Author Topic: EM Drive Developments - related to space flight applications - Thread 2  (Read 2103521 times)

Offline maciejzi

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This engine won't get us to stars. The reason is not the shape of the frutrum or cavity or frutrum material, but the ineffective process of converting mass into electricity.

E=mc^2

For MW energy to take us to stars we need to efficiently convert the mass in the ship to MW and then efficiently send it in the direction opposite to the direction the ship is going to.

Let's say 10% of the ship's  mass is propellent. We want the ship to achieve, say, 0,5 c and get to Alpha Centauri in, say, 15 years.

Hence, it is possible to calculate the required propelling energy.

Hence, it is possible to calculate the required ship's mass to energy conversion efficiency.

As far as I know it is currently much lower than the requred level.

Hence, we currently cannot create as much microwaves (or any other energy) to achieve required acceleration consistently throughout the entire journey.


The EmDrive CAN move in vacuum OR in zero gravity. It CANNOT move in vacum AND zero gravity.


Thrust readouts achieved on Earth (non-zero gravity) are incorrect because it pushes against the air cusion in air bearing with very small force but high MW frequency. That is why it moves so quickly compared to low input power.

In free space (vacuum AND zero gravity) it probably has thrust in order of nanonewtons or even smaller. I don't think its shape is efficient in sending MW in one direction.

Offline jmossman

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Interesting that breaking CofM means that translational invariance dies, and breaking Einstein's SR core principle means that inertial frame invariance dies. Interesting because you may notice that one is essentially the time derivative of the other.  And further that breaking CofE means that time invariance dies.

Perhaps that's a deep observation, but I'm not smart enough to know what it means. All I know is that, for a propellantless propulsor, we are forced to choose between killing off one or the other. If we got creative we could kill off both, maybe!

I'm sure my physics friends down the pub here in Cupertino would simply shrug and say that, since momentum appears not be conserved in the first place, there's ample room for odd statements to be correspondingly made about energy conservation (and I have made them here on this forum).

Perhaps there's an exit route out of this bind via playing off conservation of momentum against conservation of energy. Just a wild thought.

The conundrum may be resolved in two words:

Noether's theorem. 

In defining how symmetries are enforced, by extension it reveals where they are not.

Specifically, time-dependent (ie. temporally variant) interactions are, by definition, non-conservative.  Although we more commonly encounter such asymmetries in dissipative systems, there are, within electromagnetism at least, non-dissipative non-conservative systems.

And before anyone protests, this isn't half as controversial as it may seem - any electrodynamics textbook will include a section on non-conservative, temporally variant EM interactions.  By definition, CoE does not and cannot be applied to them.  See Rutherford's first paper ca 1886 on magnetic entropy viscosity (Sv)... in such a delayed response, the time-dependent rise of B to a given H means input and output FxD integrals can be non-equitable, if their mechanical displacements are varied to sub- and super-Sv speeds respectively.

Example: take two permanent magnets, at least one of which has appreciable Sv.  Allow them to attract together before B can reach Bmax, obtaining our output FxD integral, then let B peak before separating them against this now-higher force, requiring an appropriately-greater input work integral due to the higher force over the same distance.... we've input more work than the interaction has output!  Where'd the energy go?  Not dissipated to heat (the magnetocaloric profiles are almost identical, and incidental since net change in B up vs down is equal for both integrals - ie. Sv isn't a direct heating mechanism).  Rather, the answer's right there in the setup - the missing energy was spent entirely on displacement against a higher magnetic force.  Or, looking at it from the alternative perspective, squandered away by not harvesting it in the first place during the initial delayed-response output displacement.

We can repeat this interaction forever, dumping the same amount of mechanical energy into the vacuum (via the virtual photon exchanges mediating the force) each cycle.  Calorimetry will show a continuing loss...

I hesitate to interject, but I do have a quick question on the topic of calorimetry associated with the EM drive.

When a resonant cavity (such as Shawyer's frustum) is oriented with it's major resonant axis oriented parallel with a gravitation field, the resulting Doppler red shift experienced by any resonating microwaves will slowly shift their frequency away from the resonant frequency (Fr) of the cavity.  As the frequency of a trapped microwave approaches the cutoff frequency of the resonant cavity, one would expect it to be attenuated faster.

Would the faster attenuation due to the microwave frequency drifting away from the cavity's Fr be completely measured as additional thermal losses in the copper/cavity walls?  What about the energy reduction associated with the Doppler red shift?

Another forum member (@Frobnicat, IIRC) ran some quick numbers to illustrate the miniscule gravitationally induced red shift, but I've been curious whether attenuation near a resonant cavity's cutoff frequency would be expected to manifest as purely a thermal loss phenomena.  There has been the occasional use of the phrase "event horizon" to describe the resonant cavity's cutoff frequency, which invoked a mental image of a possible non-thermal loss mechanism (although probably an error of my own doing due to my very limited understanding of GR).

Thanks,
James

Offline Mulletron

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http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.110.194301

Observation of Displacement Momentum in Normal and Chiral Dielectrics
G. L. J. A. Rikken and B. A. van Tiggelen
Phys. Rev. Lett. 110, 194301 Published 10 May 2013

Would be nice if this were open access. Can't learn much from reading abstracts.

Hopefully in the future, open access to science becomes the norm.
« Last Edit: 05/09/2015 10:05 AM by Mulletron »
Challenge your preconceptions, or they will challenge you. - Velik

Offline R.W. Keyes

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Because Peltier effect can't quite reach cryogenic temperatures, for some thermodynamic reason I forgot. Maybe it changed with recent progress on the subject ? Please inquire : what are the limits of low temp. with Peltier effect, now and tomorrow ? Isn't the Peltier effect still quite low in efficiency ?

The Peltier limits are below 100K, which is enough for high-temparature superconductors. The efficiency in such temperature is low, but probably that could be economically viable because of much smaller MW input power and smaller superconducting engine size.

That said, I must sadly admit, that this engine won't probably move in free space. It may move on air cushion though, as in the experiments conducted so far on Earth.

Anyway, if so, then it is at least good for new generation of rotorless helicopters, here on Earth.

Stirling coolers are used where cryogenic temperatures are required.   They are more efficient than Peltier devices.   I have used very compact Stirling cooled IR detectors.   Several companies make them,   It takes about 1 Min. to reduce the temperature of the detector to 95 K, using 1 Watt.    However the thermal mass is very tiny.    NASA has been investigating Stirling coolers for liquifying rocket fuels (H2, O2) in space and for space telescope applications.

More efficient are coolers that utilize the Giant Magnetocaloric Effect (GME), the so-called 'solid state' refrigerators. In this device, a mass of one of several substances exhibiting the effect is placed into a magnetic field, where it heats up. This is allowed to cool to ambient temperature, and then moved into the area to cooled, and then the magnetic field removed, upon which the mass cools, and circulating coolant then creates thermal equilibrium in that system.

The problem with GME coolers it that each substance known the exhibit the GME does so over a narrow temperature range. These ranges vary, so it is possible to cascade stages with differing GME materials, but this adds complexity. I am of the believe that using a cryosystem technology with a greater range of temperatures should be used for the initial cooling, and then a single-stage GME is used to keep the temperature within its operating range.

Offline CW

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One idea just popped into my mind:

As far as I know (and please correct me if I'm wrong!), any kind of particle decays after some more or less long time (that should include photons? Although that seems to be a controversy, from what I read so far).
Let's then say we do have an EM-drive that apparently draws momentum out of nothing. Now let the EM-drive inertially move forward with its 'magically' gained momentum from nothing for an eternity via inertia, without it being active for the whole time. When, at one point in time, all atoms of the former EM-drive start to decay (and in consequence all possible 'offspring' particles of those decays, after some other more or less long time).. I think that the following question arises:

Where does the gained momentum from nothing go to, when in the end all involved particles, that had more momentum than our current understanding permits, decay into nothing?

I think that logically the answer is in the question already. Momentum is simply taken from nothing, and inevitably returns to nothing (because that's just how physics works). The additional momentum is only temporarily borrowed from nothing (even if this means an eternity from our point of view) and added as a delta to the previous momentum of the particles. You just have to give it enough time for the momentum-return to happen - because it will happen automatically.. and there's no way around it. We're just too short-lived to observe it happen eventually.
;D
« Last Edit: 05/09/2015 11:49 AM by CW »
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Online SeeShells

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I was wondering in your testing did you use a smoke stick also called a smoke pencil to check for air flows around the EM Drive in ambient air conditions?

That is a very good idea.  I don't think it has been suggested before.   There was some discussion on convective air flow and the possiblity it may explain the anomalous force measured by EW early in thread 1.   However interest in that explanation has dissipated and Dr. Rodal's analysis of thermal-mechanical effects as a conventional explanation has replaced it.
Thank you and I did review of the very nice workup by Dr. Rodal after he pointed it out.  It's not only heat convection I was thinking of, but any aberrations in air movement other than the expected thermal currents from the EM device.
« Last Edit: 05/09/2015 11:41 AM by SeeShells »

Offline Rodal

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I was wondering in your testing did you use a smoke stick also called a smoke pencil to check for air flows around the EM Drive in ambient air conditions?

That is a very good idea.  I don't think it has been suggested before.   There was some discussion on convective air flow and the possiblity it may explain the anomalous force measured by EW early in thread 1.   However interest in that explanation has dissipated and Dr. Rodal's analysis of thermal-mechanical effects as a conventional explanation has replaced it.
Thank you and I did review of the very nice workup by Dr. Rodal after he pointed it out.  It's not only heat convection I was thinking of, but any aberrations in air movement other than the expected thermal currents from the EM device.

Quote from:  Jorge Ruiz de Santayana "George Santayana"
Those who cannot remember the past are condemned to repeat it.

1873 Maxwell derives equations showing that radiation will give rise to stresses on a surface due to the electromagnetic energy density (Maxwells' stress tensor).
 
1876 Bartoli attempts to measure the radiation pressure on a reflecting surface experimentally but he is unable to overcome disturbing effects due to the heating of the reflecting surface which gives rise to convection currents of air and to the radiometer effect ( https://en.wikipedia.org/wiki/Crookes_radiometer#Explanations_for_the_force_on_the_vanes ), which are collectively described by Bartoli and other scientists of the period, as "gas action."
 
1900 Lebedew, using light waves is the first person in history to succeed in eliminating these unwanted artifact effects by performing the experiments in a partial vacuum.  He used a torsion balance and a highly reflecting mirror in his measurements.

1902 Nichols and Hull made a thorough investigation of the unwanted artifact effects collectively called "gas action" and accurately establish the accuracy of Maxwell's predicted stress tensor.  Nichols and Hull also performed experiments in a partial vacuum using a torsion balance and a highly reflecting mirror in their measurements.

1949 Carrara and Lombardini qualitatively demonstrate the existence of radiation pressure at microwave frequencies to the correct order of magnitude, but no quantitative results are obtained.  They employ a free wave method, which involves a very difficult refraction problem due to air, which precludes a quantitative assessment.

1950 Cullen is the first person to accurately measure radiation pressure at microwave frequencies.  Cullen uses power ranging from 10 to 50 watts in his microwave pressure measurements, at a wavelength of 10 cm, measuring 6.77 microNewtons/kW.  Cullen used a torsion balance and a highly reflecting mirror in his measurements.  Cullen performed his experiments in ambient air conditions.  It was impossible to obtain a stable baseline, even on a relatively short-term basis of a minute's duration.  This continual drifting of the baseline was found to be due to air convection currents set up by small and changing temperature gradients within the microwave waveguides.  The remedy was to reduce the air resistance of the reflecting end plate so that the convection currents would have no appreciable effect.  The reflecting end plate was replaced by a system of concentric wire rings (shown on Fig. 12 of Cullen's paper).  The rings acted as an almost perfect reflector of the electromagnetic waves but at the same time had a small effective cross-section to air currents.  NASA, Shawyer, Yang, and other EM Drive researchers would be well advised to experiment with replacing the end plates of the EM Drive with this system of concentric rings, in order to address the problem of air convection currents that has plagued radiation pressure experiments in ambient conditions ever since Maxwell 140 years ago.  Even in a partial vacuum, if one uses for example bilayer plates of copper/glass-fiber-reinforced epoxy with the reinforced polymer on the external surface, there is the possibility of outgassing in a vacuum producing a false positive.  The use of a mesh precludes this problem both in ambient air conditions and in a vacuum.



Attachment: ABSOLUTE POWER MEASUREMENT AT MICROWAVE FREQUENCIES
By A. L. CULLEN, Ph.D., B.Sc.(Eng.), Associate Member.
(published February, 1952.)

http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=828862
« Last Edit: 05/09/2015 03:42 PM by Rodal »

Offline Rodal

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Quote from:  Hackaday.io EM Drive project
In the first step, we will replicate the original EM-Drive thruster.
It will be driven by a high power RF source (magnetron) which is easily available.
The second step will be a miniaturization by using higher frequencies.
To achieve this, a numerical simulation of the waves inside the cone frustum must be made to obtain the optimal geometry for the cone.
A high frequency generator in the 20-30 GHz range has to be built with the power of a few watts

https://hackaday.io/project/5596-em-drive

Offline jmossman

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I was wondering in your testing did you use a smoke stick also called a smoke pencil to check for air flows around the EM Drive in ambient air conditions?

That is a very good idea.  I don't think it has been suggested before.   There was some discussion on convective air flow and the possiblity it may explain the anomalous force measured by EW early in thread 1.   However interest in that explanation has dissipated and Dr. Rodal's analysis of thermal-mechanical effects as a conventional explanation has replaced it.
Thank you and I did review of the very nice workup by Dr. Rodal after he pointed it out.  It's not only heat convection I was thinking of, but any aberrations in air movement other than the expected thermal currents from the EM device.

Quote from:  Jorge Ruiz de Santayana "George Santayana"
Those who cannot remember the past are condemned to repeat it.

1873 Maxwell derives equations showing that radiation will give rise to stresses on a surface due to the electromagnetic energy density (Maxwells' stress tensor).
 
1876 Bartoli attempts to measure the radiation pressure on a reflecting surface experimentally but he is unable to overcome disturbing effects due to the heating of the reflecting surface which gives rise to convection currents of air and to the radiometer effect ( https://en.wikipedia.org/wiki/Crookes_radiometer#Explanations_for_the_force_on_the_vanes ), which are collectively described by Bartoli and other scientists of the period, as "gas action."
 
1900 Lebedew, using light waves is the first person in history to succeed in eliminating these unwanted artifact effects by performing the experiments in a partial vacuum.  He used a torsion balance and a highly reflecting mirror in his measurements.

1902 Nichols and Hull made a thorough investigation of the unwanted artifact effects collectively called "gas action" and accurately establish the accuracy of Maxwell's predicted stress tensor.  Nichols and Hull also performed experiments in a partial vacuum using a torsion balance and a highly reflecting mirror in their measurements.

1949 Carrara and Lombardini qualitatively demonstrate the existence of radiation pressure at microwave frequencies to the correct order of magnitude, but no quantitative results are obtained.  They employ a free wave method, which involves a very difficult refraction problem due to air, which precludes a quantitative assessment.

1950 Cullen is the first person to accurately measure radiation pressure at microwave frequencies.  Cullen uses power ranging from 10 to 50 watts in his microwave pressure measurements, at a wavelength of 10 cm, measuring 6.77 microNewtons/kW.  Cullen used a torsion balance and a highly reflecting mirror in his measurements.  Cullen performed his experiments in ambient air conditions.  It was impossible to obtain a stable baseline, even on a relatively short-term basis of a minute's duration.  This continual drifting of the baseline was found to be due to air convection currents set up by small and changing temperature gradients within the microwave waveguides.  The remedy was to reduce the air resistance of the reflecting end plate so that the convection currents would have no appreciable effect.  The reflecting end plate was replaced by a system of concentric wire rings (shown on Fig. 12 of Cullen's paper).  The rings acted as an almost perfect reflector of the electromagnetic waves but at the same time had a small effective cross-section to air currents.  NASA, Shawyer, Yang, and other EM Drive researchers would be well advised to experiment with replacing the end plates of the EM Drive with this system of concentric rings, in order to address the problem of air convection currents that has plagued radiation pressure experiments in ambient conditions ever since Maxwell 140 years ago.  Even in a partial vacuum, if one uses for example bilayer plates of copper/glass-fiber-reinforced epoxy with the reinforced polymer on the external surface, there is the possibility of outgassing in a vacuum producing a false positive.  The use of a mesh precludes this problem both in ambient air conditions and in a vacuum.



Attachment: ABSOLUTE POWER MEASUREMENT AT MICROWAVE FREQUENCIES
By A. L. CULLEN, Ph.D., B.Sc.(Eng.), Associate Member.
(published February, 1952.)

http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=828862

Dr. Rodal,

How much of effect would the use of a ring (or mesh) have on ohmic losses in the endplate for some of the excited modes tested at EW?  Any hunches for the effect on the cavity Q?  (i.e. aren't the losses going to be larger for the ring/mesh versus a solid sheet of copper?)

For in-air testing, the use of a ring/mesh makes perfect sense.  I'm just curious as to the predicted effect on Q  (perhaps neglible?).  Engineering is almost always a series of tradeoffs;  minimizing a known noise source during delicate force measurements would seem like a much more important design parameter than maximizing Q at this stage.

Thanks,
James

Offline Rodal

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....

Dr. Rodal,

How much of effect would the use of a ring (or mesh) have on ohmic losses in the endplate for some of the excited modes tested at EW?  Any hunches for the effect on the cavity Q?  (i.e. aren't the losses going to be larger for the ring/mesh versus a solid sheet of copper?)

For in-air testing, the use of a ring/mesh makes perfect sense.  I'm just curious as to the predicted effect on Q  (perhaps neglible?).  Engineering is almost always a series of tradeoffs;  minimizing a known noise source during delicate force measurements would seem like a much more important design parameter than maximizing Q at this stage.

Thanks,
James
Fair point.  A detailed discussion of the effect of the ring mesh is not trivial.  I refer you to Cullen's discussion of the effect on the pressure measurement (not taking into account Q, because Cullen tested an open waveguide) in Cullen's paper attached in my post above.  The effect of a ring mesh has been further understood during the past 65 years, thanks to great advances on numerical calculations. 

Given the fact that the highest measured thrust forces, and the highest measured thrust force/InputPower were obtained with the lowest Q reported (Q~1500 see my notes concerning this) by Prof. Yang in China, while high Q force measurements at NASA Eagleworks have resulted in much lower forces and force/InputPower, a proportional relationship between force and Q remains to be experimentally corroborated (it is actually negated by the Chinese experiments).

Furthermore, the theoretical considerations advanced by Todd in these pages put more emphasis on the attenuation (which may be supported by NASA Eagleworks findings that they only measured thrust forces with an insert polymer dielectric and no forces without it). 

Finally, it is not clear that the portion of the Q due to reflection of the low frequencies (larger wavelength) of the resonant microwave spectrum would be impaired by the mesh. 

My microwave oven has a conductive metal mesh on the inside of the transparent glass, so that the microwaves are reflected,  to prevent microwaves from escaping the microwave.



BOTTOM LINE: I would suggest for experimenters to try 4 different kinds of ends:

1) A solid reflecting end (copper or aluminum)

2) A conductive wire mesh

3) A transparent glass (transparent to microwaves)

4) An open end 


And compare the results.  Such tests would be very valuable both for scientific and engineering purposes to understand what is being measured.
« Last Edit: 05/09/2015 07:09 PM by Rodal »

Offline jmossman

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....

Dr. Rodal,

How much of effect would the use of a ring (or mesh) have on ohmic losses in the endplate for some of the excited modes tested at EW?  Any hunches for the effect on the cavity Q?  (i.e. aren't the losses going to be larger for the ring/mesh versus a solid sheet of copper?)

For in-air testing, the use of a ring/mesh makes perfect sense.  I'm just curious as to the predicted effect on Q  (perhaps neglible?).  Engineering is almost always a series of tradeoffs;  minimizing a known noise source during delicate force measurements would seem like a much more important design parameter than maximizing Q at this stage.

Thanks,
James
Fair point.  A detailed discussion of the effect of the ring mesh is not trivial.  I refer you to Cullen's discussion of the effect on the pressure measurement (not taking into account Q, because Cullen tested an open waveguide) in Cullen's paper attached in my post above.  The effect of a ring mesh has been further understood during the past 65 years, thanks to great advances on numerical calculations. 

Given the fact that the highest measured thrust forces, and the highest measured thrust force/InputPower were obtained with the lowest Q reported (Q~1500 see my notes concerning this) by Prof. Yang in China, while high Q force measurements at NASA Eagleworks have resulted in much lower forces and force/InputPower, a proportional relationship between force and Q remains to be experimentally corroborated (it is actually negated by the Chinese experiments).

Furthermore, the theoretical considerations advanced by Todd in these pages put more emphasis on the attenuation (which may be supported by NASA Eagleworks findings that they only measured thrust forces with an insert polymer dielectric and no forces without it). 

Finally, it is not clear that the portion of the Q due to reflection of the low frequencies (larger wavelength) of the resonant microwave spectrum would be impaired by the mesh. 

My microwave oven has a conductive metal mesh on the inside of the transparent glass, so that the microwaves are reflected,  to prevent microwaves from escaping the microwave.



BOTTOM LINE: I would suggest for experimenters to try 4 different kinds of ends:

1) A solid reflecting end (copper or aluminum)

2) A ring-wired mesh as used by Cullen

3) A transparent glass (transparent to microwaves)

4) An open end 


And compare the results.  Such tests would be very valuable both for scientific and engineering purposes to understand what is being measured.

Your recommendations make sense to me.  RLC (resistive, inductive, capacitive) mesh analysis of power grids within microchips is similarly non-trivial (correlating the numerical values of the model elements to a given fabrication technology being the most difficult).

Probably also worth reiterating that Q of a microwave cavity can be influenced by "losses" of various types (resistive losses, dielectric losses, geometry, antenna coupling, etc).  Not to mention the lingering unanswered question of whether the EM drive has a potentially novel "loss" mechanism to help explain the anomalous thrust.  :)

If EM drive anomalous thrust turns out not to be an experimental artifact, I suspect teasing out the different "losses" currently being lumped into Q measurement will eventually be important.  However, lowering the noise-floor (via use of a grid/mesh endcap) to ensure repeatable "thrust" measurement seems like a much higher priority right now for any potential replication attempt.

Thanks,
James

Offline deuteragenie

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Quote
...
1) A solid reflecting end (copper or aluminum)
2) A conductive wire mesh
3) A transparent glass (transparent to microwaves)
4) An open end 
And compare the results.  Such tests would be very valuable both for scientific and engineering purposes to understand what is being measured.

Apart for the conductive wire mesh it would seem to me that Shawyer likely tested the other ways (why would you use something when you can use nothing? etc.) and found out that the best results were with a solid reflecting end.  BTW as we do not have a theory, we do not know if "reflective" is the right property to look after. I would be interested to know what happens when the thickness of the "reflector" is increased / decreased. I would be equally interested to know what happens when the "reflector" is replaced by non reflective crystal.
« Last Edit: 05/09/2015 07:50 PM by deuteragenie »

Online RotoSequence

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Quote
...
1) A solid reflecting end (copper or aluminum)
2) A conductive wire mesh
3) A transparent glass (transparent to microwaves)
4) An open end 
And compare the results.  Such tests would be very valuable both for scientific and engineering purposes to understand what is being measured.

Apart for the conductive wire mesh it would seem to me that Shawyer likely tested the other ways (why would you use something when you can use nothing? etc.) and found out that the best results were with a solid reflecting end.

We won't be doing ourselves any favors by making assumptions about Shawyer's undisclosed body of work.

Offline LasJayhawk

I keep looking at this and thinking it's not right.



It looks to symmetrical.

COMSOL's website says the RF module can do far field calculations, and the antenna placement would appear to put at least part of the frustum in the near field. It looks by eyeball that the software is only looking at the far field being reflecting off the small end of the frustum.

Or am I missing something?

Online RotoSequence

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I keep looking at this and thinking it's not right.

It looks to symmetrical.

COMSOL's website says the RF module can do far field calculations, and the antenna placement would appear to put at least part of the frustum in the near field. It looks by eyeball that the software is only looking at the far field being reflecting off the small end of the frustum.

Or am I missing something?

I don't have the link handy, but infrared imagery of the Eagleworks large diameter end plate did verify the thermal behavior of resonance modes predicted in COMSOL analysis.
« Last Edit: 05/09/2015 09:22 PM by RotoSequence »

Offline Rodal

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I keep looking at this and thinking it's not right.



It looks to symmetrical.

COMSOL's website says the RF module can do far field calculations, and the antenna placement would appear to put at least part of the frustum in the near field. It looks by eyeball that the software is only looking at the far field being reflecting off the small end of the frustum.

Or am I missing something?

This COMSOL Finite Element Analysis solution is a numerical solution of Maxwell's differential equations, taking into account the boundary conditions, including the losses responsible for the finite Q.  What you are looking at is the steady state of the electromagnetic fields.

The steady state electromagnetic field solution are standing waves.  Although the initial condition is not symmetrical, due to travelling waves, this is a very-short-lived transient, as the solution soon reaches a (practically) symmetric steady state. 

This has been shown by @aero with a very interesting movie based on a 2D solution of the truncated cone as a flat trapezium using MEEP which is a Finite Difference code (free from MIT alumni) that performs the full transient solution.  It was neat to see how the (practically) symmetric steady state was soon reached starting from an unsymmetric initial condition.

Furthermore, as pointed out by RotoSequence, the steady state solution for the magnetic field and a COMSOL thermal analysis was corroborated by temperature measurements using an infrared thermal camera, which verifies that the heating is due to induction heating from the magnetic field.

I obtained an exact solution for the symmetric steady state (which of course does not take into account the initial unsymmetric transient) and it fully verifies NASA's COMSOL FEA steady state solution for the electromagnetic field: the natural frequency is within 1% of the exact solution and the mode shapes are extremely close (I posted the exact solution comparison some time ago).

If one is interested in near-field far-field, transient, fully complex solution (including initial travelling waves morphing into standing waves, as well as evanescent waves) then one has to resort to a time-marching solution as with MEEP finite difference approach or a [FEA in space/FD in time] solution that imposes a finite element discretization in space and a finite difference time discretization.   (Such a transient, 3D solution containing evanescent waves is extremely time consuming.)
« Last Edit: 05/09/2015 09:55 PM by Rodal »

Offline deltaMass

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@Rodal
Have you posted your exact solution code here?
I have my Mathematica fired up and ready to go!

Offline Rodal

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@Rodal
Have you posted your exact solution code here?
I have my Mathematica fired up and ready to go!
No I only posted the graphic results and numerical comparisons.  I also posted the output graphics for the Poynting vector (I have not seen anyone else do that, including Greg Egan).  Greg Egan posted a solution for constant in the transverse (aximuthal) direction modes, but arbitrary variation in the other directions . Greg Egan's solution will not address the Cyl TM212 being shown above, but it does address other modes like Cyl TE012 that have been discussed, see: http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.html

I write "Cyl" because there is no convention on how to denominate the truncated cone mode quantum numbers, and what NASA Eagleworks has done is use the same convention as the closest mode shape for the cylinder with uniform cross-section.
« Last Edit: 05/09/2015 10:01 PM by Rodal »

Offline deltaMass

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@Rodal
Have you posted your exact solution code here?
I have my Mathematica fired up and ready to go!
No I only posted the graphic results.  Greg Egan posted a solution for constant in the transverse (aximuthal) direction modes, but arbitrary variation in the other directions . Greg Egan's solution will not address the Cyl TM212 being shown above, but it does address other modes like TE012 that have been discussed, see: http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.html
Can you possibly post your Mathematica notebook?

What I'm looking for is a frequency prediction of various modes as I vary the dimensions and frustum angle.

Offline deltaMass

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And while on the subject of simulation: Guido Fetta of Cannae tells me that his COMSOL(?unsure) sim predicts a nonzero net Lorentz force for his device. Now, we all learned that no closed system of currents can produce such a net force. There's a paradox. He insists that there are no significant cumulative rounding errors.

Anyone have insight into this?
« Last Edit: 05/09/2015 10:11 PM by deltaMass »

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