EM drive - predictive analysis

[sanman]

I think that aero  solved all our problems gentlemen (with his last remark above ), but maybe not exactly the way he described it .  We could consider positron channeling in crystals..  So we have an experimental setup where after the pair production event,  the electron transfers some momentum to the nucleus,  and the positron will channel through the crystal,  thus increasing its momentum. No pair production  - annihilation chain reaction, all laws of conservation of energy and momentum are valid, and it explains the enhanced momentum transfer.  Bingo. I think that we are on the right track here.

So based on what you've said - what is the way to optimize the effect of "enhanced momentum transfer"? Is there some kind of "mean free path" metric that needs to be increased? Is it the case that the longer a produced pair persists before anihilation, then the more momentum transfer happens? Is there some travel requirement that has to be maximized for a produced pair?

[meberbs]

Where we disagree is related to whether momentum transfer with the electron as the mediator is more efficient than a photonic drive, where momentum is transferred directly, with the photon as the mediator.

For a single event, you are correct meberbs, the momentum transferred to the nucleus is smaller than the initial momentum of the photon.

Now we get into the hairy part, the chain reaction.

Which is just the same process again, the conclusion won't change if you don't make a mistake

We are on a reference frame tied to the mirror, in particular, to the nucleus.

To be clear, we are in the initial rest frame of the surface, we are not tied to it as it accelerates, because conservation of momentum and energy need to be calculated in an inertial frame.

The electron - positron pair is created. The electron transfers momentum to the nucleus. The positron is repelled by the Coulomb field of the nucleus, and annihilates with the electron of another atom. Two gamma photons are created (at or slightly above the total threshold energy 2mc^2 , where m is the rest mass of the electron ). At about 60% of light speed, due to the relativistic Doppler effect, an observer on the mirror will see the frequency of the incoming gamma photon doubled (when moving straight towards the photon, all the possible geometrical configurations have to be considered, this is just a special case ).

You just jumped to a completely different frame, so your calculations are invalid. Why are you suddenly moving at 0.6 c anyway?

5. If this chain reaction is impossible, why is that the case? Can you prove that this chain reaction is not possible?

It isn't possible, because the energy doesn't balance, at each step, you are expecting the mirror to have gained a relative 0.6 c in speed compared to its original. This magic acceleration is where all of the bonus energy is coming from enabling the chain reaction.

By the way, QFT (in particular QED) is need, in order to calculate the probability of these types of events, in order to see which are the dominating ones. There is no going around that, and the calculations are not pretty. This is actually the heart of the problem. Speculating based on the mathematics of relativity, and intuition, is not enough.

When the energy/momentum doesn't balance, the chance of the event is 0 (QFT requires calculation of virtual particles and such, but only within a near-instantaneous event, when the smoke clears, the final answer must conserve energy/momentum). It is a useful shortcut for cases like this.

[as58]

The "engine" does not emit anything. For each pair production event, momentum is transferred to the mirror, due to the laws of conservation of energy and momentum. The problem is trying to prove that the total momentum transferred makes this "engine" more efficient that a straight photon drive. I tried it with my chain reaction model (described above), but surely I am missing something.

If it doesn't emit anything, it's not even a photon rocket. It just doesn't move.

If the device starts at rest, operates for a while and moves a distance, what has moved the other way to balance the centre of mass? 

[aero]

I think that aero  solved all our problems gentlemen (with his last remark above ), but maybe not exactly the way he described it .  We could consider positron channeling in crystals..  So we have an experimental setup where after the pair production event,  the electron transfers some momentum to the nucleus,  and the positron will channel through the crystal,  thus increasing its momentum. No pair production  - annihilation chain reaction, all laws of conservation of energy and momentum are valid, and it explains the enhanced momentum transfer.  Bingo. I think that we are on the right track here.

So based on what you've said - what is the way to optimize the effect of "enhanced momentum transfer"? Is there some kind of "mean free path" metric that needs to be increased? Is it the case that the longer a produced pair persists before anihilation, then the more momentum transfer happens? Is there some travel requirement that has to be maximized for a produced pair?

Someone with more em physics may consider how the Lorentz forces might affect the electron and positron pairs. It's fine if the x and y force components are equal and opposite, but if all 3 force directions are equal and opposite then we're back to only the radiation pressure providing a differential acceleration on the particles. That might or might not be enough. The energy gradient in the cavity is quite large relative to the particle mass after all.

[cristian]

Channeling accelerators, this is the core idea. Conduction electrons in a metal form a uniform high density plasma with longitudinal plasma oscillations. Charged particles are accelerated along atomic crystal channels by plasma waves in metal. Positively charged particles are guided by the average electric fields produced by atomic rows or planes in the crystal. The particles make a series of glancing collisions with many atoms and execute classical oscillatory motion along the interatomic channels.

For reference, read the attached file, "Channeled particle acceleration by plasma waves in metals" .

So ultimately, the energy stored in the Coulomb fields of the nuclei of the atoms in metals is the energy that will accelerate the positrons to high velocities.

Also, have a look at a comparison between the classical and relativistic momentum:

http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Relativity/relativistic_momentum.html

This is what makes the difference, the relativistic mass increase of the positrons.

From a practical perspective, how do we actually build the system? Here is how I would do it, but keep in mind that there may be other ways. The central idea is always channeled acceleration.

Stage 1. Generation of an electron beam. For reference, see the following:

http://ozradonc.wikidot.com/generation-of-electron-beams

Stage 2. Creation of a source of positrons. For reference, see the following:

http://cerncourier.com/cws/article/cern/28542

Note that channeling is also used at stage 2.

Stage 3. Channeled positron acceleration by plasma waves in metal.

The attached article is the required reference for stage 3.

Due to the relativistic momentum increase of the positrons , this will assure the enhanced thrust for the system.

Note that the "battery" energy (the energy required to set up the system), is only used at stage 1 and stage 2. Stage 3 is all about the energy stored in the Coulomb fields of the nuclei of the atoms in the metal (the crystal lattice that will accelerate the positrons generated at stage 2). This is what makes the difference, and what makes this superior to a pure photonic drive.

I must give credit to aero for the following remark:

.......But, once there are electrons and positrons inside the cavity, I'm led to believe that they will be accelerated along the energy gradient within the cavity ......

Just some thoughts.

Of course, aero was thinking about the acceleration within the cavity, but in my mind, this remark made the difference between my dilettante talk about pair production - annihilation chain reaction, and other dead ends, and the real deal, the interesting idea of using the Coulomb fields of the nuclei of the atoms in metals, in order to increase the momentum of the positrons. Thank you aero, surely two minds are better than one.

So that's it. The system will eject high velocity positrons, and will gain an enhanced thrust, as compared to a purely photonic drive or anything else. All laws of conservation of energy and momentum are valid, and no weird physics necessary. This is so far from the original design of the EM drive that I will not even try a comparison, or ask why the original design works the way it does. This is a completely different system, and no fuel necessary. Pair production is essential.

Alpha Centauri, here we come!












 

[cristian]

And if you think that electron - positron annihilation will dominate (and positron channeling won't happen for a sufficiently long time , which I don't think is the case, if you read the references  ), then you can skip step 2, and channel the electrons directly. The results will be similar.

[meberbs]

Note that the "battery" energy (the energy required to set up the system), is only used at stage 1 and stage 2. Stage 3 is all about the energy stored in the Coulomb fields of the nuclei of the atoms in the metal (the crystal lattice that will accelerate the positrons generated at stage 2). This is what makes the difference, and what makes this superior to a pure photonic drive.

False. Read the article again, you need a high energy source to generate the waves in the plasma, and even the authors of that reference you attached weren't sure how to do it. Read from the middle of page 5.

[cristian]

Compared to the way relativistic momentum increases with velocity,  that is a small price to pay (you can do the math ). The efficiency will still be higher than anything currently possible, including the photonic drive. I am glad that you are paying attention. The energy stored in the Coulomb fields of the nuclei of the atoms of  the crystal lattice that channels the particles is quite large.

[as58]

So that's it. The system will eject high velocity positrons, and will gain an enhanced thrust, as compared to a purely photonic drive or anything else. All laws of conservation of energy and momentum are valid, and no weird physics necessary. This is so far from the original design of the EM drive that I will not even try a comparison, or ask why the original design works the way it does. This is a completely different system, and no fuel necessary. Pair production is essential.

Alpha Centauri, here we come!

Ok, it will emit positrons. So it's not propellentless at all, more like a normal electric propulsion system such as ion thruster.

[meberbs]

The energy stored in the Coulomb fields of the nuclei of the atoms of  the crystal lattice that channels the particles is quite large.

You can't just magically access this energy. The energy to accelerate the particles  comes from the waves you generate, which come from your power supply. Read the article more carefully, the waves don't spontaneously exist.

Compared to the way relativistic momentum increases with velocity,  that is a small price to pay (you can do the math ). The efficiency will still be higher than anything currently possible, including the photonic drive. I am glad that you are paying attention.

Yes, lets do the math. Since all of the energy to create and accelerate the particles is coming from your power supply, (and ignoring that you would probably have a bunch of wasted power due to inefficiencies) this means the energy required is a minimum of E = sqrt(m^2*c^4 + p^2*c^2), where p Is momentum. For a given E, it is clear that p will be smaller than for the photon rocket case E=p*c.

You are moving towards the idea of an ion engine. These are efficient because you don't have to pay the energy cost to create the matter. This comes at the cost of carrying limited propellant with you. If you had antimatter available to turn the propellant into raw energy, then you would be better off doing so and emitting the energy as photons rather than sending matter out the back.

[cristian]

Thank you meberbs for keeping me on my toes.  I have to put my thinking cap back on. The relativistic energy - momentum relation is perfectly valid, but you omit the phenomenon of self-oscillation,  when the energy losses in the oscillating system are small.  In this case,  in order to sustain self-oscillations,  the quantity of energy entering the system is very small in comparison with the total energy within the oscillating system.

I will make a naive, imperfect analogy,  dealing with a simple classical situation.  We consider a sinusoidal train track, hill,  valley,  hill, valley,  and so on. A levitating train starts at the top of the first hill, we have to put it there, so we spend some potential energy. We release it. The levitating train will go up, down, up, down, and so on. Potential energy (at the top of one hill) is constantly converted to kinetic energy (in the valkey), but there are some small energy losses due to air resistance. From time to time, when it approaches the top of the hill, we have to give it a small push, in order to continue its travel. Now,  let's  imagine that every time the train is in a valley  (maximum kinetic energy), we release a small ball through the window.  In principle, we can release as many balls as we want,  at a very small expense of energy. Clearly, the analogy is far from perfect,  but you get the idea.

The electron plasma waves take advantage of the ''landscape", the distribution of the nuclei (with their Coulomb fields) of the atoms  in the crystal lattice that channels the particles. We have to spend some energy to excite the plasma, but then the energy required to maintain the self -oscillatory system is minimal (regardless of how many particles are channeled through the lattice ). This is where we take advantage of the energy stored in the  Coulomb fields of the nuclei of the atoms of the crystal lattice.

One more observation that might make you think. Just as an example,  heavily doped silicon has its plasma frequency in the infrared region,  close to microwave (so some materials have their plasma frequency close to microwave ). In some designs of the EM drive,  a dielectric resonator is added in front of the narrower end. That is interesting, isn't it? The microwave field in the cavity excites the electron plasma in the resonator,  and we could have here some sort of electron channeling, that generates the thrust. If the EM drive works,  channeling has something to do with it. The relativistic momentum increase of the channeled particles is what generates the thrust.  Could be much more efficient than a photon drive. I hope you agree. 

[sanman]

The relativistic momentum increase of the channeled particles is what generates the thrust.  Could be much more efficient than a photon drive. I hope you agree.

See, that's what makes me wonder about Laser Wakefield acceleration - because it provides such a high accelerative gradient to achieve relativistic velocities for electrons, that you can get extra action-reaction from that via relativistic momentum increase. Of course, the duty cycle on a Laser Wakefield accelerator is low, but it's still something to think about.

[aero]

The relativistic momentum increase of the channeled particles is what generates the thrust.  Could be much more efficient than a photon drive. I hope you agree.

See, that's what makes me wonder about Laser Wakefield acceleration - because it provides such a high accelerative gradient to achieve relativistic velocities for electrons, that you can get extra action-reaction from that via relativistic momentum increase. Of course, the duty cycle on a Laser Wakefield accelerator is low, but it's still something to think about.

While the SCSC was to big to put into any foreseeable spacecraft, it did accelerate protons (much more massive than electrons) to approximately 99% the speed of light in the first 20 feet of travel from the start. At least that was the design if I understand Seashells right. (she worked on the SCSC).

[cristian]

Well,  together we reached an interesting conclusion.  The principle of operation of the EM  drive has something to do with  electron channeling in a crystal lattice.  The thrust is connected to the relativistic momentum increase of the channeled particle. An interesting article to read is "Interpretation of electron channeling by the dynamical theory of electron diffraction ",  written by Kambe,  Lehmpfuhl, and Fujimoto (can be easily found for free on the net). Nonlinear dynamics, self oscillations,  and other phenomena are essential. Based on these principles,  the design of the EM drive  (with the right materials,  at the correct operational parameters,  in terms of energy and geometry)  can be vastly improved.  Compared to the tomes of nonsense that have been written about this issue,  I think that we reached a down to earth, interesting conclusion, in a relatively short period of time (and I am not aware of anybody else who followed this trail ) . I hope that experts will follow this direction of research. Thank you aero, meberbs, sanman,  as58, and everybody else who participated in this discussion.

[meberbs]

Thank you meberbs for keeping me on my toes.  I have to put my thinking cap back on. The relativistic energy - momentum relation is perfectly valid, but you omit the phenomenon of self-oscillation,  when the energy losses in the oscillating system are small.  In this case,  in order to sustain self-oscillations,  the quantity of energy entering the system is very small in comparison with the total energy within the oscillating system.
...

I am not sure how you think I am omitting something. All the the energy that got the oscillations started had to come from somewhere (your battery) and if you want to keep them going, you will need to add in just as much energy as you extracted by accelerating a particle.

To use a planetary flyby as an example: it appears to violate conservation of energy, only because you neglect the change in the planet's velocity.  You really are stealing energy from the planet, and if the planet didn't have so much energy to start with, you would have to have a giant rocket move the planet back to its proper orbit.

Well,  together we reached an interesting conclusion.  The principle of operation of the EM  drive has something to do with  electron channeling in a crystal lattice.  The thrust is connected to the relativistic momentum increase of the channeled particle.

I am not sure how you reached this conclusion. You have neither shown how your proposed mechanism could be happening in an emDrive (typical emDrives are not single crystal to start with), nor shown that any better than a photon rocket worth of thrust can be produced. You keep handwaving steps saying "relativistic momentum gives a boost" when this does not happen. If you actually did math and calculated the energy and momentum you would see this.

Also, you phrase this as an absolute statement as if this must be the mechanism of operation. The most likely explanation of emDrive force measurements remains experimental error (thermal expansion, etc.)

[cristian]

You are correct in what you are saying, but I will clarify what I mean. We write E_b for the energy of the battery. We write E_e  for the energy of the electron,  E_p for the energy of the photon. We also write a for the energy conversion coefficient for the photon (the fraction of the battery energy transferred to the photon ) , and b for the energy conversion coefficient for the electron. We write c for the speed of light.  Clearly we have a < 1 and b < 1.

The photonic drive.  In this case we have  E_p = a * E_b  = c * p.  The efficiency coefficient,  the ratio between the momentum  of the photon and the energy spent  (battery energy) to put it in that state is
 efficiency_photon = a/c , where c is the speed of light.

Electron channeling.  I  this case we have E_e = b * E_b = sqrt (m^2 * c^4 + p^2* c^2). In this case, the efficiency coefficient is  efficiency_electron = b * p/sqrt (m^2 * c^4 + p^2 * c^2).

If b is larger than a, and we assume that we do not have to spend energy to create the electrons, then we have efficiency_electron > efficuency_photon. We work with the electrons already existent in the crystal lattice  (the material ) that performs the channeled acceleration.  The operational life span of such a crystal could be many years (until structural defects in the lattice appear, or other problems).

In electron channeling,  we are dealing with nonlinear dynamics, self oscillations,  and other complex phenomena.  A good reference to start is "Interpretation of electron channeling by the dynamical theory of electron diffraction",  that I mentioned in my previous post.  It is perfectly conceivable that b > a. That is the point that I am trying to make, but the proof requires expert level solid physics,  and I do not have the required background.  Neither can you prove that my speculation is incorrect,  but the burden of proof rests with me indeed,  because I make the speculative statement (with the help of the people that participated in this discussion ). The relativistic momentum increase of the accelerated electrons (leaving the channeling crystal ) is what gives the required thrust (conservation of momentum ). The fact that the design of the EM drive includes a dielectric resonator with plasma frequency not far from the microwave region, and the fact that unexplained thrust has been observed in experiments all over the world mean something. They could not all have neglected thermal effects.

Compared to baloney theories like "relativistic pressure imbalance ",  or "virtual quantum plasma", or theories that attack the laws of conservation of energy and momentum  (and there are many other ), this model is down to earth and decent. I think that there is something interesting here that is worth further investigation.  A few decades  of operational life span of the channeling crystals are enough for a trip to Proxima Centauri.

Only in this sense,  and for a finite period of time, the efficiency of the electronic channeling drive is superior to the photonic drive.
 

[cristian]

One more short note meberbs.  Even if we spend energy creating the electrons on board (pair production ),  the relation efficiency _electron > efficiency_photon can still be satisfied if b is much larger than a, but this is less likely.  Please feel free to poke many more holes in my theoretical speculations,  I like it, and it is constructive.

[as58]

It is not strange (and definitely not new) that with the same power you get more thrust by ejecting massive particles instead of photons. But that is obviously not propellantless propulsion. I'm not seeing what is new in your proposed scheme.

[cristian]

There is no free lunch in science,  that's what I think. It's a matter of efficiency,  as defined in the discussions above. You can carry a lot of propellant on the ship,  and eject it at relatively low velocities,  for short periods of generated thrust,  or you can carry less propellant and eject it at high velocities  (taking advantage of relativistic momentum increase ),  for long time of  generated thrust. If the efficiency is high enough  (compared to a photon drive ),  you can even create electrons on board  (through pair production ),  in order to continue the journey. This is what would be needed for interstellar travel.

Related to the Woodward effect (and many related issues ),  I have no opinion whatsoever,  since I did not study the issue.  Related to particle channeling propulsion,  the principles are not new,  of course,  but the efficiency could be far superior to anything else achievable with current technology. The devil is in the details,  though.

[cristian]

Since we are in the predictive analysis section,  let's not forget the first step in all this. Related to the EM drive, when thrust is detected , electrons should be detected behind the dielectric resonator  (should look for positrons too, but less likely), in the oposite direction of thrust. Their velocity distribution should be studied. Various materials  (with plasma frequency close to the frequency of the radiation) should be tested. Experimental physicist know how to approach this problem, so that any possible sources of "noise " would be eliminated .  My bet is that high velocity electrons will be detected.