We improved the control software of the laser polishing system: now the rotation speed is large when the laser is missing the disk because of the flats.

We used S1600479 as a test. This substrate was marked as damaged and had a clear chip. It went thoruhg two different polishing runs

• CO2 power ~19.5 W, speed 0.5 mm/s
• CO2 power ~18.5 W, speed 0.25 mm/s

The second run was probably too slow, and we can see some kind of traces left on the main surface close to the edges

We then laser polished a good subtrate (S1600439) which was already measured before (137) and after annealing (144), with good Q values. This is a substrate from the first batch we received from Mark Optics. The polishing was done at ~ 18W and 0.5 mm/s.

Some pictures below:

The sample has been laser polished this afternoon, 0.5mm/s, average power 23 W.

We moved the lens that focuses the beam about one inch toward the sample, to make the beam slightly larger.

Today we laser polished S1600484, S1600485 and S1600486.

The clean room frame is built and secured to the floor and wall. Panels are being installed on the ceiling and back. Also, the optical table has been leveled.

Ceiling, back and side panels are installed. The air filters have been cabled and connected to the power supply.

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

2018-03-05

• 10:45am in chamber:
  • AK_01 in CR1
  • AK_02 in CR2
  • AK_03 in CR3
  • AK_04 in CR4
• 10:55am roughing pump on
• 11:05am turbo pump on

Annealing of 8 fused silica substrates (50mm/0.5mm) started at 3:30pm, January 25th 2018. Standard program: 9 hours ramp up to 900 C, 9 hours hold, 9 hours ramp down

2016-12-12

• 4:32pm, in chamber, balanced
• 4:33pm, roughing pump on
• 4:46pm, turbo pump on

2016-12-13

• Excitation:
  • Quiet time before excitation: 1165689679
    Excitation brodband (3 kV, 60s)
    Quiet time after excitation: 1165689920

We set up the model x3tst to acquire at 65kHz four signals coming from the PSL lab:

• X3:TST-BEAT_OUT_DQ: beat note
• X3:TST-ACC_X_OUT_DQ: accelerometer X
• X3:TST-ACC_Y_OUT_DQ: accelerometer Y
• X3:TST-ACC_Z_OUT_DQ: accelerometer Z

This morning Larry set up a network switch to create a local network for the power strip and the two Newport picomotor controllers. The laboratory workstation serves as gateway between the networks.

I still have to configure the power strip and the picomotor controllers to use the new static IP address.

I reconfigured the powerstrip and the two Newport controllers to use static IP address in the new 10.10.10.X network, using the workstation as gateway. All scripts updated and working

2017-07-31

• 1:20pm in chamber
  • S1600520 in CR1
  • S1600521 in CR2
  • S1600523 in CR3
  • S1600524 in CR4
• 1:21pm roughinp pump on
• 1:30pm turbo pump on
• Excitations:

  • Quiet time before excitation: 1185582780
    Excitation broadband: 1185582815
    Quiet time after excitation: 1185582840

  • Quiet time before excitation: 1185584070
    Excitation broadband: 1185584105
    Quiet time after excitation: 1185584130

  • Quiet time before excitation: 1185585360
    Excitation broadband: 1185585395
    Quiet time after excitation: 1185585420

  • Quiet time before excitation: 1185586650
    Excitation broadband: 1185586685
    Quiet time after excitation: 1185586710

  • Quiet time before excitation: 1185587940
    Excitation broadband: 1185587975
    Quiet time after excitation: 1185588000

  • Quiet time before excitation: 1185589230
    Excitation broadband: 1185589265
    Quiet time after excitation: 1185589290

  • Quiet time before excitation: 1185590520
    Excitation broadband: 1185590555
    Quiet time after excitation: 1185590581

  • Quiet time before excitation: 1185591811
    Excitation broadband: 1185591846
    Quiet time after excitation: 1185591871

2017-08-01

• 9:55am, valve closed, venting, pumps off

2017-08-01

• 10:05am, in chamber
  • S1600519 in CR1
  • S1600522 in CR2
• 10:11am, roughing pump on
• 10:19am, turbo pump on
• Excitations

  • Quiet time before excitation: 1185649996
    Excitation broadband: 1185650031
    Quiet time after excitation: 1185650056

  • Quiet time before excitation: 1185651286
    Excitation broadband: 1185651321
    Quiet time after excitation: 1185651346

  • Quiet time before excitation: 1185652576
    Excitation broadband: 1185652611
    Quiet time after excitation: 1185652636

  • Quiet time before excitation: 1185653866
    Excitation broadband: 1185653901
    Quiet time after excitation: 1185653926

  • Quiet time before excitation: 1185655156
    Excitation broadband: 1185655191
    Quiet time after excitation: 1185655216

  • Quiet time before excitation: 1185656446
    Excitation broadband: 1185656481
    Quiet time after excitation: 1185656506

  • Quiet time before excitation: 1185657737
    Excitation broadband: 1185657772
    Quiet time after excitation: 1185657797

  • Quiet time before excitation: 1185659027
    Excitation broadband: 1185659062
    Quiet time after excitation: 1185659087

2017-08-02

• 11:25am valve closed, venting, pumps off

2017-08-02

• 11:33am in chamber
  • S1600553 in CR1
  • S1600554 in CR2
  • S1600555 in CR3
  • S1600556 in CR4
• 11:35am roughing pump on
• 11:45am turbo pump on
• Excitations:

  • Quiet time before excitation: 1185760223
    Excitation broadband: 1185760258
    Quiet time after excitation: 1185760283

  • Quiet time before excitation: 1185767513
    Excitation broadband: 1185767548
    Quiet time after excitation: 1185767573

  • Quiet time before excitation: 1185774804
    Excitation broadband: 1185774839
    Quiet time after excitation: 1185774864

  • Quiet time before excitation: 1185782094
    Excitation broadband: 1185782129
    Quiet time after excitation: 1185782154

  • Quiet time before excitation: 1185789384
    Excitation broadband: 1185789419
    Quiet time after excitation: 1185789444

  • Quiet time before excitation: 1185796675
    Excitation broadband: 1185796710
    Quiet time after excitation: 1185796735

2017-08-03

• 11:00am valve closed, pumps stopped, venting

2017-08-03

• 11:43am in chamber
  • S1600520 in CR1
  • S1600521 in CR2
  • S1600523 in CR3
  • S1600524 in CR4
• 11:46am roughing pump on
• 11:55am turbo pump on
• Excitations:

  • Quiet time before excitation: 1185835692
    Excitation broadband: 1185835727
    Quiet time after excitation: 1185835752

  • Quiet time before excitation: 1185837582
    Excitation broadband: 1185837617
    Quiet time after excitation: 1185837642

  • Quiet time before excitation: 1185839472
    Excitation broadband: 1185839507
    Quiet time after excitation: 1185839532

  • Quiet time before excitation: 1185841362
    Excitation broadband: 1185841397
    Quiet time after excitation: 1185841422

  • Quiet time before excitation: 1185843252
    Excitation broadband: 1185843287
    Quiet time after excitation: 1185843312

  • Quiet time before excitation: 1185845143
    Excitation broadband: 1185845178
    Quiet time after excitation: 1185845203

  • Quiet time before excitation: 1185847033
    Excitation broadband: 1185847068
    Quiet time after excitation: 1185847093

  • Quiet time before excitation: 1185848923
    Excitation broadband: 1185848958
    Quiet time after excitation: 1185848983

2017-08-04

• 2:00pm valve closed, pumps off, venting

2017-08-04

• 2:04pm in chamber
  • S1600535 in CR1
  • S1600536 in CR2
  • S1600537 in CR3
  • S1600538 in CR4
• 2:06pm roughing pump on
• 2:15pm turbo pump on
• Excitations:

  • Quiet time before excitation: 1185930952
    Excitation broadband: 1185930987
    Quiet time after excitation: 1185931013

  • Quiet time before excitation: 1185932843
    Excitation broadband: 1185932878
    Quiet time after excitation: 1185932903

  • Quiet time before excitation: 1185934733
    Excitation broadband: 1185934768
    Quiet time after excitation: 1185934793

  • Quiet time before excitation: 1185936623
    Excitation broadband: 1185936658
    Quiet time after excitation: 1185936683

  • Quiet time before excitation: 1185938513
    Excitation broadband: 1185938548
    Quiet time after excitation: 1185938573

  • Quiet time before excitation: 1185940403
    Excitation broadband: 1185940438
    Quiet time after excitation: 1185940463

  • Quiet time before excitation: 1185942293
    Excitation broadband: 1185942328
    Quiet time after excitation: 1185942353

  • Quiet time before excitation: 1185944183
    Excitation broadband: 1185944218
    Quiet time after excitation: 1185944243

2017-08-05

• 1:23pm valve closed, pumps stopped, venting

We first measured the distance of the ESD from the disk in the test chamber (CR0). We had to remove the retaining ring to have reliable measurements

• distance between top of the ESD and mounting plate: 12.30 mm
• distance between top of the disk and mounting plate: 10.53 mm
• ESD thickness: 0.55 mm

So initially the distance between disk and ESD is 1.22 mm

We re-aligned the optical setup to a horizontal reference, and moved down the ESD as much as we could. It's not completely clear if the ESD is touching the disk. We'll see after pump down. The new distance from the top of the ESD to the mounting plate is about 11.80 mm, so we should have moved the ESD 0.5mm closer to the disk.

Pump down started at ~1:30pm

Excitations

• Old configuration, 1.2mm distance ESD-disk:
  • GPS before exc. 1186417492 
  • GPS after exc. 1186417546
• New configuration, 0.7mm distance ESD-disk
  • GPS before exc. 
  • GPS after exc.

2017-06-20

• The two substrates were laser polished (CO2 power ~ 23 W)
• 3:50pm installed in chamber
  • S1600541 in CR1
  • S1600542 in CR3
• 3:52pm roughing pump on
• 4:00pm turbo pump on
• Excitations

  • Quiet time before excitation: 1182045787
    Excitation broadband: 1182045822
    Quiet time after excitation: 1182045887

  • Quiet time before excitation: 1182056717
    Excitation broadband: 1182056752
    Quiet time after excitation: 1182056817

  • Quiet time before excitation: 1182067648
    Excitation broadband: 1182067683
    Quiet time after excitation: 1182067748

  • Quiet time before excitation: 1182078578
    Excitation broadband: 1182078613
    Quiet time after excitation: 1182078678

  • Quiet time before excitation: 1182089509
    Excitation broadband: 1182089544
    Quiet time after excitation: 1182089609

2017-06-21

• 1:56pm, valve closed, pumps off

2018-04-03

• 4:12pm in chamber
  • S1600541 in CR1
  • S1600542 in CR2
  • S1600545 in CR3
  • S1600546 in CR4
• 3:30pm roughing pump on
• 4:00pm turbo pump on

2018-04-20

• 3:10pm in chamber
  • S1600577 in CR1
  • S1600580 in CR2
  • S1600582 in CR3
  • S1600585 in CR4
• 3:30pm roughing pump on
• 4:00pm turbo pump on
• 4:30pm It was found IGM gauge didn't start and pressure stopped at 1.8e-3. Gabriel vented chamber and re-pumped it.
• 4:50pm roughing pump on
• 17:05pm turbo pump on
• 17:10 pm pressure 1.7e-3, IGM display " starting"
• We start measurement.

There was no problem with either the gauges nor the pressure. The IGM took a long time to go on, but finally all pressures looked good. The measurement is also good

2020-01-14

• 10:10 am in chamber
  • S2000089 in CR1
  • S2000090 in CR2
  • S2000091 in CR3
  • S2000092 in CR4
• 10:16 am roughing pump on
• 10:26 am turbo pump on

2020-01-17

• 9:16 am in chamber
  • S2000093 in CR1
  • S2000094 in CR2
• 9:17 am roughing pump on
• 9:26 am turbo pump on

2017-06-21

• 4:30 pm- Installed COMSOL, began modeling current ESD by creating parameters and the first arm of the comb

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
• 

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.

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.

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 , since fused silica is isotropic it's polarization is proportional to E so . 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.

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  and as . 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.

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*10⁶ which 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.

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.

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. 

2017-07-06

• I compared the electric field and the polarization to make sure that those calculations made sense. Since  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

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  where  is the difference in the field between the plus end and the minus end. Component wise,  where d is a unit vector. This holds for y and z, the whole thing can also be written as . Since p=qd, we can write . 

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 . This explicity explains the factor of two and is an interesting alternative explanation.

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. 

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

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 . 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. 

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. 

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.

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.

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.

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.

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.

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.

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. 

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

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

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.

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.