[Giordon, Alastair, Zach]

Alastair dropped by today and showed us how to use the HV amplifier.

When we got to the lab, we turned on the ion gauge and the pressure reading in the tank was ~10^-7 Torr, which Alastair reckoned was pretty good for one day of pumping with the large tank-mounted turbo (Giordon thought he turned this on over the weekend but it looks like a cable was unplugged). Alastair instructed us on how to rig things up and then safely turn things on and off. We tested the ESD with a maximum DC offset of 3 kV and AC amplitude of 1.5 kV @ 1 kHz, and nothing seemed to spark or explode. 

Giordon and I then did some initial sweep testing by driving the amp with an Agilent function generator. Using the frequency estimates he posted before, we set up some narrow-band, slow sweeps across some of the modes and then monitored the spectrum of the PD difference signal on a spectrum analyzer in FFT mode. Alastair recommended doing it this way instead of taking a swept sine with the analyzer alone in order to better distinguish between a real signal and a spurious EM coupling.

All in all, we weren't that successful. We did see some cases of what appeared to be modes, roughly where his COMSOL model predicted, but they each had their own problems. The differences in measured vs. predicted eigenfrequencies were all at the high end or slightly beyond the bounds that he put on them by varying sample dimensions. It could be that some other material properties are off.

Here is a list of a few modes we sought to measure (if Giordon sees this perhaps he can upload his fancy animations so we can see what the modes physically look like):

• ~5 kHz
  • This mode was completely swamped by some sort of intermittent glitching, which was apparent up to ~10 kHz or so
• ~25 kHz
  • This was the most promising one we looked at today, but we saw some sort of strange double-peaking at some FFT spans and then not when we zoomed in to lower span. The model doesn't predict two nearly degenerate modes here, so there should in fact only be one. A common feature to all of the modes we actually resolved was broadening or sidebands from low-frequency solid-body motion of the sample (e.g., pendulum, torsional, tilting).
  • I think the next step should be to look at this mode in particular but with the proper lock-in readout
  • I very roughly measured its linewidth to be ~2 Hz. If in fact the measurement is valid then it places a lower bound on the mode Q of ~10⁴
• ~44 kHz (x2)
  • The model DOES predict two nearly degenerate modes here, and we saw some very broad peaks in this region. I'm not sure yet what the degeneracy means for our measurements.
• ~80 kHz and above
  • It appears that modes of this high a frequency are too quiet for us to see, and any attempts to drive them were fruitless. Of course, the lock-in readout might help us to find them.

Lots more to come on Friday.

Giordon did see eLog post. Here are fancy gifs. Click an image to see it in a new tab/window for animation to happen. I've attached a zip file that contains all gifs (for properly downloading). Images shown below are in order of increasing eigenfrequency (from the first "non"-translational mode [re: no fixed point]) to the 9th mode as referenced based on the bolded line in the PDF linked to the comment I've replied to.

In order to accentuate the thermal noise in a silicon test cavity, it would be nice to make the ribbons a little bit thicker. Sadly, the BQuad thermal noise model seems to explode when the fibers get thicker.

The three plots I will show have the following parameters in common:

4 fibers, single pendulum silicon suspension @120K. 10g mirror mass, 5cm fiber length, 2cm cavity length. The fiber width is 2mm and the fiber thickness varies in the three plots.

The first shows a fiber thickness of 0.05mm. The second has 0.1mm, and the third is 0.2mm.

As one can see, the model sort of goes more and more nuts as the thickness is increased. I don't really understand the model enough to know why this is the case, but it seems that to have a believable noise budget we might need to make a thermal noise model from scratch, rather than using gwincdev.

Heimann (HTPA80x64d) thermopile array;

- First test to grab frames was done in my personal Win10 machine, with no success. Either I was unable to configure the server correctly, or the software "ArraySoft" is not supported in Win10. Upon contacting Heimann, I received instructions to update to a newer version but was warned that it's just a new GUI, nothing really changed from v1 --> v2. So didn't even bother.

- Instead, wrote a simple python-socket UDP server to catch the video stream. Most trouble happened when using temperature mode (command "K"). The client streams a bunch of zeros... My guess is that this unit does not have an internal temperature calibration, and one could in principle be uploaded but we probably don't care. Streaming in raw voltage mode (command "t") works well, as shown by the sample frame shown in Attachment 1.

- After recovering the CTN Win7 laptop from Radhika, I gave "ArraySoft" another change just to know the frames I was getting in python were not bogus. For this I pointed a 532 nm laser pointer straight to the sensor and got an image shown in Attachment 2. The key difference is the processing of the video stream. Attachment 1 is a single frame, while Attachment 2 is the average of 30 frames with no offsets present. 

- Another issue present during this task was a faulty USB connection. Sometimes moving the sensor around would interrupt the stream (power lost). I carefully removed the case and exposed the TO-39 package and surrounding electronics to inspect and search possible failures but after seeing none, I swaped the USB power cable with my portable battery charger and had a more robust operation... So I dumped the old USB cable, and will get a new one.

- Since this one was borrowed from TCS lab, I placed an order for another one which will be set up permanently in the lab. Hopefully this will be enough for the OSA.

Just to add a little bit more details to the previous elog:

To obtain matched magnets, we measured the magnetic field strength of the magnets. We have two type of magnets: the
first one (for fixed magnets) is 1 inch in diameter and 1/32" inch thickness; the other one (for the levitated plate) is 1/2 inch
in diameter and 1/8" inch thickness [refer to the schematic for illustration]:

In total, we bought 12 1'' ones and 12 1/2" ones [we want to get the distribution before ordering more]. We used a Gauss meter
to measure the strength [in the axial direction]. We used a plastic block to fixed the distance between the Gauss meter and
the magnets.

For the 1" ones, the measured values are {94.9, 126.3,84.6, 109.8, 117.1, 94.2, 104.8,96.5,116.3 108.5,98.0,122.6}. The histogram
is the following [normalized with respect to the total number and the horizontal axis is Gauss]:



We fitted it with a Gaussian distribution with mean of 106.1 Gauss and variance of 12.8 Gauss.

For the 1/2" ones, the measured values are {126.7,131.9,127.9,129.3,125.8,133.1,132.4,124.8,130.7,125.0,136.2,135.0}. We
fitted it with a Gaussian distribution with mean of 130.0 Gauss and variance of 3.9 Gauss.

The 1/2" ones have a much smaller variance.

Even though the quantity is small, we were able to find 4 pairs of matched ones that are differed by 5%. Interestingly, since
the force between two magnets depends on the product of their strength, we can choose the magnets in such a way that
if the fixed magnets is 5% weaker, we can compensate it by choosing the levitated magnets is 5% stronger. This needs to
be confirmed by the force measurement. Just in case, we have ordered more 1" magnets.

There is no evidence of hysteresis in the latest measurements. The plot below zooms in to the few cycles in the middle of the upper plot.

The thick black areas are created by the proper mode of the tiltmeter and air currents.

Here are some notes and pictures of what was done yesterday for the in-vac setup:

Giordon has already reported on the ESD support. To make this, I drilled the Teflon bars I had made up in the appropriate way. The two side bars have oblong holes near the center (but shifted aft a bit), so that the crossbar holding the ESD can be adjusted finely in depth. The crossbar has several holes across the middle (perpendicular to the holes that mount it to the side bars), spaced so that the ESD can be moved left or right a bit as necessary to combat cancellation from symmetry. See his entry for a good picture.

While he worked on actually attaching it to the suspension, I was working on the HV connection. I decided the best way to do it was to mount the PEEK connector to a Teflon spacer, which is mounted to the base of the chamber via 1/4-20 vented and silvered cap screw. I countersunk the hole in the Teflon for the PEEK-mounting 8-32 screw so that I could fit the nut underneath. Here's a shot:

On one side of the connector, we have the HV supply provided by cable from the SHV connection on the side of the chamber, and the ground is provided by a cable that is screwed directly into the chamber base via 1/4-20 vented and silvered cap screw. Of course, I verified that the entire tank is indeed grounded with respect to the HV amp. Here is the whole assembly in the chamber:

I'm not crazy about the angles of the cables coming out of the connector, so I may choose to shorten them.

I also connected the other cables (which will go into the PEEK connector from the other side) to the real ESD---which I also drilled beam holes into---with silver epoxy. The stuff is a bit of a pain in the ass, and I had to apply a good bit of it just to make sure the wire would be (mostly) submerged. I left it drying under foil.

With this, we should be pretty much ready to weld in the sample and pump everything down on Monday.

I used the matlab function margin() to plot the phase and gain margins for the open-loop transfer function for maglev. It seems to give an incorrect answer. Here is what I got:

As the gain margin is negative, this indicates that the system (plant + controller) is unstable. However, this is not the case.

I used the matlab function nyquist() to make a Nyquist plot, and this is what I got:

The contour circles -1 counter-clock wise once, and this satisfies the Nyquist stability criterion, as the plant (in my case the plate can be modeled as a mechanical object attached to a negative spring) has one pole on the right-half complex plane. Basically, my plant together with the controller in indeed stable, which is also the reality.

Therefore, this seems to indicate that nyquist(), instead of margin() is the right way to examine the stability in the case with an unstable plant in matlab.

To better understand the digital control system, we first tried to control a single degree of freedom (DOF) with Labview
and NI DAQ system yesterday. We relaxed the constraint on the angular motion of the levitated plate [it was constrained
by mechanical springs originally]. This allows us effectively to have a single DOF system to work with [as shown by the
figure below]:



The experimental setup and its schematic goes as follows:



We used SR560 as a low-pass filter for anti-aliasing. The corner frequency for the low-pass filter is 100Hz.

After adjusting the working point, we get the error signal. In the figures below, we showed the error signal (orange curve) from the OSEM and the control
signal (cyan curve) from the analog output of the national instrument (NI) card, before (left figure) and after (right figure) the low-pass filter is turned off. 

From the signal we can see that the system is oscillatory. It does not decrease when we apply the derivative control. From the control signal, we can
see that the sampling rate is very low, and the control signal is clearly discrete with a rate around 50ms. Probably this is why we can not have a stable
control. Can someone give us some suggestions on how to proceed? Thanks.
 

 - The previous entry showed that the sampling rate is 1ms.

If the loop is really running at 50ms, you should see an error output from the "timed-loop structure".

If the timeout error is found, the servo does not make sense anymore.

- Why don't you take the transfer function of the digital servo filter separately from the closed loop?

Thank you very much for your reply.

>> - The previous entry showed that the sampling rate is 1ms.

Yes, indeed it was. Actually, even in the current setup, the sampling rate for the channel is set to be 1kHz.
Jan told me the highest sampling frequency that we can get is of the order of 100kHz.

>> - If the loop is really running at 50ms, you should see an error output from the "timed-loop structure".

When we changed the loop time constant from 1ms to 100ms, it seems that there is no change at all. The control signal
still behaves like that. Maybe we do not know how to set it up correctly. However, there is no error output from the "timed-loop structure".
We will look into this more carefully.  Right now, we really have very poor knowledge of the digital system. I will come up to 40m
to bother you with few more questions tomorrow, if you will be around.

Since the plate is levitating, we are now in the position for real work. Here are the two major issues to investigate in the plan.

1. TF of the plate and cross coupling among different degrees of freedom (important in order to optimize the control servo)

We will measure various transfer functions to characterize the plate TF and cross couplings. We will build six degrees of freedom simulink model based on Georgios's work of three DOFs, and try to make a match between the model and the system.

2. Noise budget (to pin down the major noise source)

(a) sensing and actuation noise

We will calibrate the noise from the hall effect sensor. If it is confirmed to be the major noise, we can switch to the optical lever sensing scheme as planned. The coil is quite weak, in terms of voltage to force conversion factor, and it is 5mN/V. The thermal noise of the coil may not be important (to be confirmed with more rigorous analysis).

(c) acoustic noise

Right now the system is exposed in air, and it is anticipated that the acoustic noise is quite significant. To mitigate this noise, we can use a bell jar to cover it which can give a reasonable level of noise isolation.

(b) seismic noise

We will make a correlation measurement between the sensor output and the seismometer (or accelerometer) to see where the seismic noise dominates.

(d) ambient magnetic field noise

We will use two low-noise honeywell hall effect sensors [link] to measure the ambient magnetic field. To get a better sensitivity, we will use differential measurement by shielding one (together with instrumentation amplifier for amplifying the readout).

(e) thermal noise of the magnet

The major noise source comes from the random jitering of the magnetic moments due to thermal excitation. We can find the literature on how to analyze this kind of noise.

(f) long-term drift

We know little about the long stability of the magnets and also how the temperature drift affects the magnets. This needs to be investigated.

  This is a great find! The laser power fluctuations are limiting the interferometer noise. Now all you have to do is fix that.

You should maximize the output of the fiber after pump down. If its very sensitive to the knobs, maybe get more sensitive knobs. You will need to reduce the jitter -> intensity coupling by a factor of 1000 in order to get to the level that they had before.

Then remember that the sensitivity of the Michelson to intensity noise goes down as you reduce the Michelson offset. Instead of operating at mid-fringe, if you are able to turn up the loop gain you should be able to go to 1/100 of mid-fringe and get a nice noise reduction.

By tightening the hell out of the coupler and laser mount posts, and mounting them on an optics breadboard resting on some squishy rubber I had laying around, I am able to get better RIN coming out of the fiber.

There is still plenty of room for improvement. The coupler alignment is kind of tricky; there are little screw to lock the adjustment stage in place which I hope would reduce the amount of jitter, but when I tighten them, it hurts my coupling, probably by affecting the alignment.

Today, I'm going to try and align and take some data to check out my noise performance and try to get an upper limit (again), since I don't really trust my last attempt. We'll see how alignment goes, seeing as I spent an inordinate amount of time yesterday trying to align to no avail. 

 Lab room phone: (626) 395-3877

Also, does anyone know the password for the lab room computer? It's the one that says "controls for dhcp-123-221.caltech.edu"

 The lab floor is being mopped tomorrow. Perhaps this would be a good time to clean/put stuff away? (I did start on this a little last week, but much can still be done)

I took the liberty of tidying up the Crackling table a bit.

The Cryo people left us a friendly reminder to "get our own shit": they had found many parts from their own experiment being used or lying around on our Crackling table. Parts belonging to the Cryo experiment are labeled with a dot of gold nail polish. I'm fairly sure I found, switched out and put away all these gold-dotted parts that were lying around on our Crackling table as I was cleaning up.

After modifying the digital and analog part, we demonstrated levitation of a single degree of freedom [one corner of the
the levitation plate (as explained in the previous Elog 321)]. This time, we again use the trick of eddy-current damping
by placing an aluminum plate above the levitated magnet to obtain enough phase margin. Because we have a poor modelling
of our plant, the circuit we design [the details will be shown below] cannot provide enough phase margin. We are now
trying to measure the plant transfer function [only possible if it is levitated] and modify our circuit. In the next stage, we will try
to levitate two corners of the plate, which has two degrees of freedom, before we jump to levitate the entire plate (three degrees
of freedom that need to be controlled in the current scheme).

We took a photo of the plate corner and also the control and error signals from the oscilloscope.

(the yellow curve shows the error signal from the sensor and the blue curve shows the control signal).

Yesterday, we try to measure the entire open-loop transfer function [especially to get the TF for the plant part] by
injecting signal after the sensor with preamplifier SR560 as a summing amplifier (as shown by the figure below). Due to
the transient signal (before reaching the steady state) from the OSEM always saturate the SR560, we cannot get the right
control signal to achieve a stable levitation. We then try to use Labview to measure the transfer function by using the
build-in vi: "response function measurement. vi", but the resulting curve is very bumpy and we cannot make any sense out
of it. The possible solution is to make our own summing amplifier which allows a large voltage input and output.

___________________________________________________________________________________________________

During the last few days, we have modified both the digital and analog parts of our system. The detailed modifications and
related issues are shown as follows:

>> Digital part:

[TF measurement] We change the time-loop structure, and now the sampling rate becomes higher than what has been shown
in Elog 321. To tell the new sampling rate and the time delay of the digital path, we use SR785 to make a direct frequency
measurement, instead of using oscilloscope. We can tell the time delay from the phase. The bode plot of the TF for the digital path
[a direct path with 2-order low pass filter around 170 Hz] is shown by the figure below:

From this curve, we learn that the sampling rate is around 300Hz (from the dip of the spectrum?), and the time delay is 4.6ms
---not a very decent DAQ, but sufficient at this preliminary stage.

[issue in computational power] We found a very critical problem in our digital system---the computer does not work properly (the computer is
a quite old one) and screws up the gain if we run other programs simultaneously (even open IE) or other graphic processes. Below we show the
difference in TF of the digital part between turning on and off the waveform chart in Labview for showing real-time control signal.


As we can see that the gains at high frequencies (above 5Hz) go down significantly.

[issue in PID controller] Initially, we used the build-in "PID.vi" in the Labivew to try the digital control. As it turns out that the derivative part of the
PID does not work properly. We can clearly see many spikes in the control signal if we set the gain of the derivative control to be nonzero. This is
partially because the discreteness of the signal from the ADC, and the simply derivative control in the "PID.vi" is not band-limited. The high frequency
part of the signal screws up the derivative controller. Instead, we realize lead compensation by using an analog circuit. In the mean time, we will
try to add lead compensation by using a digital filter which is band-limited.

>> Analog part:



We have made many small changes to the analog circuit [as shown by the figure above]. Initially, channel two and three are coupled, as we want their signal difference.
Now we decouple them. We then have four parallel channels for the feedback control. We replaced many components to realize the following transfer function
[left panel shows the amplitude and the right panel shows the phase in degree (red cure is the calculated one and blue curve is measured one)]:



Initially, we thought that we have a reasonable good understanding of the plant, and the above circuit can provide a stable levitation
by using the Nyquist stability criterion, which turns out to be not the case. The design open-loop transfer function has a unit gain
frequency at 8Hz with a phase margin of 20 degree, as shown by the figure below:


The transfer function that we assumed for the plant goes as follows [based on our measurement]:

* coil to levitated magnet: 7.7 x 10^{-3} N/V
* magnet itself is modelled by a negative spring---the negative spring constant is -50N/m with mass equation to 240g
* the flag to the sensor (i.e., the displacement to the sensor output): 71 V/m

Now by using the stably-levitated system, we will be able to have more accurate measurements of the plant TF, and we can then
figure out what is the right filter for the lead compensation.

I could lock the Michelson for several seconds.
When I try to lock the Michelson, it seems that a noise at 200Hz grows up and breaks the lock. (Oscilloscope signal)
I measured a noise spectrum over a short time when the Michelson was locked. (Graph)
There are peeks at 53Hz and 214Hz.

I had tried to lock the Michelson by tow masses.
I hung another mass in a same way. (Fig)
I adjusted the filter, but I could not control.
It seems that a noise at 200Hz disturbs the control.

I measured the transfer function of the current buffer. (Graph)
It shows this circuit has gain 10.

 Here are the sample waveform results (best I could find) from the oscilloscope for my first attempt to lock the Michelson current constructed.

 [Seiji, Larisa, Vanessa]

Unsure why we weren't getting a good signal in the oscilloscope, we went over the criteria of a good/functional servo:

1. Stability (around unity gain frequency)
2. Actuator range (in terms of force and displacement)
3. Gain (is there enough?)
4. Lock acquisition

It was determined that the fourth point, lock acquisition, was the most likely cause for error. On rough estimate, we were getting about 1-2 orders of magnitude less work energy than was needed to control the mass' motion. 

One solution to this problem was to decrease the speed at which the mass was moving, which would in turn decrease the amplitude of motion. This meant we needed damping in addition to the damping that is already taking place in the configuration: something Seiji called "eddy current damping". 

Attached is one of the ways we hoped to improve our results: by shorting the actuator coils (both). As you can see, the signal is still pretty crappy...

While shorting the actuator coils, magnets have been set up close to the edges of the masses. This is part of a new scheme to use "eddy current damping", which we are using to try to lock the Michelson (one arm only, at the moment). The loop was no on.

First picture is the small Nd magnet close to the Romulus mass.

Second picture is the small Nd magnet close to the Remus mass.

Neither magnet is touching its respective mass, but it is on the order of 10^-3m closeness. We have no had any problems with the masses touching the magnets: they were successful at damping the motion quickly enough to prevent touching.

The resulting waveform was starting to looking a bit cleaner...it showed many more points where the masses were changing direction of motion (inflection points?), and this corresponds to much smaller displacement amplitude. Still no locking, but we are much closer now.

Next attempt involved "killing" the seismic isolation stack, as well as one of the blades (I can't post pictures of this because they might be a liability to Seiji's professorship). Even with the box on top of the configuration and playing with the gains, our results mysteriously did not improve.

Perhaps more (Nd?) magnets for eddy camping?

------------------------------------------------------------------------------------------------------------------------------------------------------------

TO DO:

Lock the Michelson by the end of Thursday!

Nothing new. More fiddling around got us nowhere. As proof, I've attached the waveform. 

Better luck next time.

 Maybe we just need to wait for the blades to damp longer? This is the same waveform after a few minutes of "chilling out"...

Trip to the 40m yielded these really cool magnets (see below).

We were hoping for many smaller magnets, like the ones used for the magnetic actuator set-up, but Steve Vass informed me that for masses of the magnitude we were using, the larger magnets would be more effective for eddy current damping. There was some difficulty finding a good angle/elevation to affix them so that they wouldn't attract the steel plates or the screws being used, so they were on the order of 10^-2m away, instead of 10^-3m with the smaller magnets. 

Conclusion: with these much larger magnets contributing to the eddy current damping, there was only a very marginal change. The masses are still moving too much.

 This time, we tried simplifying the configuration a lot. Changes include:

• Only one seismic stack, no rubber isolation remains
• One of the mirror-masses has been eliminated and replaced with a stationary mirror, so only one arm of the Michelson will move (when driven by actuator)

No significant changes to the oscilloscope output. It's still as crappy as before

After getting what looked like a decent cavity reflection signal, installed RFPD yesterday. For this, removed the lens that was right before the PD because the RFPD area is large enough, but keep ND filter in place. Powered with +- 18 VDC and monitor DC out on the scope, and RF out is sent to the IF of the mixer in the PDH box. For the LO, split the Marconi RF output and connected the demodulated signal into Ch2 of the scope in hopes that there was an error signal.

A hint of the error signal is present (blue trace below), although deeply buried in line noise (and harmonics up to ~180 Hz) so there really are two things to optimize now -->

1. Line noise (hunting for ground loops or equipment, e.g. power supplies, analyze LO spectrum before/after splitters, mixers, etc...)
2. Mode matching (this was the first reaction, as improving the cav refl SNR by means of mode matching makes a better pdh err signal)

Other things attempted so far -->

• Switched mixers, splitter, and RF cables
• Bypass the phase shifter completely
• Scan LO phase
• Floated RFPD power supply
• Floated PDH box power supply (really only affecting the phase shifter if anything, though unlikely to matter at this point)

Updates:

Yesterday, I stuffed the pcb boards for the hall-effect sensors (Allegro A1301 ),
and also one quadrant photodiode circuit for testing.

   [Hall effect sensor]             [QPD (before stuffed)]          [QPD stuffed (front side)]

The photodiode used is Hammatsu Si Pin photodiode S4349, and the operational amplifier
is Analog Device ADA4004-4 1.8 nV/√Hz, 36 V Precision Amplifiers. Here I attached the
schematics and the pcb layout for the QPD, which might be useful for others in other applications.
The zip file goes as follows:


Issues found (some small modifications are needed):

1. The 1/4-20 tapped holes of the fixed plate is too tight and the screws cannot go through.
2. The 0.5inch hole on the floating plate is a little bit too small and the reflector cannot be fitted in.
3. There is also a tiny problem with the slot (wrong sizing) for fixing the magnet.

Things to be done this week:

1.  Design Signal conditioning circuits (some simple filtering and amplification) for the hall-effect sensors,
   coils and also the linear DC motors.
2. Stuff the chassis power board for the binary input and output.

List of items needed (or to be ordered):

1. A rack for fixing various chassis [the analogy and digital parts].
2. Three 1-u chassis boxes for the signal conditional circuits, the front panel (BNC connectors)
   and the back panel (D-sub connectors slots).

In order to use Labview for maglev, we need to have an analog interface for the input (OSEM) and output (coil).
I have designed a new board based upon the old circuit design we had previously for the maglev. Here we only
keep the LED drive and coil drive part. The LED drive is a second-order low pass filter with Sallen-Key topology
with a corner frequency around 4.5Hz, designed by Rana.The coil drive is a voltage follower with Gain of 2 where
we use BUF634 to boost the current of quad opamp L1125.

The schematics for the LED drive is given by the figure below:

The schematics for the coil drive is given by the figure below:

The final board is

The Altium file for this board is in the attachment titled: analogy_circuit.zip

 A quick calculation of the force from a solenoid on a small magnet (which we approximate as a dipole), from which we can find the dimensions and the number of coils for the solenoid we need (not sure if it is correct; will think more on it later).

The magnet should be placed so that it is half out of the coil. At the mouth of the coil, you get a strong field gradient so you ought to calculate the force at that point. Then remember that the max current we can supply is 100 mA before the coil starts getting warm.

 Fixed my calculations from my previous post.  Hopefully they are correct now.

Calculated the magnetic force on a small magnet at the end of a solenoid (approximating the magnet as a dipole with magnetic moment mu).

 Attached is the promised circuit diagram, describing what was done yesterday in terms of configuration. 

A few notes on the diagram:

• The oscilloscope was hooked up in order to see the physical signal that was coming from the source and the signal that was seen by the photodetector (produced by the motion of the mass moving across the laser beam path)
• The laser used in the experiment was one of the two HeNe lasers on the Crackling table (so lamda~633nm)
• For those of you not familiar with what the SR780 is: a network signal analyser. This is an older machine taken from the (defunct?) LIGO lab in the High Energy Physics building, which Tara retrieved for the use of crackling experiments. It was used to measure the transfer function (of signal inputs B/A), using the Bode window type over the range of frequencies 1-10Hz.
• Again, for those of you not familiar with the SR560: we used it to get rid of the DC offset in the signal. The SR560 contains a bandpass filter with corner frequencies 0.03-300Hz (well outside the frequency range of interest by a factor of 30 on each extreme), boosts the output signal by a gain of 10, and uses DC coupling.

New magnetic actuator configuration notes:

• I soldered the wire ends of the solenoid to a couple of wires that had a BNC connector on the other end (see last image in this last post)
• We calculated the resistance of the solenoid to be R=11.3 Ohms (11.7 total - 0.3 for the cables on the multimeter)
• The inductance of the solenoid was found to be L=254uH

More to come later this afternoon...

Yi Xie and Haixing,

We used the Gauss meter to measure the strength distribution of bought magnets, which follows a nice Gaussian distribution.
We pick out four pairs--four fixed magnets and four for the levitated plate that are matched in strength. The force difference is
anticipated to be within 0.2%, and we are going to measure the force as a function of distance to further confirm this.

In the coming week, we will measure various transfer functions in the path from the sensors to the coils (the actuator). The obtained
parameters will be put into our model to determine the control scheme. The model is currently written in mathematica which can
analyze the stability from open-loop transfer function.

The source for what I've been using to calculate thermal noise.

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

* Xiaoyue will check weights for new carbon steel blades

* may start new blade run in 10 days

* RSI paper to be resubmitted this week

I made a micro-cantiliver out of SS340, single grain. Relocating the EBSD grain map in SEM is tricky, I used a self-defined coords system. However I will put the sample back for a EBSD analysis after making full use of this area:

The cantilever is of size 860 nm * 6 um which mimics the real blade in ratio width : length = 1:7.

I also made a micro-pillar (1 : 2.5 um) in order to compare the nano-pillar compressions to the nano-cantilever bending to see how the signature is different when the strain gradients are present.

Tests will be conducted soon. 

I compressed a pillar (D = 1.1 um, H = 2.5 um, made out of SS304 single grain) using G200 nanoindenter.

Using inflection point I got F_yield  = 0.3 mN, and knowing the pillar diameter to be 1 um we can estimate yield stress ~ 0.3 mN / pi (0.55 um)^2 = 316 MPa

However a more conventional definition for yielding point is the “0.2% offset” where people draw a line with slope of elasticity from 0.2% strain, and find the first cross over to be the yielding ~ 0.4 mN/ pi(0.55um)^2 = 421 MPa

I would also love to compare the pillar compression data with the indentation data.

In order to extrapolate yield stress information I need to convert the load vs. depth data to stress vs. strain ones. It involves a better knowledge of the indenter tip, as so far I got contradicting result from projected area function calibration and the tip radius claimed in the spec sheet (max projected area exceeds the claimed tip area). Also I need to learn more about how to find the actual “contact height” which excludes the non-plastic indentation from the machine loading depth.

Alastair and I popped the top on the can today and used a 3/16 balldriver to tap the optic and find the eigenfrequencies.

We achieved the ring up by lightly tapping the optic in a few different places; different taps give different modes.

Here are the list of frequencies (in kHz):

 2.696

 3.456

 4.68

 6.128

10.632

37.072

41.568

43.984

We used a few different spans, so I can't really say what the uncertainty in the frequency is.

The main finding here is that the frequencies are very different from the Blevins formulae as well as the COMSOL FEM. Perhaps we can use the measured frequencies to fix the FEM.

One feature of the disc geometry which I noticed for the first time: the edges are beveled. So this is not a right circular cylinder as we have assumed for the mode. I am also suspicious of the thickness measurements that Giordon made; the thickness of the disc should be measured at several points across the disc and the places indicated on a diagram.

Lid replaced and roughing pump restarted at ~5 PM. Hopefully we can measure in a few hours.

I disassembled the entire setup and put it back together again. I removed the rubber damping from the mirror attachments at the blades. If undamped attachment points are a problem, then we need another solution. The rubber was breaking into pieces and I am sure that it did not have a good effect on previous spectra. The mirrors attached to the blades were misaligned and covered by biochemicals. I cleaned the mirrors and aligned them again.

After realigning the rest of the interferometer, I was running some measurements of shadow sensors and photodiode signals. Locking the interferometer is still a problem, but it is not clear to me what the problem is. I think that the entire electronics part requires a bit more attention. The locking servo is still able to bring the photodiode signal into a low-variance state, but it is not clear if the interferometer is truely locked. In this "quasi locked" state and measured under vacuum (about 140mTorr), the photodiode spectra are without the usual features, but have a pretty smooth spectrum (see below). Even though this looks like something non-seismic / non-acoustic, there is still clearly response in time series to seismic disturbances (I have no idea where these end up in the spectra...).

So some more details about the locking problem. At the moment, a photodiode time series looks like this:

For a while (e.g. 1min) the variance is a bit higher, then there is a kick, and then the variance stays low all the time. Before and after the kick, the signal still shows seismic disturbances if I knock at the table. So somehow the locking servo drives the system into some strange state. The spectra before and after the kick don't show any of the typical seismic or acoustic features (left: before, right: after):

So it looks like we not able to lock the interferometer. Changing the offset of the locking servo, the DC component of the photodiode signal does not change. I am not sure what part of the system I should start to look at, but my guess is that there is a problem with the electronics and not so much with the mechanics. Anyway, maybe one of the friendly elog readers has an idea.

I tested the PD output with the new wire-up but we still see the noise. We decided to make a few changes:

1. Seprate the grounds for each signal, so we have the 9-pin connector only for the whitened/ unwhitened signals, with the flat cable ordering in signal-ground-signal-... pairs. The PD power supplies now have its own flat cable clamping through the stages, and will join the suspension OSEMs cable at the first 25-pin connector.

2. Make the cabling as short as possible, so I decided to replace the flat cable outside vacuum with shielded and twisted cable with BNC connectors.

2. Short the PCB ground to the frame.

After making all these changes, we still see the same noise in oscilloscope. Federico suggested it could be a floating ground problem, so we short the optical table (frame) to the earth (wall power ground), which is the same ground shared with the oscilloscope. This largely reduced the noise. We checked also by plugging the oscilloscope to the power strip and short the table this time to the power strip ground. Noise is reduced again. So we are pretty sure this noise we see is fake due to floating ground, and will not been seen in ADC since it's differential.

Outputing the whitened PD signal to ADC channel, we no longer see the noise in time series: with / without PD signals, the AC readings look identical. Checking also in spectrum:

In the above spectrum, red is ADC reading with no input; blue is the one with whitened PD signal, laser OFF; green is the one with whitened PD signal, laser ON. Note the spectrum is taken in a "floating ground" condition -- that is the table is not shorted to the earth, neither the PCB board is shorted to the frame.

[Federico, Gabriele, Xiaoyue] Gabriele and Federico pointed out that it's strange that in the spectra all three cases (no input, PD without light and PD with light) are sitting at a level of 1e-6. It's like we are only seeing ADC noise. We want to check if the DC output signal agrees with the level laser power on the PD: I measured directly at PD2 the laser power to be initially 0.11 mW. I cranked up the laser power so we have 1.47 mW on PD2. The DC output measured using oscilloscope is -1.10V which agrees with the power (mW) to output (V) calibration done before.

However I noticed that the whitened output responds very slowly to the laser power change, and both PD1, PD2 channels behave like the signals are low-passed! We checked the unwhitened signals and they are good as expected. So we took everything out of chamber for a thourough check: While checking the power supplies, we first found we have connection problem with the 3-pin connectors. We have to solder to make sure the cables have good conducting contact with the socket. Note this hasn't happend to the 2-pin connectors before. Then we connected a 12 kohm resistor to mimic the anode current input, and found the whitening stages (LT1128 chips) are indeed behaving like a low-pass filter. So we shortened the capacitor C43 to check if the op amp is working properly. With the oscillating Vout1 input, there's no output at all, so we are pretty sure the components are broken. We replaced the two LT1128's (U13, U14) and everything is back to normal. 

 [Vanessa]: To try to combat the problem of the end of the spring (the part between the mass clamp and the mirror clamp) oscillating at its own independent frequency (even when the mass is not moving), we are designing a setup that places the mirror on the bottom of the mass.  Attached are some of our ideas for the design parameters involved and the proposed design.

Other design problems include the dimensions of the attached mass/mirror set-up, because the larger the moment of inertia, the more apparent the undesired (horizontal) modes of oscillation.  So even if the height of the set-up is altered so the masses lie above the 45 degree mirror, this problem still must be dealt with.

ETA: I have attached a very slightly altered version of the design Larisa put up, for my own clarification.

After this we need to design/construct the mechanism to move the spring, which will be a controlled magnetic field (consisting of a small solenoid with an AC power source suspended above the spring) with a magnet (attached to the top of the spring) inside.

[Larisa]: As mentioned in my last post, it was found that attaching mirrors to the bottoms of the ETMs was the most viable option. Attached below is the final diagram of the concept design....

This model has a few advantages:

• One can easily adjust the mass load on the blade spring by adding extra masses between the "blade bend compensating mass" and "mass end cap"
• As mentioned before, having the mirror at the bottom of the mass eliminates the need to have the mass be exactly what is needed to have the blade bend exactly parallel to the optics table surface
• Screw-spring mechanism will allow the mirror to be tilted , again eliminating the need for perfect blade parallelism to optics table

After taking a few measurements on the current setup, it was found that the necessary dimensions of the ETM mass (HA, redundancy!) would be severely limited by the height of the base block holding up the blade and the 45 degree tilted mirror that guides the laser beam to the ETM.

The Romulus blade spring will probably only need about 1350g mass to make the blade sufficiently straight, but the Remus blade will need much more mass (see Vanessa's post for exact numbers)

One idea I had was perhaps to pick a material that would be heavier than the masses used...after some calculations, I found the density of one of the masses on the Remus blade (1801g) to be ~11.340g/cm³ , which corresponds most closely to lead (~11.389g/cm³). It would seem that this is one of the most cost efficient materials (compared to, say, gold) to make the room-temperature solid masses out of (lead density was the highest among those listed on this solid materials table: see here)

The other possibility is that we vertically displace the base that the blade springs are clamped to. This way we will not have to worry about the dimensions of the masses, and can just have bigger lead masses made. 

[Tara, Larisa]

As calculations for mass and dimensions began for the previous design, I found it to be unnecessarily complex and set about trying to design something simpler that would fulfill our needs just as well. A few attempts later, together with Tara, we came up with a much better design---->see first attachment:

• it utilizes parts we already have in the lab (i.e., the mirror mount, larger aluminum(?) base)
• one can easily adjust the blade-bending mass
• there are minimal calculations involved, mostly because there are a lot less screws/holes to account for
• because we have the additional larger aluminum(?) base, we are not as constrained height dimension-wise ---->see second attachment

[Vanessa]

I've added a mock-up of the new design, with dimensions, and labeled the parts we do not already have in dark red.  The particular mass values I gave are for the blade spring Remus.

Note that it is not necessary to construct a new (rectangular prism) lead mass for the spring Remus, but doing so will allow a reduction of the lead mass's height (right now, the lead mass is about 5.4 cm tall).

I think aluminum or some other light metal will work best for the side plate, so we do not create too much asymmetry in the system.  The mass end cap (also metal) can be of a  heavier metal, such as steel.

Also, since the mirror frame is L-shaped, we could put in two side screws to attach the frame to the metal plate above, creating more stability for the attached mirror.

As we mentioned in the earlier that OSEM constrained the position of working point
of the flag in our design, due to a slight drift of the equilibrium point in the horizontal
direction [as indicated by the figure below]:

In order to solve this issue, we have the following design for the sensing. This allows a flexible tuning of the
LED and PD in the horizontal direction and get the right position for sensing the flag motion.

The above scheme is not difficult to fabricate. We do not need to go to the mechanical shop and we can make them by
ourselves. Right now, we got the required components (LED, PD, Polycarbonate tube, and screws, and we need to find
something for the movable plate).

If you have any better ideas, please let us know by commenting on this log.

We tried to make our new sensors as what we designed [as shown by the figure below]:

[The reason for this new design was posted on Elog 315]

We glued the LED and PD on aluminum plates and soldered wires on them [shown by the figure below]. As it turns out,
if we simple make the gap [for holding the plate] slightly smaller than the aluminum plate, we do not need extra screws to fix
the plate, which makes the scheme a lot simpler.

In Elog 256, we showed that the 1" magnets have a mean of 106 Gauss with a variance of 12.8 Gauss.
The question would be if we want to have an imbalance of 1% how many magnets we need to buy.Here
Here we will make an estimate by assuming that the distribution of strength is Gaussian---a reasonable assumption
given what we have measured. The distribution would simply be

with and . Through numerical integration, one can find out the probability content for the
magnet strength falling into [105, 107] (within the 1% error around the mean)  is 0.062. Therefore, if we want
to have 4 matched magnets that have 1% error around the mean, the number of magnets we need to order is
approximately 4/0.062 = 64. Since we have already got 12, extra 50 would be enough (the quantity that we order
today), unless we are not lucky.

Steve: I asked  K&J  Magnetics to select matched pairs of 4, but they declined.

Today, Steve helped me to order more magnets and other mechanical parts for the maglev.
The detailed items go as follows:
1.  1" diameter and 1/32" thickness magnets (Grade N42). Quantity: 50.  The Supplier: K & J magnetics
     [The reasoning for the quantity is due to its large variance in the magnet strength, as shown in the ELOG 256]
2.  1/2" diameter and 1/8" thickness magnets (Grade N42). Quantity: 20.  The Supplier: K & J magnetics
3.  1 pack of Brass fully threaded 1/2" rods [They are used as flags in the position sensing]
4.  4 packs of 5 precision stainless spring (0.18" outer diameter and 0.018 wire)  The size of the spring is choosen
     in such a way that it can fit into a 8-32 screw. [This is for the cross coupling measurement. With spring, we can
     first create a stable setup and measure the cross coupling by driving the levitated plate with coil (see the schematics below) ]
   
5.  4 packs of 5 precision stainless spring (0.18" outer diameter and 0.026 wire). This is another size for the same
     purpose of cross coupling.

In addition, I used techmart to order another BNC terminal block [with 18 analog inputs and 2 analog outputs. The
type is 2090A, and the link is given by http://sine.ni.com/nips/cds/view/p/lang/en/nid/203462] for the national instruments
DAC card. We had already got one in the basement lab. This new ordered one gives us additional two analog outputs.
In total, we will get four analog outputs which would be enough for the first-step digital control before Cymac
will be available in one month.