Author Topic: EM Drive Developments - related to space flight applications - Thread 3  (Read 1797924 times)

Offline mwvp

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...If anyone is interested, meep does allow the source to be switched off. I could make a slightly different run so we could look at the field images immediately after power-off if that would be of interest.
...
If that would provide helpful information, let me know.

Yes! Why couldn't I have thought of that? One would think the ring down would look much like the ring-up.

Are your latest models including copper loss? The heck with the real (reactive) component of complex permittivity for a metal, just the complex/lossy component should matter?

I'd really like to see are images of a comparison of the static fields and pressure, and doppler-shifted fields and pressures.

Offline mwvp

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...I am planing to build more than just two basic designs, I have on the drawing board injected microwaveguide phase locked magnetrons that the power supply has been modified to narrow the hash and be able to sweep and phase lock the to cavity and vary the duty cycles.

I'm interested in your power-supply design, if you care to share  ;)

Offline aero

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...If anyone is interested, meep does allow the source to be switched off. I could make a slightly different run so we could look at the field images immediately after power-off if that would be of interest.
...
If that would provide helpful information, let me know.

Yes! Why couldn't I have thought of that? One would think the ring down would look much like the ring-up.

Are your latest models including copper loss? The heck with the real (reactive) component of complex permittivity for a metal, just the complex/lossy component should matter?
Yes
Quote
I'd really like to see are images of a comparison of the static fields and pressure, and doppler-shifted fields and pressures.
Don't know what that is, and so have no idea how to make it. I'll provide the data that I can and you or someone else can do the rest.
« Last Edit: 07/12/2015 06:37 PM by aero »
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Offline rfmwguy

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Frustum with copper screen mesh complete. I'm a bit OCD on building...could not form the mesh to be 100% perfect. Guess there is variation with solid copper sheeting too, but did the best I could. Took 4 hours of shaping, cutting and soldering...glad its over. Magnetron will be mounted this week. Mr Whiskers the cat seems unimpressed.

Saw some questions while I was building...thks doc, S21 Q is only Q that matters. Antennas (S11) are measured not with Q but simple return loss or more commonly VSWR. This still is only a portion of what's important in an antenna. Radiation pattern and gain are just as important. An S11 is really only used to guarantee good match to the rf source. Outside that, it does not address antenna performance...an emdrive has more to it than a simple load match to the source, its more than an antenna....at least we think it is.

Shell, saw your ebay find...too cheap not to try it out. Not sure what u want with 3dB pads other than to make a broadband match to something that's at a different impedance. Could u rephrase ur question?

Offline ThinkerX

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Quote
All Q measurements using S11 are suspect: everybody should take with a grain of salt the reported Q's from different EM Drive researchers, unless the procedure to measure the Q is detailed and they have used S21.

Perhaps this should go into the wiki?

Also, perhaps existing data results in the wiki should be crosschecked against this method, if possible.   

Might put a different spin on things.

Online Rodal

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...

Saw some questions while I was building...thks doc, S21 Q is only Q that matters. Antennas (S11) are measured not with Q but simple return loss or more commonly VSWR. This still is only a portion of what's important in an antenna. Radiation pattern and gain are just as important. An S11 is really only used to guarantee good match to the rf source. Outside that, it does not address antenna performance...an emdrive has more to it than a simple load match to the source, its more than an antenna....at least we think it is.

..
I'm glad you are here.  I don't have your experience in this area, and it took me some time to check what you were saying.   You are 100% right.  Calculating Q on S21 is much more unambiguous than using S11.
« Last Edit: 07/12/2015 06:56 PM by Rodal »

Offline DrBagelBites

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I would suggest to every EMDrive builder that having a Vector Network Analyser and understanding what it is telling you is critical to your success.

Doing 1 cable SLOW sweeps can test your excitation antenna design, impedance matching, find your cavity resonances, peak return loss dBs, VSWR, reflection coefficient, Q and cavity bandwidth.

Without a VNA, it is hard to understand how any build could achieve Force generation as there are so many VNA determinant / measurable variables that need to be all as close as possible to optimum values.

My soon to arrive 100W Rf amp has the ability to be throttled from 50dBm (100W) output to 19dBm (79mW) output and has a real time analogue VSWR output pin, which I plan to use to generate a DIY VNA as knowing the VSWR, Rf amp impedance and the frequency will enable real time calculation of the return loss db, the reflection coefficient, how well the cavity is impedance matched to the Rf amp, the cavity unloaded Q and Q bandwidth.

http://cgi.www.telestrian.co.uk/cgi-bin/www.telestrian.co.uk/vswr.pl

Seems a lot of information to get from 1 pin of analogue information, but the Rf amp is driving the cavity at it's impedance, output frequency and reporting on what is happening via the VSWR analogue output. Additionally doing it this way ensures each EMDrive is impedance matched as close as possible to it's 100W Rf amp.

Comments from the experienced microwave guys that have used 1 cable VNA measurements most welcome.
Agreed but a 1 port measurement is simply return loss or an antenna measurement not a bandpass cavity where a sample port is needed for S21. call it reflected S11 Q not forward S21 Q. This will give unnaturally high numbers leading to confusion. If u get the chance, ask shawyer for S21 plots since he had a sample port. This should illustrate assymetrical bandpass response.

What are your thoughts on this solution?

http://www.ebay.com/itm/138M-4-4G-SMA-signal-source-generator-simple-spectrum-analyzer-Tracking-source-/111493176997?pt=LH_DefaultDomain_0&hash=item19f582dea5
Add a couple of SMA 3dB attenuators for mismatch.
Add a sampling port to the frustum with the software and a laptop it should do what needs to be done.

(much thanks to someone that has been a wonderful source of information saving me hours of research)

Shell

That's the exact signal generator I have! Awesome! However, I did not buy it with the tracking source.

Just a little precaution to others who plan on buying this, there is very little documentation, and the documentation that there is was translated from German and Chinese, so it is a little unintelligible.

Just a bit of a heads up. :)

Offline TheTraveller

I would suggest to every EMDrive builder that having a Vector Network Analyser and understanding what it is telling you is critical to your success.
...
a real time analogue VSWR output pin, which I plan to use to generate a DIY VNA as knowing the VSWR, Rf amp impedance and the frequency will enable real time calculation of the return loss db, the reflection coefficient, how well the cavity is impedance matched to the Rf amp, the cavity unloaded Q and Q bandwidth.
...
Comments from the experienced microwave guys that have used 1 cable VNA measurements most welcome.

I've used VNA's to do antenna sweeps. I taught cellular engineers how to do antenna sweeps. The VNA was 2 port that went to a duplexer to make it 1 port.

Anyways, your transmitter VSWR isn't a VNA, it gives you a scalar, not vector (phase information) that is useful for determining Q. I've tuned a lot of stuff, but never needed to measure Q. BW, Ripple, insertion loss, return loss, but never was the Q of anything spec'd for the systems I worked on.

Anyways, doing the VNA thing means applying loads (open, short, 50ohm) and hitting the apt. calibrate buttons. Otherwise, how do you know your coax/waveguide isn't affecting the inferred reading you get from the return loss?

Putting a sample port on the frustrum isn't a bad idea anyways. You can make a very simple diode detector (resistor, cap, diode - costs $1) and see the peak on a $5 DVM.

Although, the ancient and venerable grid dip meter can  give you an indication of Q, but I think you'd have a heck of a time coupling to a closed frustrum. Just don't bother with that!

Best use a very lightly, barely, coupled sample port. There's a lot of power in your 100K+ Q cavity!

Thanks for the comments and suggestions.

I would suspect a typical antenna's Q would be 1, being energy in per cycle would equal energy lost (radiated) per cycle so no need to measure Q.

I understand using the Rf amps VSWR output as I intent doesn't make it a true VNA but it should give me the 1 port like S11 VNA information I desire.

1st at very low power it can sweep the output frequency back and forth, by varing the Rf gen frequency, looking for the lowest VSWR around my spreadsheets calculated resonate frequency as lowest VSWR is the same thing as the highest return loss.

Once that sweet spot is found I can lock the Rf gen to that frequency and manually adjust the load impedance screws on the cavity to get the lowest VSWR output and then repeat the sweep process and manually adjust the screws a few times.

For this application, it doesn't matter that the Rf amps output impedance is not calibrated to any standard. It only matters that the VSWR reported by the Rf amp, when driving the cavity, is as low as possible as that means the input and output impedances of the 2 devices are as closely matched as possible and that the cavity will accept the max Rf energy it can, while rejecting the min Rf energy it can.

Further by doing real time monitoring of the VSWR, while the Rf amp is driving the cavity, my embedded micro controller can detect when conditions inside the cavity have changed and the Rf gen's frequency needs to be adjusted to stay in the middle of the cavities resonance curve.

As an ex ham, I don't see why an antenna can't have a bandwidth measured at it's -3dB points as determined by converting the measured VSWR change, caused by deliberate Rf gen frequency change, into return loss dB change to determine the -3dB points from the peak return loss or lowest VSWR.

That said the same thing applies to my cavity, which to my Rf amp, is an antenna like output load, except unlike the radiant antenna which doesn't store energy, the cavity does store energy and doesn't radiate it's stored energy away to atmo or space.
« Last Edit: 07/12/2015 09:39 PM by TheTraveller »
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Offline X_RaY

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Some times ago i posted this picture. For this case i got some Results now. The qualitativ results may be interesting for the group.
I Did an experiment with a Agilent Networkanalizer in the K band regime. I got used up to 8 identical conical cavities in the setup -BD; SD; length- all got the same cone angle and all got the same resonant frequency. CNC machine builded components... The small diameter matches exact to the Cut Off diameter. The mode was TE011 for a single cavity resonator. Of course if there are 2 cavities in line the Mode will be TE012 and so on for more resonators. The antenna was optimated for this mode and installed at the bigger diameter.
Results:
A following results got same resonant frequency.
For only one resonator the S11 shows a curve whit a minimum |r|~0.1 if the small diameter was closed. If the cavity is open ended there is no detectable resonance (reference as expected).
For 2 cavitys inline in the closed case the 3dB BW is even smaller than with only 1 cavity (this is normal for higher p value) the impedance matching was a little better with |r| ~0.05. If the double resonator was open there was a very less coupled resonance with large BW in the right frequency region.
For 3 cavitys in the open ended case this resonance was couppled better- the Q was higher.
I did this strate forworth up to 8 cavitys.
In the last case the resonance in the open ended cavity was most equal to the case of a closed resonator |r|~0.12. There was only a little difference if the open end would closed up with a metal plate |r|~0.1.
conclusions:
Every half wavelength a part of the energy is reflected and goes back to the antenna. There will be a constructive interference all Lambda(0.5Lambda forward direction and 0.5Lambda backward) at the trace back to the antenna cause of the equal length of the single cavities.
Based on the periodic structure with some regions equal to cutoff there is no long way propagation of the wave along the structure.
The field strength in every single cavity in the forward direction will smaller from one to the next conical cavity in this case.
So i am no longer sure that this structure is able to increase possible net forces. It may be helpful to do research in evanescent wave theories / effects of conical resonators like posted here in the forum.
« Last Edit: 07/21/2015 07:48 PM by X_RaY »

Offline TheTraveller

Some times ago i posted this picture. For this case i got some Results now. The qualitativ results may be interesting for the group.
I Did an experiment with a Agilent Networkanalizer in the K band regime. I got used up to 8 identical conical cavities in the setup -BD; SD; length- all got the same cone angle and all got the same resonant frequency. CNC machine builded components... The small diameter matches exact to the Cut Off diameter. The mode was TE011 for a single cavity resonator. Of course if there are 2 cavities in line the Mode will be TE012 and so on for more resonators. The antenna was optimated for this mode and installed at the bigger diameter.
Results:
A following results got same resonant frequency.
For only one resonator the S11 shows a curve whit a minimum |r|~0.1 if the small diameter was closed. If the cavity is open ended there is no detectable resonance (reference as expected).
For 2 cavitys inline in the closed case the 3dB BW is even smaller than with only 1 cavity (this is normal for higher p value) the impedance matching was a little better with |r| ~0.05. If the double resonator was open there was a very less coupled resonance with large BW in the right frequency region.
For 3 cavitys in the open ended case this resonance was couppled better- the Q was higher.
I did this strate forworth up to 8 cavitys.
In the last case the resonance in the open ended cavity was most equal to the case of a closed resonator |r|~0.12. There was only a little difference if the open end would closed up with a metal plate |r|~0.1.
conclusions:
Every half wavelength a part of the energy is reflected and goes back to the antenna. There will be a constructive interference all Lambda(0.5Lambda forward direction and 0.5Lambda backward) at the trace back to the antenna cause of the equal length of the single cavities.
Based on the periodic structure with some regions equal to cutoff there is no long way propagation of the wave along the structure.
The field strength in every single cavity in the forward direction will smaller from one to the next conical cavity in this case.
So i am no longer sure that this structure is able to increase possible net forces. It may be helpful to do research in evanescent wave theories / effects of conical resonators like posted here in the forum.

Interesting.

What was your build geometry? Big dia, small dia, length and frequency? Will run the data through my EMDrive calculator and post the results.
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Offline X_RaY

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Some times ago i posted this picture. For this case i got some Results now. The qualitativ results may be interesting for the group.
I Did an experiment with a Agilent Networkanalizer in the K band regime. I got used up to 8 identical conical cavities in the setup -BD; SD; length- all got the same cone angle and all got the same resonant frequency. CNC machine builded components... The small diameter matches exact to the Cut Off diameter. The mode was TE011 for a single cavity resonator. Of course if there are 2 cavities in line the Mode will be TE012 and so on for more resonators. The antenna was optimated for this mode and installed at the bigger diameter.
Results:
A following results got same resonant frequency.
For only one resonator the S11 shows a curve whit a minimum |r|~0.1 if the small diameter was closed. If the cavity is open ended there is no detectable resonance (reference as expected).
For 2 cavitys inline in the closed case the 3dB BW is even smaller than with only 1 cavity (this is normal for higher p value) the impedance matching was a little better with |r| ~0.05. If the double resonator was open there was a very less coupled resonance with large BW in the right frequency region.
For 3 cavitys in the open ended case this resonance was couppled better- the Q was higher.
I did this strate forworth up to 8 cavitys.
In the last case the resonance in the open ended cavity was most equal to the case of a closed resonator |r|~0.12. There was only a little difference if the open end would closed up with a metal plate |r|~0.1.
conclusions:
Every half wavelength a part of the energy is reflected and goes back to the antenna. There will be a constructive interference all Lambda(0.5Lambda forward direction and 0.5Lambda backward) at the trace back to the antenna cause of the equal length of the single cavities.
Based on the periodic structure with some regions equal to cutoff there is no long way propagation of the wave along the structure.
The field strength in every single cavity in the forward direction will smaller from one to the next conical cavity in this case.
So i am no longer sure that this structure is able to increase possible net forces. It may be helpful to do research in evanescent wave theories / effects of conical resonators like posted here in the forum.

Interesting.

What was your build geometry? Big dia, small dia, length and frequency? Will run the data through my EMDrive calculator and post the results.

 :( I am sure my company doesn't allow me to post the exact dimensions. That is why i don't did that in the post. I only can talk about the quantitative effects...
You can choose a cone half angle. Lets say 12 or 14. The effect is the same if the small diameter is in the cutoff region (for the cylindrical case).
The microwave stuff is almost the same at work as the hobby stuff here. I did that experiment with Resonators for other applications.
Sorry i cant post more details like this.

Offline TheTraveller

Just to throw another log on the fire in Bringing Light into the Dark.

In the 2010 Chinese paper, Prof Yang discloses the equation they use to calculate cavity Q. Yes that is right, they don't measure Q, they calculate it from their in-house developed equation.

Search for equation 14 in the 2010 paper:
http://www.emdrive.com/NWPU2010translation.pdf

Quote
The quality factor of this resonator under no load can be calculated by the following equation:
Qu=∫|H|2dv/h/2∫|nxH|2ds+tgd∫|H|2dv = (14)
Where tg is the electric loss within the cavity, n is the normal vector of the wall, s is the cavity surface area, v is the volume of the cavity.

Who will be the 1st to post an Excel spreadsheet that duplicates Prof Yang's equation?
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Offline leomillert

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Doctor Rodal,
if I understand correctly, you are calculating the Poynting vector by hand?
Because I believe MEEP has functions to do this automatically:

(get-poynting which-band)
(output-poynting which-band)
(output-poynting-x which-band)
(output-poynting-y which-band)
(output-poynting-z which-band)

http://ab-initio.mit.edu/wiki/index.php/MPB_User_Reference#Storing_and_combining_multiple_fields


Offline rfmwguy

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Just to throw another log on the fire in Bringing Light into the Dark.

In the 2010 Chinese paper, Prof Yang discloses the equation they use to calculate cavity Q. Yes that is right, they don't measure Q, they calculate it from their in-house developed equation.

Search for equation 14 in the 2010 paper:
http://www.emdrive.com/NWPU2010translation.pdf

Quote
The quality factor of this resonator under no load can be calculated by the following equation:
Qu=∫|H|2dv/h/2∫|nxH|2ds+tgd∫|H|2dv = (14)
Where tg is the electric loss within the cavity, n is the normal vector of the wall, s is the cavity surface area, v is the volume of the cavity.

Who will be the 1st to post an Excel spreadsheet that duplicates Prof Yang's equation?
Sorry mr t, this is an arbitrary equation of limited value imo. One must ask why estimate when one can measure.

Offline TheTraveller

Just to throw another log on the fire in Bringing Light into the Dark.

In the 2010 Chinese paper, Prof Yang discloses the equation they use to calculate cavity Q. Yes that is right, they don't measure Q, they calculate it from their in-house developed equation.

Search for equation 14 in the 2010 paper:
http://www.emdrive.com/NWPU2010translation.pdf

Quote
The quality factor of this resonator under no load can be calculated by the following equation:
Qu=∫|H|2dv/h/2∫|nxH|2ds+tgd∫|H|2dv = (14)
Where tg is the electric loss within the cavity, n is the normal vector of the wall, s is the cavity surface area, v is the volume of the cavity.

Who will be the 1st to post an Excel spreadsheet that duplicates Prof Yang's equation?
Sorry mr t, this is an arbitrary equation of limited value imo. One must ask why estimate when one can measure.

My point is this equation is what the Chinese use when they quote device Q. They don't, as far as I know, measure the quoted devices Q.
« Last Edit: 07/12/2015 10:56 PM by TheTraveller »
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Offline rfmwguy

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Just to throw another log on the fire in Bringing Light into the Dark.

In the 2010 Chinese paper, Prof Yang discloses the equation they use to calculate cavity Q. Yes that is right, they don't measure Q, they calculate it from their in-house developed equation.

Search for equation 14 in the 2010 paper:
http://www.emdrive.com/NWPU2010translation.pdf

Quote
The quality factor of this resonator under no load can be calculated by the following equation:
Qu=∫|H|2dv/h/2∫|nxH|2ds+tgd∫|H|2dv = (14)
Where tg is the electric loss within the cavity, n is the normal vector of the wall, s is the cavity surface area, v is the volume of the cavity.

Who will be the 1st to post an Excel spreadsheet that duplicates Prof Yang's equation?
Sorry mr t, this is an arbitrary equation of limited value imo. One must ask why estimate when one can measure.

My point is this equation is what the Chinese use when they quote device Q. They don't, as far as I know, measure the quoted devices Q.
Seems like it mr t...with all the proper gear in their lab, why they chose not to measure is beyond me.

Online Rodal

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Doctor Rodal,
if I understand correctly, you are calculating the Poynting vector by hand?
Because I believe MEEP has functions to do this automatically:

(get-poynting which-band)
(output-poynting which-band)
(output-poynting-x which-band)
(output-poynting-y which-band)
(output-poynting-z which-band)

http://ab-initio.mit.edu/wiki/index.php/MPB_User_Reference#Storing_and_combining_multiple_fields

Thanks for your comment, that is surely useful to other users wanting to use Meep as a black box.  There have been several such requests, by many people in this thread.  It is not my interest in using computer programs as a black box, particularly for this problem (EM Drive), because its analysis (if it is not an experimental artifact) will eventually require something beyond standard-Meep, so we choose to start coding now.  (Even if it is an experimental artifact, certain standard multi-physics simulations will require going beyond Meep: thermal stress, etc.)


1) I am calculating the Poynting vector using Wolfram's Mathematica  (http://www.wolfram.com/mathematica/) (a very powerful program in its own right), and not by hand. I own two current licenses to Mathematica and I have it running Mathematica 10.1 running in two separate machines.

2) Meep's output program does not have the ability to produce vector field plots.  The Poynting vector is a vector and I would rather see the vector field plots rather than the components themselves.  I think that the vector field plots give a much better physical picture of what is going on.  I have displayed the Poynting vector fields on the planes, rather than individual components.  The actual calculation of the Poynting vector by Mathematica takes practically no time.  More time is spent on the vector field plot calculation than on the Poynting vector calculation.  Thus for my purposes there would be practically no advantage in plotting the vector field plot from components from Meep rather than computing it raw from the electromagnetic field.

3) Apparently Meep's routintes are only Cartesian or Polar.  One of my goals was to plot in the intrinsic spherical system if required (which would also mean postprocessing) as well as vector and tensor transformations.

4) The contour plots displayed by the Meep postprocessing facility (hstop spelling ?) for the components so far have been bad quality: they have not displayed the magnitude of the color contours and the contours get repeated at different magnitudes which makes for a very confusing picture, that's why I would rather plot the contour plots also by myself.

5) Ditto to show 3D plots.

6) My ultimate goal was to compute the stress tensor which is the quantity that really matters.  My understanding is that Meep does not calculate the stress tensor.  It calculates an overall force via an approximation valid for optical frequencies, whose validity remains to be shown.  I am interested in the stress tensor.

7) The power of Meep is it is an open program and many users that use Meep for publication purposes write their own processing and post-processing routines doing things that are not implicit in Meep rather than use it as a black box.

I will be showing the stress tensor shortly, which is very interesting
« Last Edit: 07/13/2015 12:07 AM by Rodal »

Offline leomillert

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Reasonable enough, Doctor Rodal. I can see how using it as a black box is limiting.

Do you plan to formalize and make available the entire process once you are done?
From rfmwguy's EM thruster to aero's MEEP modelling/simulation of it to your final computations and analysis.
« Last Edit: 07/13/2015 12:04 AM by leomillert »

Offline TheTraveller

EMDrive Control and Monitoring System (CMS)

Have attached the Raspberry Pi model 2B Control and Monitoring System I'm developing.

As you can see the control of the Rf frequency and the Rf amp power output is fully under software control. Rf amp power can be turned off or on and the power output set to between 100Ws and 79mWs via the Raspberry.

Likewise RF amp Forward power, VSWR, Rf amp temp, voltage and current is monitored. Additionally the 7,200p/rev optical encoder output from the rotary table is monitored. All monitored data is recorded in the Raspberry's 1GB of memory.

During development and static testing, the wired USB connection is used. Then when doing cordless rotary table acceleration testing, the wired USB cable will be removed and the wireless BlueTooth link will be used for monitoring and control.

Everything you see on the page, except the Laptop, Faraday Cage and 4 x 12v 6Ah SLA batteries will be supplied to the Force verifiers. Will also supply the full software suite, both PC and Raspberry.

Comments most welcome.
« Last Edit: 07/13/2015 12:29 AM by TheTraveller »
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Offline mwvp

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Nice. The graph shows the mixing of the modes as a function of cavity shape.
There is a choice of frequency, and dimension on graph. Any specific motivation?
No idea.

I'm looking for a configuration when there is one hybrid mode, followed by any other mode very close.
Why? Because I think there is another thing interacting with the electromagnetic field of cavity.
This thing probally will have a very small coupling with the electromagnetic field.
To enhance this coupling I need:
- A mode excited by a source puting the max energy on cavity
- At least one second mode with frequecy very close to the first but not excited by the source.
In this situation, when a small region of the cavity has its electromagnetics properties changed to anything different of vacuum (epslon0 and mu0), then this little "scatter" region triggers a very strong perturbation called "ghost mode".
In waveguides "ghost modes" are caused by deformations or imperfections on waveguide, but in principle, any "pertubation" can cause this effect.
This "ghost modes" can in some situations, reflect almost all power flux in the waveguide, and the "scatter" will be under very strong radiation pressure.
I don't know if this case can be considered also a type of Fano resonance, but I think if I want some type of interaction of the field inside of cavity with some "other thing", I would try  to maximize this interaction with this setup.

To me this thing is the axion field/particle. To others can be particles from "quantum vacuum" or a space-time flutuactions, but the result of the ghost mode arising is the same,  change the incidence of electromagnetic radiation on the walls of cavity.

I had to look up ghost mode and Fano reasonance, interesting stuff to know. Perhaps explains why putting a dielectric in the frustrum is a bad thing. Dielectric loss aside, it could cause ghost modes if there are nearby modes available. Lots of google hits on microwave/klystron windows pertaining to ghost modes. Wikipedia notes microwaves are associated with Fano resonance. A 1958 paper by Jaynes http://bayes.wustl.edu/etj/articles/ghost.modes.pdf notes that microwave ghost modes have a similarity to localized imperfections in crystalline periodic structures (such as dopants) leads to bound states that overlap the conduction band. If that Fano resonance too? I'll have to absorb that awhile. I have no idea how that could conjure axions out of the qv.

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