Reaction or Reactionless -- Acceleration force on a microwave antenna

[skeptic2]

A microwave transmitter, bouncing the microwaves off a parabolic dish, should have a small amount of acceleration due to the reaction of the microwaves against the dish.

Would an arrangement of two dipole antennas, 1/4 wave apart and phase shifted by 90 deg., creating a cardioid pattern, produce a similarly small acceleration in the direction of the null?

 

[BvU]

A microwave transmitter, bouncing the microwaves off a parabolic dish, should have a small amount of acceleration due to the reaction of the microwaves against the dish

Says who ?

"A soccer player should feel a slap when the keeper stops the ball"
-- and nothing when the keeper misses it ?

 

[anorlunda]

I presume your question is about radiation pressure; correct? Tiny in an antenna, huge in a thermonuclear warhead.

https://en.wikipedia.org/wiki/Radiation_pressure

 

[skeptic2]

My question was with regard to both antennas in space whether there would be acceleration with the second antenna arrangement as there would be with the first.

 

[berkeman]

My question was with regard to both antennas in space whether there would be acceleration with the second antenna arrangement as there would be with the first.

That's actually an interesting question. The "directivity" of the 2-element antenna is a result of constructive and destructive interference, not due to being concentrated by a reflective element. I'm guessing it would not result in a net force, but I'm not sure about that.

http://antennadesigner.org/cardiod_directivity.html

 

[skeptic2]

Thanks Berkeman, that's the thought I was trying to convey. I tend to think of it the same way you do that because of destructive interference there is no net force. However, now let's put an enclosure around the two dipole antennas with RF or microwave absorbing foam on the inside. The photons on the constructive interference side of the antenna will impart their momentum to the enclosure as the foam absorbs them. What will happen on the null side of the antenna? Are the photons destroyed by the destructive interference or are they still there but merely out of phase. If the latter, will their momentum likewise be absorbed by the RF absorbing foam, canceling the momentum of the photons on the opposite side. The problem I have with that argument is that if the RF power were great enough, I would expect the foam on the constructive side to get warm but not the foam on the destructive side. Does that mean there really are significantly fewer photons hitting the foam on the destructive side? Would this arrangement with an enclosure around the dipole antennas have a net force in direction of the side with constructive interference?

 

[berkeman]

I didn't quite follow your version of the setup with the absorbing material, but I think there is another version that helps to clarify what is going on with constructive and destructive interference...

Consider two high-gain microwave horn antennas, maybe even with parabolic reflectors to concentrate the output beams even more. Drive the two antennas 180 degrees out of phase, aim them in the same direction, and bring them closer and closer together. When they get (arbitrarily) close together, their radiation pattern will largely be nulled out due to destructive interference.

But it's hard to believe that there will be anything going on with that interference in the far field that will affect the reaction force (radiation pressure) caused by emitting the radiation from each transmitter/antenna.

I think I'll have to page a few physicists to have a look at this question to get better insights...

 

[skeptic2]

The RF absorbing foam is to absorb the photons in the direction they were emitted and keep the them from bouncing around inside the enclosure and complicating the results. Do I understand your comment correctly that even though the photons from the antennas destructively interfere, resulting in much less energy, i.e. photons detected in that direction, you believe they still maintain their momentum and would still cancel the momentum of the photons traveling in the opposite direction. If so, what happened to the energy of both (out of phase) photons after destructive interference? How can they still have momentum if the photons themselves can no longer be detected?

 

[Klystron]

If you have access to Microwave radiometers or similar device, you can at least calibrate the microwave emitters.

If you wish to measure RF energy in a waveguide prior to or at the feedhorn, a Bolometer with attendant test equipment can provide data including the shape of the lobes from your source. While not directly answering your momentum questions, you will have expected values that can be compared to 'reflection' from the antenna.

This thread on Microwave measurement lists several methods to measure RF depending on your experimental setup.

 

[mfb]

Would an arrangement of two dipole antennas, 1/4 wave apart and phase shifted by 90 deg., creating a cardioid pattern, produce a similarly small acceleration in the direction of the null?

If your two antennas are fixed relative to each other: Sure.
It is sufficient to consider the total momentum. You have directed emission of radiation, carrying momentum. The antennas have to accelerate in the opposite direction.

If you want to study it element by element: The radiation of antenna 1 will exert a force on antenna 2 and vice versa, but the two forces don't sum to zero. The difference is balanced by the emission of radiation.

 

[Baluncore]

Consider two parallel dipoles, excited with the same frequency signal. The dipoles would have an RF current circulating with the expected magnetic field. I would expect a force to appear between the two dipoles due to the magnetic fields, a force dependent on the phase of the currents and their separation.

 

[skeptic2]

Thank you Klystron, but as this is so far just a thought experiment we won't be making any measurements.

Yes mfb and Baluncore, the antennas are fixed and I agree that the magnetic fields of each antenna will exert force on the other but I had assumed that as they are fixed the forces between the antennas would not affect the net acceleration of the system as a whole. I may be wrong.

Consider a photon traveling from one antenna to the next in the null direction of the pattern. This photon has a certain momentum as does the photon leaving the second antenna 180 deg. out of phase from the first. When the two photons meet and destructively interfere, what happens to the momenta of both photons?

 

[Baluncore]

When the two photons meet and destructively interfere, what happens to the momenta of both photons?

RF photons do not interact like that. The waves generated by the dipoles move away at the speed of light. Their later constructive or destructive cancellation will not affect the dipoles unless energy is reflected back to the dipoles.

 

[skeptic2]

Baluncore, what about the near field effect? There is a magnetic field around each antenna that intersects the other dipole and magnetic fields do exert forces on other magnetic fields and thus the antennas from where they came. Nevertheless, like you, I do not see how these magnetic forces would affect the outcome of the experiment.

 

[Klystron]

Thank you Klystron, but as this is so far just a thought experiment we won't be making any measurements.

Even so, your mental mockup microwave system might benefit from measuring devices. I lost visualization ability about the same place (post) as Berkeman.

Also consider eliminating parabolic or any geometry reflector in favor of a Fresnel lens to focus output directly from a feed-horn emitter. [edit:assuming your are interested in efficiency.]

 

[skeptic2]

Also consider eliminating parabolic or any geometry reflector in favor of a Fresnel lens to focus output directly from a feed-horn emitter.

I'm sorry if my description hasn't been any clearer. I am not including any parabolic reflector or Fresnel lens in the example. It's really nothing more than two dipoles, 1/4 wave apart, fixed relative to each other but not fixed to anything else (think located in free space). The question comes down to whether the photons emitted in the direction of the null and therefore subject to destructive interference still have momenta (after the destructive interference), even if the photons themselves can no longer be detected due to the destructive interference. If not, what happened to their momenta?

 

[Klystron]

Got it, thanks. Despite 'dipole' I was visualizing omni-directional.

 

[russ_watters]

This is an attempted EM Drive, isn't it?

 

[berkeman]

This is an attempted EM Drive, isn't it?

Hopefully not. I'm no expert, but it seems much more like a question related to Radiation Pressure. Destructive interference is a bit strange by itself, but how it relates to Radiation Pressure seems like a reasonable question. Like, if a Solar Sail moves through a region of Constructive and Destructive EM interference, does its acceleration change?

https://en.wikipedia.org/wiki/Radiation_pressure

 

[anorlunda]

Like, if a Solar Sail moves through a region of Constructive and Destructive EM interference, does its acceleration change?

Now there's an interesting question. Do the momenta interfere? I have no idea what the answer is.

 

[mfb]

The question comes down to whether the photons emitted in the direction of the null

There is no such thing. There is no emission in that direction (at least in an idealized setup).
It is also not necessary, or even useful, to consider photons. This is much easier to analyze classically as fields.

 

[anorlunda]

It is also not necessary, or even useful, to consider photons. This is much easier to analyze classically as fields.

So EM fields interfere classically. Do the momenta of those fields interfere too?

 

[mfb]

You can calculate the Poynting vector everywhere and momentum is conserved both locally and globally in every possible configuration.

 

[skeptic2]

Do the momenta interfere? I have no idea what the answer is

Good, anorlunda, this is where I was going with my post. I don't know either but I think the answer must be yes. The reason I think yes is that I think it absurd to consider the momenta of photons which themselves cannot be detected. Also, given the double slit experiment with the interference pattern at a screen at some point behind the double slit; if that screen were to be moved farther back we would find that the photons from each slit have passed through the nulls between the interference lines and created a new interference pattern, proving the photons still retained their momenta even as they passed through the nulls. This suggests that even though the momenta have destructively interfered at the null, each photon still retains its own momentum so that after it passes the null, the momentum of each photon appears again just as does the photon's energy.

There is no such thing. There is no emission in that direction (at least in an idealized setup).

Could you please clarify mfb? Are you saying that the photons from both dipoles know that if their direction is that of the null, they are not emitted in the first place?

@russ_watters: I think if this discussion ends the way I think it will, it will show that this method will not work for an EM Drive.

 

[mfb]

Also, given the double slit experiment with the interference pattern at a screen at some point behind the double slit; if that screen were to be moved farther back we would find that the photons from each slit have passed through the nulls between the interference lines

You wouldn't. You can block the places of null intensity and it has no effect on the interference pattern.
Conversely: If you only make slits there the intensity will be null everywhere.

proving the photons still retained their momenta even as they passed through the nulls

Again: There is no such thing.

Are you saying that the photons from both dipoles know that if their direction is that of the null, they are not emitted in the first place?

That's like saying an apple knows to not grow on a banana tree.
And see above: You are needlessly making this harder to understand if you want to include photons.

 

[Baluncore]

Do the momenta interfere? I have no idea what the answer is.

If the space is linear then the resultant field is the sum of the incident fields. Destructive interference will reduce local radiation pressure while constructive interference will increase it.
We are clearly dealing here with waves, not with individual photons or quantum phenomena.

 

[sophiecentaur]

Says who ?

"A soccer player should feel a slap when the keeper stops the ball"
-- and nothing when the keeper misses it ?

In this case, the kicker and keeper are strapped together. Momentum is conserved in all cases. The keeper would feel a jolt when the kicker kicks and the kicker would feel a jolt when the keeper catches the ball. The result is that the CM of K&K & ball would be in the same place.
The net force in the whole antenna will be in the opposite direction to the centre of any beam.

Like, if a Solar Sail moves through a region of Constructive and Destructive EM interference, does its acceleration change?

If there is a variation in the Energy Flux, there will also be a variation in the Momentum in the beam. I guess the simultaneous situations of high enough beam power and high enough coherence at the same time would not be unthinkable with some fancy laser propulsion system.

Do the momenta interfere?

The waves interfere. The momentum variation is a consequence of that.

 

[anorlunda]

@mfb pointed the way. Let's pay attention to his exact words.

You can calculate the Poynting vector everywhere and momentum is conserved both locally and globally in every possible configuration.

We are talking about classical waves, not photons.

The Poynting Vector $S=\frac{1}{\mu{_0}}E\times{B}$

and the density of the linear momentum of the electromagnetic field is $\frac{S}{c^2}$

Now let's apply that to destructive interference. That question has been addressed on PF several times. Conservation laws are observed, but the distribution of energy and momentum densities are "rearranged"

https://www.physicsforums.com/insights/fabry-perot-michelson-interferometry-fundamental-approach/
https://www.physicsforums.com/threads/interference-puzzle-where-does-the-energy-go.942715/page-3
https://www.physicsforums.com/threa...erference-of-plane-waves.960024/#post-6088123
https://www.physicsforums.com/search/96537708/?q=destructive+interference+conservation&o=relevance