http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.htmlThe equations for the em fields of a tampered conical waveguide can be founded above.The expressions for the cavity( for more simple modes) are founded after matching boundaring conditons at the taps.The geometry is matched by spherical coordinates, so the fields are spherical coordinate dependent too, an this facilitate match the boundary conditions by aproximation ( the taps are not spherical but planes in real cavity).But the point is, the fields are expressed by coordinates functions, but the the wave vectors not. In fact the wave vectors are "the coordinates" the modes of propagation, where the modes are a base to span the function space of em fields inside the guide/cavity.Quote from: WarpTech on 07/05/2015 09:14 pmQuote from: Ricvil on 07/05/2015 08:54 pmYour first equation ( the definition of the wave vector K), is wrong.It establishes a erroneous z dependence on K.The K will depend at most on total geometry( including the dimensions of cavity), medium constitutive relations (mu and epslon), and boundary conditions, which defines de modes inside the sctruture, and thus the modes cut off frequencys.I am not describing a cavity. It's an open ended tapered waveguide and the radius "IS" dependent on the z coordinate. Can you provide a better way to derive the propagation vector k_{z} for a tapered waveguide than to parameterize the radius in terms of z? The radius is a variable in this waveguide, as is the transverse resonant frequency. Both are dependent on the location along the z axis of the waveguide. It is not "erroneous", it is precisely what makes the tapered waveguide different from a straight one.EDIT: You said in a previous post, Quote from: Ricvil"...The conical geometry of cavity can produce a gradient intensity of the fields inside it, and resulting on a axial non symmetric scattering of axions (produced by the stationary wave of hybrid modes), and thus the thrust is formed....". Are you saying that you believe the conical geometry can produce a gradient thrust only with axions but not with transverse, resonant EM standing waves? The equation I derived is exactly that, the gradient in the potential energy stored in the transverse standing wave as it travels down the waveguide. How else would you do it than to parameterize the potential energy wrt z?Todd

Quote from: Ricvil on 07/05/2015 08:54 pmYour first equation ( the definition of the wave vector K), is wrong.It establishes a erroneous z dependence on K.The K will depend at most on total geometry( including the dimensions of cavity), medium constitutive relations (mu and epslon), and boundary conditions, which defines de modes inside the sctruture, and thus the modes cut off frequencys.I am not describing a cavity. It's an open ended tapered waveguide and the radius "IS" dependent on the z coordinate. Can you provide a better way to derive the propagation vector k_{z} for a tapered waveguide than to parameterize the radius in terms of z? The radius is a variable in this waveguide, as is the transverse resonant frequency. Both are dependent on the location along the z axis of the waveguide. It is not "erroneous", it is precisely what makes the tapered waveguide different from a straight one.EDIT: You said in a previous post, Quote from: Ricvil"...The conical geometry of cavity can produce a gradient intensity of the fields inside it, and resulting on a axial non symmetric scattering of axions (produced by the stationary wave of hybrid modes), and thus the thrust is formed....". Are you saying that you believe the conical geometry can produce a gradient thrust only with axions but not with transverse, resonant EM standing waves? The equation I derived is exactly that, the gradient in the potential energy stored in the transverse standing wave as it travels down the waveguide. How else would you do it than to parameterize the potential energy wrt z?Todd

Your first equation ( the definition of the wave vector K), is wrong.It establishes a erroneous z dependence on K.The K will depend at most on total geometry( including the dimensions of cavity), medium constitutive relations (mu and epslon), and boundary conditions, which defines de modes inside the sctruture, and thus the modes cut off frequencys.

"...The conical geometry of cavity can produce a gradient intensity of the fields inside it, and resulting on a axial non symmetric scattering of axions (produced by the stationary wave of hybrid modes), and thus the thrust is formed....".

Quote from: SeeShells on 07/06/2015 12:45 ammeep images.https://drive.google.com/folderview?id=0B1XizxEfB23tfkF0Z184NHRtd0ViN28tNzRDY3JzSVc0WFBTOGZmSFZMcUpWLWJfcDRfZEU&usp=sharingIf you want 3d rendered version of these, let me know which...I am using a graphic ray-tracing program (www.povray.org) and have it coded and parameterized, so I can generate the 3d stuff pretty quickly...

meep images.https://drive.google.com/folderview?id=0B1XizxEfB23tfkF0Z184NHRtd0ViN28tNzRDY3JzSVc0WFBTOGZmSFZMcUpWLWJfcDRfZEU&usp=sharing

Quote from: aero on 07/05/2015 10:29 pmDr. Rodal,The yz slices along the cavity axis are up. Same top level csv file. Read and understand the description, I won't try to explain my naming convention until/unless more or different information is needed. Ask.I did not see a text file with a description.The files are labeled as follows in this example:exx-s03-m26e= Electric Field (h for magnetizing field)xx= x component in the plane with normal x (where x is the Cartesian axis oriented along the longitudinal axis of axisymmetry of the cone)s03=time step 03m = does this mean "metal model" ? (and if so, "p" stands for copper model ?)26 = this must be an identifier of the x position, if so I don't understand why the number 26 instead of 150 though

Dr. Rodal,The yz slices along the cavity axis are up. Same top level csv file. Read and understand the description, I won't try to explain my naming convention until/unless more or different information is needed. Ask.

...Over on the right margin there is a text entry labelled "Description" in my views of Google drive. Is that not shared?

Quote from: TheTraveller on 07/05/2015 08:25 amFollowing discussions with Roger Shawyer, I now understand why using a scale to measure EMDrive Force generation is a waste of time.Hey Traveller,When I asked about this back in May, you replied that Shawyer has "placed them directly on scales, hung them from springs above scales, used balance beams with scales, plus he used a rotary air bearing system to show true acceleration." Are you now saying that Shawyer does not believe that his scales based experiments returned useful results, or are you saying that they were more complicated then they appeared, and were not simply a shielded drive sitting on a scale?~Kirk

Following discussions with Roger Shawyer, I now understand why using a scale to measure EMDrive Force generation is a waste of time.

Quote from: Rodal on 07/05/2015 11:26 pmQuote from: aero on 07/05/2015 10:29 pmDr. Rodal,The yz slices along the cavity axis are up. Same top level csv file. Read and understand the description, I won't try to explain my naming convention until/unless more or different information is needed. Ask.I did not see a text file with a description.The files are labeled as follows in this example:exx-s03-m26e= Electric Field (h for magnetizing field)xx= x component in the plane with normal x (where x is the Cartesian axis oriented along the longitudinal axis of axisymmetry of the cone)s03=time step 03m = does this mean "metal model" ? (and if so, "p" stands for copper model ?)26 = this must be an identifier of the x position, if so I don't understand why the number 26 instead of 150 thoughOver on the right margin there is a text entry labelled "Description" in my views of Google drive. Is that not shared?The dash - looks like a minus sign, and I use dashes in the file name. So instead of a dash to negate, I used m, and instead of a + I used p. p and m stand-in for + and -.They are labelled 85, 26, -26 and -85 because I'm using the slice number which is based on zero at the center of the cavity. The csv line numbers aren't meaningful to h5tocsv. Maybe I could do it differently so that they were, but I didn't. So to get the csv file line number, move the origin from the center 0 to one end or the other and calculate the line number. But that is why I did both positive and negative data slices, so I'd have the right data slice no matter which way you moved to your line numbers. Either add 123 or subtract 123 to get csv file line numbers. I find it very confusing.Added - So you need to see at least one time slice including ey, ez and hy, hz. Well, I'll do that but after you let me know that you understand my file naming code. Do neither of us any good to have data that you can't associate with a place in the cavity.

http://www.microwaves101.com/encyclopedias/waveguide-mathematics#velocityInside a waveguide, the wave travels at group velocity and not at phase velocity which would be faster than c.Shawyer is correct to model end plate forces based on end plate group velocity, which is related to guide wavelength as per the attached.Any text on waveguides will tell you the energy in the waveguide propogates down the waveguide at group velocity speed.

Quote from: Ricvil on 07/06/2015 01:35 amhttp://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.htmlThe equations for the em fields of a tampered conical waveguide can be founded above.The expressions for the cavity( for more simple modes) are founded after matching boundaring conditons at the taps.The geometry is matched by spherical coordinates, so the fields are spherical coordinate dependent too, an this facilitate match the boundary conditions by aproximation ( the taps are not spherical but planes in real cavity).But the point is, the fields are expressed by coordinates functions, but the the wave vectors not. In fact the wave vectors are "the coordinates" the modes of propagation, where the modes are a base to span the function space of em fields inside the guide/cavity.1- So Todd is not modeling a cavity, just a waveguide? Ok Egan has modeled both ( traveling waves - Rplus and Rminus) and standing waves resulting from reflections on the taps ( boundary conditons forced at the taps)2- Yes, they are time harmonic solutions ( Frequency Domain) , but with they are the base to construct the called green-function, wich models any excitation inside waveguide/cavity. For a transient analysis, Time domain solutions are better to see transient responses.3-Egan has used m=0 modes to simplify the expressions, but a numerical search on boundary conditions will produce all possibles modes.4- DC solution on a Faraday cage? 5-Any RF feed can be modeled by a superposition of em modes. The modes are like base vectors on function space. Any function inside waveguide/cavity can be modeled by a mode superposition ( like a Fourier analysis). If no individual mode produce a net force, then a summ of them will not produce anything at all.6- No. RF feeds are just superposition of modes, and stand waves are just two counter propagating modes.7- Yes, closed-form solutions of this geometry would come from closed expressions for the bessel functions zeros and associated legendre polinomials. Anyone has this expressions? No? Then numeric solution is the only way.8,9,10- And you believes Todd has found closed expression of the field of a pyramidal waveguide on a very simple form? Matching the boundary conditions of the em fields at the tappered rectangular geometry? And the expressions are that with wave vectors varying with z coordinate?Ok. Quote from: WarpTech on 07/05/2015 09:14 pmQuote from: Ricvil on 07/05/2015 08:54 pmYour first equation ( the definition of the wave vector K), is wrong.It establishes a erroneous z dependence on K.The K will depend at most on total geometry( including the dimensions of cavity), medium constitutive relations (mu and epslon), and boundary conditions, which defines de modes inside the sctruture, and thus the modes cut off frequencys.I am not describing a cavity. It's an open ended tapered waveguide and the radius "IS" dependent on the z coordinate. Can you provide a better way to derive the propagation vector k_{z} for a tapered waveguide than to parameterize the radius in terms of z? The radius is a variable in this waveguide, as is the transverse resonant frequency. Both are dependent on the location along the z axis of the waveguide. It is not "erroneous", it is precisely what makes the tapered waveguide different from a straight one.EDIT: You said in a previous post, Quote from: Ricvil"...The conical geometry of cavity can produce a gradient intensity of the fields inside it, and resulting on a axial non symmetric scattering of axions (produced by the stationary wave of hybrid modes), and thus the thrust is formed....". Are you saying that you believe the conical geometry can produce a gradient thrust only with axions but not with transverse, resonant EM standing waves? The equation I derived is exactly that, the gradient in the potential energy stored in the transverse standing wave as it travels down the waveguide. How else would you do it than to parameterize the potential energy wrt z?Todd1) Those equations from Greg Egan only model standing waves frozen in place in the cavity. This is not what Todd is modeling.2) Those equations from Greg Egan assume ab initio a sinusoidal fluctuation with time of the electromagnetic field.3) Egan only gives the solutions for the m=0 mode that is constant in the azimuthal direction. It is inapplicable to higher order modes, for example TM212 used by NASA Eagleworks or the TM114 mode in the RFMWGUY recently modeled with Aero.4) Egan also ignores the DC solution.5) Egan does not take into account the RF feed at all. All EM Drive experiments have been conducted with the RF feed ON. With the RF feed off there is no measured force.6) Egans' conclusion regarding the Poynting vector is only applicable for the restricted case he considers: standing waves and no RF feed on in the cavity.7) The geometry analyzed by Egan does not lead to a closed-form solution: Egan has to solve two eigenvalue problems numerically: one in terms of Associated Legendre Functions and another eigenvalue problem in terms of Spherical Bessel Functions. Egan was not the first to solve the spherical truncated cone this way. It was first done by Schelkunoff prior to the end of WWII. In order to avoid the drastic assumptions made by Egan (that lead to no thrust whatsoever, since Egan only considers standing waves), Todd simplifies the geometry to a more amenable one that is subject to a mathematical closed-form solution (otherwise the eigenvalue problem would need to be solved numerically).9) Instead of modeling a truncated cone as done by Egan, Todd is modeling a truncated square pyramid in order to arrive at an amenable closed-form solution.10) I have not had the time to check Todd's solution, but it looks like he is taking a similar approach as Dr.Nososureofit, who in previous threads described the alternate formalism of considering the x dependence of the wavenumber k, see: http://emdrive.wiki/@notsosureofit_Hypothesisfor more details.

http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.htmlThe equations for the em fields of a tampered conical waveguide can be founded above.The expressions for the cavity( for more simple modes) are founded after matching boundaring conditons at the taps.The geometry is matched by spherical coordinates, so the fields are spherical coordinate dependent too, an this facilitate match the boundary conditions by aproximation ( the taps are not spherical but planes in real cavity).But the point is, the fields are expressed by coordinates functions, but the the wave vectors not. In fact the wave vectors are "the coordinates" the modes of propagation, where the modes are a base to span the function space of em fields inside the guide/cavity.1- So Todd is not modeling a cavity, just a waveguide? Ok Egan has modeled both ( traveling waves - Rplus and Rminus) and standing waves resulting from reflections on the taps ( boundary conditons forced at the taps)2- Yes, they are time harmonic solutions ( Frequency Domain) , but with they are the base to construct the called green-function, wich models any excitation inside waveguide/cavity. For a transient analysis, Time domain solutions are better to see transient responses.3-Egan has used m=0 modes to simplify the expressions, but a numerical search on boundary conditions will produce all possibles modes.4- DC solution on a Faraday cage? 5-Any RF feed can be modeled by a superposition of em modes. The modes are like base vectors on function space. Any function inside waveguide/cavity can be modeled by a mode superposition ( like a Fourier analysis). If no individual mode produce a net force, then a summ of them will not produce anything at all.6- No. RF feeds are just superposition of modes, and stand waves are just two counter propagating modes.7- Yes, closed-form solutions of this geometry would come from closed expressions for the bessel functions zeros and associated legendre polinomials. Anyone has this expressions? No? Then numeric solution is the only way.8,9,10- And you believes Todd has found closed expression of the field of a pyramidal waveguide on a very simple form? Matching the boundary conditions of the em fields at the tappered rectangular geometry? And the expressions are that with wave vectors varying with z coordinate?Ok. Quote from: WarpTech on 07/05/2015 09:14 pmQuote from: Ricvil on 07/05/2015 08:54 pmYour first equation ( the definition of the wave vector K), is wrong.It establishes a erroneous z dependence on K.The K will depend at most on total geometry( including the dimensions of cavity), medium constitutive relations (mu and epslon), and boundary conditions, which defines de modes inside the sctruture, and thus the modes cut off frequencys.I am not describing a cavity. It's an open ended tapered waveguide and the radius "IS" dependent on the z coordinate. Can you provide a better way to derive the propagation vector k_{z} for a tapered waveguide than to parameterize the radius in terms of z? The radius is a variable in this waveguide, as is the transverse resonant frequency. Both are dependent on the location along the z axis of the waveguide. It is not "erroneous", it is precisely what makes the tapered waveguide different from a straight one.EDIT: You said in a previous post, Quote from: Ricvil"...The conical geometry of cavity can produce a gradient intensity of the fields inside it, and resulting on a axial non symmetric scattering of axions (produced by the stationary wave of hybrid modes), and thus the thrust is formed....". Are you saying that you believe the conical geometry can produce a gradient thrust only with axions but not with transverse, resonant EM standing waves? The equation I derived is exactly that, the gradient in the potential energy stored in the transverse standing wave as it travels down the waveguide. How else would you do it than to parameterize the potential energy wrt z?Todd

Quote from: TheTraveller on 07/05/2015 04:14 amhttp://www.microwaves101.com/encyclopedias/waveguide-mathematics#velocityInside a waveguide, the wave travels at group velocity and not at phase velocity which would be faster than c.Shawyer is correct to model end plate forces based on end plate group velocity, which is related to guide wavelength as per the attached.Any text on waveguides will tell you the energy in the waveguide propogates down the waveguide at group velocity speed.Interesting fact that I have pointed out before: guide wavelength increases as cutoff dimensions approach operating frequency, however guide wavelength decreases when entering a dielectric (or higher permeability material). The effect of practical dielectrics are so strong that they override the effect of tapering for most designs. This could possibly cause a reversal of force direction depending on if the force depends on group velocity or guide wavelength.

Quote from: Ricvil on 07/06/2015 01:35 amhttp://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.htmlThe equations for the em fields of a tampered conical waveguide can be founded above.The expressions for the cavity( for more simple modes) are founded after matching boundaring conditons at the taps.The geometry is matched by spherical coordinates, so the fields are spherical coordinate dependent too, an this facilitate match the boundary conditions by aproximation ( the taps are not spherical but planes in real cavity).But the point is, the fields are expressed by coordinates functions, but the the wave vectors not. In fact the wave vectors are "the coordinates" the modes of propagation, where the modes are a base to span the function space of em fields inside the guide/cavity.Quote from: WarpTech on 07/05/2015 09:14 pmI am not describing a cavity. It's an open ended tapered waveguide and...1) Those equations from Greg Egan only model standing waves frozen in place in the cavity. This is not what Todd is modeling.2) Those equations from Greg Egan assume ab initio a sinusoidal fluctuation with time of the electromagnetic field.3) Egan only gives the solutions for the m=0 mode that is constant in the azimuthal direction. It is inapplicable to higher order modes, for example TM212 used by NASA Eagleworks or the TM114 mode in the RFMWGUY recently modeled with Aero.4) Egan also ignores the DC solution.5) Egan does not take into account the RF feed at all. All EM Drive experiments have been conducted with the RF feed ON. With the RF feed off there is no measured force.6) Egans' conclusion regarding the Poynting vector is only applicable for the restricted case he considers: standing waves and no RF feed on in the cavity.7) The geometry analyzed by Egan does not lead to a closed-form solution: Egan has to solve two eigenvalue problems numerically: one in terms of Associated Legendre Functions and another eigenvalue problem in terms of Spherical Bessel Functions. Egan was not the first to solve the spherical truncated cone this way. It was first done by Schelkunoff prior to the end of WWII. In order to avoid the drastic assumptions made by Egan (that lead to no thrust whatsoever, since Egan only considers standing waves), Todd simplifies the geometry to a more amenable one that is subject to a mathematical closed-form solution (otherwise the eigenvalue problem would need to be solved numerically).9) Instead of modeling a truncated cone as done by Egan, Todd is modeling a truncated square pyramid <snip> in order to arrive at an amenable closed-form solution.10) I have not had the time to check Todd's solution, but it looks like he is taking a similar approach as Dr.Nososureofit, who in previous threads described the alternate formalism of considering the x dependence of the wavenumber k, see: http://emdrive.wiki/@notsosureofit_Hypothesisfor more details. Dr. N. describes this as follows:<<Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency>>

http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.htmlThe equations for the em fields of a tampered conical waveguide can be founded above.The expressions for the cavity( for more simple modes) are founded after matching boundaring conditons at the taps.The geometry is matched by spherical coordinates, so the fields are spherical coordinate dependent too, an this facilitate match the boundary conditions by aproximation ( the taps are not spherical but planes in real cavity).But the point is, the fields are expressed by coordinates functions, but the the wave vectors not. In fact the wave vectors are "the coordinates" the modes of propagation, where the modes are a base to span the function space of em fields inside the guide/cavity.

I am not describing a cavity. It's an open ended tapered waveguide and...

...Thank you Jose. The equations I posted yesterday, http://forum.nasaspaceflight.com/index.php?topic=37642.msg1400288#msg1400288, are for a tapered circular waveguide with open ends. It is not a truncated pyramid because, the z-dependence (axial coordinate) is identical, regardless if I parameterize a circle, a square or a rectangle. The gradient due to the taper is the same, and the traveling wave in the z-direction is not a standing wave in a cavity.You are correct, I am trying to simplify the problem to demonstrate that the thrust of a photon rocket is not simply F=P/c. My result is very close to what @Notsosureofit has in his proposal, with more detail. I have no reason or desire to solve the eigenvalue problem for a closed truncated frustum cavity. It is not necessary or pertinent to the rocket equation I've provided.Todd

...4- DC solution on a Faraday cage? ...

I am a bit affraid about this but I don't think it will be too easy to figure out. I disclosed it and discussed it with a doctor of physics specialised in quantum. He said "I still don't belive it works but I saw it".I am interested in your thoughts about commercial application. Obviously, Shawyer has a few Patents... But there is a just a handfull of investors who could develop this into commercial tehnology.