ID 
Date 
Author 
Type 
Category 
Subject 
127

Sat Mar 17 15:27:48 2018 
rana  General  General  file size >> small 
When saving your COMSOL files do these two things to make the files much smaller (good for saving in version control and sharing):
 File > Compact History
 Preferences > Files > Optimize for File Size (not speed)

128

Mon Aug 20 15:44:56 2018 
rana  General  General  file size >> small 
Also,
 click 'Clear Mesh' under the mesh menu
 'Clear Solutions' under the Study menu
In this way the file sizes will be ~100 kB instead of 10's of MB.
Quote: 
When saving your COMSOL files do these two things to make the files much smaller (good for saving in version control and sharing):
 File > Compact History
 Preferences > Files > Optimize for File Size (not speed)


138

Tue May 12 14:16:28 2020 
Koji  General  General  FEA tutorial resources 
cf. Forwarded email from Stephen
1) Tuesday Demo  Basics of FEA Meshing G2000696
2) CIT SYS User Guides, How to Use the FEA User Group T2000295
3) CIT SYS User Guides, How to Use the ANSYS Learning Hub T2000236
Fabrice's SAMS piezo actuator second prototype E1900383 
142

Thu Jul 6 11:35:55 2023 
Rajashik  General  General  Basic Demonstration of Cavity Scan 
Attached are plots of how HOMs are introduced by defects in the mirror. This is just an example for a basic FP Cavity. 
Attachment 1: beforemin.png


Attachment 2: aftermin.png


144

Sat Jul 29 00:19:02 2023 
Rajashik  Optics  General  
I have coded a rudimentary triangular model using parameters provided by Aaron. In this model, I have kept a simple PDH signal which is the REFL power demodulated with the EO frequency. The PDH signal is then fed to the laser to modulate the frequency.
There are some points of confusion I have in this model such as the high loop gain required to achieve locking. I think this may be due to the fact that the reflective power in SI units is incredibly small while the frequency shift is considerably larger in SI units.
Then I took this model through basic operations such as determining the optimal phase angle for the PDH signal and assessing if lock can be achieved. They went as required for a sanity check.
Then I introduced a mismatch for light incident on the first mirror. This resulted in the creation of higherorder modes in the cavity as expected.
I am still analyzing the effect of this mismatch for the length control offsets. Also, I am not sure why we need a sensing matrix in this situation, because we're currently dealing with a single signal source and one degree of freedom. Or maybe a more complex readout and control scheme may be more helpful. This remains to be seen,
Nonetheless, I've attached plots that illustrate the cavity modes that have emerged due to the mismatch. 
Attachment 1: cavitymodesmin.png


Attachment 2: transmin.png


Attachment 3: download_(1)min.png


4

Thu May 2 14:00:36 2013 
Koji  General  Configuration  test mass TR with Levin's approach 
Thermorefractive noise in a finite cylindrical/infinite test mass with Levin's approach
Location of the codes: 40m SVN repository
comsol/thermorefractive/
This code realizes Levin's calculation on thermorefractive noise
doi:10.1016/j.physleta.2007.11.007
and duplicates the result of D. Heinerts paper
DOI: 10.1103/PhysRevD.84.062001
Also the result is compared with Braginsky's result in 2004.
doi:10.1016/S03759601(03)004730
 The code applies gaussianshaped heat into a cylindrical mirror.
 The heating/cooling is sinusoidal and the dissipation (heat flow) is calculated in COMSOL.
 The time series result was analyzed in MATLAB to extract the single coefficient corresponds to the transfer function.
This way the effect of the initial transient was avoided.
 Unfortunately direct measurement of frequency response in COMSOL was not available as the heat flow is not modal.
If we make a fourier analysis of the partial differential equation and solve it in COMSOL using arbitrary PDE solver,
we may turn this time dependent analysis into static analysis.
All of the calculation was driven from MATLAB. So you have to launch "COMSOL with MATLAB". 
Attachment 1: thermo_refractive_1D_axisym_result.pdf


76

Mon Sep 16 10:07:32 2013 
Evan  General  Configuration  COMSOL 4.3 on the OS X command line 
If you're running Matlab scripts that iterate over simulation parameters (à la Tara), you might find it useful to be able to run everything from the command line (instead of launching the "Comsol with Matlab" GUI application).
First, the comsol command wasn't in my path, so I symlinked it to someplace where bash could find it:
ln s /Applications/COMSOL43a/bin/comsol /opt/local/bin/comsol
I then started Comsol/Matlab using a slight modification of the commands given in the Comsol 4.3 help file "Running A COMSOL Mfile In Batch Mode Without Display":
comsol server > server_log.txt &
matlab nodesktop nosplash r "run /Applications/COMSOL43a/mli/mphstart; comsol_script; exit"
The first command starts the Comsol server in the background and cats its output into a log file. The second command launches Matlab, runs the initialization script which makes Matlab aware of Comsol, runs my Comsol/Matlab script (comsol_script.m), and then exits. 
99

Tue Sep 30 11:30:27 2014 
Nic, Dmass, Evan  General  Configuration  Gravity in Comsol 
Here is a set of slides by Yoichi Aso on how to handle gravity in Comsol. 
100

Sat Sep 5 15:04:43 2015 
Dennis Coyne  Mechanics  Configuration  summary of FEA modal model to State Space model 
At the 2014 commissioning workshop, I presented a summary of my efforts in converting finite element modal models into state space models:
https://dcc.ligo.org/LIGOG1400099
I also provided the attached written summary for a report on the workshop that Aidan Brooks and Gabriele Vajente are preparing. 
Attachment 1: FEM2SS_summary.docx

101

Sat Sep 5 15:17:41 2015 
rana  General  Configuration  FEA logs merged 
I moved the only entry from the 'ENG_FEA' log into the COMSOL log and then renamed that logbook as 'FEA' since we don't need two FEA logs.
Also renamed 'AdhikariLab' log as ATF. 
102

Fri Dec 4 18:32:02 2015 
rana  General  Configuration  COMSOL: remote server w/ matlab 
This summarizes how to get the remote comsol server to run. COMSOL 5.1.0.234 is now on tegmeni thanks to Larry.
On the server:
rana@tegmeni~> /usr/local/comsol51/multiphysics/bin/comsol server login force
This starts up a comsol server instance, listening on port 2036. 'login force' will ask you to supply a username and password which you make up. You will have to enter these later from the client side.
On my laptop, from the MATLAB prompt:
>> addpath('/Applications/COMSOL51/Multiphysics/mli/')
>> mphstart('tegmeni.ligo.caltech.edu', 2036,'uname','pword')
That's it! Now you just run the matlab script which runs the COMSOL file.
I'm attaching a tarball of the .mph file (written by Dmitry Kopstov from MSU) and the associated matlab scripts which change the parameters, as well as looping over test mass thickness to produce a plot of Brownian noise PSD v. 
Attachment 1: BrownianSweep.tgz

110

Mon Jul 24 15:35:34 2017 
Mariia  General  Configuration  Running Comsol to Matlab 
WIth Gautam's help, I have created a user directory in 40 meter Lab and copied Rana's documents (MATLAB coating files) from flash card into it. After that, from this elog by Rana : COMSOL: remote server w/ matlab from Fri Dec 4 18:32:02 2015, ran the matlab document BarrelCoating which resulted in the following error
Messages:
Could not obtain license for#LiveLink for MATLAB
Could not obtain license for LiveLink for MATLAB.
License error: 4.
Licensed number of users already reached.
Has anybody seen this before?

111

Mon Jul 24 15:54:26 2017 
Koji  General  Configuration  Running Comsol to Matlab 
The number of licenses already used by whom / still remains can be confirmed by running the following command on a comsolinstalled linux machine
$ cd /usr/local/comsol51/multiphysics/license/glnxa64
$ ./lmstat c ../license.dat a

112

Wed Jul 26 20:14:46 2017 
rana  General  Configuration  Running Comsol to Matlab 
I've just tried this out on my desktop machine using COMSOL 5.1 and its still working. Which COMSOL is installed on optimus at the 40m ? 
113

Fri Jul 28 15:48:58 2017 
Mariia  General  Configuration  Comsol batch for windows 
Using the written path from elog by ericq: Computer Scripts/Programs, Comsol can be run from the directory on the distant computer: /cvs/cds/caltech/apps/linux64/comsol51/bin/glnxa64/comsol batch inputfile Model1.mph outputfile Model_solv.mph. To transfer files from Linux to Windows : the command pscp.
The method:
1. To download PuTTY and make a coonection with a distant computer.
2. Linux terminal: ssh optimus % allows to go into the whole system
3. Windows terminal: pscp "the path of the file" controls@nodus.ligo.caltech.edu:/users/.../ % allows to transfer mphfile from Windows to Linux
4. Linux terminal: /cvs/cds/caltech/apps/linux64/comsol51/bin/glnxa64/comsol batch inputfile Model1.mph outputfile Model_solv.mph % calculation on the distant computer, without outputfile solution would be stored in the input file
5. Windows terminal: pscp controls@nodus.ligo.caltech.edu:/users/.../Model_solv.mph Documents\ % copy file from Linux to Windows, Documents is the name of the folder in Windows

139

Tue Aug 11 11:16:29 2020 
aaron  General  Configuration  COMSOL with Matlab without display 
When running comsol with matlab interface on sandbox1, it is usually most convenient to ssh with screen forwarding (eg 'CY') and launch COMSOL with matlab by following the instructions in the livelink manual.
Sometimes, it is necessary to run COMSOL without any display available. In that case, the Instructions in the manual are a little unclear. Here are the detailed steps that let me run my script '/home/amarkowi/metamaterials/run_spiral.m' with no screen forwarding.
1. ssh onto sandbox1 by entering the following at your laptop command prompt
password: [enter sandbox1 credentials]
2. start a tmux session for starting the COMSOL server
aaron.markowitz@sandbox1:~$ tmux
3. start a comsol server from the tmux session
aaron.markowitz@sandbox1:~$ comsol54 mphserver login force port 2020
Username: whoever
Password: whatever
Confirm password: whatever
4. detach the tmux session by pressing ‘ctrlb’ followed by ‘d’
5. (optionally, you can start a new tmux session for your matlab work by running tmux again at your main sandbox prompt)
6. Start matlab by running
>> matlab nodesktop mlnosplash
6. Add the comsol directory to the matlab path by running at the matlab prompt
>> addpath(‘/localhome/comsol54/multiphysics/mli/‘)
6. Start the matlab with comsol interface by running the following at the matlab prompt
7. change into the directory containing the script, and run it
>> cd /home/amarkowi/metamaterials
>> run_spiral

140

Tue Aug 11 16:35:07 2020 
aaron  General  Configuration  COMSOL: remote server w/ matlab 
To run COMSOL on sandbox1 with no graphical Interface, here are the steps that worked for me (Tue Aug 11 16:35:51 2020) from a mac on the Caltech VPN.
1. ssh onto sandbox1 with screen forwarding (Y). Make sure you have a compatible version of XQuartz or a substitute. C specifies data compression, which may be useful on slow connections
password: [enter sandbox1 credentials]
2. Launch Matlab with COMSOL 5.4, specifying no graphical interface, by running
aaron.markowitz comsol54 mphserver matlab nodesktop mlnosplash script_name’
3. If there is still a splash screen from the COMSOL server, you will have to specify nosplash by adding the following line to your .bash_profile (in your home directory)
export COMSOL_MATLAB_INIT=’matlab nosplash’
4. You can run whatever comsol script you need. Make sure that in your script you import the comsol functions by calling the following
import com.comsol.model.*
import com.comsol.model.util.*

82

Thu Apr 17 16:52:09 2014 
Evan  General  Characterization  Interpreting logfiles and picking a solver 
Here are two entries by Walter Frei on the Comsol blog that I've found useful.
Solving Linear Static Finite Element Models: Tells you how to interpret all those numbers that Comsol dumps into its logfiles.
Solutions to Linear Systems of Equations: Direct and Iterative Solvers: Explains a bit more about Comsol's solvers. Apparently, PARDISO is usually fast and SPOOLES is usually slow (the tradeoff is apparently that SPOOLES uses less memory). I've found this to be personally true with at least one model I've worked with. 
77

Wed Nov 13 23:55:44 2013 
Chris Couste  Optics  Analysis  Optical Mount Vibrational Analysis 
Project: Vibrational Analysis of Optical Mounts
Goal: Use COMSOL to run finite element analysis on simplified models of different types of optical mounts available to us, in order to find which shape/style/material reacts the least to external sound pollution. Once the few best candidates have been identified, develop test to experimentally determine optimal mount configuration and material.
Part 1: FEM
Process: Simultaneously build models in SolidWorks and design analysis in COMSOL
Solidworks: base/shaft models based on measurements of actual optical mounts, optic holder models matching mass and moment of inertia from downloaded models from their manufacturers. ~Progress: base/shaft done, optic holders almost done.
COMSOL: Design analysis that first does a general eigenfrequency analysis to find general vicinity of modes, then does a full modal frequency analysis. ~Progress: finished, ready for models to be imported. 
78

Mon Nov 18 15:56:59 2013 
Chris Couste  Optics  Analysis  Representative Models 
The simpler models of the optical mounts are finished, they will be run through the comsol analysis software soon.
see pictures below:

Attachment 1: Custom_Closed.JPG


Attachment 2: custom_open.JPG


Attachment 3: Stock_Closed.JPG


Attachment 4: Stock_Open.JPG


79

Fri Nov 22 21:04:53 2013 
Chris Couste  Optics  Analysis  analysis 
The analysis is making nice eigenmode and stress mode models, but the displacement experiment needs work. Should be fixed by monday. 
80

Fri Jan 24 17:26:38 2014 
Chris Cousté  Optics  Analysis  Mount Analysis Functional! 
The comsol eigenmode analysis is complete, and the only thing left to do on this part of the project is to run the analysis on a range of different configurations of optical mounts as well as a range of materials. This compilation will be posted on this elog in the next few weeks, due to the fairly long runtime of the analysis software. 
81

Sun Feb 16 21:10:56 2014 
Chris Cousté  Optics  Analysis  Optical Mount data compilation 1: Aluminum 
The time is finally here! this is the highest displacement of each mount in its lowest few eigenfrequencies, using 6061 Aluminum as a material. pictures will be added in a future log, because I'm going to make them into one file. Other materials will also be tested to see if there is variance in these findings, but only relevant data will be posted.
tl;dr findings: thickopen is the best combination because it has less displacement in eigenmodes and its eigenmodes are all very high/spread apart in frequency.
long:
(key) Eigenfrequency (Hz), highest displacement (mm), direction
Thin base, open mount:
315, 8.07, leaning back (laser will angle up)
316, 7.94, leaning to the side (laser won't change direction if the optic is flat, i.e. point of contact moves along surface of optic)
924, 10.50, twist to the side (laser will angle to the side)
1949, 8.89, twist about optic, slight lean forward (point of contact will move slightly, laser may angle down)
2144, 10.47, another leaning forward mode
thin base, open mount:
322, 13.29, leaning forward and translating to the side
328, 13.36, same as above
994, 17.66, twisting to the side (laser will angle to the side)
1943, 13.86, intense leaning forward
2100, 14.27, twist about optic
thick base, closed mount:
1329, 13.23, leaning back
1347, 13.32, leaning back and to the side
3577, 15.46, twisting to the side
thick base, open mount:
1326, 9.69, leaning to the side
1335, 9.77, leaning back
3504, 13.88, twisting to the side

All of these frequencies were checked for all four models, and the max displacements in those cases ranged from 100 picometers to 10 femtometers, so it's pretty reasonable to base decisions off of the displacements at the eigenmodes.
Based on this, it seems that for both thick and thin, open is the best, considering it displaces significantly less than closed (which is reasonable because there is less mass at the top to be thrown around). The choice between thick and thin depends on what frequencies we believe the mounts will be subjected to. If we are probably not going to have much sound at frequencies above 1000Hz, then thick is the better option (which is nice because it is the stock stalk instead of the custom made one). However, if there will be plenty of high noise, the thick is still probably the better option because it has fewer eigenmodes in the same range of frequencies.
here's a sample of two pictures of the relevant eigenmodes of the winner.

Attachment 1: aluminum2.png


Attachment 2: aluminum3.png


105

Tue Jun 28 15:50:45 2016 
Joy Westland  Mechanics  Analysis  A Simple Model of the Modal Analysis of a Cantilever Circular/Cylinder Cross Section in ANSYS tutorial 
Here is a tutorial to implement a simple Modal Analysis of a Cantilever Cylinder
1. Open the ANSYS workbench
2. Drop and drag the "Modal" analysis system into the project schematic
3. Right click on "Engineering Data" and edit the material. There are predetermined properties found in the "Engineering Data Sources" (Right click on the description or press the books in the top right hand corner). For this tutorial, fused silica was created with these parameters:
 Young's Modulus E: 7.2E10 Nm^2 (Isotropic Elasticity)
 Density p: 2200 kgm^3 (Density)
 Specific Heat c: 770 J/kgK (Specific Heat)
 Isotropic Thermal Conductivity k: 1.38 W/mk (Isotropic Thermal Conductivity)
 Coefficient of Thermal Expansion: 3.9E7 (Isotropic Secant Coefficient of Thermal Expansion)
 Reference Temperature: 21 C (Isotropic Secant Coefficient of Thermal Expansion)
 Poisson's Ratio: 0.17 (Isotropic Elasticity)
In order to put in the parameters, just drag and drop from the toolbox. Also make sure the filter is turned off (that's the filter symbol next to the engineering data sources/books in the top right hand corner) this will allow a user to few all the parameters.
4. Return to the project, and open/edit the geometry. The cantilever that was used for this tutorial is a cylinder with a diameter of 2 mm with a length of 200 mm, shown in image 1.
 How to Create a geometry:
 Open up the geometry
 Decide which plane you want to start drawing in: XY Plane, ZX Plane, YZ Plane
 Click on "new sketch" in the 4th row from the top after "Sketch1" it's blue sketch
 Whatever plane you decide to choose, press the "Look at Face/Plane/Sketch" icon in the top right hand corner (The person looking at a face)
 This will allow the view to go to the view where you want to sketch on
 Click on "Sketching" which is next to the "Modeling" right above the "Details View"
 Here will be Several Options
 Draw: This is where you can decide what shape you want to use
 Modify: This is the extras such as fillets, chamfers and corners
 Dimensions: This is where you can select what type of dimensions you will be using
 Constraints: This is where you can constrain lines or connect lines
 When you want to connect lines together, click on each end and make them "Coincident" this way the shape will connect when you change dimensions
 Settings: This is where you can show a grid or snap grid
 Sketch Color:
 Teal: Underdefined: The sketch does not have enough dimensions to constrain and tell the program what exactly the shape is
 Blue: Defined: The sketch is fully defined and does not need any more dimensions
 Red: Overdefined: The sketch has repeating dimensions that causes errors
 For this tutorial, draw a circle. I made mine coincident to the middle by pressing the vertex in the middle and one of the axis and then repeat the process with the second axis to center the circle
 Dimensions: The diameter is 2 mm, under dimensions to display the number, click "Display" and then "Value" instead of "name"
 To change the dimensions, the "Details View" in the bottom left hand corner will say D1 and from there you can change the diameter
 From there in order to create the length of the cylinder, press "Extrude" at the top (4th row) towards the right. From there it will ask what geometry, click on your sketch and click "Apply". Make sure the "Operation" is "Add Material" to Extrude.
 Then choose a "Depth" in this case it's 200 mm. Then click "Generate" the lightning bolt next to the "New Sketch" symbol.
 Your cylinder should look like image 1.
5. Return to the project and open the Model tab. With that open, go to the subtab of "Geometry", named "Solid". Under Solid go to "Assignment" under "Material" to assign Fused Silica or whatever material you decide to choose.
6. Go to the "Mesh" tab. In this case the "Element Size" under the "Sizing" tab is 0.04 and the "Relevance Center" as "Fine". Right click on the mesh and press "Generate mesh".
7. Under the Modal tab, go to the Analysis Settings and change the "Max Modes to Find" for ANSYS to calculate. In this tutorial, the amount of modes that were used was 17.
8. Right Click the Modal and press on "Fixed Support". This will make the bar a cantilever bar, once the geometry is set to fix one face of the bar. Press on one of the faces and click on "apply" on the Geometry.
9. Right click on the solution and press "Solve". Let ANSYS run the modes through.
10. On the Solution tab, the "Tabular Data" is listed but the Total Deformation has not been listed. In order to do so, select all the frequency of the modes in the column and right click and press "Create Mode Shape Results".
11. Once loaded, the total deformation will have a lightning bolt next to each entry, right click and press "Solve" or "Evaluate All Results". This will make all the entries have a green check mark.
12. This will give the user the ability to animate each entry. This is down by clicking the play (sideways triangle button). ANSYS will run through the simulation for that mode that is selected, shown in image 2.
13. Using Mathematica (or another computational system) input the analytical solution for a Cantilever bar fixed to one end.
 w_{n}=(k_{n}L)^{2}Sqrt(EI/mL^{4})
 Where:
 w_{n} is the frequency measured in radians/second
 E = Young's Modulus
 I = moment of cross section
 I_{rectangle }= ba^{3}/12 (b and a are the sides)
 I_{circle} = (Pi/64)(d^{4}) (d is the diameter)
 m = mass per unit length
 L = length of the bar
 k_{n} relates to the amount of nodes
 k_{1}L = 1.875, k_{2}L = 4.694, k_{3}L = 7.855, k_{4}L = 10.996, k_{5}L = 14.137
 n greater than 5: k_{n}L = (2n 1)(Pi/2)
 Convert w_{n} to f measured in Hz
14. Compare only to the bar actually bending, not twisting or contracting. There are modes that are the same due to the symmetry of the bar. In image 3 the underlined frequencies compare to the analytical calculations (Mathematica) and the computational calculations (ANSYS). 
Attachment 1: Simple_Cantilever_200_mm_Long_Geometry.PNG


Attachment 2: Simple_Cantilever_200_mm_Long.PNG


Attachment 3: Comparison_between_ANSYS_and_Calculations_Fused_Silica_200_mm_L.PNG


106

Tue Jun 28 16:54:23 2016 
Nikhil Mathur  Mechanics  Analysis  Ansys 14.5 Indroductory Tutorial: Modal Frequency Convergence 
This tutorial will go through how to show frequency convergence for a cylindrical cantilever using Ansys 14.5 and Mathematica. 
Attachment 1: ConvergenceTutorial.pdf.gz

107

Wed Jun 29 14:14:44 2016 
Joy Westland  Mechanics  Analysis  ANSYS Tutorials with Basic Meshing 
Here are a series of tutorials for basic meshing principles from ANSYS Meshing Basics:
 ANSYS Meshing Fine Mesh Basic Tutorial 1: https://www.youtube.com/watch?v=sZIX3CJkWBE
 ANSYS Meshing Method Basic Tutorial 2: https://www.youtube.com/watch?v=ATSnvFUbEk4
 ANSYS Meshing Refinement Mesh Basic Tutorial 3: https://www.youtube.com/watch?v=QVfJiydCu2g
 ANSYS Meshing Sizing Mesh Basic Tutorial 4: https://www.youtube.com/watch?v=ODJ11YDC6ac
 ANSYS Meshing Spheres of Influence Basic Tutorial 5: https://www.youtube.com/watch?v=AQlGccK_X0
 Body of Influnce 6: https://www.youtube.com/watch?v=3E1p1w32jt0
 Section Plane 7: https://www.youtube.com/watch?v=hhZOJSESJEU
 Mapped and Match Control 8: https://www.youtube.com/watch?v=3pogywR8Vgw
 MultiZone and Inflation 9: https://www.youtube.com/watch?v=vxVBvANHuB0
 Sizing Soft/Hard 10: https://www.youtube.com/watch?v=D8UzdC5Gmhs

129

Sun Aug 26 16:42:54 2018 
rana  Mechanics  Analysis  Test Mass Thermal Noise: Consistency Checks 
For the Voyager test masses, we have been considering a barrel coating to increase the IR emissivity to increase the radiative cooling power. We also seek to estimate the added Brownian thermal noise that arises from this.
Dmitry Kopstov (from MSU) made a baseline model for this which we have been modifying. The latest is in the CryogenicLIGO git repo in the FEA directory as ETM_NASAbarrel.mph.
Comparison with Analytic Estimates:
Convergence Tests:

143

Fri Jul 21 16:42:57 2023 
Rajashik  Optics  Analysis  
Initially, ideal conditions were considered, without any deformations or thermal heating effects in the mirrors. This offered a baseline model from which subsequent tests could draw comparisons.
Following this, more complex scenarios were introduced into the model: mirrorshape defects caused by suspension and thermal lensing due to heat absorption. These heat absorption rates were set at 0.5 ppm in the ETM coating and 0.3 ppm in the ITM coating.
The lensing calculations for these scenarios were performed using the power observed in the nondeformed mirror case. This lensing needs to be made dynamic in future codes to get the modeling correct. Nonetheless, introducing these conditions resulted in the emergence of higherorder modes (HOMs). Unfortunately, there seems to be a loss of power in the cavity that I haven't been able to resolve yet. Notably, this power loss persisted across the range of mirror position scans showing that this is not due to just a change in resonance length.
Also, the Hello Vinet Function in Finesse 3 seems to yield a higher degree of lensing than typically reported in the literature. I need to check with someone about what assumption I am taking incorrectly here. It's plausible that the heightened lensing effect is contributing to the observed power loss in the cavity, possibly due to high curvatures.
Looking forward, my focus will be on determining the source of this lensing discrepancy first. This analysis will involve a more detailed examination of the variables contributing to thermal lensing and potential causes for the higherthanexpected lensing observed in the simulation. Ultimately, the aim is to create a dynamic deformation model that can more accurately represent these phenomena within the aLIGO setup before introducing ring heaters and controls. 
Attachment 1: Cavity_Scan_Before_Adding_Defects.png


Attachment 2: Transmitted_Power_Before_Adding_Defects.png


Attachment 3: Cavity_Scan_After_Adding_Defects.png


Attachment 4: Transmitted_Power_After_Adding_Defects.png


3

Tue Apr 2 19:24:07 2013 
Emory Brown  Optics   First steps producing a Finite Element Model to find the internal Brownian noise of a LIGO test mass 
Motivation:
Reduction of Brownian thermal noise in future gravitational wave detectors is of significant interest. It has been suggested that changing the shape of the mirrors used may reduce the Brownian thermal noise. Before we can study how alterations in mirror shape effect Brownian thermal noise, we must be able to generate a finite element model which can compute the Brownian thermal noise in current mirror substrate so that the model may be tested against other calculations of that value using the fluctuationdissipation theorem.
Methods:
I began by constructing a model of a mirror design in COMSOL with the following parameters:
radius (R): 172.5 mm
height: 102 mm
Gaussian beam size (rBeam): 4 cm
TotalForce: 1 N (this is a placeholder force)
loge: log base 10 of e or about 0.4343
PressureCenter: TotalForce*(1/pi)*(rBeam^2)*(1e^(R^2/rBeam^2))^1
A cylinder was constructed using the radius and height above with its flat faces pointing in the z direction, and was given the properties of fused silica which COMSOL had built in.
Our first nondefault boundary condition was applying a force representing the laser beam onto one of the flat faces of the cylinder, surface 3, in the model. The force applied to this face was a Gaussian function PressureCenter*e^(sys2.r^2/rBeam^2) which was specified in COMSOL as a boundary load.
In order to keep the cylinder fixed in space, representing its being connected to wires supporting it and our ignoring violin modes, we need to apply another boundary condition. The simplest possibility would be to force surface 1 in the model, the face of the cylinder opposite the applied force, from moving, but page 5 of Liu and Thorne's paper demonstrates that we should instead apply a force of equal magnitude and opposite direction to that applied to surface 3, but distributed over the volume of the cylinder. To this end, we integrated the Gaussian force applied over the face of the mirror and determined that the total force applied was TotalForce=pi*PressureCenter(1e^(R^2/rBeam^2))rBeam^2/loge. It is more convenient to specify the total force than the pressure at the center of the mirror's face, so solving for PressureCenter we obtain PressureCenter=TotalForce*(loge/pi)*(rBeam^2)*(1e^(R^2/rBeam^2))^1. This opposing force was entered into COMSOL as a body load using the value TotalForce applied over the volume of the cylinder.
COMSOL was instructed to solve for a steady state given the above configuration and returned an error message that “The relative residual (19) is greater than the relative tolerance.” I increased the number of elements in the mesh and the analysis returned lower relative residuals (9.1) using a “finer” mesh. The computer being used did not have enough memory to use a finer mesh structure than that, but the lower relative residual indicates that using a finer mesh may solve the convergence problem.
Ideas for future work:
The simplest possibility is to perform the simulation again using a finer mesh on a computer with more memory and see if we can obtain a solution.
The function used to assign forces at the discrete points in the mesh is continuous, but the points are discrete. Using a discrete Gaussian function to determine the force at each point on the face may be worth trying.
Alternatively, the process could be handled by a Matlab script setup to first run a COMSOL simulation to determine the integrated force on the face of the cylinder, then normalize the central force based on that data such that the desired force is applied to the cylinder face. The script would then solve for the steady state solution.
We could also consider replacing the TotalForce applied over the cylinder's volume by a different boundary condition. Replacing it by a weak spring force on the back face of the mirror has been suggested. I think this is less likely to give good results than the above suggestions, but it may still be worth testing and seeing how its solution compares to values obtained from the fluctuationdissipation theorem.
Liu, Y. T., & Thorne, K. S. (2000). Thermoelastic noise and homogeneous thermal noise in finite sized gravitationalwave test masses. Physical Review D, 62(12), 122002.

83

Sun Jun 22 23:44:56 2014 
Sam Moore  Optics   Going through Heinert's 'TR noise of cylindrical test masses' paper 
At this point, my are goals are to 1) convert the timedependent heat equation into stationary, complex form, 2) use the Levin approach to calculate the TR noise given this stationary PDE, and 3) verify the results in COMSOL
I have looked at the Heinert paper and converted the timedependent partial differential Heat equation to a stationary, complex one. I did this by assuming a temperature distribution of the form T(\vec{r},t) = T_0 ( \vec{r} ) e^{i \omega t }, where \omega is the frequency of oscillation of the input heat field: q( \vec{r} , t) = q( \vec{r} ) e^{i \omega t}. Hence, I am assuming the steadystate solution of the temperature field. From this ansatz, the PDE becomes
C_p T(\vec{r}) + \frac{ i \kappa}{ \omega } \nabla^2 T ( \vec{r} ) = q ( \vec{ r} ).
This complex conversion already seems to have been done in the paper, since the stationary solution of the form
T(r, z) = \sum_{n = 0}^{\infty} \sum_{m = 0}^{ \infty} T_{n m} J_0 (k_n r) \cos ( \ell_m z) is assumed.
k_n and \ell_m are obtained from the adiabatic boundary conditions. Moreover, if I plug this form for T(r, z) into the stationary PDE, I get Heinert's eq. 12. ( although I'm not quite sure how to take the second derivative of a zerothorder bessel function).
I've started to try out the cylindrical geometry in COMSOL, using the structural mechanics and heat transfer modules. At this point, I'm not quite sure how to specify the PDE that I'm interested in, nor am I sure about how to specify the boundary conditions.

84

Mon Jun 23 11:40:17 2014 
Sam Moore  Optics   Going through Heinert's 'TR noise of cylindrical test masses' paper 
Quote: 
At this point, my are goals are to 1) convert the timedependent heat equation into stationary, complex form, 2) use the Levin approach to calculate the TR noise given this stationary PDE, and 3) verify the results in COMSOL
I have looked at the Heinert paper and converted the timedependent partial differential Heat equation to a stationary, complex one. I did this by assuming a temperature distribution of the form T(\vec{r},t) = T_0 ( \vec{r} ) e^{i \omega t }, where \omega is the frequency of oscillation of the input heat field: q( \vec{r} , t) = q( \vec{r} ) e^{i \omega t}. Hence, I am assuming the steadystate solution of the temperature field. From this ansatz, the PDE becomes
C_p T(\vec{r}) + \frac{ i \kappa}{ \omega } \nabla^2 T ( \vec{r} ) = q ( \vec{ r} ).
This complex conversion already seems to have been done in the paper, since the stationary solution of the form
T(r, z) = \sum_{n = 0}^{\infty} \sum_{m = 0}^{ \infty} T_{n m} J_0 (k_n r) \cos ( \ell_m z) is assumed.
k_n and \ell_m are obtained from the adiabatic boundary conditions. Moreover, if I plug this form for T(r, z) into the stationary PDE, I get Heinert's eq. 12. ( although I'm not quite sure how to take the second derivative of a zerothorder bessel function).
I've started to try out the cylindrical geometry in COMSOL, using the structural mechanics and heat transfer modules. At this point, I'm not quite sure how to specify the PDE that I'm interested in, nor am I sure about how to specify the boundary conditions.

I carried out the calculations for Heinert's simple model in greater detail and was able to obtain equation 12 (with the exception of a plus sign instead of a minus sign in the denominator; I guess the Fourier transform method gives a minus sign. In the end, that doesn't matter, since the modulus square yields the same result in the denominator.) I obtained the same spectral density S_z (\omega), with the exception of a missing factor of R^2. I don't know where this R^2 went, or why it is that the spectral density is associated with the extrinsic variable z (instead of r, say). It's supposed to be a "homogeneous [noise] readout along the z direction." 
85

Mon Jun 23 16:10:17 2014 
Matt A.  Optics   Going through Heinert's 'TR noise of cylindrical test masses' paper 
Quote: 
At this point, my are goals are to 1) convert the timedependent heat equation into stationary, complex form, 2) use the Levin approach to calculate the TR noise given this stationary PDE, and 3) verify the results in COMSOL
I have looked at the Heinert paper and converted the timedependent partial differential Heat equation to a stationary, complex one. I did this by assuming a temperature distribution of the form T(\vec{r},t) = T_0 ( \vec{r} ) e^{i \omega t }, where \omega is the frequency of oscillation of the input heat field: q( \vec{r} , t) = q( \vec{r} ) e^{i \omega t}. Hence, I am assuming the steadystate solution of the temperature field. From this ansatz, the PDE becomes
C_p T(\vec{r}) + \frac{ i \kappa}{ \omega } \nabla^2 T ( \vec{r} ) = q ( \vec{ r} ).
This complex conversion already seems to have been done in the paper, since the stationary solution of the form
T(r, z) = \sum_{n = 0}^{\infty} \sum_{m = 0}^{ \infty} T_{n m} J_0 (k_n r) \cos ( \ell_m z) is assumed.
k_n and \ell_m are obtained from the adiabatic boundary conditions. Moreover, if I plug this form for T(r, z) into the stationary PDE, I get Heinert's eq. 12. ( although I'm not quite sure how to take the second derivative of a zerothorder bessel function).
I've started to try out the cylindrical geometry in COMSOL, using the structural mechanics and heat transfer modules. At this point, I'm not quite sure how to specify the PDE that I'm interested in, nor am I sure about how to specify the boundary conditions.

Hi Sam,
I know it seems a bit distracting, but it's sometimes nice to write up your elog entries in a more readable form. I've reedited your comments to make them more easily read.
I used http://www.sciweavers.org/freeonlinelatexequationeditor to convert your latex to png files for easy reading.
At this point, my are goals are to:
1) convert the timedependent heat equation into stationary, complex form,
2) use the Levin approach to calculate the TR noise given this stationary PDE, and
3) verify the results in COMSOL
I have looked at the Heinert paper and converted the timedependent partial differential Heat equation to a stationary, complex one.
I did this by assuming a temperature distribution of the form:
where ω is the frequency of oscillation of the input heat field:
Hence, I am assuming the steadystate solution of the temperature field.
From this ansatz, the PDE becomes:
This complex conversion already seems to have been done in the paper, since the stationary solution of the form:
is assumed. k_{n} and ℓ_{m} are obtained from the adiabatic boundary conditions.
Moreover, if I plug this form for T(r, z) into the stationary PDE, I get Heinert's eq. 12.
( although I'm not quite sure how to take the second derivative of a zerothorder bessel function).
I've started to try out the cylindrical geometry in COMSOL, using the structural mechanics and heat transfer modules.
At this point, I'm not quite sure how to specify the PDE that I'm interested in, nor am I sure about how to specify the boundary conditions.

91

Sat Jul 5 13:04:32 2014 
Sam Moore  Optics   Heinert Model TR Noise Verification 
Agreement with Heinert's paper for cylindrical TR noise has now been achieved. Using the stationary state assumption to calculate the temperature profile, the computation time was reduced compared to the previous timedependent approach. Here are the plots showing the agreement. I have shown the plots for a 1D axisymmetric model, in addition to a full 3D model in COMSOL. Both give the same result.
What went wrong? In the 1D axisymmetric case, it turns out that COMSOL has the incorrect cylindrical coordinate Laplacian for the coefficient form PDE interface. I corrected for this by expanding the Laplacian with the product rule, giving an extra kappa/r ''convection coefficient'' in the PDE interface. Meanwhile, the 3D case worked from the beginning, since its Laplacian was in cartesian coordinates.
The next goal is to use a stationary state method to calculate TE noise for a test case.

Attachment 1: threeD_cylinderTRnoise.png


Attachment 2: oneDcylinderTRnoise_copy.png


92

Mon Jul 7 19:47:00 2014 
Koji  Optics   Heinert Model TR Noise Verification 
How close are these FEA calculations with the analytical values?
Can you plot residual too? (Put analytical values, 1D, abs(1D  analytical), 3D, and abs(3D  analytical) all together.) 
94

Fri Jul 11 10:58:18 2014 
not Koji  Optics   Heinert Model TR Noise Verification 
Quote: 
How close are these FEA calculations with the analytical values?
Can you plot residual too? (Put analytical values, 1D, abs(1D  analytical), 3D, and abs(3D  analytical) all together.)

Here are the plots with their fractional residuals: abs(S_COMSOL  S_analytical)/S_analytical 
Attachment 1: heinert_analyticalTest_residual_threeD.eps


Attachment 2: heinert_analyticTest_residual_oneD.eps


131

Thu Feb 14 12:38:51 2019 
Ching Pin  Mechanics   comsol modelling 
So I did a simple comsol model of laser heating of a silicon disk, with only radiation, to see the temperature variation at steady state, which could be the limiting factor for high Q at 123 K, due to the thermalelastic effect.
The model just uses a simple 2 inch disc, at 0.028 cm thick, with the flats not incorporated in yet.
I had to search for silicon thermal conductivity and heat capacity at low temperatures, settling with k= 800 W/(m K) and C_p= 300 j/(kg K) from refering to papers. Will check LIGO documents for more accurate versions.
I put an arbitary boundary condition of constant temperature of 123 K on a spot .2 mm in radius, to simulate a beam.
Other arbitary values include 77 K for ambient and a surface emissivity of 0.5.
The laser is off center, because that it where the laser will enter the current setup.
We can see that the power required is .02 W, which seems reasonable.
The model is consistent with the analytic model I made with the laser beam at the centre of the disc. See last two figures.
I'm still trying to get the time dependence to work, as it is just giving me nonsense right now.
Some thoughts: beam radius affects the temperature variation quite significantly, with a fat beam (1 mm radius) having half the temperature variation as a beam of .2 mm radius
I think the halo is just a trick of the eye, but I could be wrong.
Things to do:
Find the time scale of the system, as we want to modulate the laser to adjust the temperature, which will then be run though the mode ringer to measure Q to find the zero crossing
Change the heat source to be an actual laser
Add in the solid mechanics part
Add in the sapphire lens underneath 
Attachment 1: Screenshot_from_20190214_124711.png


Attachment 2: Screenshot_from_20190214_150740.png


Attachment 3: Screenshot_from_20190214_154141.png


Attachment 4: graph.pdf


132

Fri Feb 15 21:05:31 2019 
Ching Pin  Mechanics   comsol modelling 
So I got the time dependence to work, but I'm not sure what went wrong in the first time anyways. I'll trying to get a sense of how long it takes for the temerature to semiequlibrate, and coming to grips with comsol as a whole. There seems to be some inaccuracies when the timing increases, so I'm having to figure out how to increase accuracy without drastically increasing compute time. On the bright side, I switched the model to heating via deposited beam, for a more accurate model.
Attached is comsol's handling of a deposited beam modulated sinusoidally with a frequency of 0.1 Hz and screwing up badly. Y axis is the average surface tempurature across the whole disc.

Attachment 1: Screenshot_from_20190215_214001.png


133

Tue Feb 19 19:52:53 2019 
Ching Pin  Mechanics   comsol modelling 
The time step response to heating via laser (22.5 mW) is given in the attached picture, for 2 starting temperatures, 122.5 K and 122.8 K. We see that it takes fairly long to equlibrate, with a time constant of about 500 s, and is consistent across both temps. The y axis is average temperature across the surface of the disc, and the x axis is time. I believe that the heat distribution profile would be very similar with time, simply because of how much faster conduction is compared to radiation 
Attachment 1: Screenshot_from_20190219_195210.png


134

Fri Mar 1 19:33:40 2019 
Ching Pin  Mechanics   comsol modelling 
I've changed the heating to be from two heat sources, to better model the situation with a heater and a laser. The heater deposits 22 mW, with the laser deposting .5 mW. The overall temperature distribution is smaller then before, as expected, but doesn't really change much. The heater is simulated with a deposited beam with a gassian beam profile with a standard deviation (s.d.) of 8 mm. The laser to the size has a .3 mm s.d. for contrast. I learned that while the deposited beam power doesn't care for emisitivity, it cares about the area the beam is incident with, so for example, if you increase the s.d. too much, you get less power deposited then what you enter.
I've also got modes to appear using solid mechanics, and I'm trying to see if there is a good way to get the frequency dependence with temperature nicely simulated. Changing the parameters of the simulation does give me my different frequencies, but I trying to find a way to do that over the time evolution of the model. I also got to check if the frequency shift is in line with what we are measuring. 
Attachment 1: Screenshot_from_20190301_193532.png


Attachment 2: Screenshot_from_20190301_193602.png


Attachment 3: Screenshot_from_20190301_194625.png


135

Mon Mar 4 17:22:07 2019 
Ching Pin  Mechanics   comsol modelling 
I've updated the material properties to vary with temperature, mainly in the range of 90140 K. Using the parametric sweep function to vary the input power of the heater, we get the eigenfreqencies' dependence on temperature to show up. The fractional dependence of 1.3e5 /K around 123 K matches with what Aaron calculated in this elog entry, which is always a good sign that nothing is going horribly wrong. I've also added the flats to the silicon disc, for better accuracy. See the screenshots below showing the frequency shift with temperature. 
Attachment 1: Screenshot_from_20190304_191328.png


Attachment 2: Screenshot_from_20190304_191441.png


Attachment 3: Screenshot_from_20190304_191537.png


Attachment 4: Screenshot_from_20190304_191556.png


136

Wed Mar 6 09:51:18 2019 
Ching Pin  Mechanics   comsol modelling 
So I tried adding the sapphire lens to the comsol model, and I am having teething issues. I can't seem to get the solver to converge, but I'm working on it. 
Attachment 1: Screenshot_from_20190306_093124.png


137

Thu Mar 7 10:10:37 2019 
Ching Pin  Mechanics   comsol modelling 
There are no issues with the thermal side of the modeling, the issue seems to be with the structural mechanics side. I'm not sure what I'm doing wrong though, but it just isn't converging. In any case, seeing that this is my last day here, I'll just point out that the version without the lens is saved in cvs/cds/caltech/users/cp/current working model.mph, while the model with the lens is saved in the same folder under the file name testing with lens.mph, using optimus. There is also a small file edition of current working model, with a file name that is self evident. I'll leave it to aaron to upload that to git.
In any case, let me just put down some documentation and thoughts on this model: The physical parameters on the model are generally what we do know of silicon at these temperatures, with the exception of emissitivity, which was randomly given a parameter of .5. The model is currently absorbing 22 mW from the heater and .5 mW from the laser, which implies that the heater should be able to have 45 mW incident on the disc, which would in turn suggest that you would want it to at least dissapate 100 mW to account for the lack of direction from radiation. Because comsol's deposit beam power function does not care for emissitivity, it must be modified in tandem with it. 
Attachment 1: Screenshot_from_20190307_101047.png

