Author Topic: EM Drive Developments - related to space flight applications - Thread 3  (Read 1803788 times)

Offline Rodal

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@SeeShell -
Your .png and .csv files data is/are up have been uploaded here:

https://drive.google.com/folderview?id=0B1XizxEfB23tfm04QWNVVVVvT3gtcVAzRUp6T1BCLVpoV0EyeVVKR2ZxQkp2a3NKcUNPMU0&usp=sharing

I uploaded my meep data request file/form to hopefully explain what the data is, although it needs more English and fewer Scheme statements. The inside big end is at row 15 and small end at row 216 of the csv files, and the total run meep time t = 13.054 (6527 timesteps).
Thanks, interesting but not quite what we were looking to do. I'm still working out the antenna shape and placement and getting feedback like I said I was going to do on launching a Te mode. What I found out is a answer from a wonderful source that mretty much just lurks here.

Of course doing it isn't as easy as it seemed to be and I'm not sure you can do it in a meep model.
 
Quote from a email:
 "Your test setup looks great. If you use a 1/4 probe on the big end or little end you will launch a TM mode. If you use a 1/10 wave loop you will excite a TE mode at either top or bottom. I believe If you launch from the big end the net force will be toward the small end or vice versa launching from the small end as the reflected wave will be reduced by Q losses and will be smaller in magnitude than the launched wave.  A loop on the side wall will excite either mode depending on orientation wrt the frustum z axis. All walls on the frustum look like a conductive ground plane. For low power testing ,with the sweeper , the sample port I would use a probe 1/4 wavelength from the side wall, variable probe depth for the needed coupling to put the SA sampler in its optimum resolution range. If you use a loop you should place it at a low impedance point or H plane max node. <End Quote>

After hours of reading and several emails to people who are beyond my skills in antennas I would agree with this.

Shell

Here you have a Master of Science thesis on the RF fields excited by dipole and loop antennas inside a stainless steel wire mesh cage :

http://epublications.marquette.edu/cgi/viewcontent.cgi?article=1011&context=theses_open

Besides the obvious interest in the simulation of the mesh, notice the considerable effort in modeling antennas.

Quote
Three types of antennas were used for simulations; dipole, monopole, and loop. For experiments, only monopole and loops were used. The dipole was used because of its simplicity, and ability to excite the E-fields within the cage. The loop was used because it is a magnetic antenna, and well suited to excite the H-fields. 

For our case, the TMagnetic modes have an axial electric field, hence excited by the dipole antenna.  To excite a TElectric field which has a magnetic axial field, a loop antenna is needed.

Quote
Since the strongest E-fields created by the dipole are in the axial direction, to couple to a cavity it should be orientated in the same direction as the E-fields described by the mode configuration. 

The author used numerical simulation of electromagnetic fields, using The Numerical Electromagnetics Code (NEC) for simulation of the electromagnetic fields inside the cage and Matlab for post-processing of the results from NEC.

Showing once again that it is usual for researchers to use other codes to post-process data.  (Ditto for post-processing Meep data).
« Last Edit: 07/23/2015 02:01 AM by Rodal »

Offline aero

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Quote
AxialAnt-06-exSx.csv; AxialAnt-06-eySx.csv and AxialAnt-06-ezSx.csv

Actually, it looks like I completely skipped the entire 06 time slice last night. Guess I need to work on my shell command file. Hand editing is slow and obviously error prone.

It's up now.
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Offline SeeShells

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DIYer head's up. Copper flashing seems to be a cost-effect solution for frustum walls if you are not using mesh. As I was looking around for supplies, found this: http://www.acehardware.com/product/index.jsp?productId=1290779&KPID=984489&kpid=984489&pla=pla_984489

A 10ft roll seems to be the smallest length. I'd recommend the 14 inch for frustum heights to 11 inches. I can say from experience that .021 thickness will not be self-supporting and an exoskeleton will be needed. When I switched to a magnetron, the 1/8 in square copper supports were not ideal. I'd move to 1/4 in copper struts or possibly tubing.

Top and bottom plates on nsf-1701 were 1/2 oz copper clad pc board, again too flimsy for a 750g magnetron. Try the next size up. Solid copper plates would weigh too much, I stick with the pcb stuff, just make sure there are plated thru-holes or plenty of bolts to connect the 2 ground planes.

Any metal above ground potential will be subject to plasma discharge, so "mind the gaps" ;)

p.s. Bonus points for anyone who knows that phrase...
Had to do with electric trolleys I think. Before my time.

One thing you need to be aware of in copper is that it's mixed with tin to prevent corrosion, 80-90% mix is normal and if not 99% pure copper it will cause more heating signal loss and not be as a good cavity.

Shell
PS:
I'm still waiting (have some time) for my last piece of copper is holed out to my specs, was hoping to have a simulation run,  it is 99% pure the same they use in waveguides.

Shell, there are hundreds of copper alloys. Copper alloyed with tin is bronze. Copper alloyed with zinc is brass (both very generically speaking). What you are probably after is the highest possible electrical conductivity, which is commercially called 101 copper, or Oxygen Free High Conductivity (OFHC) copper.

Both brass and bronze typically have drastically lower conductivity than OFHC copper. Waveguides are often brass for structural reasons (its much stiffer and harder than OFHC), and are often silver plated internally to enhance conductivity. Cheaper waveguides are usually aluminum.

McMaster Carr (mcmaster.com) is a somewhat pricey but immediately available source for OFHC. Browse under "Raw Materials". They may even have perforated sheet.
A good heads up, I'm having to have the final copper frustum which is OFHC drilled and used for wave guides. Looked at McMaster Carr (bought a lot of stuff over the years from them) and it doesn't seem the have the right copper perforated sheets for the final build.

Thanks!
Shell

Offline rfmwguy

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To all those proposing to use Thruster in the name, I reiterate what rfmwguy said:

Electromagnetic Drive or Reactor seems safe, perhaps a little better than Thruster since we're not 100% sure its pushing rather than pulling.

What could the possible difference be between "pushing" and "pulling"?
A sign  ;D
IOW propulsion or repulsion. GUT advocates await discovery of gravity's alter ego, or repulsive force. Slim possibility in classic physics to date, but who knows what the future holds. Leaving open the small possibility of "expanding" past a propellant thrusting mentality.


Offline SeeShells

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...I wondered why that went quicker last night. Not quick but a little quicker. I guess you found out.

Check it again, they are there now.
I'm looking at the Yang/Shell Axial Antenna at Big Base case now: very unusual: the stress, and hence the force at the small base is practically zero.  The stress at the big base is a central point stress from the antenna.  Close inspection of this mode looks like another TM11 transverse magnetic mode but with drastically lower amplitude.

QUESTION1: was the mesh kept the same as in the previous csv Yang/Shell case, and you are sure this is the stress at the small base and not outside it?

Most important: QUESTION2: did Meep give you a Q value for this case ?

Thanks
He emailed me saying the Q was something like 57,000+ but was worried about the antenna position, I said run it if you want but I was still doing research into the antenna and had questions out to ppl who had 40 years + in this field. It's not one I would want to make.

Shell

Added: I certainly do not want to waste anyones time here and since Aero has been so good at running interactions in meep and interfacing with the new group getting them up to speed I didn't want to wedge into any of his time, And I still wanted to do some more research on the antenna placements.

I finally come to find out the hoop would be best for giving data but wasn't sure it Aero could model it. Not a lot of gain but highly directional, one reason they use them for the military in remote zones and also for RDFs Radio Direction Finders.
« Last Edit: 07/23/2015 02:29 AM by SeeShells »

Offline deltaMass

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I'm curious as to why the capable engineers at EagleWorks are finding Q-values around 5,000 to 6,000, and yet around here there's a lot of talk about Q-values ten times higher?

Offline rfmwguy

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...I wondered why that went quicker last night. Not quick but a little quicker. I guess you found out.

Check it again, they are there now.
I'm looking at the Yang/Shell Axial Antenna at Big Base case now: very unusual: the stress, and hence the force at the small base is practically zero.  The stress at the big base is a central point stress from the antenna.  Close inspection of this mode looks like another TM11 transverse magnetic mode but with drastically lower amplitude.

QUESTION1: was the mesh kept the same as in the previous csv Yang/Shell case, and you are sure this is the stress at the small base and not outside it?

Most important: QUESTION2: did Meep give you a Q value for this case ?

Thanks
He emailed me saying the Q was something like 57,000+ but was worried about the antenna position, I said run it if you want but I was still doing research into the antenna and had questions out to ppl who had 40 years + in this field. It's not one I would want to make.

Shell
Friendly reminder that Qs over 10K are probably impractical to consider because of the extremely narrow bandwidth; subject to wide variation of resonant freq caused by thermal/mechanical stresses. You could wind up chasing resonance around, especially with a magnetron. I'm with doc on this, high q is not a prerequisite imho.

Offline SeeShells

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@SeeShell -
Your .png and .csv files data is/are up have been uploaded here:

https://drive.google.com/folderview?id=0B1XizxEfB23tfm04QWNVVVVvT3gtcVAzRUp6T1BCLVpoV0EyeVVKR2ZxQkp2a3NKcUNPMU0&usp=sharing

I uploaded my meep data request file/form to hopefully explain what the data is, although it needs more English and fewer Scheme statements. The inside big end is at row 15 and small end at row 216 of the csv files, and the total run meep time t = 13.054 (6527 timesteps).
Thanks, interesting but not quite what we were looking to do. I'm still working out the antenna shape and placement and getting feedback like I said I was going to do on launching a Te mode. What I found out is a answer from a wonderful source that mretty much just lurks here.

Of course doing it isn't as easy as it seemed to be and I'm not sure you can do it in a meep model.
 
Quote from a email:
 "Your test setup looks great. If you use a 1/4 probe on the big end or little end you will launch a TM mode. If you use a 1/10 wave loop you will excite a TE mode at either top or bottom. I believe If you launch from the big end the net force will be toward the small end or vice versa launching from the small end as the reflected wave will be reduced by Q losses and will be smaller in magnitude than the launched wave.  A loop on the side wall will excite either mode depending on orientation wrt the frustum z axis. All walls on the frustum look like a conductive ground plane. For low power testing ,with the sweeper , the sample port I would use a probe 1/4 wavelength from the side wall, variable probe depth for the needed coupling to put the SA sampler in its optimum resolution range. If you use a loop you should place it at a low impedance point or H plane max node. <End Quote>

After hours of reading and several emails to people who are beyond my skills in antennas I would agree with this.

Shell

Here you have a Master of Science thesis on the RF fields excited by dipole and loop antennas inside a stainless steel wire mesh cage :

http://epublications.marquette.edu/cgi/viewcontent.cgi?article=1011&context=theses_open

Besides the obvious interest in the simulation of the mesh, notice the considerable effort in modeling antennas.

Quote
Three types of antennas were used for simulations; dipole, monopole, and loop. For experiments, only monopole and loops were used. The dipole was used because of its simplicity, and ability to excite the E-fields within the cage. The loop was used because it is a magnetic antenna, and well suited to excite the H-fields. 

For our case, the TMagnetic modes have an axial electric field, hence excited by the dipole antenna.  To excite a TElectric field which has a magnetic axial field, a loop antenna is needed.

Quote
Since the strongest E-fields created by the dipole are in the axial direction, to couple to a cavity it should be orientated in the same direction as the E-fields described by the mode configuration. 

The author used numerical simulation of electromagnetic fields, using The Numerical Electromagnetics Code (NEC) for simulation of the electromagnetic fields inside the cage and Matlab for post-processing of the results from NEC.

Showing once again that it is usual for researchers to use other codes to post-process data.  (Ditto for post-processing Meep data).
I'll be the first to say, need to learn more on antennas and looks like a good bedtime story. The mesh I understand why it's not a good reflector being almost 1/2 inch openings but I'll take it all in.

Thnaks,
Shell

Offline aero

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I'm curious as to why the capable engineers at EagleWorks are finding Q-values around 5,000 to 6,000, and yet around here there's a lot of talk about Q-values ten times higher?

Because EW is using real world materials with analog sources, not discretized sources and idealized copper that doesn't seem to heat or suffer significant losses of any sort. Perhaps, just guessing here, perhaps if the node granularity was less than the skin depth of the copper, we could see more realistic skin effects. But its not so we can't.
Retired, working interesting problems

Offline rfmwguy

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Speaking of magnetrons and antenna matching, read a lot of design papers on microwave ovens lately. An empty microwave is designed for ideal match. Food or liquid changes impedance match, yet magnetrons are not recommended to be fired into an empty microwave cavity. Since therrs nothing to absorb the em, the radome/monopole heats up on the reflected or standing waves.

Also read waveguide launchers for magnetrons are not designed for 50 ohms. One I read about was 550 ohms. In addition, standard mw magnetrons or designed to accept a mismatch up to 3:1 vswr. average mtbf is about 6k hours.

Perhaps we see why spr cooled their magnetron, to bleed of heat due to high standing waves. Wonder if the dielectric insert at ew was perhaps a radiation "sink". so many questions, so few data runs...hope to fix that.

Offline deltaMass

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I think I've lost track of all the DIYers now. Let's see:
1. TheTraveller
2. SeeShells
3. rfmwguy
4. Mulletron (?)
5. klm(?)

Is this on the wiki?
Is the wiki link not supposed to be at the top of the page btw? - can't find it.

Offline SeeShells

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I think I've lost track of all the DIYers now. Let's see:
1. TheTraveller
2. SeeShells
3. rfmwguy
4. Mulletron (?)
5. klm(?)

Is this on the wiki?
http://emdrive.wiki/Main_Page
http://emdrive.wiki/Building

I guess it's a dirty dozen so far
Is the wiki link not supposed to be at the top of the page btw? - can't find it.

Offline SeeShells

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...I wondered why that went quicker last night. Not quick but a little quicker. I guess you found out.

Check it again, they are there now.
I'm looking at the Yang/Shell Axial Antenna at Big Base case now: very unusual: the stress, and hence the force at the small base is practically zero.  The stress at the big base is a central point stress from the antenna.  Close inspection of this mode looks like another TM11 transverse magnetic mode but with drastically different amplitude.

QUESTION1: was the mesh kept the same as in the previous csv Yang/Shell case, and you are sure this is the stress at the small base and not outside it?

Most important: QUESTION2: did Meep give you a Q value for this case ?

Thanks

Everything about the run was identical except the antenna. The csv files are the same size aren't they? If something were changed likely they would change size. And really, the bases should be in the same place they were previously. I looked at this data set with HDFview. But note that the row numbers I gave you I had 1 added, to start at 1 like the csv matrices, instead of 0 as HDFview uses. If you also added 1, that would be the problem. The model skin is three matrix rows thick, adding an extra 1 would make the small base row be inside the skin.

It was also the same 58 mm antenna centered quarter wavelength from the inside face of the big base but rotated 90 degrees to an axial orentation. Note that 1/4 wave length is only slightly more than half of 58 mm, so the end of the antenna near the big base was about 1.5 mm away from the base, and excited with ez component although hy would have been more natural.

Q? Yea, Q was ridiculously high, like 60 million and the resonant frequency was like 2.463 GHz, which I ignored and made the run at 2.45 GHz.
I was looking for this Aero but models of a loop are hard to do. Any ideas out there?
Shell

Offline SeeShells

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Speaking of magnetrons and antenna matching, read a lot of design papers on microwave ovens lately. An empty microwave is designed for ideal match. Food or liquid changes impedance match, yet magnetrons are not recommended to be fired into an empty microwave cavity. Since therrs nothing to absorb the em, the radome/monopole heats up on the reflected or standing waves.

Also read waveguide launchers for magnetrons are not designed for 50 ohms. One I read about was 550 ohms. In addition, standard mw magnetrons or designed to accept a mismatch up to 3:1 vswr. average mtbf is about 6k hours.

Perhaps we see why spr cooled their magnetron, to bleed of heat due to high standing waves. Wonder if the dielectric insert at ew was perhaps a radiation "sink". so many questions, so few data runs...hope to fix that.
Just like this 2D simulation.
http://www.met.reading.ac.uk/clouds/maxwell/microwave_oven.html
Shell

PS:
Looks just like evanescent waves inside of the potato, not bad for an imaginary wave function that carries no energy.

Back to sleep.
« Last Edit: 07/23/2015 08:24 AM by SeeShells »

Offline SeeShells

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ACD
Asymmetric Cavity Drive

This debate is actually not really helpful.  :-\ The one who explains the physics correctly will give it a name in his paper, or do it democratically, but let's go back to science right now ::)

This for example:
ghost modes in imperfect waveguides
http://bayes.wustl.edu/etj/articles/ghost.modes.pdf
Thanks, a good ghost story at bedtime. Nice info in there.

Shell

Offline mwvp

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Use a simple internal working name...and take a hint from the marketing gurus in big pharma...the BIG EASY TO REMEMBER MARKETABLE NAME
...Brand it when there is a device that you want to have the masses interested enough in to fund it. Big companies may invest in it, but the masses still fund it, whether they want to ride on it or have it bounce reruns of Cheers to them from orbit.                                       

Then how 'bout "E-Jet; Shawyer-tron electrodynamic propulsor:D

Very sorry for that.

I need a laugh after watching the Woodward interview last night. Perhaps I was too vicious to the Eagleworks crew for marketing hype. Isn't the first time I've heard good scientists, engineers & professors lament corruption, politics and funding woes.

Offline mwvp

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Regarding using wire mesh,

A wire mesh waveguide is described in https://www.jlab.org/ir/MITSeries/V9.PDF pg 287 with a loss of .4db/m, compared to (typical?) .02db/m. Only ~10%. However, wouldn't one have to multiply that by the expected number of reverberations the wave will traverse? My math on factorials or series is a bit rusty.

$120 for a roll of copper looks pricey compared to the $15 aluminum next to it. Perhaps it can be copper plated? Pretty simple to copper plate.

Another paper on how to hack a magnetron, to work as an amplifier, CW and very (relatively) narrow bandwidth, and use magnetic solenoid tuning:
http://n5dux.com/ham/files/pdf/The%20Magnetron-A%20Low%20Noise%20Long%20Life%20Amplifier.pdf

Offline Rodal

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The question was not what name to use to market this device, or what name to use to write an article on a paper.  The question was whether to continue to use "EM Drive" for this thread in its next chapter #4, or to change it, to better describe what the thread should be about (motivated by the fact that we are close to starting a new thread and by the fact that Wikipedia decided to stop calling it "EM Drive" and have switched to "RF resonant cavity thruster").  The name "EM Drive" is trademarked in the UK and in the US to mean something completely different dealing with electric motors (http://www.trademarkia.co.uk/uk/em-drive-827809.htm  and  https://trademarks.justia.com/778/89/emdrive-77889765.html).

Yang, et al's 2008-2014 papers called it a microwave resonant cavity thruster.
« Last Edit: 07/23/2015 11:36 AM by Rodal »

Offline graybeardsyseng

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DIYer head's up. Copper flashing seems to be a cost-effect solution for frustum walls if you are not using mesh. As I was looking around for supplies, found this: http://www.acehardware.com/product/index.jsp?productId=1290779&KPID=984489&kpid=984489&pla=pla_984489

A 10ft roll seems to be the smallest length. I'd recommend the 14 inch for frustum heights to 11 inches. I can say from experience that .021 thickness will not be self-supporting and an exoskeleton will be needed. When I switched to a magnetron, the 1/8 in square copper supports were not ideal. I'd move to 1/4 in copper struts or possibly tubing.

Top and bottom plates on nsf-1701 were 1/2 oz copper clad pc board, again too flimsy for a 750g magnetron. Try the next size up. Solid copper plates would weigh too much, I stick with the pcb stuff, just make sure there are plated thru-holes or plenty of bolts to connect the 2 ground planes.

Any metal above ground potential will be subject to plasma discharge, so "mind the gaps" ;)

p.s. Bonus points for anyone who knows that phrase...
Had to do with electric trolleys I think. Before my time.

One thing you need to be aware of in copper is that it's mixed with tin to prevent corrosion, 80-90% mix is normal and if not 99% pure copper it will cause more heating signal loss and not be as a good cavity.

Shell
PS:
I'm still waiting (have some time) for my last piece of copper is holed out to my specs, was hoping to have a simulation run,  it is 99% pure the same they use in waveguides.

Shell, there are hundreds of copper alloys. Copper alloyed with tin is bronze. Copper alloyed with zinc is brass (both very generically speaking). What you are probably after is the highest possible electrical conductivity, which is commercially called 101 copper, or Oxygen Free High Conductivity (OFHC) copper.

Both brass and bronze typically have drastically lower conductivity than OFHC copper. Waveguides are often brass for structural reasons (its much stiffer and harder than OFHC), and are often silver plated internally to enhance conductivity. Cheaper waveguides are usually aluminum.

McMaster Carr (mcmaster.com) is a somewhat pricey but immediately available source for OFHC. Browse under "Raw Materials". They may even have perforated sheet.
A good heads up, I'm having to have the final copper frustum which is OFHC drilled and used for wave guides. Looked at McMaster Carr (bought a lot of stuff over the years from them) and it doesn't seem the have the right copper perforated sheets for the final build.

Thanks!
Shell

A good source of copper sheet, bar etc we use for grounding and other electrical apps is:

Georgia Copper 
http://www.gacopper.com/

Somewhat pricey on some things but they are fast with good customer service.   Also have some copper fittings - i.e.  nuts, bolts etc.

Herman
EMdrive - finally - microwaves are good for something other than heating ramen noodles and leftover pizza ;-)

Offline RERT

Folks - this is a contribution to theory, not replication. It demonstrates a solution to Maxwell's equations in a theoretical infinite two-dimensional cavity which describes a net total Lorentz force on the conductors. There are some reasons why this might be an academic curiosity, but it may be of interest.

The reason that the net force is not zero is that I've postulated that reflected waves at a conducting surface experience a small delay before being reflected. Since electrons have non-zero mass, this is a reasonable assumption, though the exact form of a constant delay is clearly an approximation. The second assumption is that the environment at either face of the cavity is asymmetric, and that consequently the delay experienced at each end may be different.

The scale of delay I'm contemplating is around 10^-13 seconds.

The 'cavity' is the space between two perfectly conducting planes at x=0 and x=-L. The fields are polarised with the Electric field in the y direction and and magnetic field in the z direction.

The classic solution (with no delays) is for the fields to be zero for x>0 and x<-L, and to be

E = 2A*sin(wt)*sin(wx/c)
B = (2A/c)*cos(wt)*cos(wx/c)

between the planes, where A is the amplitude of the electric field in the incident wave (travelling towards increasing x). w is the angular frequency of the wave, i.e. w = 2*pi*f, where f is the real frequency, and t and c are the time and speed of light respectively.

w is constrained by the geometry so that the incident wave is identical to itself reflected off both planes, giving w =2n*pi*c/L

Thinking first about reflection off a single plane with delay d, the fields within the cavity become

E = 2A*sin(w(t-d/2))*sin(w((x/c)-(d/2)))
B =(2A/c)*cos(w(t-d/2))*cos(w((x/c)-(d/2)))

This is interesting in itself, in as far as they are the same as the original, with the time origin displaced by around 10^-14 seconds and the position of the wall out by c*d/2 or about 10^-5 metres.

For x>0, i.e. outside the cavity to the right, the fields are:

E = -2A*sin(wd/2)*sin(w(t-(x/c)-(d/2)))
B = -(2A/c)*sin(wd/2)*sin(w(t-(x/c)-(d/2)))

This is a plane wave travelling to the right. The factor sin(wd/2) makes these fields small. For 3 GHz radiation the scale is around 10^-3.

We can find the surface current in this plane by using Maxwell's equations:

J = (1/mu)(Curl(B))-(epsilon)dE/dt

The non-zero component is in the y direction and is

J = 4A*(epsilon)*w*sin(wd/2)*cos(w(t-d/2))

We can now calculate the Lorentz force density  on the wall, by averaging the force J^B due to B on either side:

F (x direction) = 4*(epsilon)*(A^2)*(w/c)*sin(wd/2)*g(x,t)

where, resetting the origin of t so that t-d/2 ->t,

g(x,t) = cos(wt)[cos(wd/2)*cos(wt) - sin(wd/2)*sin(wt)]

The time average of the second term is zero, as it is like sin(2wt). The time average of the first is

cos(wd/2)*0.5

and this gives the time average force density at the wall of

F = (epsilon)*(A^2)*(w/c)*sin(wd)

I guess the punchline is just to observe that this depends on d. The situation at the opposite face is reversed, and so if there are two different delays at each face, the net force per unit area on the system is

F = (epsilon)*(A^2)*(w/c)*(sin(wd1) - sin(wd2))

Where d1 is the delay at x=0 and d2 the delay at x=-L.

To put a scale on this, observe that (epsilon)*(A^2) is the time average radiation pressure due to the incident plane wave. Switching to a more practical context, we can see that as

2*Q*P/c

where P is input power and Q is some quality factor. That gives

F = (2*Q*P/c)*(w/c)*(w*d1-w*d2)

(having used sin a ~ a for small a)

So say we have approximately:

(d1-d2) = 10^-14 seconds
w = 2*pi*3*10^9
c= 3*10^8 m s-1
Q=10^4
P = 1000 Watts/m^2

F = 2*10^4*1000*36*(pi^2)*10^18*10^-14/(9*10^16)
F = 8*10^-4 N/m^2

Since I think not many people will have read this far, I will post some more comments in a separate reply.

For those who have, thank you. If any of you have the time and inclination, I would really appreciate any efforts to find and fix any conceptual or algebraic errors in the above.

R.

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