch misalignment was acquired with only ~10% of power increase. One might wonder, if we see a geometrically induced wire heating run away.

I modeled how much the two front wires have to heat up to casue a bottom mass pitch of 1 microradian. A very small temperature increase is needed to predict this.

* Assuming a constant temperature profile along the wire length (I'm sure this is not the case, but it is easy to calculate), it is

0.003 [C]

* Assuming a linear temperature profile where with the max temperature is in the middle, and the ends of the wire have no temperature increase

0.006 [C]

So we can say an order of magnitude estimate is greater than 1 mC / urad and less than 10 mC / urad.

Calculations:

From gwinc, the thermal coefficient of expansion for C70 steel wire is

alpha = 12e-6 [1/C].

From the HLTS model at ../SusSVN/sus/trunk/Common/MatlabTools/TripleModel_Production/hltsopt_wire.m

wire length L = 0.255 [m]

front-back wire spacing s = 0.01 [m]

The change in wire length for pitch = 1 urad is then

dL = s * pitch = 0.01 * 1e-6 = 1e-8 [m]

* For uniform wire heating of dT, this change comes from

dL = alpha * L * dT

So, solving for dT

dT = dL / (alpha * L) = 1e-8 / ( 12e-6 * 0.255 ) = 0.0033 [C]

* For a linear temperature increase profile (max at middle, 0 at ends), I break the wire into many constant temperature segments of length Lsegment.

The temperature increase profile is a vector defined by

dT = dTmax * TempPrile

where TempProfile is a vector of the normalized shape of the temperature prodile. It is triangular, 0 at the ends and 1 at the peak in the middle. Each element of the vector corresponds to a constant temperature segment of the wire. dTmax is a scalar representing the maximum temeprature increase at the middle of the wire.

The change in wire length is then given by

dL = sum( alpha * Lsegment * TempProfile ) * dTmax

solving for dTmax

dTmax = dL / sum( alpha * Lsegment * TempProfile )

with 101 segments, this gives us

dTmax = 0.0063 [C]

about double the uniform heating case.

* I also considered that since the wire has significant stress due to the test mass weight, the Young's modulus's temperature dependence might cause a different effective thermal expansion coefficient alpha_effective. This appears to be a negligible effect.

From gwinc, the temperate dependence of the young's modulus E is

dE/dT = -2.5e-4 [1/C]

and young's modulus E is

E = 212e9 [Pa]

from https://alog.ligo-la.caltech.edu/aLOG/index.php?callRep=12581, we know that the change in spring length due to the modulus of eleasticity dependence is

dL = -dE/dT * dT * Tension / Stiffness

where Tension is the load in the wire and Stiffness is the vertical stiffness of the wire.

The Stiffness is given by

Stiffness = E * A / L = E * pi * r^2 / L

where A is the cross sectional area of the wire, and r is the radius.

So plugging this in above

dL = -dE/dT * dT * Tension * L / ( E * pi * r^2 )

We get the correction on alpha by dividing this by L and dT, which eliminates both from the equation. From the HLTS model, the bottom mass is 12.142 kg and the wire radius is 1.346e-4 m.

Tension = 12.142 * 9.81 / 4 = 29.8 [N]

The correction on alpha is then

-dE/dT * Tension / ( E * pi * r^2 ) = 2.5e-4 * 29.8 / (212e9 * pi * 1.346e-4^2) = 6.2e-7 [1/C]

This changes alpha from

12e-6 to 12.6e-6 [1/C]

Not enough to matter for the estimates above.

Localizing the heat source:

I made a calculation of the heat absorption by wires.

Based on Brett's temperature estimate, assuming the radiation as the only heat dissipation mechanism, the heat the front wires should be absorbing is about 1uW total per two wires when SR3 tilts by 1 urad regardless of the temperature distribution.

If you only look at the power, any ghost beam coming from PRC power (about 800W per 20W input assuming recycling gain of 40) can supply 1uW as each of these beams has O(10mW) or more.

I looked at BS AR reflection of X reflection, CP wedge AR both ways, and ITM AR both ways. I'm not sure about the first one, but the rest are mostly untouched by anything and falls on SR3 off centered.

The attachment depicts SR3 outline together with the position of CP wedge AR (green) and ITM AR (blue) reflections, assuming the perfect centering of the main beam and the SR3 baffle on SR3. Note that ITMX AR reflection of +X propagating beam falls roughly on the same position on SR3 as ITMY AR reflection of +Y propagating beam. Ditto for all ITM and CP AR reflections. The radius of these circles represent the beam radius. The power is simply 20W*G_rec(40)*(AR(X)+AR(Y))/4 (extra factor of 2 due to the fact that the AR beam goes through the BS) for ITM and CP, and 20W*40*AR/2 for BSAR of -X beam.

I haven't done any more calculations and I don't intend to, but just by looking at the numbers (total power in green and blue beams in the figure is about 240mW, 5 orders of magnitude larger than the heat absorbed by wires), and considering that the centering on SR3 cannot be perfect, and that SR3 baffle is somewhat larger than SR3 itself, and that CP alignment is somewhat arbitrary, it could be that these blobs seeps through the space between the baffle and the SR3 and provide 1uW.

The red thing is where BSAR reflection of -X beam would be if it is not clipped by the SR2 scraper baffle. If everything is as designed, SR2 scraper baffle will cut off 90% of the power (SR2 edge is 5mm outside of the center of the beam with 8mm radius), and remaining 10% comes back to the left edge of the red circle.

Any ghost beam originating from SRC power is (almost) exhonerated, because the wire (0.0106"=0.27mm diameter) is much smaller than any of the known beams such that it's difficult for these beams to dump 1uW on wires. For example the SRC power hitting SRM is about 600mW per 20W input, SRM AR reflection is already about 22uW.

Details of heat absorption:

When the temperature on a section of wire rises, the stretching of that section is proportional to the length of that section itself and the rise in temperature. Due to this, the total wire stretch is  proportional to the temperature rise integrated over the wire length (which is equial to the mean temperature rise multiplied by the wire length) regardless of the temperature distribution as is shown in effect by Brett's calculation:

stretch prop int^L_0 t dL = mean(t) * L

where L is the length of the wire and t is the difference from the room temperature.

Likewise, the heat dissipation of a short wire section of the length dL at temperature T+t via radiation is

sigma*E*C*dL*[(T+t)^4-T^4] ~ 4*sigma*E*C*dL*T^3*t

where sigma is Stefan-Boltzmann constant, E the emmissivity, C the circumference of the wire, T the room temperature (about 300K). The heat dissipation for the entire length of wire is obtained by integrating this over the length, and the relevant integral is int^L_0 t dL, so again the heat dissipation via radiation is proportional to the temperature rise integrated over the wire length regardless of the temperature distribution:

P(radiation) ~ 4*sigma*E*T^3*(C*L)*mean(t).

I assume the emmissivity E of the steel wire surface to be O(0.1). These wires are drawn, couldn't find the emissivity but it's 0.07 for polished steel surface and 0.24 for rolled steel plate.

I used T=300K, t=3mK (Brett's calculation for both of the temperature distributions), C=pi*0.0106", L=0.255m*2 for two front wires, and obtained:

P(radiation) ~ 0.8uW ~ 1uW.

ITM AR:

ITM has a wedge of 0.08 deg, thick side down.

ITM AR reflection of the beam propagating toward ETM is deflected by 2*wedge in +Z direction. For the beam propagating toward BS, ITM AR reflects the beam, deflecting down, and this beam is reflected by ITM and comes back to BS. Deflection of this beam relative to the main bean is -(1+n)*wedge.

AR beam displacement at BS is +14mm for +Z-deflection and -17mm for -Z-deflection. Since the BS baffle hole "radius" seen from ITMs is 100+ mm, and since the beam radius is about 53mm, AR  beams are not blocked much by BS baffle and reaches SR3.

ITM AR reflectivity is about 300ppm.

CP AR:

Similar calculation  for CP except that they have horizontal wedge, thick part being -Y for CPX and -X for CPY.

CP wedge is about 0.07 degrees.

I only looked at the surface of CP that is opposite of the ITM, and assumed that the surface facing ITM is more or less parallel to ITM AR, within an accuracy of O(100urad).

I assumed that S1 is the surface close to the ITM, and took S2 AR numbers from galaxy web page (43.7ppm for X, 5ppm for Y).

BS AR propagation:

BS wedge is 0.076 degrees, with a reflectivity of 50ppm.

Deflection of BS AR reflection of -X beam relative to the main beam is NOT -2*wedge as BS is tilted by 45 degrees. With some calculation it turns out that it is about -0.27 degrees, with a displacement of +48mm (positive = +X).

This beam is not obstructed at all by the BS baffle, hits SR3 and makes it to SR2 baffle edge. What made it to the SR2 surface doesn't go to SRM and instead comes back to SR3 as SR2 is convex  and the beam is heavily off-centered.

If there's no SR2 baffle and if SR2 is much larger, the center of the reflected beam is going to be  50cm in -X direction from the center of SRM, which happens to be on SR3.

I don't know what happens to the edge scattering and the reflection from SR2, but both of these are highly dependent on SR2 centering.