Author Topic: EM Drive Developments - related to space flight applications - Thread 3  (Read 1881370 times)

Offline flux_capacitor

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What I can't understand about Tajmar's build is he could have easily duplicated Shawyer's 1st Experimental EMDrive as it was driven by a non water cooled low cost 2.45GHz magnetron just as Tajmar used.

His vacuum chamber is more than large enough to handle the 160mm diameter big end.

At 16mN Force output, his measurement system could have easily measured the Force generated.

This Tajmar mini EMDrive is really a very strange build.

I read a few pages ago that you guys speculated the dimensions of Tajmar EmDrive may actually be twice what we thought (because the dimensions in the paper may be radii instead of diameters). Whatever, the cavity is still very small, and the reason is quite obvious even if Tajmar didn't explain it in the paper.

Tajmar had to build the cavity so small so the system "cavity + waveguide + magnetron" is light enough to hang on the torsion pendulum inside the vacuum chamber. The vacuum chamber is large, but the torsion pendulum, like Eagleworks', can sustain a limited weight.

Paul March expressed the same doubts in Thread 2 when he thought about hanging a heavier magnetron on Eagleworks torsion pendulum instead of the lighter coax cable and RF amp:

Quote from: Star-Drive
So yes, a wide bandwidth RF source seems to be called for and one that can be both AM and FM modulated at the same time.  From my readings to date, that appears to be a hard nut to crack for solid state RF amplifiers at the desired kW power levels due to their limited RF power bandwidth capabilities, so we may be forced into using magnetrons and just learn how best to feed their 4-to-20 kV high voltage anode requirements while working in a hard vacuum.  However the more difficult problems are finding ways of reducing their mass and size so we can "fly" them on our torque pendulum.  Cooling the magnetrons in a hard vacuum is also another problem we need to deal with since air cooling is out of the question and liquid cooling is a giant pain to deal with as well.  About the only other way to cool these beasts in a hard vacuum is to use phase change material like paraffin wax that could give us several minutes of run times before we had to let the accumulated heat in the paraffin radiate to the vacuum chamber walls.

So It seems that for now we are stuck with high power magnetron = large thrust in ambient air with the risk of spurious effects; and low power solid state RF amp = precise but small thrust in a vacuum.

The third way is to use 100W to 1kW solid state RM amps in ambient air, as @TheTraveller.
« Last Edit: 07/27/2015 08:55 AM by flux_capacitor »

Offline SeeShells

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Got it figured.

Tajmar's cavity has a measured 50MHz input bandwidth from 2.40GHz to 2.45GHz or the lower portion of the WiFi band.

Most magnetrons output in the upper half of the WiFi band, 2.45GHz to 2.50GHz range as attached.

If his magnetron output bandwidth was like that Paul March measured (as attached) then only about ~25% of the magnetron energy (2.40GHz - 2.45GHz) would be getting inside the cavity and the other ~75% (above 2.45GHz would be rejected.

Which means the 663Ws forward power (at VSWR 1.622:1) drops to 167 real watts inside the frustum with 533W reflected back to heat the magnetron.

With 167W in the cavity and a Q of 48.8 the predicted Force generation is 31uNs and at a Q of 20.2 is 13uNs. A SnowFlake is ~30uN, to give an idea of the magnitude of the Forces being generated here.

This same effect of mismatched input and output bandwidths caused the serious dip in Prof Yang's Force versus power curve. The lower left rectangles, in the group of 6 charts, are the cavity input bandwidth and the other curve is the magnetron output bandwidth. Clear to see the massive mismatch that occurred and that totally messed up her data until they went back and found the reason for the massive dip.

So history has maybe repeated itself and this cavity input / magnetron output bandwidth mismatch may have struck again.
I got my little USB SA a couple days ago and the first thing I did it look at the microwave oven. What a mess, sweeping up and down in frequencies with a FM looking spectrum, power levels fluctuating like a AM band, for me it would be tough to say what percentage anyone could get from that malstrom unless the magnetron tended to want to seek and lock a little through the waveguide and that's a stretch.

Next week I'm planning to hook up my magnetron to a large rheostat and lower the 110 VAC input voltage and monitor the frequency output with the Spectrum Analyser to see if I can stabilize it some, narrow the bandwidth some and reduced output power is just fine.

Shell

Offline SeeShells

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A post over on reddit attributes the thrust to a phenomenon called sputtering.  I was wondering how valid this interpretation is.  It appears to depend on oxidation, which seems unlikely in a vacuum.  Link:

http://www.reddit.com/r/Futurology/comments/3emk49/direct_thrust_measured_from_propellantless_em/cthg9uo
You can answer that question by filling the enclosed Frustum with Sulfur hexafluoride,

Sulfur hexafluoride is an inorganic, colorless, odorless, non-flammable, extremely potent greenhouse gas which is an excellent electrical insulator. SF 6 has an octahedral geometry, consisting of six fluorine atoms attached to a central sulfur atom.

But it is hard to keep in a perforated cavity. It is used in high power systems to prevent arcing.

Shell

Another thing I like about SF6 is that is a dense gas so if the thrust is dependent on gas being present then there is a lot to work with.  That said, I have no idea what frequency you would need to use it as a resonant gas.
They used it in tuning for the super colliders magnetrons power supplies and those frequencies was just shy of the GHz range and some just over. It would prevent arcing and plasma discharges and I'm not sure if we want to prevent that yet for it could be a component of thrust.

Shell

Offline SeeShells

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What I can't understand about Tajmar's build is he could have easily duplicated Shawyer's 1st Experimental EMDrive as it was driven by a non water cooled low cost 2.45GHz magnetron just as Tajmar used.

His vacuum chamber is more than large enough to handle the 160mm diameter big end.

At 16mN Force output, his measurement system could have easily measured the Force generated.

This Tajmar mini EMDrive is really a very strange build.

I read a few pages ago that you guys speculated the dimensions of Tajmar EmDrive may actually be twice what we thought (because the dimensions in the paper may be radii instead of diameters). Whatever, the cavity is still very small, and the reason is quite obvious even if Tajmar didn't explain it in the paper.

Tajmar had to build the cavity so small so the system "cavity + waveguide + magnetron" is light enough to hang on the torsion pendulum inside the vacuum chamber. The vacuum chamber is large, but the torsion pendulum, like Eagleworks', can sustain a limited weight.

Paul March expressed the same doubts in Thread 2 when he thought about hanging a heavier magnetron on Eagleworks torsion pendulum instead of the lighter coax cable and RF amp:

Quote from: Star-Drive
So yes, a wide bandwidth RF source seems to be called for and one that can be both AM and FM modulated at the same time.  From my readings to date, that appears to be a hard nut to crack for solid state RF amplifiers at the desired kW power levels due to their limited RF power bandwidth capabilities, so we may be forced into using magnetrons and just learn how best to feed their 4-to-20 kV high voltage anode requirements while working in a hard vacuum.  However the more difficult problems are finding ways of reducing their mass and size so we can "fly" them on our torque pendulum.  Cooling the magnetrons in a hard vacuum is also another problem we need to deal with since air cooling is out of the question and liquid cooling is a giant pain to deal with as well.  About the only other way to cool these beasts in a hard vacuum is to use phase change material like paraffin wax that could give us several minutes of run times before we had to let the accumulated heat in the paraffin radiate to the vacuum chamber walls.

So It seems that for now we are stuck with high power magnetron = large thrust in ambient air with the risk of spurious effects; and low power solid state RF amp = precise but small thrust in a vacuum.

The third way is to use 100W to 1kW solid state RM amps in ambient air, as @TheTraveller.
Lower the power of the magnetron and stabilize the output so less is lost in spurious non-Q effects and one last thought I've had is modifying a fanless CPU cooler to keep the magnetron cooler.
http://www.acousticpc.com/images/a_nofan_cr-95c_copper_fanless_cpu_cooler.jpg
I'm still thinking about this one.

Shell

PS: This is important... <quote> So yes, a wide bandwidth RF source seems to be called for and one that can be both AM and FM modulated at the same time.  From my readings to date, that appears to be a hard nut to crack for solid state RF amplifiers at the desired kW power levels due to their limited RF power bandwidth capabilities...
« Last Edit: 07/27/2015 09:12 AM by SeeShells »

Offline SeeShells

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Finally got tired and I'm off to a little sleep time. GN.

Shell

Offline TheTraveller

What I can't understand about Tajmar's build is he could have easily duplicated Shawyer's 1st Experimental EMDrive as it was driven by a non water cooled low cost 2.45GHz magnetron just as Tajmar used.

His vacuum chamber is more than large enough to handle the 160mm diameter big end.

At 16mN Force output, his measurement system could have easily measured the Force generated.

This Tajmar mini EMDrive is really a very strange build.

I read a few pages ago that you guys speculated the dimensions of Tajmar EmDrive may actually be twice what we thought (because the dimensions in the paper may be radii instead of diameters). Whatever, the cavity is still very small, and the reason is quite obvious even if Tajmar didn't explain it in the paper.

Tajmar had to build the cavity so small so the system "cavity + waveguide + magnetron" is light enough to hang on the torsion pendulum inside the vacuum chamber. The vacuum chamber is large, but the torsion pendulum, like Eagleworks', can sustain a limited weight.

Paul March expressed the same doubts in Thread 2 when he thought about hanging a heavier magnetron on Eagleworks torsion pendulum instead of the lighter coax cable and RF amp:

Quote from: Star-Drive
So yes, a wide bandwidth RF source seems to be called for and one that can be both AM and FM modulated at the same time.  From my readings to date, that appears to be a hard nut to crack for solid state RF amplifiers at the desired kW power levels due to their limited RF power bandwidth capabilities, so we may be forced into using magnetrons and just learn how best to feed their 4-to-20 kV high voltage anode requirements while working in a hard vacuum.  However the more difficult problems are finding ways of reducing their mass and size so we can "fly" them on our torque pendulum.  Cooling the magnetrons in a hard vacuum is also another problem we need to deal with since air cooling is out of the question and liquid cooling is a giant pain to deal with as well.  About the only other way to cool these beasts in a hard vacuum is to use phase change material like paraffin wax that could give us several minutes of run times before we had to let the accumulated heat in the paraffin radiate to the vacuum chamber walls.

So It seems that for now we are stuck with high power magnetron = large thrust in ambient air with the risk of spurious effects; and low power solid state RF amp = precise but small thrust in a vacuum.

My design predicts around 100mN from 100W narrow band Rf. Maybe 50% more if the Prof Yang short cylinders at each end trick works and eliminates the need for highly accurate and highly polished end plates.

BTW that is 1N/kW. As Prof Yang's team has already achieved that back in 2010 and without the 2013 short cylindrical flat end plates, 2N/kW should be doable and maybe bettered. Prof Yang has also shown 4N/kW but only over a small power span.

Above 4N/kW, further gains may be hard won without going superconducting but can't see that tech getting the reliability needed for deep space human rated applications. Probably better to then turn to scale up a 400N/100kW EMDrive and start doing human exploration and colonisation of the solar system.

Might even help Paul March fund & build his WarpStar1. Hey not so crazy a private EMDrive powered space ship. Only need 126,000Ns. Yeah just dreaming. Maybe.........
"As for me, I am tormented with an everlasting itch for things remote. I love to sail forbidden seas.”
Herman Melville, Moby Dick

Offline flux_capacitor

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Lower the power of the magnetron and stabilize the output so less is lost in spurious non-Q effects and one last thought I've had is modifying a fanless CPU cooler to keep the magnetron cooler.
http://www.acousticpc.com/images/a_nofan_cr-95c_copper_fanless_cpu_cooler.jpg
I'm still thinking about this one.

Shell

Yes. Every DIYer planning to use a magnetron should look at the already discussed paper "The Magnetron - A Low noise, Long Life Amplifier" (also attached to this message).

To summarize here (I try to advertise the content of the paper for those who would still not have read it) the tricks to transform a noisy magnetron into a cleaner RF amp is to add a feedback mechanism limiting the temperature and thus emission of the cathode in a more subtle way and control over the anode current. To do this you need to:

- Add a switch to disconnect the included lower-end DC power supply off the magnetron, whose sole purpose was to continuously heat the cathode filament, after the tube has started. So after heating has started, let the cathode be heated by back bombardment power alone.

- Use an external, well filtered DC power supply to run the magnetron as a reflection amplifier also more specifically known as a directional amplifier, where the drive power injected through a ferrite circulator becomes indistinguishable from the power reflected by a mismatched load.

- In such a configuration, there is a phase difference between input and output which also limits the gain, because the free running frequency of the driver is not tuned. Forcing the magnetron to operate at the same frequency as the driver can be done by using the natural magnetron's frequency dependence upon the anode current which is called magnetron pushing, or conversely the reactive component of load (magnetron pulling). The former is used more often.

- Add a little solenoid called a buck-boost coil in the magnetic circuit, to control the anode current which changes the free running frequency of the magnetron, into a phase locked amp. The coil creates a magnetic field which increases or reduces the operating voltage, hence the anode current intercept of the load line with a fixed voltage power supply. The coil is ran with low power (< 5 W) from an op-amp that amplifies the phase error signal.



- How to acquire noise data and add a feedback control loop is detailed in the paper so I won't rewrite it there. All you need to know is with that basic tuning the author decreased the noise in a frequency band of 300 kHz at 10 MHz from the carrier by more than 100 dB below the carrier level over a broad range of operating voltage, magnetic field, load and gain. With only 0.6 W drive, the gain was 30 dB at 560 W output. Noise at 10 kHz from the carrier can also be decreased in an even finer way.

This way you obtain a high-gain, phase-locked, long-life, low noise microwave amplifier from a very cheap commercial oven magnetron.

Offline aceshigh

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My design predicts around 100mN from 100W narrow band Rf. Maybe 50% more if the Prof Yang short cylinders at each end trick works and eliminates the need for highly accurate and highly polished end plates.

BTW that is 1N/kW. As Prof Yang's team has already achieved that back in 2010 and without the 2013 short cylindrical flat end plates, 2N/kW should be doable and maybe bettered. Prof Yang has also shown 4N/kW but only over a small power span.

Above 4N/kW, further gains may be hard won without going superconducting but can't see that tech getting the reliability needed for deep space human rated applications. Probably better to then turn to scale up a 400N/100kW EMDrive and start doing human exploration and colonisation of the solar system.

Might even help Paul March fund & build his WarpStar1. Hey not so crazy a private EMDrive powered space ship. Only need 126,000Ns. Yeah just dreaming. Maybe.........

the WarpStar1 however was ME (Mach Effect) right?

Speaking of which, Tajmar and Heidi Fern will tomorrow be speaking about both EM and ME drives at AIAA.


here, LiveFeed for tomorrow

edit: found the right one!

http://livestream.com/AIAAvideo/events/4212872?origin=event_published&mixpanel_id=136b121d63432e-06c456027-316f6852-13c680-136b121d635aad&acc_id=10115456&medium=email

AIAA Propulsion & Energy 2015
« Last Edit: 07/27/2015 12:13 PM by aceshigh »

Offline Chrochne

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My design predicts around 100mN from 100W narrow band Rf. Maybe 50% more if the Prof Yang short cylinders at each end trick works and eliminates the need for highly accurate and highly polished end plates.
.
Might even help Paul March fund & build his WarpStar1. Hey not so crazy a private EMDrive powered space ship. Only need 126,000Ns. Yeah just dreaming. Maybe.........

the WarpStar1 however was ME (Mach Effect) right?

Speaking of which, Tajmar and Heidi Fern will tomorrow be speaking about both EM and ME drives at AIAA.


here, LiveFeed for tomorrow

edit: found the right one!

http://livestream.com/AIAAvideo/events/4212872?origin=event_published&mixpanel_id=136b121d63432e-06c456027-316f6852-13c680-136b121d635aad&acc_id=10115456&medium=email

AIAA Propulsion & Energy 2015

Thanks a lot! I did not know it will be live!
« Last Edit: 07/27/2015 12:23 PM by Chrochne »



Speaking of which, Tajmar and Heidi Fern will tomorrow be speaking about both EM and ME drives at AIAA.


http://livestream.com/AIAAvideo/events/4212872?origin=event_published&mixpanel_id=136b121d63432e-06c456027-316f6852-13c680-136b121d635aad&acc_id=10115456&medium=email

AIAA Propulsion & Energy 2015

Excuse me, but i don't see any of those 2 listed on the schedule. Any info on what time they are supposed to talk ?

Thanks

Offline aceshigh

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Speaking of which, Tajmar and Heidi Fern will tomorrow be speaking about both EM and ME drives at AIAA.


http://livestream.com/AIAAvideo/events/4212872?origin=event_published&mixpanel_id=136b121d63432e-06c456027-316f6852-13c680-136b121d635aad&acc_id=10115456&medium=email

AIAA Propulsion & Energy 2015

Excuse me, but i don't see any of those 2 listed on the schedule. Any info on what time they are supposed to talk ?

Thanks

and unfortunatelly you are right. This conference seems to be much bigger and I guess the panel, whatever, where Heidi Fern and Tajmar will speak won´t be streamed I guess... the live streaming as far as I know is only of the Plenary and Forum 360 sessions...

they are in the conference...
NFF-04. Future Flight Propulsion Systems
Chair(s): Gregory Meholic (The Aerospace Corporation)
Co-Chair(s): Heidi Fearn (California State University, Fullerton)
2:30 PM - 5:30 PM; Lake Nona A

but the type of the conference is labelled as "Technical Paper"
Session Title:Future Flight Propulsion Systems
Session Notes: Monday Afternoon
Session Type: Technical Paper
Session Topic: 51st AIAA/SAE/ASEE Joint Propulsion Conference
Chair: Gregory V Meholic
Co-Chair: Heidi Fearn
Location: Lake Nona A

https://aiaa-mpe15.abstractcentral.com/s1agxt/com.scholarone.s1agxt.s1agxt/S1A.html?
&a=3277&b=1593989&c=27404&d=17&e=28618011&f=17&g=null&h=BROWSE_THE_PROGRAM
&i=N&j=N&k=N&l=Y&m=LplFTrirj27I9oyXeGO7TJHjTMQ&r=c-gnY+1FRMR+OuWei-g4gw**.c832eqys1as_ac&n=0&o=1438002443351&q=Y&p=
https://aiaa-mpe15.abstractcentral.com
« Last Edit: 07/27/2015 01:26 PM by Chris Bergin »

Offline rfmwguy

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DIYers, heres my plan...I will fire the magnetron in the frustum this week. I will not attempt any matching with launchers or stub tuners. This, I feel, will compress the output bandwidth and limit the ERP into the frustum. IOW, all the magnetron power will be fired into the frustum, complex modulation and all.

I will directly measure the core temp and will not allow it to exceed about 90 deg C. 160 deg C is typical thermal shutdown.
« Last Edit: 07/27/2015 01:46 PM by rfmwguy »

Offline Ricvil

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http://www.google.com.br/url?sa=t&rct=j&q=legendre%20equation
%20boundary%20conditions%20conical&source=web&cd=7&ved=0CDoQFjAGahUKEwicvI2nuPvGAhUCQ5AKHediDc0&
url=http%3A%2F%2Fcee.northwestern.edu%2Fpeople%2Fbazant%2FPDFs%2FPapers%2520-%2520Backup%
25202_20_2013%2F067.pdf&ei=LDW2VZz2MoKGwQTnxbXoDA&usg=AFQjCNFOyFVYVL6_crh3B7BYQINNKm_2SA

Zeng not solve the boudary condition for the conical problem. He uses the standard solutions for free space.

The  numeric procedure for set the boundary conditions for a conical problem is explained on the link above (a math analogous problem).


...
I haven't used perturbation theory since circa 1992. That would take a great deal of effort for something I find to be trivially obvious. Look at the attached equation for the wave vector in a circular waveguide. If w0 = wmn, there is no propagation. There can be however, periodic boundary conditions and localized standing waves. On the other hand, even if w0 > wmn such that it is a traveling wave. There is an inertial frame where the group velocity is zero, and the same situation applies, periodic in z, with a stationary resonant standing wave.

Now, what is the difference if I slowly increase w0, or slowly decrease wmn by introducing a taper? Nothing, as far as I can see. The end result is the same, a traveling wave that is accelerating. Why does this need to be proven? it's obvious. If not, why isn't it? 

I am not considering a closed ended frustum here. Only the tapered waveguide vs a straight waveguide. It is only a resonant cavity in 2D, the circular cross section, not the length. Bessel function is the solution for a circle. It shifts frequency for the same reason "time dilation" occurs in a gravitational field. It is in a potential energy gradient.
Todd
It is the difference between a spherical wave and a flat wave.  The flat wave solution with the cylindrical Bessel function in the cross section applies to a perfect cylinder.  The tapered, conical waveguide does not have the flat wave solution in general, only as an approximation.  The flat wave solution does not respect the boundary conditions of the lateral surface of the cone.  See the paper of Yang and Fan: they consider an open waveguide and they had to use the spherical wave solution. 

You asked for comments. Your solution is an approximation to the spherical wave solution.  The objection can be raised that the accuracy of the amplification factor is unknown, as the solution is predicated on a flat wave that does not exactly respect the boundary conditions for an open conical waveguide (or section of a cone).  The cylindrical Bessel function is assumed ab initio.  Satisfaction of boundary conditions is not discussed in your paper.

I appreciate the help. Now i understand the issue. However, wouldn't a ray-vector approach show the same behavior without the need for spherical harmonics?

Below is what Zeng & Fan wrote for impedances. Impedance is basically u0*velocity. The TE mode is the phase velocity, the TM mode is the group velocity. How do we plot this as a function of kr?  I can't interpret something I don't understand and this just looks like gibberish to me, without some way to plot it out and visualize it. Sorry, I'm an engineer not a mathematician.
Todd

I think they are Henkel spherical functions.  I could plot it with Mathematica but I have some $$$ work to do.  Didn't Zeng and Fan have some plots of impedance in their paper?
« Last Edit: 07/27/2015 03:46 PM by Chris Bergin »

Offline Rodal

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[Huge URL needs to be shortened with URL shortener]

..Zeng not solve the boudary condition for the conical problem. He uses the standard solutions for free space....
Zeng and Fan (https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-17-1-34&id=175583 ) express the boundary conditions for the conical problem in Equations 4 (for TE modes) and 7 (for TM modes) of their paper.
The solution is an eigenvalue problem.
In Table 1 of their paper they give eigenvalues for TE11,TM01,TM11 and TE01 modes as a function of the cone half angle from Pi/24 to Pi/2.

Thank you for the paper by Bazant and Keer. 
« Last Edit: 07/27/2015 03:09 PM by Rodal »

Offline rfmwguy

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Offline Ricvil

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[Huge URL needs to be shortened with URL shortener]

..Zeng not solve the boudary condition for the conical problem. He uses the standard solutions for free space....
Zeng and Fan (https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-17-1-34&id=175583 ) express the boundary conditions for the conical problem in Equations 4 (for TE modes) and 7 (for TM modes) of their paper.
The solution is an eigenvalue problem.
In Table 1 of their paper they give eigenvalues for TE11,TM01,TM11 and TE01 modes as a function of the cone half angle from Pi/24 to Pi/2.

The Zeng expressions do not solve equation (1) .
You may use the the "eingen values" expressions into (2) ,(3), (5) ,(6) and no one of that solves (1).

Offline zellerium

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...
which will launch a TE mode that is coupled to the resonant iris which then reflected a matched source to the frustum sidewall which should then excite a TM mode in the frustum transverse axis which is at approx a right angle to  rectangular waveguide. The diagram which shows a similar setup with the E-probe in the rectangular wave guide end wall will launch a TM mode which will be matched by the iris and reflect a matched source to the frustum wall but should excite a TE mode in the frustum. It will interesting to see his mode data.

Do we know for certain he used an iris? I don't believe it was mentioned or pictured...


...

If his magnetron output bandwidth was like that Paul March measured (as attached) then only about ~25% of the magnetron energy (2.40GHz - 2.45GHz) would be getting inside the cavity and the other ~75% (above 2.45GHz would be rejected.
...

I don't think we should assume their magnetron output distributions are the same. Not all magnetrons are created equally; Tajmar's happened output 700 W, most used in ovens today are ~900~1000 W. Different kinds of strapping, number of spokes, shape of internal resonant cavity, etc all will impact the power output and distribution.
source: https://www.jlab.org/ir/MITSeries/V6.PDF

Offline Rodal

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[Huge URL needs to be shortened with URL shortener]

..Zeng not solve the boudary condition for the conical problem. He uses the standard solutions for free space....
Zeng and Fan (https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-17-1-34&id=175583 ) express the boundary conditions for the conical problem in Equations 4 (for TE modes) and 7 (for TM modes) of their paper.
The solution is an eigenvalue problem.
In Table 1 of their paper they give eigenvalues for TE11,TM01,TM11 and TE01 modes as a function of the cone half angle from Pi/24 to Pi/2.

The Zeng expressions do not solve equation (1) .
You may use the the "eingen values" expressions into (2) ,(3), (5) ,(6) and no one of that solves (1).

See

R. F. Harrington, Time-harmonic electromagnetic fields (Wiley-IEEE, 2001), Chap. 6, 
Hardcover: 496 pages
Publisher: Wiley-IEEE Press; 2nd edition (September 13, 2001)
Language: English
ISBN-10: 047120806X
ISBN-13: 978-0471208068

to see how Eqns. 2,3, (and 5 and 6) in Zeng and Fan can follow (under suitable conditions)  from Eqn 1 in Zeng and Fan
« Last Edit: 07/27/2015 03:40 PM by Rodal »

Offline DrBagelBites

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@rfmwguy

Chatted up some of the companies at the conference, asked the ones in R&D about any sort of electromagnetic engines/propulsions they may be working on. No dice. Most or all are researching hall thrusters/ion propulsion/etc.

Just a quick update from the conference. Tajmar's talk is tomorrow.

-I

Offline zen-in

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@rfmwguy

Chatted up some of the companies at the conference, asked the ones in R&D about any sort of electromagnetic engines/propulsions they may be working on. No dice. Most or all are researching hall thrusters/ion propulsion/etc.
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That isn't surprising.

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