-
#820 by Notsosureofit on 18 Feb, 2015 20:03
-
@ RODAL
(Almost) anything is possible if I get the time
Can you generate a dispersion relation from the exact solution ?
This work done whenever I take a break from $$$ paying work
It continues to snow over here
Same here, and snowing again. -
#821 by Mulletron on 18 Feb, 2015 20:09
-
At 16:30 the dispersion relation is focused on building on the last several minutes.
It should be able to be adapted to a cone using the same methodology.
Probably need to break out a straight edge and graph paper. -
#822 by Rodal on 18 Feb, 2015 21:13
-
@ RODAL
@NotSoSureOfIt
Can you generate a dispersion relation from the exact solution ?
I think that the relation between the wavenumber k and the angular frequency omega is perfectly linear for a truncated cone homogeneously filled with a medium having constant, isotropic, electric permittivity and constant magnetic permeability. It follows from the homogeneous electromagnetic wave equation, which for the truncated cone is solved in spherical coordinates via spherical waves (this involves an assumption of spherical ends, instead of flat ends).
Is your question what is the effective dispersion relation for a truncated cavity containing a dielectric (with constant properties) filling only a portion of the truncated cone?
Or is your question what is the dispersion relation for a truncated cavity containing a dielectric with nonlinear properties? Or anisotropic properties?
Or am I wrong, or missing something, ...
-
#823 by Notsosureofit on 18 Feb, 2015 23:11
-
@ RODAL
@NotSoSureOfIt
Can you generate a dispersion relation from the exact solution ?
I think that the relation between the wavenumber k and the angular frequency omega is perfectly linear for a truncated cone homogeneously filled with a medium having constant, isotropic, electric permittivity and constant magnetic permeability. It follows from the homogeneous electromagnetic wave equation, which for the truncated cone is solved in spherical coordinates via spherical waves (this involves an assumption of spherical ends, instead of flat ends).
Is your question what is the effective dispersion relation for a truncated cavity containing a dielectric (with constant properties) filling only a portion of the truncated cone?
Or is your question what is the dispersion relation for a truncated cavity containing a dielectric with nonlinear properties? Or anisotropic properties?
Or am I wrong, or missing something, ...
I was just thinking of the simplest case but based on your exact solution, rather than using that of the cylindrical cavity evaluated at both ends, which is what I have been using. The radii of both ends would presumably be already present in the single (presumably quadratic ?) expression. -
#824 by Rodal on 19 Feb, 2015 00:05
-
@ RODAL
@NotSoSureOfIt
Can you generate a dispersion relation from the exact solution ?
I think that the relation between the wavenumber k and the angular frequency omega is perfectly linear for a truncated cone homogeneously filled with a medium having constant, isotropic, electric permittivity and constant magnetic permeability. It follows from the homogeneous electromagnetic wave equation, which for the truncated cone is solved in spherical coordinates via spherical waves (this involves an assumption of spherical ends, instead of flat ends).
Is your question what is the effective dispersion relation for a truncated cavity containing a dielectric (with constant properties) filling only a portion of the truncated cone?
Or is your question what is the dispersion relation for a truncated cavity containing a dielectric with nonlinear properties? Or anisotropic properties?
Or am I wrong, or missing something, ...
I was just thinking of the simplest case but based on your exact solution, rather than using that of the cylindrical cavity evaluated at both ends, which is what I have been using. The radii of both ends would presumably be already present in the single (presumably quadratic ?) expression.
1) The resonant cylindrical cavity is solved in terms of its natural coordinates: a cylindrical coordinate system rho(radius), phi(angle) and z (longitudinal coordinate).
1a) The resonant cylindrical cavity (with a single medium inside it) has a linear dispersion relationship between frequency and wavenumber
2a) the eigenvalue problem has a closed form solution (http://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity) expressing the frequency in terms of the SquareRoot of the sum of the square of the zero Bessel function m.n (Xm,n and X'm,n are the eigenvalues ) divided by the Radius of the cylinder plus the Square of the longitudinal quantum number "p" divided by the cylinder's Length
3a) the only issue with the closed form solution (http://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity) is a side equation necessary to satisfy cut-off of mode shapes that cannot take place in the cylindrical cavity ( http://en.wikipedia.org/wiki/Cutoff_frequency#Waveguides )
2) The resonant truncated cone cavity is solved in terms of its natural coordinates: a spherical coordinate system r(radius), theta (polar angle), and phi(azimuthal angle). Please note that the radial coordinate "r" is entirely different in the spherical coordinate system than the radius "rho" in the cylindrical system. In the spherical system the radius "r" defines the length of the walls of the truncated cone.
2a) The resonant truncated cone cavity (with a single medium inside it) has a linear dispersion relationship between frequency and wavenumber
2b) There are two eigenvalue problems to solve in the truncated cone: one eigenvalue problem deals with the spherical angle theta (polar angle) and another eigenvalue problem deals with the spherical radius "r". Neither of these two eigenvalue problems has a closed-form solution. Hence the frequency for the truncated cone cannot be expressed as a closed-form solution (using classical functions). The two eigenvalue problems need to be solved numerically. . There is an exact solution, but it is not closed-form.
3c) while in the cylindrical cavity, the radius (or the diameter) of the cylindrical cavity appears, in the truncated cone this is not the case. In the truncated cone the
cylindrical coordinate radius "rho1" of the small base of the cone = r1*Sin[thetaw]
and the
cylindrical coordinate radius "rho2" of the big base of the cone = r2*Sin[thetaw],
where thetaw is the cone-half-angle and r1 is the radial distance from the origin of the spherical coordinate system to the small base and r2 is the radial distance from the origin of the spherical coordinate system to the big base. The cone-half-angle appears in the eigenvalue problem for the polar angle theta and the radial distances r1 and r2 appear in the eigenvalue problem for the spherical radius r. Therefore the big and small diameter do not appear explicitly in the truncated cone solution. Instead the truncated cone solution parameters are the cone-half-angle thetaw and the spherical radii r1 and r2. And there is no closed-form solution: the frequency is the result of the numerical solution of two eigenvalue problems (which can be solved with numerical root finding procedures).
3d) The first eigenvalue problem contains Legendre functions (http://en.wikipedia.org/wiki/Legendre_function) of the Cosine of the cone-half angle.
3e) The second eigenvalue problem contains Spherical Bessel functions (http://mathworld.wolfram.com/SphericalBesselFunctionoftheFirstKind.html) in terms of the wavenumber K and the spherical radius.
3f) No cut-off auxiliary equation is necessary for the solution of the truncated cone problem. Purely evanescent modes get cut-off automatically when solving the eigenvalue problem if one is seeking real solutions. There are also interesting degenerate modes in the truncated cone which are resonant within a portion of the cavity and evanescent on another portion of the cavity.
-
#825 by Notsosureofit on 19 Feb, 2015 00:32
-
Mmmm...I see the problem.
-
#826 by Rodal on 19 Feb, 2015 00:42
-
Mmmm...I see the problem.
One could construct a table of eigenvalues (as done for the cylindrical cavity for Xm,n and X'm,n) in terms of discrete values of the spherical polar angle theta at the walls of the cone (Boundary Conditions thetaw the half-angle of the cone), and some papers for conical waveguides (as in radar) have done this. This is of limited usefulness because it is only useful if one's truncated cone half-angle is in the table (otherwise one has to interpolate), and that solves only the first eigenvalue problem, but for a resonant cavity you still need to solve the second eigenvalue problem for spherical Bessel functions to get the frequency. It would be unwieldy to build a table of eigenvalues for the second eigenvalue problem of the truncated cone in terms of the wavenumber k and the spherical radius r with boundary conditions at r1 and r2.
And notice that the table of eigenvalues would not be in terms of diameters or radii of the bases of the truncated cone. -
#827 by Notsosureofit on 19 Feb, 2015 02:15
-
Might need to rethink this approach if the goal is to find the optimum thrust cavity configuration rather than an analytic solution for this particular cavity.
-
#828 by Star-Drive on 19 Feb, 2015 03:39
-
Folks:
While you all talk about various ways to accomplish the E&M simulations of these frustum cavities, I thought you might like to take a look at the COMSOL derived resonances of the Eagleworks Lab's copper frustum resonant cavity driven with a ~16mm OD loop antenna located 15% up the side wall of the frustum from the large OD end of the cavity.
BTW, the EMPower amplifiers were delivered to the Lab yesterday and I'll be calibrating the power metering for one that was installed yesterday on the torque pendulum.
Best, Paul M,
Thank you, Paul, for posting this, the attached pdf with COMSOL plots (which I first missed, my bad, thanks to Mulletron for pointing it out to me ) is very useful for all of us (those like me working on the exact solution of the frustum, and those working with numerical methods like MEEP, COMSOL, ANSYS-multiphysics, etc.).
I could not find in the pdf attached to your post, or in your post. language to indicate whether the COMSOL calculations in the attachment (http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=796287) include or do not include a dielectric inside the truncated cone (frustum). My impression is that these COMSOL calculations do not include the dielectric inside the truncated cone (this impression is based on the frequency calculated for TE012).
Still a clarification for some readers like me, may be useful (to those to whom what I write below is obvious, please forgive me for taking your time):
1) Clarification: the jpg image you posted are not "COMSOL derived resonances of the Eagleworks Lab's copper frustum resonant cavity", the COMSOL plots are in the pdf attached to your post (http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=796287)
2) The mode shapes in the slide are for a different geometry: a circular waveguide (instead of a truncated cone/frustum like NASA's EM Drive) , that had been plotted in published journals since 1936, without using a digital computer. The actual reference's date is 1985 (instead of 1966): http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1132998. Since COMSOL was started in 1986, Lee, Lee and Chuang did not use COMSOL: they had no need to use a finite element program, because an exact solution exists for what they plotted: the mode shapes of a circular waveguide.
The circular waveguide exact solution is present in the 1943 textbook by Schelkunoff, and in papers he published in the 1930's. The mode shapes look identical to the plots that Schelkunoff published in the 1930's without the benefit of a digital computer: http://forum.nasaspaceflight.com/index.php?topic=36313.msg1332981#msg1332981. The article by Lee, Lee and Chuang states: "The earliest plots of modal field distribution in rectangular/circular waveguides were given by Southworth (1936), Barrow (1936), Schelkunoff (1937), and Chu and Barrow (1937)"
3) The solution for a truncated cone (the geometry of the NASA frustum, and the geometry analyzed by COMSOL in the attached pdf) is different from the solution for a circular waveguide in several respects: the natural frequencies are quite different, and while in a circular waveguide different mode shapes are either resonant or cutoff, in a truncated cone some mode shapes are resonant, some are evanescent and some have a transition from resonant to evanescent (a characteristic not present in circular waveguides). Also, the attenuation and focusing aspects of the truncated cone (frustum) are not present in the circular waveguide.
Dr. Rodal:
Sorry I wasn't more explicit with my commentary this morning, but I plead not enough coffee! But to answer your first and second questions, the circular waveguide picture was supplied just as a marker from where we started from, that led us to the conclusion that we would have to model the E&M resonances in the copper frustum in the best manner possible before going forward with our testing. I was NOT trying to imply that COMSOL was used to generate this circular waveguide modes table and the source given was where I found it.
That said the NASA/JSC/EP group where we work had one COMSOL license seat that had to be shared amongst all the engineers who had a need for its analytical capabilities. We were also lucky enough to have one EP5 electrical engineer, Frank Davies, from Rice University who had taken an interest into what Sonny and I were doing in the Eagleworks Lab because his office mate also had a deep interest in the topic. And as it turned out Frank also knew how to work COMSOL for his battery research work that he does for his day job at NASA/JSC. Where this interest led is demonstrated in Frank's COMSOL summary report I posted this morning. And yes this COMSOL analysis was for the copper frustum without any dielectric discs in in it.
For question 3, I agree with you on all counts, but you have to remember that we were a bunch of electrical and aerospace engineers that only vaguely remembered their E&M from 20 to 40 years ago so we had to learn or relearn a lot of E&M basics before getting around to nit picking the details you are worried about.
Best, Paul
-
#829 by Mulletron on 19 Feb, 2015 06:13
-
Well this is a gut check moment and there is no doubt this post will be controversial and might get me in trouble for being off topic and for the subject matter. I am being serious here. I'm no dummy. Either we didn't figure out jack or we actually did. It seems very likely that we did. If we did, we weren't the first.
We all know how the world works. If a bunch of guys on an internet forum can figure out the basic principles of "q-thrusters".... someone else has already perfected them and kept them black; rightfully so. The cat is now out of the bag gentlemen. We want to explore space. I want to see human space missions to the planets. We all do. Please give what you have to the world.
This isn't tin foil hat wearing nonsense. NOT UFO conspiracy theory bs. It is no different than this:
http://www.aviationweek.com/technology/skunk-works-reveals-compact-fusion-reactor-details
http://en.wikipedia.org/wiki/Skunk_Works
#giveusthegoods
Sorry moderators. This won't happen again. I don't want the thread to devolve into this kind of discussion. I am pointing out the obvious. I'll delete the post if asked to do so. -
#830 by JPLeRouzic on 19 Feb, 2015 07:35
-
Symetry violations are hot topics in physic since decades.Strong H field at dielectric disc. Just like theory suggests.
Wow. Those are quite remarkable papers. It seems like a very likely cause for the thrust, with previous published results availing it.
I wonder why the research wasn't pursued to its logical conclusion (a thruster). Maybe the researchers didn't believe they could get usable forces?
For example for someone who don't attempt to detect electrons, Wu's experiment may looks like some kind of propellantless drive, but actually it isn't: http://en.wikipedia.org/wiki/Wu_experiment
Maybe EMDrive is some weird version of Wu's device, but as I wrote nearly one year ago, there are many possible explanations and one man life is not enough to try all of them. It's much more efficient to carefully select and focus on problems that would help us create new knowledge and to build controlled experimentations based on what we already know. That the way science is done since centuries. One step at a time.
-
#831 by Star One on 19 Feb, 2015 11:39
-
Well this is a gut check moment and there is no doubt this post will be controversial and might get me in trouble for being off topic and for the subject matter. I am being serious here. I'm no dummy. Either we didn't figure out jack or we actually did. It seems very likely that we did. If we did, we weren't the first.
We all know how the world works. If a bunch of guys on an internet forum can figure out the basic principles of "q-thrusters".... someone else has already perfected them and kept them black; rightfully so. The cat is now out of the bag gentlemen. We want to explore space. I want to see human space missions to the planets. We all do. Please give what you have to the world.
This isn't tin foil hat wearing nonsense. NOT UFO conspiracy theory bs. It is no different than this:
http://www.aviationweek.com/technology/skunk-works-reveals-compact-fusion-reactor-details
http://en.wikipedia.org/wiki/Skunk_Works
#giveusthegoods
Sorry moderators. This won't happen again. I don't want the thread to devolve into this kind of discussion. I am pointing out the obvious. I'll delete the post if asked to do so.
All I'll say is if it wasn't meant to be discussed publicly it wouldn't be, the fact that is, is your answer and that's the end of that OT post by me. Sorry for going off track. -
#832 by Notsosureofit on 19 Feb, 2015 11:59
-
FYI
https://www.dropbox.com/s/xiw9mq7dawhp00c/other1.jpg?dl=0
What I would really like to do is stack these 2 puppies on the left into a single vertical chamber and try the Cavandish type experiment under battery power w/ a solid-state oscillator.
OK, couldn't get the pic to post but the link works ... so that would be my retirement plan (fat chance) -
#833 by Rodal on 19 Feb, 2015 12:16
-
FYI
https://www.dropbox.com/s/xiw9mq7dawhp00c/other1.jpg?dl=0
What I would really like to do is stack these 2 puppies on the left into a single vertical chamber and try the Cavandish type experiment under battery power w/ a solid-state oscillator.
OK, couldn't get the pic to post but the link works ... so that would be my retirement plan (fat chance)
-
#834 by Notsosureofit on 19 Feb, 2015 13:25
-
?? can't get pics to post directly .. must be the Alzhiemers !
(Chris Edit: Hmmm, needs to be attached from your hard drive, as I tried correcting the link, but it doesn't like showing embedded via dropbox it seems). -
#835 by Notsosureofit on 19 Feb, 2015 13:31
-
A little less fantasy;
https://www.dropbox.com/s/cxfcrf822n0dpsa/IMAG0359.jpg?dl=0
I'm (slowly) collecting parts for an X-band miniature version in the cans shown in the middle of the picture.
Higher frequency and lower power. (we have a lot of experience w/ battery power in vacuum and/or plasma)
Anybody have a short taper section from X to something smaller ? -
#836 by Rodal on 19 Feb, 2015 13:40
-
A little less fantasy;
https://www.dropbox.com/s/cxfcrf822n0dpsa/IMAG0359.jpg?dl=0
I'm (slowly) collecting parts for an X-band miniature version in the cans shown in the middle of the picture.
Higher frequency and lower power. (we have a lot of experience w/ battery power in vacuum and/or plasma)
Anybody have a short taper section from X to something smaller ?
<<the frequency range of X band is rather indefinitely set at approximately 7.0 to 11.2 gigahertz (GHz). In radar engineering, the frequency range is specified by the IEEE at 8.0 to 12.0 GHz >>
For similar dimensions as present, that's going to result in high natural frequency mode shapes with lots of different mode shapes bunched up next to each other at nearby frequencies...
It will indeed have to be a smaller diameters, shorter section...
If you have a truncated cone geometry in mind, I can compute the frequencies and mode shapes from the exact solution to the truncated cone (I need: axial length, Big Diameter and Small Diameter) -
#837 by Notsosureofit on 19 Feb, 2015 13:58
-
Yes, oscillator called for, mode = unknown, F down by 1000, but more sensitive ??
The power heads are on X-band rectangular waveguide fittings, so a rectangular taper is what I was thinking as these are out there (EBay ?) -
#838 by Rodal on 19 Feb, 2015 14:01
-
?? can't get pics to post directly .. must be the Alzhiemers !
Only .jpg, .png, .gif etc. file formats can show. For example .bmp file extension does not post.
You have to insert the following: [img] before the link (no spacing allowed)
and you have to insert: [/img] at the end of the link (no spacing allowed)
For example:
[img]http://ep.yimg.com/ca/I/yhst-37994427369291_2241_23717082[/img]
will show this image
This can also be done by clicking on the InsertImage button right underneath the B (bold) button, if you prefer
Try it again like this, it's fun and informative
Or you can attach the image where it says "Attach" with a button saying "Choose File"
EDIT: Apparently the problem is with the way that Dropbox posts the image in a webpage: the dropbox link does not show like other links
-
#839 by Chris Bergin on 19 Feb, 2015 14:21
-
Firstly, I want to thank people on here for really focusing this thread, especially after the first thread had some problems. I can tell you it has the attention of some big hitters at NASA - who I've invited to post in this thread (at least one is already, but I'm not allowed to name him).
It has also been suggested we look at summarizing the progress made in this thread into a news article. Obviously, this is out of my comfort zone of things like current launch vehicles, but I'm going to sit down this weekend and read every single post in this thread.
Regardless, as I've always said, there's so many members here who would be able to write better articles than I, because they are well versed in the specific subject - which is half the battle. That is even more the case with this thread.
So, per the suggestion, I'm looking to crowd source members posting in this thread to look at being part of creating an article to cover this subject. I already have one offer to be part of that team and if you're interested in helping out, then please PM me and we'll set up a joint PM between all interested people as we go.....because probably setting up a thread (private or otherwise) to build it.
This is a 81,000 viewed thread, but that's over time and the news site article is where you can get that in a day. The benefit to all is it would get it into a much wider audience and likely bring in a lot more folk who may be able to help with the thread, by nature of the news site being interlinked with the forum.
