Author Topic: EM Drive Developments - related to space flight applications - Thread 3  (Read 1805529 times)

Offline lmbfan

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Like this?

(run-until 200 (synchronized-magnetic output-poynting output-tot-pwr))

I don't know for sure, I'm not at my home computer, so take the following with a grain of salt.  I can't find a reference to the "output-poynting" flag except on the "synchronizing" page, the reference page has "output-Xfield-p" to mean the poynting field, so I'd imagine:

(run-until 200 (synchronized-magnetic output-Xfield-p))

The "output-tot-pwr" is optional, it does not directly affect outputting the poynting field as far as I can tell.  It appears to be mentioned on that page because it also benefits from being synchronized.
« Last Edit: 07/03/2015 08:42 PM by lmbfan »

Offline VAXHeadroom

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Due to the planar nature of the dipole antenna effect, the Poynting vector field in the xy plane has significantly smaller amplitude than the one in the xz plane.  However, it in increasing with time, the amplitude at Time Step 13 clearly being much larger than at TS03 and TS08 (which are similarly located in the time cycle).
3D animation rendering, please stand by :)
I'm thinking I need to maybe switch the 'flat' and 'upright' images in the animation...  I swear the Poynting vectors look like they're rowing :)

« Last Edit: 07/03/2015 08:49 PM by VAXHeadroom »
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Offline aero

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Could you give us an example of the actual code showing the imposition of boundary conditions at a finite difference gridpoint on the conical wall?

Sure, here - https://github.com/stevengj/meep/blob/master/src/meep.hpp#L169-L172

Dr. Rodal, you are asking about the internals of Meep. I have no idea how to answer that.

In my understanding, wall thickness does not matter with perfect metal.  With copper, wall thickness and a PML box encompassing the drive would be needed.

deuteragenie - I think the first sentence is right. As for the second sentence, well, any fields that escape the cavity will bounce around in the computational lattice. But look at some of the .csv files. You can see that the energy outside the cavity is down by nearly 30 orders of magnitude compared to the energy inside the cavity. To me, that seems negligible.
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Offline Rodal

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Considering that Dr. Rodal's analysis shows only 3 slices of the frustum, what are the odds that there are some vectors in the field that are not show actually point the other way?  Is there some way to sum the entire Poynting field, including those not shown in the cross sectional views?  I notice that in Meep there is the option to output the Poynting vectors here:

 http://ab-initio.mit.edu/wiki/index.php/Meep_Reference#Output_functions

Notably this section:

Quote
output-Xfield-x, output-Xfield-y, output-Xfield-z, output-Xfield-r, output-Xfield-p Output the x, y, z, r, or φ component respectively, of the field X, where X is either h, b, e, d, or s for the magnetic, electric, displacement, or Poynting field, respectively. If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively. Note that for outputting the Poynting field, you might want to wrap the step function in synchronized-magnetic to compute it more accurately; see Synchronizing the magnetic and electric fields.

I wonder if there is a HDF5 reduction tool that can sum up fields in the file and reduce the entire field to one vector, or how complicated it would be to write such a tool.  Seems to me to be just adding up a bunch of numbers... which computers are rumored to be good at.
Nothing left to chance here.  In Cartesian coordinates three views should suffice, plus common knowledge of transverse electromagnetic variation with the azimuthal angle.  There are only two planes shown at azimuthal angles of 0 and 90 degrees, but the variation with azimuthal angle is shown in the base view and it is a conventional harmonic m=1, n=1 variation.

It is for higher modes, m>1 that what you are discussing would apply, not for m=1, n=1.

We know what the antenna looks like: it is a dipole antenna, the plane views are consistent with it.

To double check this all that is needed is to provide other circular cross-sections: I would favor one at the antenna location, another one close to it, within the same longitudinal wave-pattern, and another one in the next longitudinal wave pattern away from it towards the big base.

Concerning <<seems to me to be just adding up a bunch of numbers... which computers are rumored to be good at.>>, the csv files are available to the public, so anybody can perform their own postprocessing calculations based on the csv, all you have to do is to calculate  this can be done by anybody without using HDF5

Somebody sent me a Personal Message asking "How can you be sure that nothing is left to chance ?"

ANSWER: Because this is not a Monte Carlo analysis where statistical uncertainty is inherent in the model.  This is a Finite Difference analysis where Maxwell's equations are solved with a Finite Difference discretization scheme both in time and space.  As such we are solving Maxwell's equations.   The complication comes in through the RF antenna feed, but it is a dipole antenna with a simple geometry: we know what is the field variation produced by such an antenna.  We also know what the standing waves look like, because I have run the exact solution for this model (so the truncated cone geometry does not introduce uncertainty).  We know that the mode is m=1, n=1 and therefore we know the variation in the azimuthal direction.

These are the errors that can be present:

1) Human error. Human errors in @aero's modeling or human error in my postprocessing to compute the Poynting vector.  I have double-checked my solution.  The best way to further address this is through indepedent post-processing by others of the same csv files.

2) Finite Difference discretization errors:  time space FD discretization was recently addressed by aero by doubling the number of FD gridpoints.  This serves to analyze the FD discretization in space.  FD discretization in time can be addressed by halving the FD time step and marching to twice the number of time steps to arrive at the same time: compare the results

3) Not having reached steady state:  we could examine further marching for another 100 time steps for example.

4) As previously discussed to double check the results I advise to output other circular cross-sections closer to the antenna, to see whether the mode shape deviates from m=1, n=1 closer to the antenna.

Offline lmbfan

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I need more details on what boundary conditions you are imposing and exactly how are you imposing them at the nodes to understand the model.  I am NOT discussing the copper modeling.  I am interested in the boundary conditions you implement such that the transverse electric fields Ez, Ez, Ey are zero at a boundary and that the normal magnetizing field Hx, Hy and Hz is zero at a boundary as appropriate to each boundary.  In particular for the side conical walls.

Could you give us an example of the actual code showing the imposition of boundary conditions at a finite difference gridpoint on the conical wall?

The following page may be of interest to you:

http://ab-initio.mit.edu/wiki/index.php/Meep_Introduction#Finite-difference_time-domain_methods

Specifically the following (particularly the bolded sentences):

Quote
The illusion of continuity in Meep

Although FDTD inherently uses discretized space and time, as much as possible Meep attempts to maintain the illusion that you are using a continuous system. At the beginning of the simulation, you specify the spatial resolution, but from that point onwards you generally work in continuous coordinates in your chosen units (see units in Meep, above).

For example, you specify the dielectric function as a function ε(x) of continuous x, or as a set of solid objects like spheres, cylinders, etcetera, and Meep is responsible for figuring out how they are to be represented on a discrete grid. Or if you want to specify a point source, you simply specify the point x where you want the source to resideŚMeep will figure out the closest grid points to x and add currents to those points, weighted according to their distance from x. If you change x continously, the current in Meep will also change continuously (by changing the weights). If you ask for the flux through a certain rectangle, then Meep will linearly interpolate the field values from the grid onto that rectangle.

In general, the philosophy of the Meep interface is pervasive interpolation, so that if you change any input continously then the response of the Meep simulation will change continuously as well, and so that it will converge as rapidly and as smoothly as possible to the continuous solution as you increase the spatial resolution.

For example, the ε function used internally by Meep is not simply a discretely sampled version of the ε(x) specified by the user. Rather, each grid point is a kind of average of the ε in the surrounding pixel. Our subpixel average is specially designed in order to minimize the "staircasing" and other errors caused by sharp interfaces, and we believe it is a substantial improvement over past methods used for FDTD. See the paper by Farjadpour et al. in Citing Meep.

A quick look at Meep's source code does not reveal any obvious references to exactly how the "subpixel average" is computed (which is actually a subdivision of the finite difference grid, if I got the gist of the previous discussion).

If this isn't what you were asking about, please ignore.  I'm still learning all the jargon that goes along with this field.

Offline Rodal

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Due to the planar nature of the dipole antenna effect, the Poynting vector field in the xy plane has significantly smaller amplitude than the one in the xz plane.  However, it in increasing with time, the amplitude at Time Step 13 clearly being much larger than at TS03 and TS08 (which are similarly located in the time cycle).
3D animation rendering, please stand by :)
I'm thinking I need to maybe switch the 'flat' and 'upright' images in the animation...  I swear the Poynting vectors look like they're rowing :)



This is great !!!

Could you

1) look at this from an angle so that one has a better view of the horizontal plane?

2) Can you rotate it more so that one gets to see the circular cross-section better?

Or would it be too much to ask to get 3 separate movies for each plane separately?

Offline VAXHeadroom

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Due to the planar nature of the dipole antenna effect, the Poynting vector field in the xy plane has significantly smaller amplitude than the one in the xz plane.  However, it in increasing with time, the amplitude at Time Step 13 clearly being much larger than at TS03 and TS08 (which are similarly located in the time cycle).
3D animation rendering, please stand by :)
I'm thinking I need to maybe switch the 'flat' and 'upright' images in the animation...  I swear the Poynting vectors look like they're rowing :)



This is great !!!

Could you

1) look at this from an angle so that one has a better view of the horizontal plane?

2) Can you rotate it more so that one gets to see the circular cross-section better?

Or would it be too much to ask to get 3 separate movies for each plane separately?

Your wish is my command. *vanishes in a greasy puff of smoke*
Emory Stagmer
  Executive Producer, Public Speaker UnTied Music - www.untiedmusic.com

Offline deuteragenie

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Could you give us an example of the actual code showing the imposition of boundary conditions at a finite difference gridpoint on the conical wall?

Sure, here - https://github.com/stevengj/meep/blob/master/src/meep.hpp#L169-L172

Dr. Rodal, you are asking about the internals of Meep. I have no idea how to answer that.

In my understanding, wall thickness does not matter with perfect metal.  With copper, wall thickness and a PML box encompassing the drive would be needed.

deuteragenie - I think the first sentence is right. As for the second sentence, well, any fields that escape the cavity will bounce around in the computational lattice. But look at some of the .csv files. You can see that the energy outside the cavity is down by nearly 30 orders of magnitude compared to the energy inside the cavity. To me, that seems negligible.

If it helps: the below will output the Poynting vector and the total energy density. Tested locally. Works.

(run-until 200 (at-end synchronized-magnetic output-poynting output-tot-pwr) )

Offline aero

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Could you give us an example of the actual code showing the imposition of boundary conditions at a finite difference gridpoint on the conical wall?

Sure, here - https://github.com/stevengj/meep/blob/master/src/meep.hpp#L169-L172

Dr. Rodal, you are asking about the internals of Meep. I have no idea how to answer that.

In my understanding, wall thickness does not matter with perfect metal.  With copper, wall thickness and a PML box encompassing the drive would be needed.

deuteragenie - I think the first sentence is right. As for the second sentence, well, any fields that escape the cavity will bounce around in the computational lattice. But look at some of the .csv files. You can see that the energy outside the cavity is down by nearly 30 orders of magnitude compared to the energy inside the cavity. To me, that seems negligible.

I am asking about your model.

Let me put the question this different way:

You input a square grid for the cross-section.  The truncated cone circular cross-section is inside this square grid.

How did you let Meep know where the circular boundary gridpoints of the metal are located ?

How did you let Meep know where the copper is located ?

Is this what you want to see?
(define cavity (list
    (make cone (center 0 0 0) (radius bwmeep) (height hconemeep)
    (radius2 swmeep)
    (material (make medium (epsilon 1) (D-conductivity CU-D-conduct)))
    (axis axex axey axez) )   ; Use (axis 0 0 1) for end view.
    (make cone (center 0 0 0) (radius bwicmeep) (height hicconemeep)
    (radius2 swicmeep) (material air) (axis axex axey axez) )
)) ; end cavity

I start with the 3 internal numbers you have posted, 2 radii and height in inches, convert them to meters, add the simulated skin thickness (I use 1/4 inch copper because of cpu time and memory issues). I now have 6 numbers, 3 inside and 3 outside. I convert them to meep units and use them in the above concentric frustums, leaving copper skin with air inside.

As for where the copper falls within the computational lattice, you can see that in the csv files.
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Offline kitsuac

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inline direction stop_at_direction(ndim dim) {
  return (direction) (dim + 1 + 2 * (dim == D1));
}

I could bet dim never equals to D1 in practice; if that is the case the whole expression can be simplified and moved upstream.  But we should discuss this in a Meep forum, not here.

int num_direction(direction d) const {
    return num[((int) d) % 3];
  };

Maybe a candidate for optimization: is it using ivec ? Can the direction be made of a special form which guarantee that the modulo is always 0 or 1 ? or that mod can be optimized because of the special form of d (ie d is a Mersenne prime etc.)

See http://stackoverflow.com/questions/1697358/fast-modulo-3-or-division-algorithm?lq=1

idiv cycles: approx. 43
shift/add approach cycles: approx 30, so at first glance there is something to be won to optimize %3
 
Does it beat -O3 ?

Also, what is the value of direction for one run? Does it change or is it set once the .ctl file is loaded? If it is constant troughout a run, this can be simplified a lot of course.

I'm getting more sensible profiler results using ./configure CFLAGS="-pg -O3" CXXFLAGS="-pg -O3" which keeps inline routines in-tact. The top routine (step_curl_stride1) is a great candidate for SIMD optimization, but looking at the disassembly this is already being done by GCC via -O3's auto-vectorization. It could be improved with hand written assembler, but it wouldn't be enough to make a huge impact on overall performance.

 28.28     10.66    10.66    11664     0.00     0.00  meep::step_curl_stride1(double*, meep::component, double const*, d 13.53     15.76     5.10     9678     0.00     0.00  meep::step_update_EDHB_stride1(double*, meep::component, meep::gri 12.02     20.29     4.53 325045889     0.00     0.00  meep::grid_volume::big_corner() const
  9.79     23.98     3.69        3     1.23     2.65  meep::fields::find_metals()
  7.07     26.65     2.67 521866872     0.00     0.00  meep::grid_volume::owns(meep::ivec const&) const
  7.00     29.29     2.64        3     0.88     2.26  meep::fields::connect_the_chunks()
  6.07     31.58     2.29       36     0.06     0.93  meep::fields::step()
  1.83     32.27     0.69 63836343     0.00     0.00  material_of_unshifted_point_in_tree_inobject
  1.78     32.94     0.67 42557562     0.00     0.00  geom_epsilon::eff_chi1inv_row(meep::component, double*, meep::volu
  1.34     33.44     0.51 42557562     0.00     0.00  meep::grid_volume::dV(meep::ivec const&, double) const
  1.33     33.94     0.50      135     0.00     0.02  meep::structure_chunk::set_chi1inv(meep::component, meep::material
  1.27     34.42     0.48        1     0.48     0.48  meep::fields::require_component(meep::component)

I did some experiments running the MPI version of meep with various numbers of concurrent threads, and it speeds up only until about 4 threads and after that the overhead of synchronizing the threads seems to overtake any speed gains. It looks like scaling up performance would require finding a way to divide the work into sections without interdepencies.. but the math is beyond me so I don't know if that's even possible.

From what I can see so far, it looks like the best approach to making good use of CPU power would be to run many instances across 4-threaded cloud servers each with differing initial conditions, allow them all to churn away, and get back a batch of results.

Three dimensional runs are by far the slowest so they could use some help.

Hmm, how do you perform a 3-dimensional run? I'll check that too.
« Last Edit: 07/03/2015 09:53 PM by kitsuac »

Offline Rodal

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Quick notes:

We have shown that there is a definite Poynting vector, meaning an energy flux in the longitudinal direction, that persists over integer periods of time.

This has very important consequences regarding the Stress-Energy tensor, regarding momentum.  See:  https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor



The Poynting vector is the momentum density part of the Stress-Energy tensor.

We still have to show that the flux goes into momentum of the copper and does not get all dissipated into the walls as heat.

Even if there would be momentum we would have to show that the amount is anywhere close to what experimenters are claiming.

As to how momentum could be produced, notice that Aero has a FD grid outside the cavity.

Aero: do you have any gaps through which evanescent waves can escape? when you had an evanescent wave field in the past, was it achieved through intentional gaps you had placed on purpose?

A possible gap in the EM Drive of experimenters is between the bases and the truncated cone walls: not a perfect conductive seal, as I recall.  NASA uses fiber reinforced epoxy bases coated with a very thin layer of copper on the inside.  Other experimenters seem to have a gasket between the base and the truncated cone walls.
« Last Edit: 07/03/2015 09:46 PM by Rodal »

Offline aero

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@Dr. Rodal - You wrote
To double check this all that is needed is to provide other circular cross-sections: I would favor one at the antenna location, another one close to it, within the same longitudinal wave-pattern, and another one in the next longitudinal wave pattern away from it towards the big base.

Would you care to look at a csv file  with x,y or x,z and tell which row (x dimension is rows, isn't it?) that contains the fields you want to see? I can then take slices of the y,z plane containing those rows. Slicing the cavity in the y,z plane, and uploading to Google drive is faster than doing same for the other two planes, so more slices will not be a big burden.
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Offline aero

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Aero: do you have any gaps through which evanescent waves can escape? when you had an evanescent wave field in the past, was it achieved through intentional gaps you had placed on purpose?

No, there are no gaps, as is evident in the code snippet posted above.

Yes, in the past my frustum was modelled as perfect metal, hence intentional gaps were the only method to allow evanescent waves to escape. I did model the Copper Kettle with perfect metal and the gasket they had used at one point. See image attached. I don't remember anything more about that gasket, but it did make a pretty picture  :)
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Offline SeeShells

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Quick notes:

We have shown that there is a definite Poynting vector, meaning an energy flux in the longitudinal direction, that persists over integer periods of time.

This has very important consequences regarding the Stress-Energy tensor, regarding momentum.  See:  https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor



The Poynting vector is the momentum density part of the Stress-Energy tensor.

We still have to show that the flux goes into momentum of the copper and does not get all dissipated into the walls as heat.

Even if there would be momentum we would have to show that the amount is anywhere close to what experimenters are claiming.

As to how momentum could be produced, notice that Aero has a FD grid outside the cavity.

Aero: do you have any gaps through which evanescent waves can escape? when you had an evanescent wave field in the past, was it achieved through intentional gaps you had placed on purpose?

A possible gap in the EM Drive of experimenters is between the bases and the truncated cone walls: not a perfect conductive seal, as I recall.  NASA uses fiber reinforced epoxy bases coated with a very thin layer of copper on the inside.  Other experimenters seem to have a gasket between the base and the truncated cone walls.
I know in Feynman's lectures on physics he talks about the energy-flux for a finite space just looping back to cancel to 0 but here we seem to hold it in one place in the small of the cone preventing it from leaking out. If it could the Emfield would seem to want to loop back and sum to zero it can't we have it trapped
But evanescent waves escaping couldn't make that loop back to cancel. Evanescent waves will penetrate the copper walls to a depth of what 2-5um and degrade about 1/3 of a
wavelength out  from there they were created.

GTG be back neighbor needs help will finish ideas later but think about this... good, bad or wrong.

Offline aero

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Take a look at the image above and tell me if they are evanescent waves or propagating waves outside of the cavity. They must squeeze through the gap as evanescent waves but maybe they self-organize into propagating waves on escaping. What ever they they are, they certainly go farther than 1/3 wavelength from the cavity. Cavity is 9 - 10 inches high and the frequency is like 1.95 GHz.
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Offline VAXHeadroom

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Due to the planar nature of the dipole antenna effect, the Poynting vector field in the xy plane has significantly smaller amplitude than the one in the xz plane.  However, it in increasing with time, the amplitude at Time Step 13 clearly being much larger than at TS03 and TS08 (which are similarly located in the time cycle).
3D animation rendering, please stand by :)
I'm thinking I need to maybe switch the 'flat' and 'upright' images in the animation...  I swear the Poynting vectors look like they're rowing :)



This is great !!!

Could you

1) look at this from an angle so that one has a better view of the horizontal plane?

2) Can you rotate it more so that one gets to see the circular cross-section better?

Or would it be too much to ask to get 3 separate movies for each plane separately?

Your wish is my command. *vanishes in a greasy puff of smoke*
Same data, higher viewpoint, only run at 5 frame/sec (the 10frame/sec seemed really hard to look at).
Original frames have been overlaid on the 3D animation.  The 3D animation is now 100 frames and looped 5 times.

We really need this at about 100 frames for one microwave cycle...



Emory Stagmer
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Offline wallofwolfstreet

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I don't know if there is the same issue here because I haven't read the forum in a while, but there seems to be a bit of a misconception on the Poynting vector and what it indicates over on the reddit forum.

Alot of people seem to have confused the idea of a net, non-zero time averaged poynting vector with a net thrust.  This is not true.  Such a poynting vector would indicate that their is a store of linear momentum within in the cavity, so at some point a force (the rate of change of linear momentum) must have occured. 

To be honest, isn't the result that there is net poynting vector from the small end, where the antenna is located, to the big end rather intuitive?  The antenna is "injecting" power into the cavity, so it flows from the small end to the big end.  The reflected power from big end to small is less due to losses, so there ought to be a net poynting flow from small end to big end.  It's actually much like this picture from the wikipedia article on the poynting vector.  Note that there is a net poynting vector to the right, from battery to resistor.  Clearly there is no net force on a battery + resistor circuit.

A net poynting vector, even averaged over all time, is NOT indicative of a net force.  Force is the rate of change of the poynting vector, so a constant force would have to come from a monotonically increasing poynting vector, such that at any given time step we would need to see a poynting vector greater than the time step before.

I want to stress this point because this is something I've personally stumbled over too many times. 

Offline Rodal

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Aero: do you have any gaps through which evanescent waves can escape? when you had an evanescent wave field in the past, was it achieved through intentional gaps you had placed on purpose?

No, there are no gaps, as is evident in the code snippet posted above.
Yes, in the past my frustum was modelled as perfect metal, hence intentional gaps were the only method to allow evanescent waves to escape. I did model the Copper Kettle with perfect metal and the gasket they had used at one point. See image attached. I don't remember anything more about that gasket, but it did make a pretty picture  :)

If there are no gaps, and (assuming that Meep is not modeling any quantum tunneling and/or that the walls are too thick for quantum tunneling to take place) then the asymmetric Poynting vector in the model must be getting dissipated into the copper (eventually resulting into heat).  Currents are magnetically induced in the walls by the electromagnetic field, and these currents will meet resistance (eventually dissipating) energy into heat.

Is there a way to look into the current into the walls in Meep ?

Offline SeeShells

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Take a look at the image above and tell me if they are evanescent waves or propagating waves outside of the cavity. They must squeeze through the gap as evanescent waves but maybe they self-organize into propagating waves on escaping. What ever they they are, they certainly go farther than 1/3 wavelength from the cavity. Cavity is 9 - 10 inches high and the frequency is like 1.95 GHz.
EM that would be about a 6 inch wavelength at 1.95Ghz and it fits the pattern size. Plus Evanescent  carry no information to propagate as a wave. 

Offline WarpTech

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Dr. Rodal- Time slices 3 thru 7 have been added to the csv folder on Google Drive. Same place as the other ones, I just changed the name to reflect 3 thru 13.
@aero:

two important questions to investigate this further:

1) How do you impose boundary conditions? What are your boundary conditions and how do you actually implement them in Meep (I read that boundary conditions can be imposed such that the problem becomes nonlinear, which would also partly explain the results)

2) TS013 : does this mean that you only marched the FD solution through 13 time steps total?  If so, this is way insufficient to make sure that this is not just a transient, if so we would need to investigate marching forwards many more time steps to investigate the time evolution

It appears from what we're seeing in the gif movies and what I've calculated for a tapered waveguide, that the two match. For a very long frustum waveguide, starting at the small end with a k vector perpendicular to the x-axis, the axis of the frustum;

k2 = 0 + ky2 + kz2, initially.

This is the rocket equation (per photon);

dpx = (E(w)/(c2*px))*[dE(w) + (c/p)*hbar2*(Xmn2/x^3)*dx]

Xmn2 = [(m*pi/A*tanθ)2 + (n*pi/B*tanθ)2], for a tapered rectangular waveguide of width and height;

x*A*tanθ and x*B*tanθ


Multiple reflections from the side wall will rotate k into kx, thereby transferring all of the momentum that was perpendicular to the axis, to be parallel to the axis. That rotation occurs a little bit, each time it reflects from the side walls. You can see this clearly in the Hx-z images from @aero's work. (Thank you @aero and @VAXheadroom) This is WHY a smaller cone angle and a longer frustum is better. "If it were long enough", there would be so many bounces that no energy would reach the big end, it would all be converted into thrust.

I retract my previous statement that I've given up on the microwaves, thanks to all the work done here. Theory and simulation seem to be merging. :)
Todd
« Last Edit: 07/04/2015 12:32 AM by WarpTech »

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