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#280 by Rodal on 23 Jan, 2015 12:28
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Meep (an acronym for MIT Electromagnetic Equation Propagation) solves the Maxwell partial differential equations with the old Finite Difference numerical technique (developed decades before the Finite Element Method or the Boundary Element Method and other numerical techniques), albeit with an interesting implementation (and it is free, of course).
I would be curious to know if anyone can explain why the difference between the Wikipedia formula calculation of resonant frequency and the resonant frequency obtained by integrating Maxwell's equations in the time domain then doing Fourier analysis to calculate the resonant frequencies. In a nutshell, meep ...
Before embarking on a solution of a more complicated geometry (truncated cone) and materials (dielectric inside the cavity) it is always advisable to compare your numerical solution for a problem having an exact solution to see whether your finite difference spatial and time discretization have converged, to examine possible ill-conditioning of the matrices and to make sure that there are no human errors of input or bugs or theoretical problems with the software. Any numerical solution is always inferior to an exact solution, the only point of a numerical solution is to solve problems for which an exact solution is not possible. Thus you are doing the right thing by testing the solution vs the exact solution for a cylindrical empty (no dielectric) cavity. Your present numerical results are so far from the exact solution for an empty cylindrical cavity that it is not meaningful yet to discuss your solution for a dielectric included until you can show good convergence between your numerical result towards the exact solution for the empty cylindrical cavity (of course, besides discretization convergence problems there is always the possibility that you have made a human error somewhere or that the software has a bug or a theoretical problem).
The starting point of any finite difference solution is the discretization of space and time into a grid. Meep uses the standard Yee grid discretization (see http://ab-initio.mit.edu/wiki/index.php/Yee_grid )
which staggers the electric and magnetic fields in time and in space, with each field component sampled at different spatial locations, allowing the time and space derivatives to be formulated as center-difference approximations. Meep further divides the grid into chunks that are joined together into an arbitrary topology via boundary conditions.
To examine the convergence of your solution you should do a convergence study: run different cases with finer spatial grids and smaller time increments (output the frequencies for each spatial and time discretization). The time discretization is very important as it has been known for a long time that the central finite difference time discretization has a stability problem (the time increment needs to be small enough for a good result). This is assuming that one uses the time stepping technique (that I would start with). For a frequency-domain solver you will have to examine convergence of the frequency-domain solver. Also, I assume of course that you are using at least double precision. Examining the convergence should give you an idea of how much finer spatial and time discretization you need in order to arrive to results that match the exact solution. Only once you have been able to accurately match your numerical discretization output with the exact solution for the empty cylindrical cavity you should pursue more complicated geometries containing dielectric materials, problems for which there is no closed-form solution.
Godspeed and carry on
NOTE: The frequency-domain solver assumes a time dependence of e^(−iωt) for all currents and fields, and solves the resulting linear equations for the steady-state response or eigenmodes. Thus if you eventually want to solve problems with nonlinear dielectric materials or active systems, be forewarned that the frequency domain solver is inadequate for nonlinear materials and for active systems in which frequency is not conserved.
To obtain the frequency-domain response of a cavity with multiple long-lived resonant modes, in the time domain, is very challenging for numerical techniques, like Meep. These modes require a long simulation to reach steady state, whereas in the frequency domain the resonances correspond to poles that increase the condition number ( http://en.wikipedia.org/wiki/Condition_number ) and hence slow convergence due to ill-conditioning of the matrix. (R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, PA, 1994, http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.83.867&rep=rep1&type=pdf ) -
#281 by RanulfC on 23 Jan, 2015 14:58
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Lightly following this thread but you folks are veering into territory I DO actually understand and I felt the need to correct some misconceptions.
Why is there the "assumption" that no matter how much (or little) an operational EM-Drive would generate it would be of military/geo-political value beyond, say, extending the service life of spy, communications, etc satellites? That it provides for greatly enhanced (or even practical) kinetic bombardment weapons? That it has some sort of huge military purpose that will ignite an arms race?
Really? No. Only if it has enough thrust to power an aircraft with a reasonable (turbine-generator) amount of power and is more efficent AND more powerful than current jet or rocket engines. Otherwise its simply a low-thrust station keeping and manuever system with a long service life
A thrust of 0.09lb to 0.9lb per KW as noted in the cited paper isn't that great really. Again the main advantge is you don't have to carry propellant/reaction mass. The main "geopolitical" ramification of the EM-Drive would be that satellite servicing is going to look a lot LESS attractive since with it you'd (supposedly) never have to fill up maneuvering system every again which was the major driver for that concept.
Hidden "Rods-From-Gods" in deep space ready to rain down on anyone, anywhere and "undetectable" due to the EM-Drive? Uh, NO just no.
First of all: There is no "stealth" in space. Period.
http://www.projectrho.com/public_html/rocket/spacewardetect.php
Your rod carrier is going to be spotted and tracked. The EM-Drive requires power, which is going to have heat that is going to have to be rejected, which is going to be "visible" to anyone looking in the right direction. The EM-Drive itself (according to one post above) "emits" radiation which can be detected with the right sensor set up. And lastly you CAN see objects in space if you look carefully enough. Even if you used solar panels to provide the power for the EM-Drive they are going to "reflect" some of the energy they recieve AND they are going to be sources of waste heat for the energy they absorb but do not use.
I wonder if anyone has pointed out that IF this "works" the way it would seem to what they've invented is basically the "Space:1889" Ether Propeller
Randy -
#282 by Rodal on 23 Jan, 2015 15:03
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#283 by JasonAW3 on 23 Jan, 2015 15:24
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Lightly following this thread but you folks are veering into territory I DO actually understand and I felt the need to correct some misconceptions.
Why is there the "assumption" that no matter how much (or little) an operational EM-Drive would generate it would be of military/geo-political value beyond, say, extending the service life of spy, communications, etc satellites? That it provides for greatly enhanced (or even practical) kinetic bombardment weapons? That it has some sort of huge military purpose that will ignite an arms race?
Really? No. Only if it has enough thrust to power an aircraft with a reasonable (turbine-generator) amount of power and is more efficent AND more powerful than current jet or rocket engines. Otherwise its simply a low-thrust station keeping and manuever system with a long service life
A thrust of 0.09lb to 0.9lb per KW as noted in the cited paper isn't that great really. Again the main advantge is you don't have to carry propellant/reaction mass. The main "geopolitical" ramification of the EM-Drive would be that satellite servicing is going to look a lot LESS attractive since with it you'd (supposedly) never have to fill up maneuvering system every again which was the major driver for that concept.
Hidden "Rods-From-Gods" in deep space ready to rain down on anyone, anywhere and "undetectable" due to the EM-Drive? Uh, NO just no.
First of all: There is no "stealth" in space. Period.
http://www.projectrho.com/public_html/rocket/spacewardetect.php
Your rod carrier is going to be spotted and tracked. The EM-Drive requires power, which is going to have heat that is going to have to be rejected, which is going to be "visible" to anyone looking in the right direction. The EM-Drive itself (according to one post above) "emits" radiation which can be detected with the right sensor set up. And lastly you CAN see objects in space if you look carefully enough. Even if you used solar panels to provide the power for the EM-Drive they are going to "reflect" some of the energy they recieve AND they are going to be sources of waste heat for the energy they absorb but do not use.
I wonder if anyone has pointed out that IF this "works" the way it would seem to what they've invented is basically the "Space:1889" Ether Propeller
Randy
I don't know Randy. All the talk about Dark Energy, Dark Matter and Quantum Vacume are starting to sound a lot like the Aether concept!
I guess everything old is new again. -
#284 by RanulfC on 23 Jan, 2015 15:32
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http://en.wikipedia.org/wiki/Space:_1889
But is it the Edison, Zepplin, or Armstrong type?I don't know Randy. All the talk about Dark Energy, Dark Matter and Quantum Vacume are starting to sound a lot like the Aether concept!
I guess everything old is new again.
As I recall SEVERAL people working in quantum mechanics have pointed out that its FAR to easy to "slip" into that description when talking to us "laymen," however it has the dangers of being taken TOO far way to fast as is a problem with most analogies
It probably does not help though that I've noted many of those same people tend to have "steampunk" leanings
Randy -
#285 by Rodal on 23 Jan, 2015 15:40
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#286 by aero on 24 Jan, 2015 01:10
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@RodelQuote
The first subscript (m) is the azimuthal mode number: it indicates the number of full-wave patterns around the circumference of the waveguide. It is zero for modes in which there is no variation in the circumferential direction.
The second subscript (n) is the radial mode number: it indicates the number of half-wave patterns across the diameter. The radial mode number (n) plus one indicates the number of nodes across the diameter (counting as nodes the end nodes).
The third subscript (p) is the longitudinal mode number. It indicates the number of full-wave patterns along the longitudinal length of the waveguide. It is zero for modes in which there is no variation in the longitudinal direction.
I did double check everything as you advised and there does not seem to be anything wrong with my meep simulation. Neither could I find any questions related to my problem on the Internet. That leads me to think that my problem is still my understanding of mode shapes and cavity dimensions. I thought I had TE1,1, but from the above, for the mode to be TE 1,1, the cavity radius needs to be 1/4 wavelength and the circumference should support 1 full wave pattern. The wavelength for 2.45 GHz is 0.1223642686 in vacuum. So, for the vacuum filled cavity to resonate at 2.45 GHz in the TE 1,1 mode the radius needs to be 0.0305910671 meters. But simply plugging that radius into the formula calculates a resonance frequency of ~2.92GHz in air. So it seems evident that I am still confused about modes and use of the formula to calculate resonance frequencies. Would you lead me through the example of a resonant cavity dimensions for 2.45 GHz resonance?
I also note that driving the cavity from my previous post at 2.45 GHz, R = 0.0377449, there is no sign of resonance in the field images. So the cavity does not resonate at 2.45 GHz and therefore my dimensions must be wrong.
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#287 by Rodal on 24 Jan, 2015 07:57
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Please provide the convergence study you have done, to analyze the convergence rate of your Meep calculation. I can't help you without seeing, and thus being able to analyze, the convergence study data.
I did double check everything as you advised and there does not seem to be anything wrong with my meep simulation.........
Incorrect dimensioning is one of several kinds of numerical simulation errors possible.
So the cavity does not resonate at 2.45 GHz and therefore my dimensions must be wrong.
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#288 by aero on 24 Jan, 2015 21:03
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@Rodel -
I am going to explain my understanding of meep in excruciating detail. If you detect a misunderstanding, PLEASE tell me. First, I am setting my simulation in 2-D, running in 64-bit single precision. To run in double precision would require a re-compilation of meep from source code and I am not prepared to do that.
Here is what I have:
Drive frequency 2.45 E+9 Hz, so wavelength = 0.1223642686 meters.
Geometry actual inside dimensions L= 0.1223642686, Dia = 0.0754898000 meters air filled cylindrical cavity with no dielectric. I am ignoring the difference between speed of light in air and vacuum.
Scale factor, 0.01, but is a parameter to adjust
The above gives geometry simulation dimensions in scaled units = 012.23642686, 007.54898000
There is a boundary layer, PML layer around the inside of the computational lattice.
The PML layer thickness is set to 1.
Through an abundance of caution I have set my computational lattice (cell) to twice the geometry dimensions plus twice the PML layer thickness.
Twice the PML layer is correct because there is a layer within on all 4 sides.
Twice the geometry dimensions separates the geometry by one-half its width/height from the PML layer.
This results in -
Computational cell is 26.8729 x 17.498 x 0 (it is a 2D model)
The geometry model is in the center of the computational cell.
The antenna is located at x = 0. and y offset to the radius of the cylinder, and inward - the length is 0.007 meters, or 0.7 scaled units.
The other significant parameter is Resolution, that is, the density of the pixel grid within each distance unit of the computational cell. If resolution = 1, then there would be about 12 pixels lengthwise and 7.5 pixels crosswise in space within the geometry. That is not actually enough density to resolve the wave pattern across the search bandwidth. The tutorial indicates that meep likes a minimum of 10 pixels per wavelength of the frequency, or the frequency to be detected. It happens that the minimum frequency to be searched for is the drive frequency minus half the search band width. In other words, to detect resonance frequency as low as 1.75 GHz, (wavelength = 0.171309976 meters, 17.13 units). The corresponding highest frequency in the bandwidth is 3.15 GHz. The wavelength at 3.15 GHz ~ .095 meters or 9.5 simulation units. This constrains resolution to be no less than 2. Time descretization is the significant constraint.
Time in meep is normalized to the speed of light, that is, c =1. The meep literature is very confusing on time scaling, but by setting the resolution and simply running the simulation for 1 time unit, meep displays the number of time steps. In this way, I find the the number of time steps = 2 times resolution.
Now, running the simulation, using cylindrical coordinates (effectively a 1D simulation) and setting resolution sequentially to 1, 2, 3, 4 meep gives no results. With resolution = 5, meep does give a result. I made these low resolution runs for the purpose of this convergence study, in reality, I rarely use resolution less than 40. And from the meep tutorial document, " Note: this error is only the uncertainty in the signal
processing"
Here are my results.
Resolution number of time steps resonant frequency Q error
1 2 none detected
2 4 none detected
3 6 none detected
4 8 none detected
5 10 1.84921E+009 negative 2 e-4
10 20 1.85128E+009 negative 2 e-4
20 40 1.86441E+009 ~ 500 6 e-4
40 80 1.87262E+009 ~ 1200 3 e-4
80 160 1.86992E+009 ~ 300 13 e-4
160 320 1.87042E+009 ~ 80 47 e-4
The detected frequency bounces around consistently with the error which can be taken as estimating the number of significant digits of the frequency detected.
The quality is very low. I take that to be a result of the cavity dimensions being incorrect for the resonant frequency detected as they are also incorrect for the drive frequency.
I would seriously like to know how to properly design a resonant cavity for a selected resonant mode. I can tinker with the dimensions in meep and get higher quality factors, but that is not very efficient and forces me to guess the mode by looking at images of the wave pattern. -
#289 by Rodal on 24 Jan, 2015 21:35
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....
Here are my results.
Resolution number of time steps resonant frequency Q error
1 2 none detected
2 4 none detected
3 6 none detected
4 8 none detected
5 10 1.84921E+009 negative 2 e-4
10 20 1.85128E+009 negative 2 e-4
20 40 1.86441E+009 ~ 500 6 e-4
40 80 1.87262E+009 ~ 1200 3 e-4
80 160 1.86992E+009 ~ 300 13 e-4
160 320 1.87042E+009 ~ 80 47 e-4
The detected frequency bounces around consistently with the error which can be taken as estimating the number of significant digits of the frequency detected.
The quality is very low. I take that to be a result of the cavity dimensions being incorrect for the resonant frequency detected as they are also incorrect for the drive frequency.
....
Well, there is a lot of stuff here for me to digest, I will need some time to read your post very carefully, and consider what to do, but my first impression is that there is a convergence problem that is most evident from the Q:
Resolution number of time steps resonant frequency Q error
1 2 none detected
2 4 none detected
3 6 none detected
4 8 none detected
5 10 1.84921E+009 negative 2 e-4
10 20 1.85128E+009 negative 2 e-4
20 40 1.86441E+009 ~ 500 6 e-4
40 80 1.87262E+009 ~ 1200 3 e-4
80 160 1.86992E+009 ~ 300 13 e-4
160 320 1.87042E+009 ~ 80 47 e-4
Notice how the Q is completely wrong ("negative") even for
10 20 1.85128E+009 negative 2 e-4
then reaches a maximum for:
40 80 1.87262E+009 ~ 1200 3 e-4
which, as you wrote, it is still a very low value for Q, and then as you increase the time step discretization, the Q gets worse rather than better:
80 160 1.86992E+009 ~ 300 13 e-4
160 320 1.87042E+009 ~ 80 47 e-4
And notice that the error also increased, as you increased the time step for those two cases.
I don't see how the convergence problem can be due to the geometry. By "geometry" I mean the dimensions of the cavity (in meters or whatever consistent unit of length). The geometry stayed constant (I presume) for the different discretizations. Therefore the wrong geometry can lead to a wrong solution but not to a solution that gets worse (increasing error and decreasing Q) with increased discretization.
I'll be back.
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#290 by Rodal on 24 Jan, 2015 21:55
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.. I am setting my simulation in 2-D, running in 64-bit single precision....
Just to be speaking the same language, are you really using 64-bit: Double Precision as defined by the IEEE 754 standard ?
64-bit: Double Precision see http://en.wikipedia.org/wiki/Double-precision_floating-point_format
32-bit Double Precision: Computers with 32-bit storage locations use two memory locations to store a 64-bit double-precision number (a single storage location can hold a single-precision number).
32-bit: Single Precision see http://en.wikipedia.org/wiki/Single-precision_floating-point_format -
#291 by Rodal on 24 Jan, 2015 23:39
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.....
The quality is very low. I take that to be a result of the cavity dimensions being incorrect for the resonant frequency detected as they are also incorrect for the drive frequency.
I would seriously like to know how to properly design a resonant cavity for a selected resonant mode. I can tinker with the dimensions in meep and get higher quality factors, but that is not very efficient and forces me to guess the mode by looking at images of the wave pattern.
What did you use for the bandwidth (df) source around the frequency of interest (Drive frequency 2.45 E+9 Hz)?
Could you try running all these cases again, everything the same as before except with a significantly narrower bandwidth (df) source around the frequency of interest ? . Reportedly harminv does a better job the narrower the source is around the frequency of interest . -
#292 by aero on 25 Jan, 2015 00:57
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Ok, I did run it again with bandwidth = 0.2 * Drive frequency, for cases up to resolution of 80, but I didn't get anything. Once I narrow the bandwidth to exclude the resonant frequency at 1.87 GHz, there are no resonances within the bandwidth......
The quality is very low. I take that to be a result of the cavity dimensions being incorrect for the resonant frequency detected as they are also incorrect for the drive frequency.
I would seriously like to know how to properly design a resonant cavity for a selected resonant mode. I can tinker with the dimensions in meep and get higher quality factors, but that is not very efficient and forces me to guess the mode by looking at images of the wave pattern.
What did you use for the bandwidth source around the frequency of interest (Drive frequency 2.45 E+9 Hz)?
Could you try running all these cases again, everything the same as before except with a significantly narrower bandwidth source around the frequency of interest ? . Reportedly harminv does a better job the narrower the source is around the frequency of interest .
Harminv does work better at identifying the resonant frequency with narrower bandwidth, when the frequency is within the bandwidth. I set the drive frequency to 1.873 GHz, narrowed the bandwidth to 0.07 * frequency and got this:
frequency Quality factor error
1,873,339,229.3075 Hz 18,325,307.0778158 1.673972608680621e-7+0.0i
As you can see the quality factor is much higher and the processing error is much lower. The only problem is that it is not the frequency I had hoped for.
I did some further searching and found two things.
1 - The value of the J'0(1) Bessel function = 1.8411837813 which agrees with the number we have.
2 - Meep doesn't actually excite the cavity with Gaussian noise, rather it uses the derivative of a Gaussian signal, whatever that means.
I really don't think this particular problem is in the meep software. As I wrote before, I searched the discussion list, which goes back at least 8 years, and there is no mention of this particular problem. If it were in meep, some user would have encountered it long ago. A 25% discrepancy is hard to overlook. There is a chance that it is in my general understanding of how to model using meep, but my knowledge of meep is far superior to my knowledge of resonant cavity design so using Occam's razor, it is most likely that my cavity design is the problem.
Dr. Rodal, I really appreciate your efforts on my behalf. I will continue to look into the details of resonant cavity design. Maybe it has something to do with the cavity length. But actually, that doesn't seem very likely at all. What do you know about Gaussian noise derivatives and could that be a simple frequency correction? But, when generated with a continuous wave at 2.45 GHz, the field images don't show any resonance.
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#293 by Rodal on 25 Jan, 2015 01:13
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Ok, I did run it again with bandwidth = 0.2 * Drive frequency, for cases up to resolution of 80, but I didn't get anything. Once I narrow the bandwidth to exclude the resonant frequency at 1.87 GHz, there are no resonances within the bandwidth......
The quality is very low. I take that to be a result of the cavity dimensions being incorrect for the resonant frequency detected as they are also incorrect for the drive frequency.
I would seriously like to know how to properly design a resonant cavity for a selected resonant mode. I can tinker with the dimensions in meep and get higher quality factors, but that is not very efficient and forces me to guess the mode by looking at images of the wave pattern.
What did you use for the bandwidth source around the frequency of interest (Drive frequency 2.45 E+9 Hz)?
Could you try running all these cases again, everything the same as before except with a significantly narrower bandwidth source around the frequency of interest ? . Reportedly harminv does a better job the narrower the source is around the frequency of interest .
Harminv does work better at identifying the resonant frequency with narrower bandwidth, when the frequency is within the bandwidth. I set the drive frequency to 1.873 GHz, narrowed the bandwidth to 0.07 * frequency and got this:
frequency Quality factor error
1,873,339,229.3075 Hz 18,325,307.0778158 1.673972608680621e-7+0.0i
As you can see the quality factor is much higher and the processing error is much lower. The only problem is that it is not the frequency I had hoped for.
I did some further searching and found two things.
1 - The value of the J'0(1) Bessel function = 1.8411837813 which agrees with the number we have.
2 - Meep doesn't actually excite the cavity with Gaussian noise, rather it uses the derivative of a Gaussian signal, whatever that means.
I really don't think this particular problem is in the meep software. As I wrote before, I searched the discussion list, which goes back at least 8 years, and there is no mention of this particular problem. If it were in meep, some user would have encountered it long ago. A 25% discrepancy is hard to overlook. There is a chance that it is in my general understanding of how to model using meep, but my knowledge of meep is far superior to my knowledge of resonant cavity design so using Occam's razor, it is most likely that my cavity design is the problem.
Dr. Rodal, I really appreciate your efforts on my behalf. I will continue to look into the details of resonant cavity design. Maybe it has something to do with the cavity length. But actually, that doesn't seem very likely at all. What do you know about Gaussian noise derivatives and could that be a simple frequency correction? But, when generated with a continuous wave at 2.45 GHz, the field images don't show any resonance.
Ok, that (drive frequency to 1.873 GHz, bandwidth to 0.07 * frequency) takes care of the Q and error problems :
frequency Quality factor error
1,873,339,229.3075 Hz 18,325,307.0778158 1.673972608680621e-7+0.0i
I hope that tomorrow I have some time to go over the equations and the dimensions (which I did not have the time to go over yet) to check if I find any reason why you calculate it should be 2.45 GHz and Meep resonates at1.873 GHz instead.
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#294 by aero on 25 Jan, 2015 04:07
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It was partly due to a misunderstand of the formula. I changed modes, to T?-?,?,0 and found that with p=0, while the cylinder length has no effect on frequency from the formula, it has a strong effect in meep. It is understandable that changing length should effect the resonance. In fact the effect of changing length is stronger than the effect of changing radius but that is likely due to having a radius not associated with any given mode. The nearest frequency mode is TM0,1,0
I didn't notice that I was looking at the wrong table of frequencies until after I iterated meep to the 2.45 GHz frequency. I'll look at it again tomorrow, but it's getting tired here now. -
#295 by Mulletron on 25 Jan, 2015 08:56
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Went back to investigate what I reported in post #233 http://forum.nasaspaceflight.com/index.php?topic=36313.msg1318683#msg1318683 about the RF and Microwave Toolbox app. I found that the app is reporting the correct solutions for TE and TM. The help file just had a typo. I verified it against the KWOK lectures http://www.engr.sjsu.edu/rkwok/EE172/Cavity_Resonator.pdf slide 16. KWOK and the APP match. So this works as a quick and easy way to find resonant modes! There really is an app for everything.
I remain unconvinced that calculating resonant modes for cylinders is a good approximation for conical frustums though.
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#296 by Stormbringer on 25 Jan, 2015 09:39
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people have mentioned Dr Dr. Michael McCulloch a few times. i though i would drop a link to one of his papers. though actual discussion should be taken up elsewhere. it is related to the present topic because he has alternate views of how these EM devices (Shawyer, Cannae, White, the Chinese, etc) work.
http://www.ptep-online.com/index_files/2015/PP-40-15.PDF -
#297 by Mulletron on 25 Jan, 2015 11:18
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@Rodel
QuoteThe first subscript (m) is the azimuthal mode number: it indicates the number of full-wave patterns around the circumference of the waveguide. It is zero for modes in which there is no variation in the circumferential direction.
The second subscript (n) is the radial mode number: it indicates the number of half-wave patterns across the diameter. The radial mode number (n) plus one indicates the number of nodes across the diameter (counting as nodes the end nodes).
The third subscript (p) is the longitudinal mode number. It indicates the number of full-wave patterns along the longitudinal length of the waveguide. It is zero for modes in which there is no variation in the longitudinal direction.
I did double check everything as you advised and there does not seem to be anything wrong with my meep simulation. Neither could I find any questions related to my problem on the Internet. That leads me to think that my problem is still my understanding of mode shapes and cavity dimensions. I thought I had TE1,1, but from the above, for the mode to be TE 1,1, the cavity radius needs to be 1/4 wavelength and the circumference should support 1 full wave pattern. The wavelength for 2.45 GHz is 0.1223642686 in vacuum. So, for the vacuum filled cavity to resonate at 2.45 GHz in the TE 1,1 mode the radius needs to be 0.0305910671 meters. But simply plugging that radius into the formula calculates a resonance frequency of ~2.92GHz in air. So it seems evident that I am still confused about modes and use of the formula to calculate resonance frequencies. Would you lead me through the example of a resonant cavity dimensions for 2.45 GHz resonance?
I also note that driving the cavity from my previous post at 2.45 GHz, R = 0.0377449, there is no sign of resonance in the field images. So the cavity does not resonate at 2.45 GHz and therefore my dimensions must be wrong.
I want to point out a discrepancy I found. Perhaps I'm the discrepancy, because I don't agree with my old post or any of the other sources, which is highly unlikely.
First here's what I have about mode numbering from various sources:
ME from thread 1: T(MorE)mnp. m is the # of 1/2 wavelengths around a half circumference, n is the # of 1/2 wavelengths across a radius, p is the # of 1/2 wavelengths of length of the cavity.
Navy Neets mod 11 (screenshot below): The first subscript indicates the number of full-wave patterns around the circumference of the waveguide. The second subscript indicates the number of half-wave patterns across the diameter.........(p left out).
Oracle: http://en.wikipedia.org/wiki/Transverse_mode In circular waveguides, circular modes exist and here m is the number of half-wavelengths along a half-circumference and n is the number of half-wavelengths along a radius.......(p left out).
Rodal: The first subscript (m) is the azimuthal mode number: it indicates the number of full-wave patterns around the circumference of the waveguide.
The second subscript (n) is the radial mode number: it indicates the number of half-wave patterns across the diameter. The third subscript (p) is the longitudinal mode number. It indicates the number of full-wave patterns along the longitudinal length of the waveguide.
So there is conflicting information. Rodal and the Navy agree, the oracle and me are different. I'll see if I can clear it up.....and find deal here.
Using the coke can example from http://www.engr.sjsu.edu/rkwok/EE172/Cavity_Resonator.pdf slide 17, for a radius of 1.25"(or diameter of 2.5"), depth of 5". This comes out to a TE111 f,res of 3.01ghz, which gives me a wavelength of 3.923". So first, to test the first subscript m, the circumference of a circle with r 1.25" is 7.85". 7.85"inch is 2 wavelengths @3.01ghz.
So it appears that m should be the # of full wavelengths around half a circumference.
or
If you don't do any rounding with the coke can example, @3.01ghz you get 3.923928113636958 inches, multiply that by 2 you get 7.847856227273916 inches, which is just shy of the calculated circumference of 7.85, which technically is not a FULL cycle of 2 wavelengths. Which means this example sits on the edge of TE111 and TE211. Technically that 0 wasn't crossed yet.
So is that the answer? FULL wavelengths must be counted, the rest is dropped? Meaning if you go around 2.6 times for example, you just get an m of 2?
###Resolution:
http://forum.nasaspaceflight.com/index.php?topic=36313.msg1321080#msg1321080
http://forum.nasaspaceflight.com/index.php?topic=36313.msg1321196#msg1321196
This is important because soon I'm going to be cutting copper shapes and making stupid mistakes can be very expensive.
I've found fault with the Navy references before on other things, and we all know that everything on the Oracle needs to be verified, and I'm frequently wrong, but Rodal is usually right. So what's going on there?
As far as n or p go, I'm not even going to look at them until I get some feedback about the m discrepancies. I just want to clear this up. I don't mind getting egg on my face.
Break:
You know, I think this got overlooked: "We performed some very early evaluations without the dielectric resonator (TE012 mode at 2168 MHz, with power levels up to ~30 watts) and measured no significant net thrust."
I got a lot of grief before for my approach to deriving the cavity dimensions (starting with the 6.25 inch small end, using the dimensions of the PE discs from 14 of Brady et al Anomalous thust...., but I think those dimensions, (see screenshot below) are exactly spot on and here's empirical proof. So my calculated cavity length in Autocad after scaling based on 6.25inch small ends size, was 10.88". If you look at the frequency of 2168mhz, you'll find the wavelength is 5.4479". Take two wavelengths of this, you'll arrive at 10.8958, my cavity length was 10.88". Converted to meters, it is:
Dsmall=0.15875m (0.159m)
Dlarge=0.30098m (0.3m) amazingly round number
Length=0.27637m (.276m)
###Edit: Added link to resolution with current and correct info.
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#298 by Stormbringer on 25 Jan, 2015 13:47
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The Rational Wiki has an interesting page on these EM drives.
http://rationalwiki.org/wiki/EmDriveQuoteNASA plans to upgrade their equipment to higher power levels, use vacuum-capable RF amplifiers with power ranges of up to 125 W, and design a new tapered cavity analytically expected to produce thrust in the 0.1 N/kW range. Then, the test article will be shipped to other laboratories for independent verification and continued evaluations of the technology, at Glenn Research Center, the Jet Propulsion Laboratory and the Johns Hopkins University Applied Physics Laboratory.
I know that has been discussed here but thought there might be additional info in it that may have not been noticed before. -
#299 by Rodal on 25 Jan, 2015 13:55
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....
As far as "m" goes, I don't see any discrepancy whatsoever. They all agree:
First here's what I have about mode numbering from various sources:
ME from thread 1: T(MorE)mnp. m is the # of 1/2 wavelengths around a half circumference...
Navy Neets mod 11 (screenshot below): The first subscript indicates the number of full-wave patterns around the circumference of the waveguide....
Oracle: http://en.wikipedia.org/wiki/Transverse_mode In circular waveguides, circular modes exist and here m is the number of half-wavelengths along a half-circumference....
Rodal: The first subscript (m) is the azimuthal mode number: it indicates the number of full-wave patterns around the circumference of the waveguide.
....
So there is conflicting information. Rodal and the Navy agree, the oracle and me are different....
As far as n or p go, I'm not even going to look at them until I get some feedback about the m discrepancies....
Mulletron (from thread 1) "the # of 1/2 wavelengths around a half circumference"
Wikipedia " the number of half-wavelengths along a half-circumference"
US NAVY: the number of full-wave patterns around the full circumference
Rodal: the number of full-wave patterns around the full circumference
" the number of half-wavelengths around a half-circumference" is exactly the same as the number of full-wave patterns around the full circumference of the waveguide because a full wave around the full circumference is exactly one half-wave around the half-circumference, or 1/3 wave around 1/3 the circumference, or 1/nr wave around 1/nr circumference where nr is an arbitrary integer.
And the definition of wavelength is exactly the same length as the definition of "full wave pattern".
