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ID Date Author Type Category Subject
1191   Thu Jan 15 18:27:02 2015 ZachDailyProgressSiFi - ringdownSapphire washers added, ringdown setup rebuilt, higher Q measured

[Nic, Zach]

Yesterday, we opened up the small cryostat and installed the sapphire washers (SwissJewel SP-175). This is hypothesized to increase the resonator Q by reducing the strain energy leaking into the lower-Q steel clamp.

We found that the inner diameter of the washers is slightly too small to accomodate the inner lip of the lower part of the clamp. We were able to make do just by having the lower sapphire washer sitting on this lip---rather than on the full wider area of the lower clamp section---but it is not ideal.

Nevertheless, we clamped it, resealed and pumped the chamber down. As it pumped, I rebuilt the HeNe optical lever readout. When I finished, I was quickly able to tap the cryostat and see a mode ringing at almost exactly 250 Hz, which is known to be the frequency of this cantilever at room temperature. At a respectable pressure of several x 10-5 Torr, I made a quick-and-dirty ringdown measurement using a scope and a stopwatch. I estimated $\tau$ at roughly 2.5 seconds, giving Q ~ 2000. This was already a few times higher than Marie was able to measure at room temperature (see below).

I went down today and did an actual measurment, using the Zurich box sampling at 7 kHz as DAQ. Fitting the envelope by eye, I found a time constant closer to $\tau$ = 5.55 s, giving Q ~ 4300 (I don't think my stopwatch method was all that wrong yesterday, but I do think the residual gas might have been contributing at the time---the pressure is now at 10-7 Torr). This is not only much better than the previous result, but also within a factor of less than 3 of the expected result for Si, according to Marie's data. Given how cavalier we were with the clamping, I'm fairly confident that the sapphire washer idea (and therefore also the monolithic thicker-clamp idea) works as intended.

1193   Thu Feb 5 02:04:39 2015 ZachDailyProgressSiFi - ringdownNo big Q increase at low temperature

Dmass helped me solve the Great Funnel Problem of 2015 by fashioning a foil extender to put in the tip of his metal funnel, since my glass funnel has a spout that is too narrow to get enough nitrogren through it. We spent some time yesterday afternoon filling the reservoir, after which I waited and then came back to see if it was still holding liquid. It was, so I added some more and left it overnight, and there still seemed to be some liquid by late this afternoon.

Assuming the cold volume had had enough time to reach low temperature, I made a quick ringdown measurement, only to find that the Q had only increased from ~4000 to ~8000 between room temperature and now. I think this means that the clamp integrity afforded by the sapphire washer sitting on just the lip of the steel clamp is not good.

I'm going to wait for things to warm up and then vent the chamber so that we can:

1. Improve the clamp
2. Fix our wiring issues
1194   Fri Feb 6 04:23:20 2015 ZachDailyProgressSiFi - ringdownNo big Q increase at low temperature

I monitored the reservoir level periodically over the day and night. As of the evening, there appeared to be ~1 cm of LN2 still there. As of around 4am, it appears empty, so it should be OK to open tomorrow. I've sealed the vacuum and shut off the pump in preparation.

 Quote: I'm going to wait for things to warm up and then vent the chamber so that we can: Improve the clamp Fix our wiring issues

1197   Sat Feb 7 03:50:14 2015 ZachDailyProgressSiFi - ringdownElectrical connections fixed, clamp adjusted, chamber repumped and cooling

I vented the chamber today to redo the clamping and investigate our wiring issues.

## Clamp

Since I observed relatively low Q even at cryogenic temperatures, I assumed there was some jankiness with how we clamped the cantilever when we installed the sapphire washers. Recall that the lower part of the steel clamp has a circular lip near the center around the screw hole, and it was too wide to allow the sapphire washers to fit around it. This meant that the lower washer was only being held by this lip, and not by the full surface area of the clamp. Also, when we installed the washers, we didn't remove the smallest can around the physics package, so we were doing a bit of guesswork as to how well aligned the entire clamp stack was. This meant that there could have been some slight rubbing, for example. Here is a photo of what it looked like in profile when I did remove the can today:

You can see what I mean about the lip, and it's also clear that the stack was not very well aligned. To fix the lip problem, I found a steel washer that was just about the right thickness and drilled the center hole out wide enough that it fit around the lip. This way, the lower sapphire washer will be supported by a larger surface from below (of course, the real solution will be to either design a new clamp or get wide-enough-ID sapphire washers). The picture on the left below shows the washer around the lip.

There was also some dust and other gunk visible to the eye, so I thoroughly cleaned all parts in the stack with methanol and isopropanol. I then carefully restacked the components and reclamped (a little tighter than we did last time, as well). The final stack is shown below at right.

## Wiring

I checked each connection from the feedthrough to the heater or RTD, and found that everything seemed to be in order, so there must have just been a short when we closed up last time. I wrapped some extra kapton around each connector solder joint to provide insulation and extra strain relief, and everything stayed as it should be when I resealed the chamber. I *did* accidentally break a joint on the wire for the ESD while closing up---whoops---but I decided it was more hassle to fix it than necessary for this next run. I'll resolder it when we cycle again.

The chamber is under vacuum now and I filled the reservoir with nitrogen. The clamp was at 200 K when I left around 10pm, so I'm hoping things will be calm and cool when I come in tomorrow.

1198   Sun Feb 8 02:49:27 2015 ZachDailyProgressSiFi - ringdownQ still low after clamp adjustments, mode cross-coupling suspected

The cantilever was fully cooled by the time I got in this afternoon. I measured some quick ringdowns by looking at the amplitude on the scope, and estimated a Q of 2-2.5 x 104. This is slightly better than what I measured the other day before improving the clamping (see CRYO:1193), but not good---still a few orders of magnitude below what we expect. I heated the system up near 120 K and found a slight reduction in Q.

Unlike before, I noticed a strange sort of sloshing of energy into a higher-frequency mode (~1350 Hz). It was hard to tell, but I got the sense that energy was being dissipated out of the fundamental mode through this higher-order one. I looked at a time-lapse spectrum of the ringdown, and it seemed to confirm this effect. If you look at the movie below (which is just about real time), you can see that the RMS of the two modes between 1-2 kHz pump up and down, while the fundamental mode around 215 Hz monotonically decreases. If you squint, it appears that the full RMS stays constant in most cases while the high-frequency modes ring up, while they all decrease together. This, coupled with the fact that everything rings down to zero if left alone, indicates to me that energy is leaking from the fundamental mode out through these others. As an order-of-magnitude estimate, the amount of energy pumped through these modes as the amplitudes increase and decrease is not inconsistent with the energy lost from the fundamental based on the observed Q.

I did some COMSOLing to try and figure out what is going on, and at first I couldn't explain it; it appeared that even the higher-frequency modes should have too little strain energy density leakage into the steel to explain the effect, especially with the sapphire spacers. In looking a little more carefully, though, I realized that we have not been careful enough in modeling our system: at the bottom of the clamp stack, there is a PEEK platform between the clamp post and the cold plate. This is there by design, to thermally insulate the clamp from the bath (for heating), but it also considerably softens the contact there.

This PEEK piece shouldn't have much of an effect on the fundamental mode, as the energy ratio for that mode is of order 10-4. The second mode at 1350 Hz is nearly as well isolated. However, for the third mode around 1800 Hz, something like 70%(!!) of the energy is expected to reside in the PEEK layer. Since PEEK has very high loss, this is not good. Here are some COMSOL screenshots, with the first 3 showing the first 3 mode shapes, and the fourth showing the (log) strain energy density for the 3rd mode. Note that this model is run at room temperature, so the eigenfrequencies are somewhat higher than in my spectra.

### So, my hypothesis is that somehow energy is leaking from the (otherwise well-isolated) fundamental mode into these higher-order ones, where it is immediately lost to friction in the PEEK. One possible step is to get rid of the PEEK piece, but that doesn't address the question of why the cross-coupling exists in the first place. My intuition fails me, so I'm not sure what the right thing to do is.

1199   Mon Feb 9 02:59:28 2015 ZachLab InfrastructureSiFi - ringdownNew vacuum chamber for rapid room-temperature iteration

It is a little tedious waiting for a full cryo cycle to iterate on the clamp. Also, in many cases we can learn a lot from just running at room temperature, but opening and closing the cryostat to get at the experiment takes a fair bit of effort. So, tonight I repurposed one of the gyro corner chambers to serve as a rapid-iteration room-temperature testbed. I used the northeast chamber since it had the pump connection. It has 2 KF flanges (on which I have put blanks) and 2 CF (one which goes to the gauges and valve, and the other which used to have a blank that I have replaced with a window).

I set it up next to the cryostat so that we only have to move 2 mirrors to switch between setups.

Given my revelation about the energy leakage and PEEK loss last night (see CRYO:1198), I resurrected the old rectangular block clamp to try a new idea. Namely, I just tried sandwiching the silicon cantilever (the central region with the hole, that is) between two sapphire washers, and then clamping the whole sandwich using the block clamp. The block clamp also has a PEEK base, but it should have provided a much stiffer clamp than the newer, cylindrical one, and that should result in less energy getting to the base. Here is what it looked like:

I pumped the chamber down and took a quick ringdown measurement. Unfortunately, the result was a Q in the ~2000 region, similar to what it was when we first installed the sapphire washers in the newer clamp and the bottom one was sitting on the clamp's lip (see CRYO:1191). Never fear---I have a new suspect: in looking at my photos, I'm noticing that the sapphire washers are not particularly flat. This could mean that the clamp contact is some strange shape and/or that the silicon is being stressed in some strange way.

Instead of the washers, I think I'm going to try sandwiching the cantilever between some other spare pieces of silicon that we have. If I use enough pieces to make a decently thick clamping region, this should serve the same purpose that we hoped the sapphire washers would. I'll try this tomorrow.

I sealed the cryostat vacuum line so I could use the pump for the new chamber. The LN2 reservoir was empty before I did so, and the clamp was registering around 250 K when I left. In any case, I'm going to keep iterating with the new chamber, and I think we shouldn't bother with the cryostat again until we can demonstrate a Q of close 104 at room temperature.

1200   Mon Feb 9 18:49:55 2015 ZachDailyProgressSiFi - ringdownQ ~ 6800 at room temp with Si sandwich

As I planned yesterday (CRYO:1199), I tried out a new clamp using spare pieces of broken silicon instead of sapphire washers to sandwich the cantilever (as with the last run, I used the old, stiff rectangular block clamp---the newer cylindrical one is still in the cryostat).

I didn't take a photo, but this was basically just a sandwich consisting of the cantilever (still attached to the central wafer region) as the meat and two scrap broken-off cantilevers on each side as the bread. This was all put near the center of the steel block clamp so that the clamping force was normal, and I made sure that the protruding cantilever had enough room not to be clipped by the block as it swings.

I put it in the new chamber and pumped down, and immediately measured a fairly high Q of ~6800 (ringdown tau ~ 6.4 s, while the mode frequency is ~340 Hz---slightly higher than before due to the clamping being a bit further along the cantilever).

This is the highest room-temperature Q I've yet measured, beating the ~4300 I measured after we first installed the sapphire washers on the newer cylindrical clamp (see CRYO:1191), and is within a factor of 2 of Marie's prediction in the absence of clamping loss (also shown in that post). This is also by far the cleanest ringdown I've seen: there are a few high-frequency modes present when I first deliver the impulse, but they die away and do not return. The Q also seems far less amplitude-dependent than I've noticed before.

1201   Tue Feb 10 04:37:05 2015 ZachDailyProgressSiFi - ringdownQ consistently lower in cryostat

A lot of things happened tonight (mostly in the realm of setbacks followed by recovering frome them), but the take-home is that the measured Q of my silicon sandwich clamp seems consistently lower when measured in the cryostat, compared to in the new chamber from the gyro. Here's a rundown of what happened today/tonight:

• Before dinner, I made a first measurement on the silicon sandwich idea (cantilever sandwiched between a couple spare pieces of silicon on each side --- see CRYO:1200). This gave me the highest room-temperature Q I've measured yet at ~6800.
• After dinner, I wanted to port this to the cryostat and potentially do a cooling run. Unfortunately, to fit it in the cryo volume, I had to flip the sandwich around so that it was protruding from the clamp in the other direction (for the first run, I had it sticking out over the power resistor to avoid clamping in the region on the other side that has the groove for the Glasgow-style cantilevers, but there wasn't enough room for that orientation in the cryostat, so I had to flip back---I made it work so I didn't clamp over the groove anyhow).
• Unwittingly, I made the dumb mistake of not first testing this freshly-clamped system again in the simple chamber, and after I closed the whole cryostat again and pumped down, I measured a much lower Q (back down around 3000).
• So, I opened the cryostat again, and then spaced out and made the further mistake of still not testing this apparently bad clamp job in the simple chamber, just to verify that I got the same low Q. Instead, I went straight to cleaning all the pieces and re-clamping.
• This time, I put it into the simple chamber and immediately recorded a high Q around 7000 again.
• This is when some setbacks kicked in:
• In opening the chamber, one of the RTD wires came loose from the feedthrough.
• Not realizing that these were just press-fit sockets, I unscrewed the feedthrough to have access so I could reattach the single loose wire, only to have several others fall off.
• So, I disconnected all the wires, spent some time mapping which one went where, re-soldered some and re-kapton shieled all, then reattached all wires, bunch taped them and taped the bunch to the feedthrough so that none could easily come loose. I also took this time to resolder the ESD wire that I broke the other day.
• In moving stuff around, I accidentally tugged on the ribbon cable between the QPD and its vectorboard readout circuit, pulling a couple connections.
• So I spent some time fixing that
• Now I was ready to do science again, so I transferred the (known good) clamp from the simple chamber back into the cryostat and carefully closed it all up again.
• After seal and pumpdown, I again measured a low Q around 3000.

So, it seems that the Q is repeatably lower for a particular clamp in the cryostat vs. in the simple chamber. To be sure, I'm going to do the final step of returning the clamp back to the simple chamber tomorrow and see if I again get a higher Q.

I'm not exactly sure why this could be happening. The only mechanical differences from one chamber to the other are:

1. The clamping block is screwed via holes in the PEEK base to the cold plate in the cryostat, while it is dogclamped to the breadboard in the simple chamber.
2. In the cryostat, there are wires soldered to the power resistor attached to the clamping block as well as a wire-attached Pt RTD kapton-taped to it. None of this is present in the simple chamber.

I'm tempted to think that (2) could be causing some excess damping, so one thing I will try is simply not connecting these just to see if that makes the probem go away.

1202   Wed Feb 11 03:15:02 2015 ZachDailyProgressSiFi - ringdownOnly some extra damping is from wires

Following my preliminary conclusion from yesterday (CRYO:1201), I set out to confirm or deny this seeming decrease in Q for a given clamp when going from the simple vacuum chamber to the cryostat.

One potential source of extra damping I considered was the wires attached to the block for the power resistor and RTD, so, while I still had the clamp in the cryostat assembly, I just disconnected these wires and pumped down the cryostat to see if I saw an improvement. I did see an increase in Q from ~3000 to ~5500, but not to the full 7000 I saw before in the standalone chamber. So, I conclude that there is some appreciable damping added by this kapton wiring. We need to use less rigid wire for the last stretch between the coldplate-mounted strain releif and the block.

The last step was to transport the clamp back into the simple chamber and see if I could recover the Q of 7000 that I measured initially. I did, completing the circle of repeatablility. I'm not sure what else could be causing the excess damping in the cryostat.

It is a shame, because I would be very interested to see what this particular silicon sandwich clamp looks like at 120 K, but I seem to have now way of doing so without the extra losses empirically associated with putting it in the cryostat.

1211   Wed Feb 25 04:29:49 2015 ZachDailyProgressSiFi - ringdownTaiwan cantilever has higher Q, going for cryo cycle now

[Nic, Zach]

Nic got a Glasgow-style cantilever from a group in Taiwan, and a quick test in the rapid cycle chamber showed that it had pretty low loss, so we are running it in the cryostat now. As a reminder, these are the rough dimensions of this style cantilever:

Below is a photo of the box it came in, showing the actual 92-um thickness of this sample, as well as a shot of it in the vacuum chamber. For some reason, this particular sample's clamping tab did not fit in the groove that Nic had built into the clamping block for the other Glasgow cantilevers, so I had to mount it to the side against the flat faces of the clamp (as I've been doing with our larger samples).

This evening, we transferred it over to the cryostat and restored all the electrical connections for what will hopefully be a fruitful cryo run. Here is a ringdown of the fundamental mode (~106 Hz) at room temperature:

The measured decay time of 41 seconds corresponds to a Q of around 14,000, which is about as good as we expect at room temperature. This sample is probably better than our other ones for at least 2 reasons:

1. It is made from a better-quality (FZ) wafer, and
2. It has been manufactured monolithically with a thicker clamping tab, which our modeling suggests is a very effective way to evade clamping losses by keeping strain energy within the silicon.

Given that we didn't see much improvement at all with our other samples when going to low temperature, I believe (2) is by far the biggest effect. The Glasgow wafers only have the clamp-region thickness extended to one side, which is modelled to be worse than if you go both ways, but it is still much better than we can do with our discrete sandwiching.

I filled the LN2 reservoir and the volume is cooling overnight. I did some rough ringdowns at a point when the steel block was registering around 160 K and found greatly improved Qs already (approaching and perhaps exceeding 105). We will continue to make measurements tomorrow.

1213   Fri Feb 27 05:47:27 2015 ZachDailyProgressSiFi - ringdownTaiwan cantilever fundamental mode Q

[Nic, Zach]

We measured the Q of the fundamental (~106 Hz) mode of the Taiwan cantilever in two ways. First, we used Nic's active steady-state method, and then we did a traditional ringdown. The results seem to agree, but the precision of the first method is much better due to the dynamic range of the readout for this mode: the motion becomes nonlinear at an amplitude only a few times greater than the background excitation level. Over a ~4-hr average, the loss is measured to be 1.45 x 10-6 ± 2.9 x 10-7, giving a Q of ~6.9 x 105.

Here is a plot of the instantaneous phi from the calibrated control signal. This data has already been fed through a ~1-hr lowpass, and then the data from the initial settling time has been truncated away. The mean and standard deviation of the rest of the points are what is reported.

After this measurement was made, we shut off the servo and allowed the mode to ring down. Here is that ringdown, along with a predicted range of theoretical curves using the result from above. As you can see, they are fairly consistent with what is measured, considering that the system quickly reaches a regime where it is excited by the environment (that is, only the initial part of the ringdown, where the agreement is good, is very trustworthy).

This Q is a couple orders of magnitude lower than what is expected for this mode at this temperature, but it is also only a factor of 2-3 worse than the best measurements using a similar apparatus at Glasgow (to my knowledge).

It bugs me that we don't seem to have any information about what steel looks like at low temperatures. Given my COMSOL strain energy modeling, the energy ratio for this mode is about 3 x 10-4, so this could be explained by clamp loss if the steel Q is as low as a few hundred. I'm looking into other modes to try and support or refute this hypothesis; since different modes have different energy ratios, we may be able to see what's going on. In parallel, I'm asking Matt and others to find out what is really known about cryogenic steel.

1214   Wed Mar 4 02:32:45 2015 ZachDailyProgressSiFi - ringdownSi spacer added to clamp holding Taiwan cantilever

The most recent measurements on the Taiwan-sourced Glasgow-style cantilver (see CRYO:1213) are encouraging, but the best Q measurement at low temperature is still a couple orders of magnitude worse than what is theoretically achievable, and about one order of magnitude worse than our conservative clamp loss estimates. Also, I've done some measurements on other modes (that have different expected clamp loss contributions due to the relative strain energy ratios) to try and sort out what is going on, with little success. Finally, some modes---including the 2nd bending mode at ~650 Hz---exhibited very low Q for no known reason.

One thing I thought about is that, since the Taiwan cantilever did not fit in the groove that was built into the block for the Glasgow-style cantilevers and therefore is just sandwiched between the two large pieces making up the clamp (see CRYO:1211), the clamp is likely pushing down at somewhat of an angle, which could lead to all sorts of non-idealities. Since the other Si samples we have lying around are roughly the size of the clamping region of this cantilever (~300-500 um), I opened up the cryostat today and reclamped the cantilever using a spare broken-off 300-um-thick cantilever piece as a spacer on the other side:

Pumping it all back down, I immediately measured Qs a bit higher than what we saw last time around at room temperature. The last measurement I made before leaving was tau ~ 135 s ==> Q ~ 46000, though it had been increasing up to that point, likely from the residual pressure, which was at ~10-3 Torr when I left. Compare this with the Q of ~14000 from the last time around, though admittedly I did not record the pressure at which this was measured.

1216   Thu Mar 5 22:35:43 2015 ZachDailyProgressSiFi - ringdownTaiwan room-temp Q > 10^5, cooling now

On Tuesday night, when I added the Si spacer to the clamp, I measured a Q of ~46000, but I noted that it had been increasing up to that point, likely due to the residual gas damping (see CRYO:1214). Last night, I made another measurement and found it to be much higher, at ~1.2 x 105 (tau ~ 350 s). This is much better than we have seen at room temperature thus far, so it looks like my spacer addition has helped.

I remeasured this an hour or so later and saw no appreciable increase. I checked again today and it appears as though it may have increased slightly, but it was hard to say for sure due to higher environmental noise. Really, we need the steady-state ringdown to make a good measurement at this level.

The LN2 dewar was refilled today, so I filled the cryostat and we'll see how it looks at low temperature tomorrow.

1217   Fri Mar 6 19:02:28 2015 ZachDailyProgressSiFi - ringdownQ at low temperature after reclamp… worse?

The cantilever had cooled to around 100 K by this morning, so I set up the mode ringer and began an active measurement on the fundamental mode. The online loss angle measurement for a 3-hr period beginning around an hour after lock is shown below (this is the control signal filtered by a 2nd-order low pass at 0.2 mHz.

As you can see, the loss is hovering around 3 x 10-6, giving a Q around 3 x 105, which is slightly but significantly lower than what we measured before I added the Si spacer to avoid skewing the clamp (CRYO:1213). I would chalk this up to the spacer actually making the clamp worse, but we did in fact see a huge improvement at room temperature (CRYO:1216). So, like, what the hell man?

I've left it running to collect more data over the weekend. I haven't gone over the temperature readout/control system with Nic, so I set up a simple temperature readout in the meantime so that we can have at least a coarse Q(T) measurement as it warms. To do this, I simply put a 1k resistor inline with the RTD and put 5V across with a lab supply. The second set of RTD leads goes to the temperature readout input in the digital system, so this is now just a DC readout of the voltage across the RTD. The lockin input channel X1:SCQ-TEMPERATURE_LOCKIN_DEMOD_SIG_OUT is calibrated to volts, and is equal to 5 V * RRTD/(1k + RRTD).

 Quote: The LN2 dewar was refilled today, so I filled the cryostat and we'll see how it looks at low temperature tomorrow.

1223   Tue Mar 10 03:19:49 2015 ZachComputingSiFi - ringdownTemperature calibration and control changes

It was a little unclear to me how the digital temperature control was supposed to work as it was built, so I made some modifications today.

The previous implementation used a digital lockin setup (as does the new one), but the output of this was converted to an error signal for the temperature control loop using a relatively primitive calibration, so I added some math into the model to make it a little more exact. The changes can be divided into two sections: 1) the demod voltage to RTD resistance section and 2) the RTD resistance to temperature section.

### Demod voltage to RTD resistance

To get a nice linear temperature signal using the 4-lead sensing method, the RTD current should not be determined solely by the RTD (otherwise, the readout just sees the excitation directly). So, I have added a 1-kOhm resistor in series with the RTD in the LO path, just as I did with the temporary setup described in CRYO:1217. The series resistor and the RTD now form a voltage divider where the RTD resistance can be inferred to high precision in the limit RRTD << Ri (= 1 kOhm). This is almost always true, but the model does include the exact expression for RRTD(Vout). To set the calibration, one must enter 2 values:

• RISET (aka Ri): The input series resistor (1 kOhm presently)
• VLO: The (pk) amplitude of the LO signal in volts across Ri+RRTD

### RTD resistance to temperature

For this, I have implemented the full, quartic formula from the ASTM standard (see our RTD manufacturer's page). Other than 4 preprogrammed empirical constants (and the Kelvin conversion of +273.15 at the end), this only requires one input from the user:

• R0: The RTD resistance at 0° C (100 Ohms for our RTDs).

## Heater actuation

The heater actuation section was in pretty good shape, so I didn't really have to make any modifications there. One thing I did do was add a heater power calculation, which requires the user to enter the heater resistance.

On the hardware end, since I'm using the bigger steel block clamp which also has the higher-resistance (100-Ohm) power resistor, I found that I needed more juice than what the DAC -> voltage amp/buffer that Marie and Nic used could provide (this circuit was regulated to 15 V, giving a max power of 2.25 W, which just isn't enough). I stole my Sorensen HV supply back from the CTN lab for now, as it seems to be unused, and used it as a HV amplifier via the external control feature. Since this unit doesn't allow voltage range limiting in remote mode, I added a 1/10 divider between the DAC and it so that I didn't have to trust software limiters. Really, I should attenuate the HV output, but I couldn't think of an easy way to do that with the stuff I had on hand. Anyway, the railed heater voltage from a +10 V DAC signal is ~40 V --> 16 W.

Finally, I edited the SCQ master screen to reflect all these changes. Here, you can see the system being held at 120 K:

1224   Tue Mar 10 03:51:42 2015 ZachDailyProgressSiFi - ringdownTaiwan cantilever long-term low-temperature phi

I reported in the replied-to entry that the Q of the Taiwanese cantilever at low temperatures actually appeared to have gotten lower at low temperatures, relative to the case before the Si spacer was added to the clamp to avoid skewness. However, the data from the longer run over this past weekend (see the ~20-hr stretch below) seem to suggest a Q not significantly different from that measured in CRYO:1213.

Interestingly, the online phi measurement starts out at the higher level I indicated in the previous post, but then slowly approaches a level not inconsistent with the ~1.5 x 10-6 number from before the spacer addition. The title is misleading, as the system actually approached a minimum temperature of ~90 K on Saturday, but the thermoelastic noise prediction is roughly flat over this temperature band, so that shouldn't be a factor, and the associated deflection from this temperature shift should not be enough to account for this drift via calibration error.

As I discuss in the quote, I had hoped to make a continuous phi measurement as the system warmed leading up to today, but at the time I neglected to consider the thermal deflection, which over such a large temperature swing completely rasters the beam off the QPD. In retrospect, I'm lucky that this effect didn't break the cantilever as the sensing gain was reduced from the misalignment---thankfully, the loop destabilized quickly enough that the watchdog script killed the feedback before anything happened.

So, it looks like we'll have to make this measurement the old fashioned way, point-by-point, which is why I spent time reconfiguring the temperature control today. I'm running an active measurement overnight at 120 K to see if we see a Q bump there.

 Quote: As you can see, the loss is hovering around 3 x 10-6, giving a Q around 3 x 105, which is slightly but significantly lower than what we measured before I added the Si spacer to avoid skewing the clamp (CRYO:1213). I would chalk this up to the spacer actually making the clamp worse, but we did in fact see a huge improvement at room temperature (CRYO:1216). So, like, what the hell man? I've left it running to collect more data over the weekend. I haven't gone over the temperature readout/control system with Nic, so I set up a simple temperature readout in the meantime so that we can have at least a coarse Q(T) measurement as it warms. To do this, I simply put a 1k resistor inline with the RTD and put 5V across with a lab supply. The second set of RTD leads goes to the temperature readout input in the digital system, so this is now just a DC readout of the voltage across the RTD. The lockin input channel X1:SCQ-TEMPERATURE_LOCKIN_DEMOD_SIG_OUT is calibrated to volts, and is equal to 5 V * RRTD/(1k + RRTD).

1229   Thu Mar 26 20:06:02 2015 ZachCryostatSiFi - ringdownSmall cryostat reassembled, Taiwan cantilever in clamp, pumping down

[Den, Chris, Nic, Zach]

Since my snafu before the LVC meeting (CRYO:1225), the small cryostat has been in pieces being thoroughly cleaned and aired out. Nic wanted to have the ringdown setup rebuilt so that we can demo the steady-state Q measurement technique for our visitors, so we did some work today to make that happen.

This morning, I re-lined the main chamber walls and floor with aluminum tape. This model came with some thin foil lining the walls, attached by periodic thin strips of double-sided paper tape. We have been intermittently scraping some foil off each time we cycle, and since a nasty residue was present on the floor of the chamber after the epoxy incident, I figured it was time to replace the lining. I just used aluminum tape since a.) it is stronger and will be less prone to scraping off, and b.) if and when we need to replace it again, it should come off much more easily.

This afternoon, we rebuilt the cryo package on the cold plate (clamp with Taiwan cantilever installed, ESD, and 45º mirror). Since we don't want to use epoxy to mount the power resistor anymore and we don't have any tapped holes in the clamp, we have not equipped any heat source or temperature sensor. This is fine, since we really just want to use it as a demo this time around, and room temperature should be sufficient. If we want, we can still cool it down to LN2 temperature, but we won't have any actuation or readout.

Upon pumpdown, we noticed that the pressure had stalled at around 20 mTorr after a good 20 mins of pumping, indicating that we had a leak. We checked the top seal and electrical feedthrough (which had also been freshly reattached during the rebuild), and found no issues. With nothing else to try, we decided it was most likely the seal between the chamber floor and the main section (I had to foil this with rectangular sections of tape, which I then XActo cut into a circle at the o-ring groove, so it was possible that a foil flake was blocking the seal). With everything still in place, we flipped the cryostat over and removed the bottom. We found a couple places where a tiny piece may have extended into the seal, so I re-cut the circle more conservatively. When re re-sealed, we found the pumpdown profile to be much closer to what we usually expect. The pressure was a few mTorr after ~10 minutes and showed signs of healthy decline.

We rebuilt the optical readout, then tested the MODERINGER amplitude sensing and found everything seemed to be working. We did not want to test the ESD at this high pressure. When I left, the Q was relatively low at maybe a few thousand, but gas damping was likely still a limiting factor. Also likely is that there is still some residue on the cantilever that I didn't get off, or perhaps even that some irreparable damage might have been done. We should be able to tell when the pressure is low enough.

1230   Fri Mar 27 00:26:02 2015 ZachSummarySiFi - ringdownTaiwan cantilever phi vs. T (old but unreported)

Before the LVC meeting, I had just done a long steady-state Q measurement on the Taiwan cantilever. I got too distracted by the melted epoxy disaster (CRYO:1225) to actually post the data.

Below is a plot of the ~16 hour stretch of data (second trend), showing the temperature and instantaneous loss angle. The temperature was stepped in 10-K increments from 90 to 130 K, holding at each temperature for 3 hrs to allow the system to equilibrate and integrate (except for some of the early steps which required some manual intervention).

The main result is that the loss seems relatively constant at ~10-6 from low temperature to ~120 K, where it starts to increase. Towards the end of the 130-K stretch, the LN2 ran out, and the system started heating to room temperature uncontrolled (i.e., heater output was railed at zero).

This level is too high to be from the Si, so I assumed it was some residual clamping loss. I was dubious that the figure from the one reference that Matt A. found and gave me for the cryogenic Q of stainless steel would be applicable to our particular clamp, so I thought I might try to measure it directly, in parallel with the cleanup of mess in the cryostat. To do this, I got some spare steel wire from Gabriele and made a makeshift suspension, hanging the top piece of the clamp, hoping to measure the loss of its lowest vibrational mode. I knew it was a long shot, since this mode should be around 17 kHz, but I set it up in the simple vacuum chamber anyway, and tried to excite it and read it out optically. The first bending mode should have nodes *near* the suspension points, so I thought I might get some kind of meaningful results if I could actually see a ringdown.

I was unsuccessful. I tried various excitation schemes, from broadband (banging stuff) to narrowband (bandpassed white noise, amplified with the boom box and blasted out of a speaker touching the chamber), and none revealed any mode excitation. I was able to see broadband noise increase with the excitation profile, but no lines, so most likely I was seeing some alternate path.

I still think it would be nice to get an empirical measurement of the cryogenic Q of the steel we use for our clamps. Maybe we can set up a laser vibrometer measurement like Norna and her student did a few years back on the steel gyro PMC?

1264   Sun Jun 7 17:33:31 2015 ZachUpdateSiFi - ringdownNew clamp received, second prototype cantilever made, some measurements

This is a recap of some things that have happened over the last couple days that I have yet to elog.

New clamp

We received the new clamp for the ringdown cryostat. The drawings are attached, but to jog the memory:

• It has similar dimensions to the old clamp
• Mounts to the same PEEK insulating base as the old clamp
• The clamping surfaces are polished to mirror finish
• There are tapped holes near the corners for guide rods to ensure level clamping. The guide rods themselves were ordered from McMaster-Carr, but they were lost by CIT mail services. I'll find them this week.
• There are 3 pairs of 8-32 holes for clamping (one pair at any given time---just to be able to clamp in different places).
• Holes on the side for mounting of the power resistor for heating
• a channel on the side for taping on the RTD

It looks pretty good. Here is a shot of it, and then a second shot focusing on my camera in reflection, to give you an idea of the finish quality:

New prototype cantilever

Justin and I made a second prototype cantilever. It is 50 mm long, with 10 mm of clamping/mirror region on either side. We estimate the thickness of the central region after etching to be ~200 um.

As you can see, the "un-etched" regions were etched a bit, particularly on one face of the cantilever. We believe this to be caused by cleanliness issues that are difficult to avoid when prepping/etching both faces in one go. We're going to iterate on this somewhat, but we may need to do the prep and maybe the etch on one face at a time.

I also did some very rough testing of the optical quality of the tips. Shining the 1550nm laser on it, I got some strong etalon action. The max transmission I got was around 90%, and the minimum was on the order of a few percent---I need to do this more methodically. The TRANS and REFL beams seemed to have good quality, but I'd like to see them on the CCD to look for aberrations.

Some ringdowns

With these new toys, I did a few more ringdowns.

Prototype 1 in old clamp at room temperature: Q ~ 4000. Not so great.

Prototype 2 in old clamp at room temperature: Q ~ 40,000. Pretty good. The best we've seen is around 100,000 with the Taiwan cantilever (see CRYO:1216), but this was after pumping much longer. The Taiwan cantilever showed Q ~ 40,000 at similar pressures, so it could be that this prototype is as good.

Taiwan cantilever in new clamp at 120 K: Q ~ 400,000. This is about what we measured with the old clamp (see CRYO:1230). The point of this measurement was to see if the result improved with the new clamp, with the hypothesis that we were limited by clamping effects from the poor finish of the old clamp before. At this point, this seems not to be the case.

Attachment 7: Clamp_base_v2.PDF
Attachment 8: Clamp_top.PDF
1265   Wed Jun 10 18:09:39 2015 ZachUpdateSiFi - ringdownSecond prototype cantilever cryogenic Q not great

I measured the Q of the second prototype with the new clamp in the cryostat at low temperature. The result was ~60,000, which is not much better than what was measured at room temperature (see quote from last post).

My next hypothesis as to what's going on is that the new cantilevers are thus far dominated by surface loss. If you compare the apparent quality of the surface of the Taiwan cantilever (photo in CRYO:1211) with those of the first (CRYO:1260) and second (CRYO:1264) prototypes, it's obvious that it's much better, at least visually. There is also some clear macroscopic blemishing on the first prototype, which could be leading to its abysmal Q of 4,000 at room temperature.

Two parallel courses of action that are underway:

1. Use an estimate for the roughness of the etched portion of the prototype cantilevers to see how bad the surface loss would have to be to explain our measured Qs. I'm waiting for Justin's answer on this.
2. Start trying some surface treatments. It could be that we just need to get a little better at fabrication at this point, but it can't hurt to try a treatment and see if we get a noticeable chage in Q. This is certainly only worth it for the second prototype, which at least appears fairly uniform in roughness.

We are also going to get started with a third prototype soon. For that, we'll be working on our cleanliness procedures.

 Quote: Prototype 2 in old clamp at room temperature: Q ~ 40,000. Pretty good. The best we've seen is around 100,000 with the Taiwan cantilever (see CRYO:1216), but this was after pumping much longer. The Taiwan cantilever showed Q ~ 40,000 at similar pressures, so it could be that this prototype is as good.

1266   Thu Jul 2 16:15:40 2015 ZachDailyProgressSiFi - ringdownQuick update on recent measurements

[Matthew, Nic, Zach]

Over the last few days, we've done 2 significant measurements:

Flower Mound propeller resonator sandwiched between sapphire washers at room temperature

We clamped one of the propeller resonators between two of the new, larger sapphire washers, using the cylindrical mount in the room-temperature chamber. Unfortunately, the inner diameter of these washers is also too small to fit around the lip in the bottom part of the clamp (as it was with the old washers---see CRYO:1197), so I needed to reuse the steel washer that I fashioned before.

We measured the Q to be a rather low ~2,000.

It's unclear exactly why it should be so bad, but we have never measured a good Q with these thick, uniform resonators. It may be caused by the effect I noted in CRYO:1198, where the mode is highly coupled to the relatively soft and high-loss PEEK. It could also be from clamping non-idealities from the fact that the bottom sapphire washer does not sit flush on the clamp over its whole surface.

Matthew has designed a revised version of the cylindrical clamp. The main improvements are 1) it is bigger and therefore should not allow for as much coupling of the silicon modes to the PEEK base, and 2) it will be made to accomodate the sapphire washers we have. Nic put the order in and it should be in late next week.

Painter fab prototype 2, after surface treatment, in new polished block clamp at ~100 K

I finally got a chance to meet with Justin again to do a surface treatment of the second prototype resonator (the one in CRYO:1264). This consisted of 10 minutes in "piranha" etch (this is 3:1 hot H2SO4 and H2O2), followed by 10 minutes in room temperature HF. According to Justin, this is a passivation treatment that only affects the surface chemistry of the resonator; it does not repair the surface in terms of the roughness. Since our leading hypothesis was that our low Q for this thin resonator is related to the rough surface, I didn't have high hopes for a big improvement.

Matthew and I put it in the cryostat yesterday and cooled it overnight. This morning, we measured a Q of around 30,000 at 100 K. This is about a factor of 2 lower than before, which is certainly surprising...

Matthew did some real data analysis on this ringdown, and I'll have him attach it to this post.

Update (Matt):

I just attached a couple data analysis plots that I used for determining Q. I calculated a Q of ~28,000 at f0 = 145Hz. I'm taking an FFT of the ringdown measurement, filtering around the resonant frequency (in the time domian), and then fitting an exponential to the filered signal to measure tau.

Attachment 1: data_analysis_plots.jpg
1267   Wed Jul 8 20:07:21 2015 ZachSummarySiFi - ringdownSummary of all ringdowns thus far
 Resonator f0 [Hz] T [K] Q Comments Si, 300 um uniform thickness (symmetric design) 241 300 530 From Marie's original measurements. T1400668 " 160 1790 " 77 10,500 Same as above, but with sapphire washers 250 300 4300 Washer didn't fit around clamp lip. CRYO:1191 " ~100 8000 Same as above, but steel washer added to make contact flush 250 ~90 20,000 CRYO:1197, CRYO:1198 Same as above, but in large rectangular clamp rather than cylindrical one 250 300 2000 Attempt at removing potential coupling to lossy PEEK CRYO:1199 Same silcon resonator as all above, but sandwiched between 2 other 300-um pieces of silicon (rather than sapphire washers) 340 300 6800 Thinking non-flatness of sapphire could have been the issue. CRYO:1200 Taiwanese Glasgow-style cantilever 92 um thickness 106 300 14,000 Possibly gas damping limited. CRYO:1211 " 95 6.9 x 105 CRYO:1213 " 300 1.2 x 105 Improved clamping with spacer, waited for much lower pressure CRYO:1216 " 100 6.7 x 105 No significant change at low temp vs. pre-spacer (2 rows up) CRYO:1224 " 90-120 0.5 - 1 x 106 Measured continuously over temperature range CRYO:1230 " 120 4 x 105 In new rectangular clamp. No improvement (slightly worse, in fact). CRYO:1264 Painter prototype 1 ~350(?) 300 4000 In old rectangular clamp CRYO:1264 Painter prototype 2 ~150 300 40,000 In old rectangular clamp CRYO:1264 " 100 60,000 CRYO:1265 " 100 30,000 After HF surface treatment (worse!) CRYO:1266 Flower Mound propeller resonator 300 um, uniform thickness, asymmetric 145 300 2000 In old cylindrical mount, with newer sapphire washers CRYO:1266

1268   Thu Jul 9 17:45:03 2015 MattUpdateSiFi - ringdownRingdown measurement with new clamp

Today Zach and I tried out the new clamp setup. The clamp is much thicker than the previous post design and has a lip to constrain the sapphire washer. There's also a large SS washer on top to (hopefully) distribute the force of the 1/4 20 screw more evenly. We forgot to take pictures of the new assembly, so I've attached the SolidWorks model:

We estimated a 1/e decay time tau ~5s and a resonant frequency f0 = 150Hz, so the Q was around 2,300 at room temperature. This is comparable to the old cylindrical mount with sapphire washers.

1269   Fri Jul 10 11:12:16 2015 ranaUpdateSiFi - ringdownRingdown measurement with new clamp

I wonder about the mode beating effect on the ringdown. Can you post the spectrum so we can see what the overlap is? If the frequencies came out too close, then the Q would look low because of energy sloshing.

1270   Fri Jul 10 11:44:27 2015 ZachUpdateSiFi - ringdownRingdown measurement with new clamp

The modes aren't close enough. We designed these to be different in frequency by increments of 20% for exactly that reason.

Spectrum-wise, we can measure each cantilever individually, but the response of one to another's fundamental mode should be very small...

 Quote: I wonder about the mode beating effect on the ringdown. Can you post the spectrum so we can see what the overlap is? If the frequencies came out too close, then the Q would look low because of energy sloshing.

1271   Sun Jul 12 01:21:22 2015 ranaUpdateSiFi - ringdownRingdown measurement with new clamp

Probably right, but hard to be sure.

20% sounds like a lot, but its really not if the tolerances were not held in the machining. We wouldn't be at all surprised if the frequencies were 5% off from spec.

It should be easy to measure / calculate if the beating is an issue. It mostly depends on the coupling which is there through the clamp; hard to quantify I think unless COMSOL does time domain ringdowns.

Also, I wonder why PEEK is necessary at all. Can we not replace that with a hard base? e.g. a hard ceramic or some easily machinable glass? I don't have a great suggestion for material, but I expect that there is one out there (low conductivity, high Young's modulus). Or is the base already so big that the PEEK being soft doesn't matter? In this paper (http://arxiv.org/abs/gr-qc/0504134) from Glasgow, they use Macor.

1276   Thu Jul 23 23:40:51 2015 DmitryDailyProgressSiFi - ringdownTaiwan cantilever - Ringdown - Continuous Q-measurements

[Nic, Zach, Matthew, Dmitry]

On Tuesday we opened the cryostat and switched the Painter 2 cantilever for the Taiwanese one (CRYO:1211). ESD seemed to be a bit too high above the cantilever and was turned upside down (the cantilever was facing the wrong side of the ESD). Nevertheless it provided enough force to excite both the first mode (106Hz) and the second one (663Hz).

Quality Factor (1st variant)

Date Frequency, Hz Q Pressure, Torr Technique
07/21/15 106 (7-8)*103 10-2 continuous Q
07/21/15 106 9*103 10-3 continuous Q
07/21/15 633 1.3*104 10-3 ringdown
07/22/15 106 3*104 10-(4-5) (*) continuous Q
07/22/15 663 1.6*104 10-(4-5) (*) ringdown

(*) it is an estimate, the gauge actually showed 10-7 torr

On Wednesday we opened the cryostat again, cleaned the surface of the cantilever (there were several smears on both surfaces), lowered the ESD (so that it is now closer to the cantilever and the side with electrodes is facing the cantilever – see the photo below) and Zach installed the guiding rods for the clamp.

Quality Factors (2nd variant)
Date Frequency, Hz Q Pressure, Torr Technique
07/22/15 106 7*103 10-3 (*) ringdown
07/22/15 663 (9-10)*103 10-3 (*) ringdown
07/23/15 106 2.3*104 10-5 (**) ringdown
07/23/15 663 8*103 10-5 (**) ringdown

(*) it is an estimate; evacuation time - ca 1.5 hours, the gauge already showed 10-7 torr.

(**) also an estimage - evacuation time - about 12 hours.

Either the surface became actually dirtier or more dusty, or the previous clamping was better.

Today with Nic's help Matthew and I were getting ourselves familiar with continuous Q measurements technique. We were able to repeat continuous Q measurement for the first mode and got close to setting up one for the second mode. The ESD is close to the node of the second mode, so the excitation is not as effective as for the first one, and the frequency is higher so it is difficult to get UGF high enough.

Nevertheless we were able to perform “proof of concept” experiment where we were driving both frequencies simultaneously and were able to change amplitudes of both modes independently.

After that we once more estimated the current quality factor values:

160Hz  - 3.2*104

663Hz -  7*103

I made a COMSOL model of the cantilever and the clamping. For some reason (most probably the big aspect ratio of cantilever's length to it's thickness) COMSOL's results are mesh dependent, no matter how coarse/fine the meash is. 3D model failed, but 2D one gives consistent results using specially designed mesh (it predicts correct 106 and 663 Hz frequencies and correct quality factors given some bulk loss factor value). Using this model I calculated the dependence of the clamping loss (through energy leakage) on the length of the part of the cantilever that is clamped (L=0..10mm). COMSOL predicts minimum loss if almost all of the cantilever's thick part is clamped  L(min)~9.7mm.

Attachment 1: COMSOL_ClampingLoss_on_length.png
1278   Sat Jul 25 16:50:13 2015 DmitryDailyProgressSiFi - ringdownTaiwan Cantilever - Update

Yesterday Matthew and I opened the cryostat in order to reclamp the cantilever (hoping to get higher Q) and move the ESD to make it face the middle of the cantilever so that the second mode would be excited more effectively.

In attempt to compensate the angle between the upper and the lower parts of the clamp and make the pressure distribution more even, we removed guiding rods and replaced them with screws:

We tried ti clamp it with 4 screws using the central holes, but the holes in the upper and lower parts of the clamping did not match so we used two guiding rod holes instead. We also left about 1/10 of the thick part of the cantilever outside the clamping. This resulted in frequencies shift (105.5Hz for the first mode and 655Hz for the second) and bad quality factor:

Pressure, Torr Frequency, Hz Q
5e-3 105.5 5.3e3
5e-3 655 2.4e3
1.5hrs evac. time, gauge reading 1e-7 105.5 9.6e3
-------------------------------------//--------------------------- 655 3e3
13hrs evac. time, gauge reading 1e-7 105.5 1.5e4
---------------------------------//--------------------- 665 1.4e3

We failed to make continuous Q measurements for the 2nd mode, as we got almost no excitation, and the effectiveness of the ESD at the 1st mode also was poor.

Today we reclamped the cantilever (holding it now by almost the full length of the thick part - minimum clamping loss according to COMSOL, two front screws only. Using 500um Si shim we were able to compensate the angle between the upper and the lower part of the clamp). We also removed part of the ESD support to make it closer to the cantilever:

The quality factor of the first mode is worse than the one achieved with the first clamping (CRYO:1276), the one of the second mode - better. We were able to repeat continuous Q measurements for the second mode, got excitation for the second mode but the UGF is still too low.

Pressure, Torr Frequency, Hz Q Comments
1e-2 106 5e3 ringdown
1e-2 663.5 1.5e4 ringdown
1e-3 106 9e3 continuous
1e-3 663.5 2.1e4 ringdown
3hrs evac time (gauge shows 2e-7) 106 1.4e4 continuous, laser attenuated (attenuator's transmission - 25%)
-----------//--------- 663.5 3.0e4 ringdown, exponential fit, laser attenuated
-----------//--------- 106 1.4e4 continuous, full laser power
-----------//--------- 663.5 3.0e4 ringdown, exponential fit, full laser power
9hrs evac time 106 2.3e4 ringdown, exponential fit
----------//---------- 663.5 3.2e4 --------//-------------------------

1292   Tue Aug 11 12:04:41 2015 ZachUpdateSiFi - ringdownReceived new Glasgow samples

I returned to my desk to find 4 new uncoated silicon samples sent from Glasgow, thanks to Stuart Reid and Iain Martin. We'll toss these into the Q setup and see how they compare to the Taiwain cantilever (which has almost the same mechanical design, but was made in a different facility using a different recipe).

1294   Tue Aug 11 21:09:32 2015 MattDailyProgressSiFi - ringdownNew Glasgow cantilever measurements

I have started taking measurements with one of the new Glasgow cantilevers (CRYO:1292). First I took some pictures out of curiosity and to see what the cantilever surface looks like before we handle them:

I think that the surface quality looks pretty comparable to the Taiwan cantilever, but I'm not being at all quantitative.

I also replaced the pressure gauge, since the old gauge wasn't giving accurate readings at low pressures (gauge would get stuck and display 2e-7 torr).

I began the measurement process by looking at the impulse response of the oscillator to find the first couple modes:

It looks like the first three modes are at 66, 417, and 1198Hz. I can easily excite the first two modes, so I'm focused on measuring the quality factor at these resonances. The first mode has a very long decay time (~450s) and starts to get clipped at medium to large amplitudes, so I wasn't able to measure the Q with a ringdown very accurately. I suspect the clipping is due to a bad clamping position, but I'll play with the optics some more to see if I can get better alignment. I measured the decay time of the 2nd mode to be ~80s, so Q=1e5. Pretty comparable to the Taiwan cantilever. This is at room temperature and 2.6e-4 torr. The filtered 2nd mode ringdown is shown below:

I tried to set up continuous measurements on the first two modes to look at Q as the pressure continues to decrease, but got the error message:

Cannot open related display:

Check EPICS_DISPLAY_PATH

when I try to set up the UGF block on the amplitude locked loop stage. It looks like the UGF.adl file in this directory has gone missing! I spent some time trying to fix this but was unsuccessful, so I'll ask around. Hopefully I will be able to take some continuous and cryogenic measurements tomorrow.

1332   Wed Sep 23 18:11:25 2015 ZachDailyProgressSiFi - ringdownRoom temp Q of most recent CIT cantilever > 10^5!

Over the past couple weeks, I have been iterating on the production process for our cantilevers, trying to get as close to Shiuh Chao's recipe as possible, but with our different design. I will make an entry dedicated to explaining the evolution of the process, but for now I want to happily report that I just measured the most recent sample that I brought over from the KNI today, and its room temperature Q appears to be in excess of 105, which is as good as we have ever seen even for the Glasgow/Taiwan cantilevers.

Here are a couple shots of the cantilever itself. I should note that there are *many* nonidealities with this sample (e.g., it is single-side polished, so the backside is very rough; it was masked using a lo-fi technique that has left the etch pattern slightly wiggly; finally, I feel that the mask can stand to be a bit thicker, as I think we had some etch-through in a few regions that should have been protected), so there is still room for improvement. The second photo here is focused on the reflection of the ceiling, so you can see the surface finish of the protected end regions and the central etched region.

Here is the ringdown. The mode frequency is about 100 Hz, so this tau of 400 s corresponds to Q ~ 1.25 x 105.

1334   Fri Oct 2 19:20:10 2015 ZachDailyProgressSiFi - ringdownCryogenic Q of CIT cantilever ~500k

After having the LN2 dewar refilled, I transferred the newest cantilever (which performed well at room temperature---see CRYO:1332) into the cryostat to make a cryogenic measurement. I had to adjust the clamping block position on the cold plate to put the smooth reflective surface of the cantilever within line of sight of the laser beam, and I think the RTD may have come loose from the block during closeout because it is registering ~100 K after 2 days of cooling.

In any case, I made several-hour measurements at two different amplitudes using the steady state technique, and found a consistent Q of about 5 x 105. This is a bit lower than what is expected given the room temperature performance---when the Glasgow/Taiwain cantilevers showed Q > 105 at room temperature, they almost always had Q $\geq$ 106 at low temperature.

I can think of at least 2 reasons we may be seeing this effect:

1. The clamp state is not good. It is well known that "bad" clamping can happen, and this can only really be evaulated empirically. I will probably try a re-clamp on this once it heats up.
2. Some kind of lossy oxide/gunk has grown on the cantilever since the nicer measurement. When the room temperature measurement was made, the cantilever had just been removed from a hydrofluoric acid clean (to remove the hard nitride etch mask). I cleaned it, carried it across campus, and installed it into the chamber. It sat in that chamber for a few days, then in the lab air for on the order of an hour while the cryostat was cycled. So, conceivably, it could have gotten dirtier in the meantime.

I will also re-measure the cantilever at room temperature in the simple chamber, to see if I can recover the result from the other day.

(P.S.: Why do images automatically get reduced now and even when you try to set their size larger upon upload it just magnifies the low-resolution copy? Pooey.)

 Quote: Over the past couple weeks, I have been iterating on the production process for our cantilevers, trying to get as close to Shiuh Chao's recipe as possible, but with our different design. I will make an entry dedicated to explaining the evolution of the process, but for now I want to happily report that I just measured the most recent sample that I brought over from the KNI today, and its room temperature Q appears to be in excess of 105, which is as good as we have ever seen even for the Glasgow/Taiwan cantilevers.

1336   Thu Oct 8 13:18:45 2015 ZachDailyProgressSiFi - ringdownPEEK problems again?

I re-measured the same cantilever in the room-temperature chamber again, and again its Q was above 100,000.

I re-installed it into the cryostat chamber, under the hypothesis that the clamping condition was bad in the previous cryogenic measurement. Instead of cooling, I left it pumping overnight at room temperature (the small pump aperture makes it take several hours to reach a good vacuum without cryopumping). When I came back the next day, at 10 uTorr, the Q was measured to be only around 30,000. So, it seems that---as I have noticed in the past---the Q is consistently lower in the cryostat.

I then took the clamp and PEEK base from the cryostat coldplate and put it in the simple chamber. I wanted to repeat the measurement in this chamber without reclamping the cantilever, but unfortunately I had to becasue I needed the reflective side up instead of down (the 45 deg mirror is below the cantilever on the coldplate but above it in the room temperature chamber). So, I reclamped it, and then measured the Q to be roughly as low as it was just before in the cryostat. So, perhaps it is the PEEK and/or newer clamp, and not the cryostat itself, which is adding the loss.

Finally, I went to take off the PEEK base and just measure with the clamp alone, but within the simple chamber and not the cryostat. Sadly, in this process, I broke the cantilever. I installed another one from the same batch and recorded a Q near 100,000 again.

So, this needs to be repeated with a better control now that I broke the original cantilever, but it seems that the PEEK spacer has been causing extra loss in the measurement. We will likely need to get a glass spacer.

 Quote: I will also re-measure the cantilever at room temperature in the simple chamber, to see if I can recover the result from the other day.
1717   Wed Sep 6 19:07:31 2017 ZachUpdateSiFi - ringdownQ measurement setup built on SiFi table, first ringdown

I began building the Q measurement setup on the W edge of the SiFi table. As before, I want to have both the IRLabs cryostat for low-temperature measurements as well as the gyro corner chamber for rapid room-temperature iteration:

I installed one of the new cantilevers (one of the hole-less ones from CRYO:1714) into the gyro chamber, then set up the laser and QPD and aligned the oplev beam.

After pumping down to ~1 mTorr, I measured the first ringdown in this new configuration:

This is the fundamental mode, with a frequency of 115 Hz. The ringdown time is ~32 seconds, giving a Q of ~11,500.

I'll need to calculate the thickness (from the mode frequency) to estimate the thermoelastic loss, which should be dominant.

1720   Thu Sep 7 14:03:24 2017 ZachUpdateSiFi - ringdownFirst new cantilever room-temperature Q ~ 10,000 (low)

Using COMSOL, I estimated the cantilever central thickness to be ~240 um. This puts the expected thermoelastic loss at room temperature at ~10-5, so there is a wide discrepancy here.

I am going to reclamp this cantilever (and/or switch it out for another one) and try again at room temperature. Remember, the best room-temperature Q we've seen for our CIT-made cantilevers has been about 105, which, again is thermoelastic-loss limited (see CRYO:1332).

 Quote: This is the fundamental mode, with a frequency of 115 Hz. The ringdown time is ~32 seconds, giving a Q of ~11,500. I'll need to calculate the thickness (from the mode frequency) to estimate the thermoelastic loss, which should be dominant.

1722   Fri Sep 8 14:48:41 2017 ZachUpdateSiFi - ringdownHole & no-hole cantilever room-temperature Q >= 10^5

I inspected the cantilever that registered the low-ish Q of 10,000 yesterday and found it to have some scratches and stuff on the underside, so I skipped trying to reclamp it and went straight onto measuring another sample from the same batch.

This sample had a lower fundamental mode frequency of ~77 Hz (I etched half of the samples in this batch for longer than the other half, making them thinner---this one is about 190 um). To my delight, it exhibited a much longer ringdown time:

For some reason, there were some odd low-frequency fluctuations (in the 10s of seconds range) evident on the decay envelope of this measurement. I investigated several possible sources, but couldn't make them go away. Nevertheless, there was a clear decay profile in every case, and the fluctuations only led to some uncertainty in the decay time. (NOTE: Today's measurements were all made by observing the decay of the mode amplitude over the maximum scope trace time of 100 s, then extrapolating.) For this sample, I estimate a decay time of 450-550 seconds, giving a Q of 1 - 1.4 x 105. For reference, the estimated thermoelastic Q limit for this sample is ~3 x 105.

After this success, I made the first measurement on a holey cantilever. I wasn't super optimistic, since the surface quality of these holed cantilevers doesn't look so great by eye after the 2nd round of etching (i.e., the thinning etch):

A first measurement of this sample gave a Q of only 10,000-20,000. However, after I reclamped it a second time, the quality shot up dramatically:

The fundamental mode is at a frequency of ~83 Hz. The ringdown time---which was much less uncertain this time---is about 400 s, giving a Q of just about 105. This sample is the longest we've ever made at 7 cm---COMSOL estimates a thickness of around 240 um. The predicted thermoelastic limit in this case is ~1.5 x 105, so we seem to be very close to it. I am pleasantly surprised by the performance of this first batch.

I started preparing the IRLabs dewar so I can take some cryogenic measurements. Unfortunately, after putting it back together (incuding with some replacement valve parts), it is not holding vacuum very well. I also want to replace the rigid Kapton wiring inside that chamber with some of the more pliable stuff Aaron and Brittany are using in their cryostats, so there is some work to be done on this unit. Fortunately, the thermoelastic loss prediction at 77 K is already quite low (i.e., no need to stabilize at 125 K to get a low-loss measurement). So, while I'd like to get some Q vs. T data with full stabilization in the near future, I can already get some good data at low temperature with minimal wiring once the vacuum problem is fixed.

Finally, one more nice result from yesterday. As you can see in the photo above, the steel clamp is mounted on a standard ThorLabs base. This is fine for doing the room temperature measurements in the gyro chamber, but it needs to have the usual PEEK base attached when it goes into the cryostat. To test the repeatability of the Q measurement, then, I vented the gyro chamber, exchanged the aluminum base for the PEEK one, then put it all back together. When I remeasured the ringdown, I found the Q to be right at 105 again. This seems to show that---so long as the actual clamping of the cantilever in the steel clamp is not disturbed---the quality of the system is fairly robust against reconfiguration/transfers/etc.

 Quote: Using COMSOL, I estimated the cantilever central thickness to be ~240 um. This puts the expected thermoelastic loss at room temperature at ~10-5, so there is a wide discrepancy here. I am going to reclamp this cantilever (and/or switch it out for another one) and try again at room temperature. Remember, the best room-temperature Q we've seen for our CIT-made cantilevers has been about 105, which, again is thermoelastic-loss limited (see CRYO:1332).

1723   Tue Sep 12 14:28:42 2017 ZachUpdateSiFi - ringdownHoled cantilever Q worse at low temperature (~30k)

I replaced a couple o-rings and that made the vacuum situation on the smaller cryostat much better. On Friday evening, I transferred the clamp-cantilever assembly onto the cryostat cold plate and pumped it. The pumping with this chamber is pretty slow, so I got impatient at about 1 mTorr and started filling it with LN2. Before doing so, I measured a Q of a few tens of thousands, the lowness of which I chalked up to residual gas damping (as I've seen lower-than-optimal Qs in the past at this pressure level). As the system started cooling, the pressure dropped more dramatically from cryotrapping, but the vibration noise was too high to get another clean Q measurement.

On Saturday, I came in after things had settled and cooled, and made another ringdown measurement:

Again, the Q came in at about 30,000, which is disappointing. I rechecked it again yesterday, after the temperature had come back up, and it was simlarly low.

I'm not sure what would cause this pretty significant Q decrease. Typically, when we are close to the thermoelastic limit at room temperature, we would see at least a slight increase in going to low temperature---or at least the same Q, in cases where we are dominated by some clamping effect at room temp.

More investigation to follow...

 Quote: The fundamental mode is at a frequency of ~83 Hz. The ringdown time---which was much less uncertain this time---is about 400 s, giving a Q of just about 105. This sample is the longest we've ever made at 7 cm---COMSOL estimates a thickness of around 240 um. The predicted thermoelastic limit in this case is ~1.5 x 105, so we seem to be very close to it. I am pleasantly surprised by the performance of this first batch. I started preparing the IRLabs dewar so I can take some cryogenic measurements. Unfortunately, after putting it back together (incuding with some replacement valve parts), it is not holding vacuum very well. I also want to replace the rigid Kapton wiring inside that chamber with some of the more pliable stuff Aaron and Brittany are using in their cryostats, so there is some work to be done on this unit. Fortunately, the thermoelastic loss prediction at 77 K is already quite low (i.e., no need to stabilize at 125 K to get a low-loss measurement). So, while I'd like to get some Q vs. T data with full stabilization in the near future, I can already get some good data at low temperature with minimal wiring once the vacuum problem is fixed. Finally, one more nice result from yesterday. As you can see in the photo above, the steel clamp is mounted on a standard ThorLabs base. This is fine for doing the room temperature measurements in the gyro chamber, but it needs to have the usual PEEK base attached when it goes into the cryostat. To test the repeatability of the Q measurement, then, I vented the gyro chamber, exchanged the aluminum base for the PEEK one, then put it all back together. When I remeasured the ringdown, I found the Q to be right at 105 again. This seems to show that---so long as the actual clamping of the cantilever in the steel clamp is not disturbed---the quality of the system is fairly robust against reconfiguration/transfers/etc.

1728   Wed Sep 20 15:23:58 2017 ZachUpdateSiFi - ringdownRecent progress

Here's a few things that have happened over the last week or so.

Opened up the cryostat a tad early

After trying some cryogenic Q measurements out for the first time in a while (see CRYO:1723), I was a bit overeager and opened up the cryostat before it had warmed all the way to room temperature (recall that I have yet to redo the wiring in the smaller cryostat, so I didn't have a temperature monitor, and the system took longer to heat up than I thought it would). So, I there was a good bit of condensation/frost on the system when I got it all the way open.

I let it dry in the air for a while, and then I figured I would try some vacuum drying/baking:

I put the clamp in the gyro chamber and tried pumping it down. Unsurprisingly, it stalled as high as a few mTorr. I made a bake setup by wrapping the chamber in heating tape and powering it through a variac. I monitored the temperature on a flange a bit away from the heating with a thermocouple. Using a slow human servo, I found a good operating point that kept the chamber outside temperature at about 60° C and let it go for a few hours. By the end, the pressure had gone below the 10-5 Torr floor of the gauge.

I then let the system cool, vented it and repumped it. It reached 10-5 Torr again within an hour or so, which is better than it ever was. As an added bonus, it will now hold below that pressure for on the order of a few minutes when sealed, which is pretty nice.

Roughing pump vibration influence on ringdowns

This is something I had looked into somewhat with the old setup, but never had a definitive result. I have been noticing that the baseline (ambient) excitation level of mode vibrations for certain cantilevers is anomalously high, leaving a very narror amplitude range above it and below the linear limit of the oplev setup in which to make a ringdown measurement. This manifests itself as a rattiness in the ringdown profile as these background excitations exchange with the resonator as it rings down. For lack of much else to try, I sealed the chamber and turned off the vacuum pump, and I noticed an immediate improvement in the smoothness and repeatablility of the ringdown.

Here is a comparison of a particular ringdown with the pump on (left) and off (right)

Presumably, this effect---which is often much more pronounced---depends on the mode overlap with the background vibrations, but I will likely make all future measurements with the pump off. The increased vacuum hold time is a boon in light of this.

I have spent most of this week at the KNI. (Thankfully, under the new management, the PECVD user group switching is being done on a regular, weekly basis, so I am on a sort of one-week-on/one-week-off schedule between here and there at the moment.) I had some holed cantilevers mid-production (the kind in part 2 of CRYO:1714), which I just finished etching today. I also made a fresh batch of the non-holed kind, using the RCA cleaning protocol that seemed very effective with the newest (holed) versions I made. These are ready for etching and should be done tomorrow.

Why am I still making no-hole cantilevers? Well, I'm noticing that the double-etch process needed to make the holed ones may be too much to expect them coming out looking very clean. I was able to get a good room temperature measurement (CRYO:1722) with one of them, but not with others, and it also didn't end up looking good at low temperature (though it's unclear why this is). I still need to try some of the passivation treatments Rana has mentioned based on what the Painter group has done.

Regardless, I have started to wonder whether making these holed cantilevers is really worth it. We need some way to attach a mirror, but this could be done in principle by mechically/laser cutting a slot on one end before the thinning takes place. If I can etch the holes myself and they turn out well, great; but, investigation of this kind of fabrication is not necessary for Voyager-type applications, and it may not be worth my time.

To that end, I'm still making the simpler cantilevers to see if they yield better and more stable quality. I'm also talking to wafer cutting/dicing companies to see if they can cut silicon pieces to look like one of these:

Attachment 4: APD_designs_9_13_17.pdf
2005   Thu Apr 5 15:28:38 2018 ZachUpdateSiFi - ringdownNewest hole cantilevers RT Q = ~80k

I performed ringdowns on the most recent batch of hole cantilevers (see CRYO:2004). This is the first set of ringdowns done with the newer clamp design (i.e., the ones that go into the main experiment) and with the precise clamp alignment procedure.

Both cantilevers had a frequency of 94 Hz. I made two ringdown measurments on each one, with a full removal and reclamp between trials.

Sample "2/27/2018 #1A1" exhibited a Q of 83k on the first trial, and again 83k on the second trial. This is near the thermoelastic limit for this specimen, and the reproducibility is very nice.

Sample "2/27/2018 #1A2" exhibited a Q of 88k on the first trial, but only 74k on the second trial.

Therefore, it seems that while the new clamps are capable of being very robust, it is still possible for clamping effects to come into play.

Also, I found the odd triangular-connector breakout cable that I need to interface with the feedthrough on the smaller cryostat! After tearing the Cryo Lab up looking for it, I found it in the EE Shop :-)

2072   Sat Jun 16 22:45:31 2018 ranaSummarySiFi - ringdownModeringer: commissioning the MR4 servo for the 497 Hz mode of the current cantilever

With Zach's advice, I got the settings set up for Moderinger Q measurements of the 497 Hz mode of the existing cantilever.

Steps:

1. In the Differentiator button, I put a filter which is a differentiator. It has a zero at DC and a pole at 900 Hz. It has unity gain at 497 Hz. This filter bank should firmly saturate the "saturation" block, so increase the gain in there until the output is > 1000 cts p-p at the desired oscillation amplitude.
2. In the "Deqsquare" button, put a low pass filter to remove the harmonics of the square wave, changing it back to a sine wave.
3. In the bandpass bank, put a 4th order Butterworth bandpass with a ~10 Hz width around the desired frequency.
4. In the "Energy" bank, put a low pass filter (~5-10 Hz) to remove the high freq signal components from the RMS.
5. In "PWRCTRL", put the loop shaping filter. At the moment, I just have a pure integrator.
6. The UGF servo is disabled and the screen doesn't work, so don't worry about it for now. Fix it later.

The attached stripchart shows the performance. Once the loop is engaged, stepping aroun the setpoint changes the amplitude of the oscillation at 497 Hz. The loop itself is sort of ringy with a UGF of a couple minutes. We could tune this up later if we wanted.

The Q of this mode (at some? low temp -- the dipstick shows ~1" of LN2) is (Q = pi * f * tau) pi * 497 * 120 ~ 190k.

Earlier today, we noticed that banging on the cryostat with a wrench can change the Q of some modes. This implies that maybe somethings touching or that there is a burr or piece of schmutz between the clamp and the cantilever. Banging on the can didn't change this mode by more than 10%, so maybe this is a good candidate to measure in the cavity setup.

Attachment 1: mr4.png
Attachment 2: ModeRinger4-performance.png
209   Fri Jun 24 01:16:35 2011 FrankHowToSimulationMultilayer Control of an Optical Reference Cavity

found this one while looking for publications on thermal modeling of refcavs:

http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5447814

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4416756

done in comsol see here:

Simulation of a Multilayer Thermal Regulator for an Optical Reference      http://www.comsol.com/papers/7236/

214   Mon Jun 27 15:28:43 2011 JennyDailyProgressSimulationMaking COMSOL solution match analytical solution part II

I ran this new simulation of silicon and foam. Here's a picture of the model (again with the foam in red and the silicon in blue):

I changed the dimensions to two cylinders, each of length 1 mm and each of radius 10 cm for two main reasons:

1) A short, wide silicon cylinder has a lower thermal resistance than a long one. The approximation in which I neglect its resistance becomes more accurate.

2) I didn't want to make the foam cylinder so long that its thermal resistance was so large that the time constant of the system was on the order of days. These dimensions gave a time constant (in my pen-and-paper calculations) of 43.6 seconds.

My first run popped out a time constant of 50 seconds. That's a 13% difference from my calculations.

Then I noticed that the solver was only updating the solution every ~10 seconds. I told it to update every second instead and got a time constant of 46 seconds, a 5% difference.

In summary:

Percent difference between calculated time constant and COMSOL time constant

• Si w/o foam, computer-generated timesteps: 40%
• Si w/ foam, computer-generated timesteps: 13%
• Si w/ foam, max timestep of 1 second: 5%

Here's a plot of temperature at each end of the silicon cylinder.

It just looks like one line because there is essentially no temperature gradient over the cylinder. Both ends are at the same temperature to the 4th decimal place.

217   Tue Jun 28 22:24:14 2011 JennyDailyProgressSimulationRadiation in COMSOL

I built this model today:

Info:
•    2D axisymmetric model
•    120 K cryo cavity and 120 K shield
⁃   cavity height: 10 cm
⁃   dx=1 cm (thickness of shield AND distance from outer radius of cav. to inner radius of shield AND distance from top and bottom of cav. to top and bottom of shield)
•    All materials: silicon, bulk
⁃   emissivity: 0.9 for shield, 0.1 for cavity
⁃   everything else: from material
•    Physics
⁃    ambient temp: 120 K
⁃    no heat flux from boundaries via conduction
⁃    conduction within cavity and shield
⁃    both cavity and shell initially at 120 K
⁃    step function
⁃    outside boundary of shield set to 120.1 K at time t=0
•    Results: time-dependent
⁃    probing temp of inside of cavity
⁃    time constant tau= 3.72*10^5 s = 103 h

The time constant DMass calculated was 640 h for similar dimensions and material properties... The reason for this discrepancy is still unclear.

Inside center of cavity:

Next I'm going to change the dimensions, materials, and temperature conditions to more closely reflect the room temperature cavity on which I can take real measurements. Then I'll work on fitting the simulation point-probe output in Matlab and try to identify the both the radiative pole and the pole for conduction through the materials.

Also I'm going to go through the radiative heat transfer calculations and see if the COMSOL output for the time constant matches what I'd expect.

222   Thu Jun 30 19:10:08 2011 JennyDailyProgressSimulationSimple model of room temp cavity

I changed the geometry, material properties, and temperature of my model to more closely mimic the cavity and vacuum tube in the lab downstairs.

I've now saved all of my comsol models, images, and text files to the SVN in case anyone wants to look at or fiddle with them.

File title: 6-29_cavity_vactube
•    2D axisymmetric model
•    Materials
⁃    295 K fused silica cavity (Corning 7940, solid, NIST SRM 739 Type I)
⁃    295 K stainless steel vacuum tube (UNS S30400, solid, polished)
•    Geometry
⁃    cavity diameter = 2"
⁃    cavity length = 8"
⁃    vacuum tube diameter = 8"
⁃    vacuum tube length = 22" (this is not counting flanges)
⁃    vacuum tube thickness = 0.12"
•    Physics
⁃    ambient temp: 295 K
⁃    no heat flux from boundaries
⁃    strain reference temperature: T
⁃    conduction within cavity and shield
⁃    both cavity and shell initially at 295 K
⁃    boundary step function
⁃    outside of tube set to 295.1 K at time t = 0
•    Results: time-dependent
⁃    probing temp of inside of cavity
⁃    Time constants:
1) Conduction through vac tube: 5 seconds
2) Radiation to cavity: 2 hours

It looks like this at time t = 0:

Videos, demonstrating conduction through vacuum tube and radiation between tube and cavity

• Video #1 (First 8 seconds show heat propagating through stainless steel vacuum tube.)
• Video #2 (All 30,000 seconds of simulation, showing heat  propagating to inner cavity from outer tube.)

I probed the temperature evolution of the point at the very center of the inner cavity. I fit it to an exponential on Igor Pro and got the following fit:

T(t)=T_0-A*exp[-t/tau] with

• T_0 = (295.10000 +- 0.00005) K
• A = (-0.10268 +- 0.00008) K
• tau= 7180 +- 15 s

Here's the plot (bottom curve, blue dots) and fit (red line) with residuals plotted up top (also blue dots).

My next task is to find a function that fits better, that takes into account the conduction through the stainless steel and fused silica.

Notes on materials:

• Corning 7940 is the only kind of fused silica in the COMSOL model library.
• NIST SRM 739 Type I is one of many orientations/variations for Corning 7940. I don't know which, if any of the options, is the kind we're using.
241   Thu Jul 14 15:12:43 2011 JennyDailyProgressSimulationSimple model of room temp cavity

Update: More exciting video (by which i mean the same video with some Bach music added and a slightly faster frame rate)

252   Wed Jul 20 09:19:52 2011 JennyUpdateSimulationModel parameter sweeps: temp step and emissivities

I did some simulations of my simplified cavity and surrounding enclosure while changing parameters. The parameters I changed were

• cavity emissivity
• surrounding stainless steel enclosure emissivity
• temperature step

I recorded the time constant (assuming a single pole and looking at where the curve reaches 1-1/e of the temperature step).

Temperature Step Sweep

I used 10 second time steps in the simulation and got the following table (with cavity emissivity e_cav = 0.7 and surrounding enclosure emissivity e_s = 0.1)

 temp step [K] time const [s] 10 9820 1 10340 0.1 10400 0.01 10400 0.001 10400 0.000001 10400

As the temperature step gets smaller, variation between any step responses diminishes. If I normalize the responses so that the all start at 0 and end at 1, as the

following graph shows, the curves that correspond to smaller temperature steps lie on top of each other, whereas those corresponding to larger temperature steps differ more.

Top Graph: Temperature response to a boundary step function for different temperature step sizes, as a fraction of the temperature step.

Bottom Graph: Difference between fractional temperature response for different step sizes relative to temp response for Tstep=0.01K (absolute value)

So for smaller temp steps it appears that I am limited by the number of decimal places recorded in the solver. Currently the solver is outputting 10 decimal places,

which may be fewer than the number it's actually using in its calculations, so I may be able to go to even smaller temp steps if necessary. The

responses are essentially identical for 0.1 K temp steps and below. For larger temperature steps, it is likely that the linear approximation no longer holds,

and the time constant begins to depend on the temperature step.

I also tried a range of temperature steps for different input emissivities and saw the same trend.

Emissivity Sweeps:

I chose a temp step of 0.01K. Here are my data and fits:

For e_s=0.01: tau(e_cav)=(3100±30)*e_cav^(0.994±0.004)+(27870±50)

For e_s=0.05: tau(e_cav)=(3080± 20)*e_cav^(-0.996 ± 0.003)+(5980± 40)

For e_s=0.2: tau(e_cav)=(3070± 30)*e_cav^(-0.997 ± 0.003)+(1800± 40)

For a constant surroundings emissivity, the time constant goes as 1/e_cav. For a constant cavity emissivity, the time constant goes as 1/e_s.

This is consistent with David's calculation which gave , assuming small e1 and e2 such that the e1e2 term can be neglected.

Here's a 3-D Plot:

And here''s the actual data in a table:

 temp step=.01K e_ cav e_s tau (s) notes 0.1 0.01 58400 100 s timesteps 0.2 0.01 43200 0.3 0.01 38100 0.4 0.01 35600 0.5 0.01 34000 0.7 0.01 32300 0.9 0.01 31300 0.1 0.05 36500 0.2 0.05 21300 0.3 0.05 16200 0.4 0.05 13650 50 s timesteps 0.5 0.05 12100 100 s timesteps 0.7 0.05 10400 0.9 0.05 9400 0.1 0.2 32300 50 s time steps 0.2 0.2 17100 0.3 0.2 12000 0.4 0.2 9450 0.5 0.2 7900 20 s timesteps 0.7 0.2 6200 0.9 0.2 5220

279   Mon Aug 8 12:57:44 2011 JennyUpdateSimulationSimplified cryo cavity simulation

I made a simplified cryogenic model.

This is a 2D axisymmetric model. The inner cavity is silicon and the outder shields are both aluminum.

The dimensions are the same as those in the drawings for the physical cryogenic cavities being built.

I wanted to see how long the inner radiation shield took to cool to the temperature of the outer shield, first first with no conductive links between the cavity and either of the shields.

I set the entire system to 120K initially except for the outer edge of the outer radiation shield, which is set to 125K at time t=0. The cavity and inner shield cool to 120K during the duration of the simulation.

The inner radiation shield has changed by 1-1/e of the temperature step after 3.0 x 10^5 s or 83 hrs

The cavity interior hadschanged by 1-1/e of the temp step after 4.25 x 10^5 s or 118 hrs.

This further supports Frank's finding that if time constants of the thermal coupling in this system are to be on the order of an hour, the dominating form of heat transfer will be conduction through the links between the shields and the cavity.

It makes sense that this system I have modeled would have two radiative poles. Fitting this on matlab may allow for identifying them separately from one another.

My next step in modeling is to add a conductive link and run the same simulation. Since I'm working in 2D axisymmetric mode, the link will be a thin disk. To account for the added cross-sectional area through which heat can flow, I'll decrease the thermal conductivity of the material accordingly.

673   Sun Feb 3 21:39:20 2013 DmassComputingSimulationSpice on MAC

Keeping a checklist (to become a recipe) for installing LTSpice on OS X via Wine. Some info was found here helpful hacker dude

1. Install Macports (via .dmg file for OS 10.7)
2. >  sudo port -v selfupdate      % update macports
3. check shell: bash
4. Install and update XCode (can do via app store)
5.  Build Wine
• section title "Build Wine, the MacPorts way"
•  >  sudo port install git-core wine-devel   (from "Build Wine git version, the MacPorts way"
• Took a while installing things - ~
• Error: org.macports.build for port wine-devel returned: command execution failed
To report a bug, follow the instructions in the guide:
http://guide.macports.org/#project.tickets
Error: Processing of port wine-devel failed
• Googled a small amount, idk what the problem is
• sudo port install wine   (installs 1.4.1 instead)
• Install seemed successful based on messages
• sudo port -v selfupdate
• Total number of ports parsed:    19
Ports successfully parsed:    19
Ports failed:            0
Up-to-date ports skipped:    16414
• checked ~/.profile as per instructions in above link
• added this command to profile as per recommendation in above link:
• export DYLD_FALLBACK_LIBRARY_PATH="/usr/X11/lib:/usr/lib:/opt/local/lib"
•  >   if [ sysctl -n hw.cpu64bit_capable -eq 1 ] ; then echo "+universal" | sudo tee -a /opt/local/etc/macports/variants.conf; else echo "not 64bit capable"; fi
• This command suggested by helpful hacker dude
• output "+universal" -> macports knows whether or not it is good with 64 bit
• > sudo xcodebuild -license   (agree to xcode license)
> wine LTspiceIV.exe
errors came up, but installer window also came up - clicked install @ C:/program files etc...
LTSpice opened
error on opening LTSpice in Wine:   Dynamic session lookup supported but failed: launchd did not provide a socket path, verify that org.freedesktop.dbus-session.plist is loaded!
Drawing things seems to work. I will play more tomorrow. Also fix the terrible formatting in this elog.

The above tells macports to start up D-bus each time, and made that error go away



Up soon: use dropbox to get my spice topology set up and synched between my machines.

677   Tue Feb 5 00:19:31 2013 DmassComputingSimulationLISO

I have talked to Zach and he has sent me the working LISO model of the PDHv2 schematic. Instead of burying my head in this problem, I have borrowed a second LB1005 box, since we know that works to get a ~150kHz loop, and am going to try to get initial beat that way.

843   Thu Sep 5 15:57:26 2013 EvanDailyProgressSimulationFirst go at cavity seismic coupling in Comsol

Nic gave me Tara's Comsol model (and associated matlab code) for computing cavity sag, and I've begun adapting it to the cryo cavities. The model currently uses a four-point support for the cavity, with two planes of symmetry to simplify the computation (see attached picture). I've changed the cavity dimensions to match the cryo cavity dimensions and changed the material to amorphous silicon. I've used amorphous silicon as a stand-in until I verify that the monocrystalline silicon option in Comsol is going to give the right behavior; since the elasticity is anisotropic, the crystal direction must be chosen correctly.

The support geometry is parametrized by (a) the distance between the supports and (b) the angle of the supports from the horizontal (so a support angle of 90° means the supports are directly underneath the cavity). I ran a series of simulations varying these parameters; the resulting mirror tilt is shown in the attached color plot. The color plot preserves the sign of the tilt, so zero tilt is a soothing aquamarine. The Airy point (L/rt(3)) is 2.3 inches, so the zero tilt from the simulation seems reasonable.

This modified Comsol model to is checked into the svn at /trunk/CryoLab/comsol.

From here, the next steps are

1. Find papers on existing suspension geometries to figure out existing designs as well as what figures of merit they use to characterize seismic coupling.
2. Change the material to be monocrystalline silicon. [2013–09–11: I've done this, and I've put the longitudinal axis of the spacer to be the (100) axis of the silicon. There is still freedom to pick the orientation of one of the other two axes, (010) and (001), and this will slightly affect the elasticity matrix. But so far the results don't look earth-shatteringly different from the results with amorphous silicon.]
3. Compute both the sag and the tilt of the mirrors, and convert these numbers into effective change in cavity length. [2013–09–19: This is done, and the result is further converted into frequency change per g of acceleration. See elog 863.]
4. Look for a minimum or zero crossing in the seismic coupling as a function of support geometry; try to extract the appropriate derivatives to arrive at a simple model of the sensitivity of the coupling w.r.t. small changes in support point positions and in other parameters. Specifically, these are
1. sensitivity w.r.t. support angle,
2. sensitivity w.r.t. support angle,
3. sensitivity w.r.t. variations in g [to test the validity of interpreting the sag (in meters) as a seismic coupling (in meters per g)], and
4. sensitivity w.r.t. variations in area of contact with the support.
5. See how items (2) and (3) are affected by small common mode errors in the support points, since we found the differential minimum (e.g. support points at -49 and +51 deg, and similarly for distance between spacer COM and support points) [2013–09–19: Comsol says there is a zero crossing for very shallow support angles (<5° or so). Rana said at last week's meeting that going for a zero crossing and tons of sensitivity optimization is overkill; we should just pick something that gives frequency noise on par with existing low-noise cavities.]
6. Some time in the future: estimate the dynamic response of the cavity sag in response to small oscillatory accelerations.

Edit: after discussion with David I think we're in agreement that mirror tilt is not the important effect here for changing the effective cavity length. More important is the change in the mirror separation distance. Quantitatively, the change in the effective cavity length is Δx + R(Δφ)2, where Δx is the change in mirror separation and Δφ is the tilt in radians. I've included a color plot of Δx below. I'm currently trying to figure out whether it makes physical sense for the separation to go through a maximum as the support distance is varied.

Attachment 1: cryo_cav_comsol.jpg
Attachment 2: cryo_cav_sagging.pdf
Attachment 3: cavity_length_change.pdf
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