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 Coating Ring-down Measurement Lab elog, Page 1 of 18 Not logged in
 New entries since: Wed Dec 31 16:00:00 1969
ID Date Author Type Category Subject
128   Tue Sep 27 08:53:46 2016 GabrieleGeneralVacuumEtched disk installed

Installed the etched disk: using manually the centering ring allowed me to get the beam on the QPD. A couple of taps to the disk were enough to get the beam centered.

Pump down started at 8:52am

133   Mon Oct 17 10:50:50 2016 GabrieleGeneralVacuumNo sign of problems in the electrostatic drive

I opened the chamber and took the etched disk out. Inspection of the electrostatic drive does not show any sign of burn or damage.

So it seems that the problem we had previously was due to contamination of the chamber (in the first case) or of the ESD (in the second case)

142   Fri Oct 21 14:03:17 2016 GabrieleGeneralVacuumRoughing pump moved

I moved the roughing pump out of the clean room, adding an extension hose.

This reduced a lot the vibrations induced by the pump. In the past when the pump was running we often saw very large noise, see the red trace in the figure below. Now, in the same conditions, we get the blue trace, which is much better.

The plot below shows a comparison of different configurations:

• blue: what I sometimes manage to get tewking the pump position and keeping it on top of a plastic box
• red: now, with the pump far away
• green: with the pump off

We are quite close to the pump off condition.

165   Mon Nov 7 11:27:16 2016 GabrieleGeneralVacuumTurbo pump excites some resonance at 58 Hz

I looked into a couple of turbo pump switch on periods, and in both cases when the pump speed hits 58 Hz, a resonance is excited. I'm not sure what's resonating.

Today I let the roughing pump reduce the pressure to a level lower than usual, and this seems to mitigate the effect. The disk wasn't shaking as much as it did in previous pump-downs.

186   Mon Nov 14 11:28:33 2016 GabrieleGeneralVacuumViton pads

I added three 1"x1" viton pads below the base plate, and realigned the entire optical system to the horizontal reference

The pads seem to reduce a bit the vibrations in the QPD_X direction, but significantly improve the situation in the QPD_Y direction, see below:

195   Thu Nov 17 12:06:39 2016 GabrieleGeneralVacuumSwitching on the IGM moves the disk

Here's a trend of the QPD signals when the IGM was turned on:

Turning it off does not bring the disk back.

264   Thu Jan 19 07:32:33 2017 AlenaGeneralVacuumNew chamber first pimp down

The new chamber was build. The first attempt to pump down was unsuccessful because of dislocated lid. After the lit was placed properly, the chamber was pumped down to 0.1 torr within 8 min. In future a sky hook will be used to help placing the lid properly. The clamps should not be placed on the lid before the roughing pump turned on.

The turbo pump controller failed. Error code 698 – call the vendor.

265   Thu Jan 19 12:49:17 2017 GabrieleFacilityVacuumSkyhook installed

The SkyHook has been put in place and bolted down to the floor.

Attachment 1: IMG_4241.JPG
Attachment 2: IMG_4241.JPG
Attachment 3: IMG_4241.JPG
267   Thu Jan 19 14:27:02 2017 AlenaGeneralVacuumFirst vacuum test new chamber

Turbo pump controller (new chamber) was configured. Need to reduce the frequency or setup a standby mode. First pump down: E-7 range reached within about an hour. See plot: blue - old crime chamber, pink - new crime chamber.

285   Tue Jan 31 16:50:55 2017 Gabriele, AlenaGeneralVacuumFirst pump-down with setup

This afternoon we started the pump-down with all the system installed into the chamber. Unfortunately the IGM vacuum gauge isn't working, so we can't be sure what the pressure is. To be fixed

498   Tue Mar 27 16:37:22 2018 GabrieleGeneralVacuumTurbo pump for test chamber CR0 set point

I changed the set point of the test chamber turbo pump to 666 Hz. This was done by setting the "standby rotation speed" to 80% and enabling the standby condition.

517   Thu Apr 12 10:33:06 2018 GabrieleGeneralVacuumRead-out of vacuum gauges

I failed to interface in a reliable way the datalogger with Linux. So i hooked up the four analog outputs of the vacuum gauge controller to the fast ADC. The voltages are read and saved to disk at a reduced rate (16 Hz, throught the epics channels):

X3:CR0-VACUUM_VAC1_OUTMON
X3:CR0-VACUUM_VAC2_OUTMON
X3:CR0-VACUUM_VAC3_OUTMON
X3:CR0-VACUUM_VAC4_OUTMON

A python script running on the workstation (~/pycrime/automation_scripts/vacuum.py) reads the voltage every second and update four epics channels:

X3:CR0-VACUUM_CG0 = convection gauge of test chamber (high pressure gauge)
X3:CR0-VACUUM_IGM0 = ionization gauge of test chamber (low pressure gauge)
X3:CR0-VACUUM_CG1 = convection gauge of main chamber (high pressure gauge)
X3:CR0-VACUUM_IGM1 = ionization gauge of main chamber (low pressure gauge)

See below for an example during pump down (the test chamber is at a too high pressure for the IGM to work, so it returns a bogus number).

Here's an example of venting and pumping down

703   Tue May 28 15:48:42 2019 AlenaGeneralVacuumLow pressure gauge exchange

After venting the vacum chamber (CR14) a few times, checking for leaks and trying to tune settings to the gauges controller, I gave up. I removed the low pressure gauge from the newer vaccum system (CR14). Inspection did now show any obviouse depositions around the electrode (due to some burns). I will pack the gauge ans send it to the manufacture for an RMA. Took the same gause from the older vaccum system (CR0) and installed it on CR14. Started pumping down. The low pressure gause turned on just fine. Will check the preassure in an our before starting a measurement.

170   Wed Nov 9 15:32:11 2016 GabrieleGeneralNoise huntingNoise below 2 kHz is not due to the roughing pump, but to the clean air filters

The two spectra below show basically no difference (blue roughing pump on, red, roughing pump off)

Instead, below is another comparison: blue same as before, standard condition, red with one of the two clean air filters momentarily off. There is some clear improvement. The second filter is too hard to switch off!

176   Thu Nov 10 17:04:05 2016 GabrieleGeneralNoise huntingTemporary second QPD

This morning I installed temporarily a second QPD to monitor the input beam. The goal was to understand where the vibrations at frequencies below 2kHz couple from. As shown in the photo, the second QPD was close to the first one.

The signals in the two QPDs were quite different, and the coherence between them wasn't great. So I concluded that the main coupling path is not through input beam of QPD vibration, but more likely real motion of the disk.

I removed the additional QPD and restored the setup to its nominal configuration. The readout infrastructure is still in the model.

181   Sun Nov 13 10:11:19 2016 GabrieleGeneralNoise huntingNoise due to air

The plot below compares the QPD signal spectra in different configurations (roughing pump on/off, air on/off).

The noise below ~<2kHz is making very hard to measure the Q of the first mode at 1100 Hz

The main source of noise are the clean air filters. I switched them to minimum for the moment being.

209   Wed Nov 23 08:55:41 2016 GabrieleGeneralNoise hunting"Advanced" vibration isolation

In normal conditions the RMS of the QPD signals is dominated by the 58 Hz line generated by the roughing pump. Also, when the modes are excited, they exhibit large sidebands at +- 58 Hz that are an annoyance for the analysis.

I improved a bit the level of the 58 Hz in the QPD signals by putting the roughing pump on top of a "Very Useful Box":

Despite the fact that this advanced vibration isolation is already a little bit effective, it might be good to try to build some better suspension and maybe add an acoustic isolation around the pump.

216   Tue Nov 29 17:02:06 2016 GabrieleFacilityNoise huntingSuspending the roughing pump

I suspended the roughing pump with four springs. The reduction of the 58 Hz peak is similar to what I got when the pump was sitting on a box. So most of the coupling is due to acousting noise.

Attachment 1: 2016-11-29_11.08.17.jpg
287   Wed Feb 1 15:23:42 2017 GabrieleOpticsNoise huntingWandering line is due to the laser

The wandering line I mentioned in my previous elog, which is spoiling most of the sensitivity, turns out to be power noise of the laser.

I used a Thorlabs PDA100 and a SR785 to measure the power noise out of the laser directly, and saw a huge forest of peaks above 20kHz. Among them, a couple of peaks are moving up and down in frequency very fast. The plot below compares two different times of the Thorlabs HNL210L laser (the new one, 21 mW) with the old JTSU laser we are using for the test setup:

The noise of the new laser is cleary much larger (even after the laser has been on for some time) and non stationary. This is a big issue for us. I will contact Thorlabs to inquire if this behavior is normal.

The attached video file shows the peaks dancing around on the SR785 screen.

Attachment 2: Untitled.avi
326   Thu Mar 2 11:27:47 2017 GabrieleGeneralNoise huntingTurbo pump of CR0 pollutes CR1

The turbo pump of the CR0 chamber runs at 833 Hz. It causes vibrations that pollute the measurements in the CR1-4 chamber. In particular CR1 is extremely sensitive and the line is highly up-converted. It's not clean why CR1 is more sensitive than CR2-3-4.

351   Thu Jun 22 13:16:37 2017 ZachElectronicsModelingBeginning with COMSOL

# 2017-06-21

• 4:30 pm- Installed COMSOL, began modeling current ESD by creating parameters and the first arm of the comb
352   Thu Jun 22 15:37:20 2017 ZachElectronicsModelingBeginning modeling

# 2017-06-22

• Created the geometry of the ESD by creating blocks and joining them with Unions. I then created a block to serve as the domain and added air to that region
• This plot is a combination of a Surface plot of the potential and a Streamline plot of the electric field
• I created another model of the ESD with more accurate measurements to the real thing and added the silica disc to the model
353   Fri Jun 23 12:02:12 2017 ZachElectronicsModelingPlots

# 2017-06-23

• I created plots of the E field and potential from my rough model of the ESD. This model has 1mm electrode arm widths and spacings, the length of each arm is 16 mm, and the resulting total size is 38mm x 20 mm x 0.1 mm. One comb has ten arms while the other has nine to match the actual ESD currently in use in the lab.
• I set the ten arm comb to a potential of 100 V and the other to ground. I then used physics controlled mesh with an extremely fine element size to computer the simulations. With mesh sizes larger than extra fine, there was clearly non-physical error in the electric field and potential graphs that appeared as inexplicable field lines, spikes, and coarseness in the plots.
• To create readable plots of the potential I created a Cut Plane in the center of the ESD perpendicular to both the arms and the plane of the device. The plots are attached with a milimeter length scale. I created a filled contour plot of the potential that is very clean, I tried a couple of different options for the electric field because it is harder to represent well. I created a contour plot for the norm of the electric field as well as superimposing a streamline plot of the field lines over that. Everything behaves generally as expected though I do suspect the spikes in electric field at the edges of each electrode are due to the fact that they are sharp corners and not smooth edges.

Attachment 1: Potential.png
Attachment 2: E_w_Lines.png
Attachment 3: Mesh.png
356   Tue Jun 27 14:17:47 2017 ZachElectronicsModelingFurther plots and improving models

# 2017-06-27

• I built a new model of the ESD to determine whether or not the spikes in the electric field at the corners was affecting the results enough that it had to be accounted for in further models. To create the model, I created a 2D profile of the arm used in my original model and filleted the corners at a radius of .05 mm, since the electrode model is .1 mm thick, this made completely rounded edges. In creating this model I caught an earlier mistake in the original one, I only set one half of the surface of the electrodes to have a potential or to ground, the "bottom" was left with no charge. I fixed this mistake and then compared the two models at a potential of 1000 V. For speed of computation I ran both models with a finer mesh size and then calculated the electric field at approximately the middle of the ESD, 1mm above the fourth electrode arm. For the rounded electrodes the field had a value of 84024 V/m and for the rectangular electrodes the field had a value of 80728 V/m, which is less than a 4% difference in field magnitude. Furthermore, the field shapes appear nearly indistinguishable; I am confident from this test that I can proceed modelling the arms of the ESD as rectangles.
Attachment 1: E_field_corner.png
Attachment 2: E_field_round.png
359   Thu Jun 29 16:40:41 2017 ZachElectronicsModelingAccurate model and force profile

# 2017-06-29

• I created a much more accurate model of the current ESD setup from the technical drawings. My resulting ESD has dimensions of 21.3x24.3x.1mm with 1 mm spacings and 17.5 mm long electrode arms. The sample has a diameter of 75 mm and thickness of 1mm, the ESD is 1mm below the sample in the current model. I still have to compare the technical drawings to confirm that is the actual distance in the current lab setup.
• I was able to calculate the force profile on the disk from the ESD. COMSOL struggled to resolve the data with a small mesh size over the whole domain, so I created a region of extremely fine mesh around the ESD and the disk and then made the rest of the mesh size normal sized. Over the domain near the ESD my mesh size ranges from 2.5*10-3 to .25 mm and over the rest of the domain it's automatically setup at the normal size.
• The force on a single dipole is given as $F = (P \cdot \nabla)E$, since fused silica is isotropic it's polarization is proportional to E so $F = \chi_e \epsilon_0 \nabla (E^2)$. The electric suscepitibility of fused silica is 1.09, I plotted the profile of the force perpendicular to the plane of the disk and exported data files of the full vector quantity of the force for use with Matlab.

360   Fri Jun 30 11:02:18 2017 ZachElectronicsModelingMatching Forces

# 2017-06-30

• I adjusted the plot parameters slightly so that it only showed the actual force profile on the sample in the direction perpendicular to the sample surface. Additionally I compared the two methods of computing the force, as $\vec{F} = -(\vec{P}\cdot \nabla)\vec{E}$ and as $\vec{F} =- \chi_e \epsilon_0 \nabla \vec{E}^2$. The profile of the force in both instances appear equal, but they differ in magnitude by exactly a factor of 2, I plotted the force computed with the explicit polarization doubled and the force magnitudes matched exactly. I'm still not entirely sure where this factor of two could be coming from.

361   Fri Jun 30 16:27:56 2017 ZachElectronicsModelingDouble Checking Model

# 2017-06-30

• In order to confirm the accuracy of my model I checked some easily computable quantities between what real values and what COMSOL produced. My expected electric field magnitude between the electrodes is 106 V/m and COMSOL reads out 1.015*10which is less than a 2% error. When I went to compute the electric field gradient however, I discovered that I had been calculating my derivatives wrong, I was calculating full derivatives when I needed partial derivatives. Due to some subtleties of the numerics involving curl calculations are the order of the variables, in order to calculate a partial I belive that I have to map the results of the electric field to Lagrange elements.
363   Wed Jul 5 12:01:51 2017 ZachElectronicsModelingForce plots-Correct plots, force issue

# 2017-07-05

• I sorted out my mathematical lapse in logic and computed the correct force profiles in the perpendicular direction in both disks. The issue is that now the force profiles don't match up. The fact that there is a measured force distribution for the E^2 case outside the disk is only an artifact of the numerics because it is being calculated only from the electric field data which is defined outside the sample. It can be easily removed for final plots once the force distributions are matched by either redefining the cut plane or putting a data filter specifically on the E^2 plot. The jumps in the E^2 plot suggest that the meshing is still too large, I will try to fix this first, hopefully it will help resolve the difference.

364   Wed Jul 5 16:40:51 2017 ZachElectronicsModelingForce disparity-improvement

# 2017-07-05

• In order to improve my data I shrunk the region of the finer meshing slightly and made the mesh even smaller and then recalculated the force profiles. This time I tried sampling regions inside the disc rather than immediately at the surface. The attached graphs were sampled at the center of the disc. These two techniques vastly improved the data, now the profiles appear the same, but the magnitudes differ by a factor of 2 again. Previously this was due to an error in my calculation of the force, now I do not believe this to be the case. I will leave my work here for the purposes of my first report, it is an interesting result. I also restricted my data set to the finely meshed box which resolved the earlier data display issue.

365   Thu Jul 6 12:08:35 2017 ZachElectronicsModelingChecking physical parameters

# 2017-07-06

• I compared the electric field and the polarization to make sure that those calculations made sense. Since $P = \epsilon_0 \chi_e E$ due to the linear dielectric, I plotted the electric field and the polarization divided by the proportionality constant and they match exactly.
• This confirms both the constant value and the polarization distribution but gets me no closer to resolving the factor of two

366   Thu Jul 6 12:48:54 2017 ZachElectronicsModelingResolving the factor of two

# 2017-07-06

I resolved the factor of two from Griffiths' discussion of dipoles in non-uniform electric fields. The force on a dipole in a non-uniform field is $\textbf{F}=\textbf{F}_+ + \textbf{F}_-=q(\Delta \textbf{E})$ where $\Delta \textbf{E}$ is the difference in the field between the plus end and the minus end. Component wise, $\Delta E_x = (\nabla E_x) \cdot \textbf{d}$ where d is a unit vector. This holds for y and z, the whole thing can also be written as $\Delta \textbf{E} = (\textbf{d} \cdot \nabla) \textbf{E}$. Since p=qd, we can write $\textbf{F} = (\textbf{p} \cdot \nabla) \textbf{E}$

Jackson derives it differently by deriving the electrostatic energy of a dielectric from the energy of a collection of charges in free space. He then derives the change in energy of a dielectric placed in a fixed source electric field to derive that the energy density w is given by $w = -\frac{1}{2} \textbf{P} \cdot \textbf{E}_0$. This explicity explains the factor of two and is an interesting alternative explanation.

367   Wed Jul 12 15:08:59 2017 ZachElectronicsModelingModel of actuator and sample

# 2017-07-12

• I am attaching the first fully functioning model of the actuator and sample. I cleared both meshes and solutions to make the file a reasonable size, but they can quickly be built/solved again.
Attachment 1: Force_Model.mph
368   Fri Jul 14 16:43:24 2017 ZachElectronicsModelingForce profile matlab script

# 2017-07-14

• I have completed a rough, but functioning script that calculates the modal force profiles. The force values are still coming out incorrect (on the order of 10^14) but the script can take in my model as a .m file and return an array with a force value per mode. I am attaching both the .m file and the matlab script
• I have done very little work with the numerical integration itself, based on the 2D numerical integration code I received I just appended a z component and left it at that so when I return from Livingston I will  fix that component
Attachment 1: forces.m
par.a = 75e-3/2;    % radius [m]
par.h = 1.004e-3;   % thickness [m]
par.E = 73.2e9;     % Young's modulus [Pa]
par.nu = 0.155;     % Poisson's ratio
par.rho = 2202;     % density [kg/m^3]

%Calculate fundamental modes of the disk
[freqs, modes, shapes, x, y] = disk_frequencies(par, 10000, 1, 'shapes', 0.5e-3);

%Now we extract the force profile from the COMSOL model

... 41 more lines ...
Attachment 2: faster.m
function out = model
%
% faster.m
%
% Model exported on Jul 14 2017, 14:47 by COMSOL 5.2.1.262.

import com.comsol.model.*
import com.comsol.model.util.*

model = ModelUtil.create('Model');

... 403 more lines ...
371   Thu Jul 20 11:37:01 2017 ZachElectronicsModelingMatlab Script

# 2017-07-20

• I believe my MATLAB script successfully calculates the force distribution into each of the modes specified by the parameters. My previous error was caused by my neglecting the proportionality factor of $\frac{1}{2}\chi_e\epsilon_0$. Now the force order of magnitude is on the order of 103. I am currently unclear how to think about the units of the mode shapes from the disk_frequencies script, but I will pick it apart more carefully and try to figure that out. Then it will be a matter of converting units so that it matches with the N/m^3 from the COMSOL script and then comparing with real lab results. It seems to me that the error in force distribution should be inversely proportional to the number of modes calculated, in which case it would be useful to determine an appropriate number of modes to calculate.
Attachment 1: forces.m
par.a = 75e-3/2;    % radius [m]
par.h = 1.004e-3;   % thickness [m]
par.E = 73.2e9;     % Young's modulus [Pa]
par.nu = 0.155;     % Poisson's ratio
par.rho = 2202;     % density [kg/m^3]

%Calculate fundamental modes of the disk
[freqs, modes, shapes, x, y] = disk_frequencies(par, 10000, 1, 'shapes', 0.5e-3);

%Now we extract the force profile from the COMSOL model

... 27 more lines ...
375   Mon Jul 24 09:13:45 2017 ZachElectronicsModelingParametric Sweep

# 2017-07-24

• I wrote a MATLAB script that is capable of sweeping parameters, the code is attached. The next step is to create nested loops so that I can sweep multiple parameters in a single run. I also should add a function in the script to eliminate the modes that cannot be measured by the experimental setup.
• My first sweep was for the gap between electrodes and swept from 1 to 2 mm. In the plot the gap grows from steps 1 to 6 and the only obvious effect in the plot is a decrease in force from the highest mode. Intuitively it makes sense that a wider gap would decrease the force because the electric field is diminished by spreading out the electrodes.
• I would like to add a parameter for the overlap of the electrodes, but this would require substantial redesigning of the COMSOL model due to the multilevel dependency on parameters.

Attachment 2: forcesweep.m
fpro = zeros(6, 27);
no = 1;
for count = 1:.2:2
gap = strcat(num2str(count), ' [mm]')
model = fst2(gap);
forces;
fpro(no, :)= product(:);
no = no + 1;
end
378   Tue Jul 25 13:38:30 2017 ZachElectronicsModelingParametric Sweep of ESD gap

# 2017-07-25

• I completed a short sweep of the gap between the drive and the sample, between .5 and 1 mm in .1 mm increments. It appears that a 1 mm distance is the ideal distance by approximately a factor of two. I will next sweep larger distances and see how the force profile behaves at greater distances.

379   Wed Jul 26 09:27:40 2017 ZachElectronicsModelingSweeping the space between ESD and sample

# 2017-07-26

• I ran a sweep of the gap between the ESD and the sample, first from .5 mm to 1 mm. That sweep suggested that there is a significant jump in force across almost all of the modes at 1 mm. To confirm this I double checked the geometry and it appears that COMSOL is building everything as expected when changing the spacing parameter. Then I ran a finer sweep in .02 mm increments for the spacing between .9 and 1.1 mm. Once again it appears there is a large jump as the gap approaches 1 mm, but the behavior does not seem to be symmetric about that point, the force appears to diminish linearly as the gap increases beyond 1 mm. I will run a sweep of the ESD arm spacing along with the vertical gap to confirm that the jump occurs when the gap between the ESD and the sample is equivalent to the spacings between the ESD arms.

Attachment 1: Gap_near_one.jpg
381   Wed Jul 26 21:22:50 2017 ZachElectronicsModelingParametric Sweep Results

# 2017-07-26

• I resolved the major bugs in the parametric sweep scripts and ran low resolution sweeps of the gap between the ESD and sample (Gap Sweep) and the spacing between the ESD arms (ESD Arm Gap Sweep).
• The arm gap sweep largely behaved in a reasonable way with a maximum excitation at a 1.25 mm gap. However modes 14, 19, and 25 did not follow the general trends and had sharp drops and increases compared to the other modes.
• The sample gap sweep had less intuitive behavior, all of the modes followed the same general double peak trend that drops to zero when the gap is 1.5 mm. I cannot explain exactly why it is behaving that way, I will run a higher resolution sweep and examine the geometry in greater detail.

382   Thu Jul 27 13:37:31 2017 ZachElectronicsModelingCorrected sample gap sweep

# 2017-07-27

• I resolved a couple more data processing bugs and calculated a sweep of the ESD-Sample gap from a distance of .5 mm to 1.5 mm. The resulting data behaves far more like I would expect from a force generated by an electric field, it seems to drop off like distance squared. This is a very strong correlation with a good intuitive explanation, and would suggest that it is prudent to place the ESD as close to the sample as possible.
• I also computed a higher resolution sweep of the gap between the arms of the ESD. It did not resolve the strange behavior at all, so I will investigate coupling into the mode pairs as a possible source.

Attachment 1: Fine_sample_gap.jpg
Attachment 3: fine_arm_gap.jpg
383   Thu Jul 27 16:56:03 2017 ZachElectronicsModelingOffset Sweep

# 2017-07-27

• I ran a low resolution sweep of the offset in the arms of the ESD, the space between the end of the arm and base of the opposite combs. The trends are much more subtle and are not coherent across as many of the modes. The lower frequency modes decrease slightly, while the force in the higher frequency modes increase more drastically. This is an interesting parameter, I will definitely run another sweep once I have written code that accounts for the mode pairs. Assuming the apparent trends are physically accurate, this could be a useful parameter because a greater offset gives a greater relative increase to the higher order modes while still leaving a substantial force on the lower order modes that are excited more easily anyway.

Attachment 1: Offset.jpg
386   Tue Aug 1 16:10:42 2017 ZachElectronicsModelingImproved Gap Sweep

# 2017-08-01

• I completed an improved sweep of the gap between the ESD arms. I resolved some code issues, since it was passing the maximum value not the most extreme, smaller magnitude positive values were being included rather than the strongest force calculation.
• There are still three modes that show unique behavior relative to the others: 14, 19, and 25. Mode 14 is the (2,2), mode 19 is the (2,3) and mode 25 is (3,2).
• Plots of the mode shapes are included for reference. The black rectangle represents the region covered by the ESD.

388   Wed Aug 2 13:47:47 2017 ZachElectronicsModelingArm width Sweep

# 2017-08-02

• I ran a sweep of the width of the ESD arms. There appears to be a linear relationship across the modes except for mode 25. Mode 25 exhibits a very similar behavior as in the arm gap sweep. I realized that the abrupt change in direction (also noticeable in mode 14) is likely caused by the fact that the force profile is calculated as absolute value, there might be an exponential relationship that gets converted into that shape by the absolute value function.

389   Wed Aug 2 15:40:00 2017 ZachElectronicsModelingParameter diagram

I am posting a diagram of the geometric parameters that I swept. The only one not included is the vertical space between the ESD and sample that sweeps perpendicularly out of the image

394   Mon Aug 7 13:19:48 2017 ZachElectronicsModelingNormalized data

# 2017-08-07

• I included the modal mass factors in the code and renormalized my data. The normalization has a noticeable impact, but does not change the general trends of the data
• In fact the impact is not even significant enough to warrant a change in the ideal parameters I picked for the rectangular ESD in my interim report

Attachment 1: Arm_gap.pdf
Attachment 2: Arm_width.pdf
Attachment 3: Offset.pdf
Attachment 4: Sample_Gap.pdf
398   Tue Aug 8 16:20:24 2017 ZachElectronicsModelingRotated ESD

# 2017-08-08

• I rotated the ESD and calculated it's modal projections by rotating the data array that MATLAB extracts from COMSOL. I confirmed that this was properly done by plotting the profile and then computed and plotted both the rotated and normal projections.
• The rotated ESD actually increases the force in some of the modes but decreases the forces in others. It markedly improved the force in 7 of the modes: 3, 6, 12, 18, 19, 22, and 26 while being quite weaker in about 4 of the modes: 9, 13, 14, and 15. This suggests that it may actually be useful to rotate the ESD as it excites some of the higher order modes a noticeable amount more. I am including plots of both modal profiles as well as a chart with mode numbers, shapes, and frequencies.

Attachment 1: ESD.pdf
Attachment 2: Rotated.pdf
Attachment 3: resonantmodes.pdf
399   Wed Aug 9 12:10:47 2017 ZachElectronicsModelingPreliminary improvement from ESD optimization

# 2017-08-09

• I created a plot of the ratio of the force in the optimized design to the force in the original design. The improvement factor is huge, some modes are excited by more than a factor of 100. I took the same ratio keeping the gap between the ESD and the sample constant and it decreased the excitation by almost a factor of 10. Keeping that gap constant, the geometric modifications to the ESD give an improvement factor ranging from almost 2 to almost 4 for most of the modes. Modes 10 and 25 are outliers but in the original geometry they are barely excited at all, so this could easily be a numerical artifact where those modes were excited at a minimum in the original geometry.

Attachment 1: Ratio.jpg
400   Wed Aug 9 15:57:28 2017 ZachElectronicsModelingTriangular Geometry

# 2017-08-09

• I compared the triangular geometry to the original geometry and the excitation was only improved in 7 of the of 20 modes. In four of those modes the improvement factors ranged from almost 2 to over 3 while the other modes where only improved by about 25%. The other 13 modes were diminished drastically, 9 of them where less than half as excited. Given more time it may have been interesting to try and optimize the geometry of a triangular drive, but that would easily take the better part of a week.

401   Wed Aug 9 17:07:57 2017 ZacharyElectronicsModelingOptimization Summary

# 2017-08-09

• From the data I have gathered from a variety of MATLAB sweeps, I think that the optimal geometry I can produce has the parameters in the attached image. Neither the original or optimized drawing is to scale. The gap between the arms of the electrodes should be 1.25 mm, the arm width 0.55 mm, the arm length 16 mm, and the offset of the arms 3.5 mm.

• It is also optimal to place the ESD as close to the sample disk as can reasonably be achieved, at around 0.5 mm away. Since the force on the disk scales exponentially with the distance from the ESD, decreasing that gap is the most substantial way to impact the excitation. Decreasing the gap from 1 mm to .5 mm increases the excitation of the modes by approximately a factor of 8.

• From my simulations, the shift in geometry alone still has a useful impact on the excitation. Modes 1 and 3 are the only two modes that are less excited by the new geometry, mode 1 is 10% weaker  and mode 5 is 5% weaker. Modes 5 and 6 are nearly unaffected by the shift, mode 5 is 2% stronger and mode 6 is 5% stronger.  Modes 7, 18 and 19 are outliers, 7 is excited by a factor of 7, 18 by a factor of 4 and 19 by a factor of 17. The rest of the modes are improved by between a factor of 1.5 and 3. For mode numbers, shapes, and frequencies a plot is included.

Attachment 1: resonantmodes.pdf
402   Thu Aug 10 10:47:54 2017 ZachElectronicsModelingGeometry Ratios

# 2017-08-10

• The attached plots compare the new and old geometries with .5 mm and 1 mm sample gaps. They are the same plot on linear and logarithmic axes respectively

Attachment 1: Optimization_plot_lin.pdf
Attachment 2: Optimization_plot_log.pdf
407   Tue Aug 15 00:09:01 2017 ZachElectronicsModelingESD Improvements

# 2017-08-14

• I did my best to increase the excitation in the higher order modes. By making the ESD narrower (a 6mm electrode overlap) the higher order excitation is improved drastically, by factors of between 10 and 30 for most modes.  I also created a double ESD (see image) that excited the modes by a factor of 3 or more better than the thinner drive. The plotted ratios are relative to the original geometry, but both of these geometries do better than previous geometries by factors of 2 or 3.
• After a lot of experimentation, I think that there are non-trivial numerical artifacts from the force projection method. I have noticed that in the modes that are almost entirely unchanged by modifications, both the mode and its doublet have equal regions of positive and negative antinodes directly above the ESD force profile. This can be more clearly seen in the attached mode plot, the rectangle represents the region of the ESD. As a result of this, when the mode shape and force profile are multiplied and integrated the resultant force is very small. I expect this does not appear in the lab because the modes could be rotated at a different angle relative to the ESD. I am not sure how to effectively resolve this, perhaps checking other rotations of the mode shapes could be productive though I am unsure how to effectively accomplish this.

Attachment 1: double.pdf
Attachment 2: double.jpg
Attachment 3: offset10.jpg
Attachment 5: offset10.jpg
Attachment 6: double.jpg
Attachment 9: thin.png
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