...A gradient force in the waveguide, the evanescent wave propagates at a frequency which is less than the cutoff frequency.How did you find it?

Quote from: rfmwguy on 06/01/2015 01:30 AMQuote from: aero on 05/31/2015 04:43 PMI think it is important for all to remember that the EM drive is a physical system, not a mathematical one. In the physical system, cutoff is not a line in the sand that you shall not cross, rather it is (probably) the center of a range where propagation drops below some relative value of db. The EM drive will do as it does over a range of frequencies, plus or minus, just some will do better than others.Add: Its also important that the magnatron drive is a noisy source so the cavity will select its own operating frequency. It would be nice to have the maximum power transfer from source to cavity but very often "Perfect" is the enemy of "Good enough."Classic definition of cutoff is 3db. A single cavity will not have a steep shape factor in stopbands, no brickwall is correct. Return loss will be much more transitional in the passband... IOW i'd design and tune for best S11 performance at center frequency simply to keep the signal source protected as a matter of safety and efficiency. Also the bessel function has a shallower shape factor. Its best known characteristic is flat group time delay in passband for radar/pulse applications. Really, the frustum is a poor bandpass, being so assymetrical around a center frequency....but maybe that's part of the mystery These high Q frustums may be difficult to deal with. As example assuming 3.85GHZ resonance at Q = 60,000. Bandwidth at -3db points of 64kHz or 32kHz either side of ideal resonance. Then assuming we wish to operate at max 50% of that deviation, we need to hold excitation frequency to +-16kHz of the ideal and at the same time track resonate changes due to thermal expansion.This is doable but not so easy as blasting away with a wide band magnetron into a lower Q cavity with flat end plates as against spherical end plates and a narrow band Rf generator.Will shortly present the system I'm putting together to enable resonance tracking as the frustum warms up and alters it's length and end plate diameters.Intend to use a very slow sweep spectrum analyser, over a tight frequency range, via an Rf coax switch that samples what is happening to the cavity via the same antenna that excites the cavity, then adjusts Rf frequency to get close, then use real time closed loop thrust feedback to centre the external Rf to the centre of the thrust curve.Also intent to do thrust bandwidths to see how much external freq variance affects generated thrust, at the same -3db down points. So will measure both conventional bandwidth and thrust bandwidth. Then will start to get a feel for how sensitive this beast is to frequency variance versus generated thrust.Using a wide band magnetron Rf source, there is little chance of being able to directly measure thrust bandwidth or even cavity Rf Q. So while the narrow band pathway will be slower to get there, it should yield much more interesting data.

Quote from: aero on 05/31/2015 04:43 PMI think it is important for all to remember that the EM drive is a physical system, not a mathematical one. In the physical system, cutoff is not a line in the sand that you shall not cross, rather it is (probably) the center of a range where propagation drops below some relative value of db. The EM drive will do as it does over a range of frequencies, plus or minus, just some will do better than others.Add: Its also important that the magnatron drive is a noisy source so the cavity will select its own operating frequency. It would be nice to have the maximum power transfer from source to cavity but very often "Perfect" is the enemy of "Good enough."Classic definition of cutoff is 3db. A single cavity will not have a steep shape factor in stopbands, no brickwall is correct. Return loss will be much more transitional in the passband... IOW i'd design and tune for best S11 performance at center frequency simply to keep the signal source protected as a matter of safety and efficiency. Also the bessel function has a shallower shape factor. Its best known characteristic is flat group time delay in passband for radar/pulse applications. Really, the frustum is a poor bandpass, being so assymetrical around a center frequency....but maybe that's part of the mystery

I think it is important for all to remember that the EM drive is a physical system, not a mathematical one. In the physical system, cutoff is not a line in the sand that you shall not cross, rather it is (probably) the center of a range where propagation drops below some relative value of db. The EM drive will do as it does over a range of frequencies, plus or minus, just some will do better than others.Add: Its also important that the magnatron drive is a noisy source so the cavity will select its own operating frequency. It would be nice to have the maximum power transfer from source to cavity but very often "Perfect" is the enemy of "Good enough."

Quote from: WarpTech on 06/01/2015 04:42 AMQuote from: txdrive on 06/01/2015 03:00 AM...What are you suggesting here, that EagleWorks didn't actually run the cavity at the resonance? From what I recall they had actually measured the Q with a sense antenna. There's a well known formula for calculating resonant modes of a truncated cone. It is certainly correct - tested to death in many practical devices. And they're also tuning the frequency to hit the actual resonance if the shape is a little off (due to thermal heating for instance).The point missing is, if you tune it for the highest Q and resonance, it reduces the thrust. I've proven to myself anyway, that the thrust happens due to the interference between the standing wave k and the evanescent wave Beta, phase factors. Where they interfere is where the phase shift is happening due to attenuation, as it propagates into the small end. Optimal thrust will occur when the amplitude of the standing waves is nearly the same as the amplitude of the evanescent waves and the two are out of phase. If you concentrate only on higher Q at resonance like EW did, it will minimize the evanescent waves that drive the thrust. Therefore, a lower Q is more likely to have positive results. Perhaps @TheTraveler's point is true, that had EW tested it at the Df frequency, it may have provided more thrust. So nothing is falsified by their test except the idea that they understand how it works.I'm still trying to crunch all this into design equations that are hopefully, more accurate and informative. It may take me a while.ToddAgain, this doesn't make any sense. When the RF that is coupled into a cavity is at the resonant frequency the Q will be maximal. That means the return loss is also at a maximum and almost all the power goes into the cavity. Any frequency that results in a lower Q will have a lower return loss and so there will be more power reflected back from the cavity. If the return loss is 10 dB lower at the frequency with a lower Q and "better for producing thrust" then the effective RF power transmitted to the cavity is just 1/10 of the power transmitted to the cavity at the resonant frequency where the Q is maximal. So maybe less RF power is the key. Reduce the RF power and get more thrust. Reduce it further and get even more thrust... ad infinitum until with no power you get infinite thrust.

Quote from: txdrive on 06/01/2015 03:00 AM...What are you suggesting here, that EagleWorks didn't actually run the cavity at the resonance? From what I recall they had actually measured the Q with a sense antenna. There's a well known formula for calculating resonant modes of a truncated cone. It is certainly correct - tested to death in many practical devices. And they're also tuning the frequency to hit the actual resonance if the shape is a little off (due to thermal heating for instance).The point missing is, if you tune it for the highest Q and resonance, it reduces the thrust. I've proven to myself anyway, that the thrust happens due to the interference between the standing wave k and the evanescent wave Beta, phase factors. Where they interfere is where the phase shift is happening due to attenuation, as it propagates into the small end. Optimal thrust will occur when the amplitude of the standing waves is nearly the same as the amplitude of the evanescent waves and the two are out of phase. If you concentrate only on higher Q at resonance like EW did, it will minimize the evanescent waves that drive the thrust. Therefore, a lower Q is more likely to have positive results. Perhaps @TheTraveler's point is true, that had EW tested it at the Df frequency, it may have provided more thrust. So nothing is falsified by their test except the idea that they understand how it works.I'm still trying to crunch all this into design equations that are hopefully, more accurate and informative. It may take me a while.Todd

...What are you suggesting here, that EagleWorks didn't actually run the cavity at the resonance? From what I recall they had actually measured the Q with a sense antenna. There's a well known formula for calculating resonant modes of a truncated cone. It is certainly correct - tested to death in many practical devices. And they're also tuning the frequency to hit the actual resonance if the shape is a little off (due to thermal heating for instance).

Quote from: zen-in on 06/01/2015 05:39 AMQuote from: WarpTech on 06/01/2015 04:42 AMQuote from: txdrive on 06/01/2015 03:00 AM...What are you suggesting here, that EagleWorks didn't actually run the cavity at the resonance? From what I recall they had actually measured the Q with a sense antenna. There's a well known formula for calculating resonant modes of a truncated cone. It is certainly correct - tested to death in many practical devices. And they're also tuning the frequency to hit the actual resonance if the shape is a little off (due to thermal heating for instance).The point missing is, if you tune it for the highest Q and resonance, it reduces the thrust. I've proven to myself anyway, that the thrust happens due to the interference between the standing wave k and the evanescent wave Beta, phase factors. Where they interfere is where the phase shift is happening due to attenuation, as it propagates into the small end. Optimal thrust will occur when the amplitude of the standing waves is nearly the same as the amplitude of the evanescent waves and the two are out of phase. If you concentrate only on higher Q at resonance like EW did, it will minimize the evanescent waves that drive the thrust. Therefore, a lower Q is more likely to have positive results. Perhaps @TheTraveler's point is true, that had EW tested it at the Df frequency, it may have provided more thrust. So nothing is falsified by their test except the idea that they understand how it works.I'm still trying to crunch all this into design equations that are hopefully, more accurate and informative. It may take me a while.ToddAgain, this doesn't make any sense. When the RF that is coupled into a cavity is at the resonant frequency the Q will be maximal. That means the return loss is also at a maximum and almost all the power goes into the cavity. Any frequency that results in a lower Q will have a lower return loss and so there will be more power reflected back from the cavity. If the return loss is 10 dB lower at the frequency with a lower Q and "better for producing thrust" then the effective RF power transmitted to the cavity is just 1/10 of the power transmitted to the cavity at the resonant frequency where the Q is maximal. So maybe less RF power is the key. Reduce the RF power and get more thrust. Reduce it further and get even more thrust... ad infinitum until with no power you get infinite thrust.The Brady report shows these cases where a lower Q produced a higher force.Mode Frequency(MHz) , Q Input Power (W) Peak Thrust (μN)TM211 1932.6 7,320 16.9 116.0 TM211 1936.7 18,100 16.7 54.1 Same mode, (practically) same frequency and power :Notice that reducing the Q to only 2/5 of the higher one (7320 instead of 18100) resulted in greater than twice as high a thrust force (116 instead of 54)(...)

Hi TravellerYour proposals sound fine to me.Note that the Q you achieve will also be dependent on how well you tune and match the impedance of the input antenna. We have used probe, loop and waveguide iris plates as input circuits. All have their own problems, but you should first calculate the wave impedance of the cavity at the input position. Standard text book equations work, as they always do. You can then design your chosen input circuit to match the wave impedance at the cavity resonant frequency.All successful EmDrive thrusters that I know of have incorporated a tuning element of some sort at the input. Also no successful design used COMSOL without correction, as the software does not seem to cope with conditions close to cut-off.Best regardsRoger> Hi Roger,>> Thanks again for the assistance.>> With my EM Drive Calculator now matching your numbers, I'm starting to get> a good gut feel for how the variables interact. Thanks again for your advise. >> It is beyond me why EW never took the time to do this and instead used> COMSOL to determine their cavity resonance frequencies.>> The copper pieces for the frustum will be laser cut from 1mm thick> sheet, professionally rolled / formed for the spherical end caps and the 2> end flanges turned on a lathe to match their inside diameter and slope to> that of the frustum side walls. All joints will be silver soldered. Any> silver solder that gets inside the butt side wall joint or flanges will be> removed before all internal surfaces are highly polished. External end caps> will also be produced to clamp the spherical end plates between the flanges> and the end caps.>> I assume it is ok to apply a protective anti oxidation film over the outer> frustum surfaces? Of course none inside the frustum, just highly polished> copper.>> If after the Flight Thruster replicator frustum is built and a spectrum> scan is run across your suggested 3.9003GHz resonance frequency +- 250> MHz should I expect to see and be able to measure the cavity Q at the> resonant frequency?>> I assume you measure frustum Q as the bandwidth at the -3bd points divided> into the centre frequency?>

Interesting email corro with Roger Shawyer. There is much useful information here.Quote...Also no successful design used COMSOL without correction, as the software does not seem to cope with conditions close to cut-off.Best regardsRoger...>

...Also no successful design used COMSOL without correction, as the software does not seem to cope with conditions close to cut-off.Best regardsRoger...>

@RodalDoc, so I haven't lost my way, what is your recommendation for frustum diameters and height using a conventional 2.45 GHz magnetron and the TM mode of your choosing? Thanks...

Quote from: TheTraveller on 06/01/2015 02:51 PMInteresting email corro with Roger Shawyer. There is much useful information here.Quote...Also no successful design used COMSOL without correction, as the software does not seem to cope with conditions close to cut-off.Best regardsRoger...>Discordant dissonant comment about COMSOL Finite Element Analysis software "not seeming to cope with conditions close to cut-off" falsified by this peer-reviewed article (hat tip to Otto):http://www.jpier.org/PIER/pier151/07.15022404.pdfWhere the authors of the peer reviewed article calculate how a particle in a rectangular waveguide can be pulled towards the light source or pushed away from the light source just by varying the frequency around the waveguide cutoff frequency. All of the fields and forces analytical calculations were validated using COMSOL Multiphysics Finite Element Analysis. The peer-reviewed literature contains numerous other reference of analysts successfully using COMSOL to analyze conditions below, near and above cut-off.COMSOL Finite Element Analysis is a very powerful tool with a huge number of modules available. COMSOL, as well as ANSYS, ABAQUS, ADINA, and other multiphysics packages are routinely used for such analysis at top companies, universities and research institutions (like CERN). Most large companies and research institutions have their own finite element packages as well.Just like any tool, what an analyst may achieve depends on the expertise and experience of the analyst and the COMSOL modules available, as anything else.

Also no successful design used COMSOL without correction, as the software does not seem to cope with conditions close to cut-off.

http://www.jetpletters.ac.ru/ps/1407/article_21374.shtmlChiral anomaly and the law of conservation of momentum in 3He-A.

Quote from: Mulletron on 06/01/2015 01:12 PMhttp://www.jetpletters.ac.ru/ps/1407/article_21374.shtmlChiral anomaly and the law of conservation of momentum in 3He-A.Thank you Mulletron !This is a particularly good article, not because of He3, but because he elaborates on the interaction of the Bose particles (the photon standing waves in our case) and the Fermi (principally the electrons in the cavity wall) to show the existence of a momentum current term in the interaction. This does remind me of the current term in the Sachs-Schwebel quaternion formulation for GR.

...Sounds like an advert for COMSOL. Do you sell or rep or support it?...

Quote from: Notsosureofit on 06/01/2015 03:24 PMQuote from: Mulletron on 06/01/2015 01:12 PMhttp://www.jetpletters.ac.ru/ps/1407/article_21374.shtmlChiral anomaly and the law of conservation of momentum in 3He-A.Thank you Mulletron !This is a particularly good article, not because of He3, but because he elaborates on the interaction of the Bose particles (the photon standing waves in our case) and the Fermi (principally the electrons in the cavity wall) to show the existence of a momentum current term in the interaction. This does remind me of the current term in the Sachs-Schwebel quaternion formulation for GR. Notsosureofit , could you please explain as to whether this interaction, and the existence of this momentum current term could relate (somehow) to your Notsosureofit hypothesis for the EM Drive or the other possible explanations put forward ?Concerning your example of the photon standing waves, would the interaction also take place with evanescent waves, as contemplated by WarpTech? Thanks

..Added: A comment by Schwinger: "Incidentally, the probability of actual pair creation is obtained from the imaginary part of the electromagnetic field action integral. " ... for S. White