Probably a Dumb Idea

[john_auerbach]

Good evening everyone,

I originally got into fusion after seeing the late Doug Coulter's ideas involving alternating between AC and DC currents to induce stable oscillations. From what I have read it seems that the primary difficulty is the coulomb collisions of ions inside the chamber. Statistically the ions will want to go to a higher entropy state, fighting the uniformity caused by the plasma spheres. As they reach the inside of the cathode, their momenta has nowhere to go, and they bounce back in extremely unstable ways, meaning fusion can only occur in periodic sparks after the ions disperse, rather than engaging in any sort of resonance.

I am wondering what the implications would be if one were to attempt to apply this idea to tokamak fusion devices, as in trying to create a fluctuating volume toroid of sorts, with ion collisions occurring radially in the plane normal to the direction of ion flow, (i.e. oscillating compression and expansion along the x and y coordinates in a Frenet-Serret coordinate system). My intuition says that the radial components of these elastic collisions would mostly cancel, though I suspect there may be a differential in field strength and stability along the inner and outer edges of the plasma ring, and even a possible coriolis drift that must be taken into account. In response to the compression forces in the xy plane, particles would theoretically want to be squeezed out along the s direction (along the path of the ring). Due to the relativistic velocities of these ions however, an individual ion would theoretically see the ions in front of it as dramatically closer, and the ring as a whole would appear to be a smaller radius if I am not mistaken.

My experience in relativistic electrodynamics and beaming is extremely limited, so I apologize if I am utterly butchering the physics that go into something like this. My illiteracy in this area should wane as I get further into my studies, especially as I move on to graduate school in a few years. What I am wondering is this: would the closer perceived distance between the ions at relativistic velocities imply they feel a greater compression force between them? Or is this simply cancelled by a relativistic contraction of their electromagnetic fields? I feel like it would simply be cancelled and they would feel no 'extra force' per-se, otherwise it would imply that there is extra energy available in modern tokamaks, not to mention it would open a whole new can of worms. In the case that I am wrong and they actually do feel a relativistic compression along the ion ring, would that imply that a periodically oscillating plasma could derive a force from this interaction in a tokamak to fuel a more energetic outward expansion?

The whole idea came from 'the hairy ball theorem' and I was thinking that any non-radial velocity of an ion in an oscillating plasma sphere would be wasted, and due to coulomb forces it would be hard to have a geometry where the ions would want to interact in any sort of nice, non turbulent way. But with a toroidal shape, a buildup of velocity in any non radial direction would theoretically be conserved as part of that oscillation, naturally reaching a stable state. I am almost certain that the whole virtual relativistic force thing is wrong and would probably also be detrimental to efficient fusion assuming it exists at all, though I don't see why an oscillating toroid wouldn't be more stable than a sphere as long as it is possible to properly tune the electromagnetic fields.

I'm not posting this because I believe I've had some sort of unique revelation about fusion that nobody else has thought of or anything, it just seems like a curious idea and I have been unable to find any information about similar ideas online.

I mostly just want to know how I should go about exploring these ideas and the physics behind them, if there are any important considerations in a set up like this, or if anyone can explain why an idea like this is unfounded or unviable.

Thanks for taking the time to read this long post from an amateur who is way out of his depth, hope there are some people on here that would enjoy discussing something like this

John

[Liam David]

There's a lot to unpack here and I haven't gone through your ideas in that much detail, but a couple of incomplete thoughts in response:

1. I'm not sure what you mean by "As they reach the inside of the cathode, their momenta has nowhere to go...". Indeed the density increases and therefore the probability of coulomb scattering, but this doesn't seem to be what you're talking about.

2. In the ion frame of reference, assuming a monoenergetic distribution for simplicity, locally the ions do not see each other as closer. Indeed, the ring shape will be contracted, but only in the direction of motion and hence it will look like an ellipse (or some oblate look-alike, haven't done the math but probably a conic section given how they tend to show up in SR). If we set up a toroidal curvilinear coordinate system with toroidal angle theta = [0,2pi), an ion at theta=0 will indeed see an ion at theta=pi/2, say, as contracted closer. Ignoring debye shielding, only if the minor radius of the torus is comparable to the major radius will the vessel wall not occlude them.

In the lab frame, the ion electric fields are contracted along their direction of motion.

I'm not sure how you jump from contraction to an extra force that "fuels a more energetic outward expansion".

3. You will never get relativistic ions in a tokamak, or likely any fusion reactor present or future, for myriad reasons. The rest mass of deuterium is ~2 GeV, and we ain't building a reactor on that energy scale. Even for reactions like p-B11 that would benefit from MeV-scale systems, the relativistic correction is of the order (1e-3)^2 = 1e-6, or entirely negligible. The electron bremsstrahlung would be ridiculous. Also, fusion will not happen at those energies. At best, you might have some stripping reactions among the mess of reactions that are best left to the particle physicists.

4. The hairy ball theorem is intrinsically a 2d problem (ok, a 2n dimension, n = 1,2,3... but we don't live in 4D). If you nest tangent (velocity) fields on infinitely many spherical shells to form a volumetric sphere, the cusps would just correspond to radial motion. These spheres will be randomly oriented (if we use the cusps as points of reference). Moreover, due to isotropy, the tangent field will average to zero everywhere and so the theorem does not apply. I'm not sure exactly how you're mapping ion phase space to the tangent space of a sphere/torus, or how you're getting no conservation/conservation, respectively.

Interesting ideas, you've gotten me thinking about a few things as well.

[Richard Hull]

Liam's point #3 is spot on and shows his study of issues related fusion and its limitations in simplistic theoretical machination and suggestion related to that which he commented on. In any theoretical situation, we not only need to examine the physics limitations but also be able to conceive of how the hardware might be put forth to do what theory predicts and demands. Relativistic deuterons relate to accelerating energies that are just not doable in any reasonable assembly attempting to do fusion.

All of the limitations and exceptions are well covered by Liam who has his feet in both worlds. These worlds are complimentary. They are a good grounding the fusion physics, and in the mechanization and engineering issues in making things in the theoretical models come to pass. That is, come to pass in a real world filled with "gotchas" that definitely are against any atoms fusing to a degree where real net energy is available for use in a well controlled device or system.

Still, Liam thinks of your ideas as interesting and admits to getting him thinking. Learning by reading and classical, instruction followed up by theoretical assertion arising from same, must be bounded by experience in the doing. The mind can readily go anywhere, but will that anywhere find a place in the real world? In short, if you can dream it up, are you also capable of imagining how to actually mechanize it? The latter is typically filled with flies in the ointment. Relativistic deuterons in a fusion system rolls of the theoretical tongue with ease. Obtaining relativistic deuterons in a fusion system is a bridge too far.

In the end, for a useful fusion system, the actual distributable, usable, electrical energy should be an order of magnitude greater than that input into the system to obtain the fusion output. We have discussed that if fusion will be accepted as an energy source in future, the power company "bean counters" will be the final arbiters, not the physicists or the engineers who brought forth over unity fusion. Fusion has to not only pay for itself, but deliver a suitable profit to the company at a price the electrical customers will be willing to pay for it.

There are many choke points or "strangle holds" in useful fusion's path.....The physics bounding the universe fusion within it. The material science and engineering to mechanize any successful physics. The power company bean counters accepting fusion, as a physical construction in being profitable before a public willing to buy it at their stated price. Naturally, all physics and engineering efforts over the past 70 years and billions spent, have all failed miserably at doing useful fusion on a corporate and publicly viable 24-7-365 delivery rate. ITER is sure to join this fail list, "real soon now"

Richard Hull

[john_auerbach]

Thank you Liam and Richard for the incredibly thoughtful and in-depth responses!

In regards to your first question, that was definitely not the most elegant way I could have worded it. What I meant was that for an oscillating plasma sphere, you ideally want all the particles in phase, passing through the center of the cathode at the same time. As they approach the center however, we often get insufficient fusion interactions because most of the ions do not have trajectories that directly pass through the center, with the increase in repulsive coulomb interactions. In theory, if someone were to have a system that was perfectly balanced, with all ion trajectories passing through a single point, it would be far easier to constrain the motion to a resonant frequency than if you have completely unpredictable (elastic?) interactions going on.

I'm not sure what the exact distribution is for ion trajectory in a POPS, most of the papers on it appear to be blocked by paywalls, but I would assume that coulomb scattering would widen the distribution of particle velocities, positions, and angular momenta which would mean only a small portion of these interactions would have sufficient collision energies for fusion during any realistic resonance. This isn't even taking into account the energy losses and disruption due to a grid, since there isn't really an effective method of initially lensing particles toward a point in the first place (as far as I know). I believe there have been attempts to do it without a grid with various field designs (quadrupoles, etc.), injecting electrons into the center to try to neutralize the space charge and limit electrostatic repulsion to create a stable harmonic oscillator potential, but I haven't seen anything that has truly fine-tuned control over every aspect of the ion's motion in a way that can squeeze that distribution into more uniform and precise oscillation.

In terms of angular momenta, a small net 'spin' of particles due to random interactions or intentional perturbations around the center point might not be a problem, as ion densities in a perfectly uniform collapsing ion sphere should still be efficient enough to induce fusion at higher energies, even if its radius does not go directly to 0. Along the equator of this sphere, would having that extra angular momentum among all particles allow these oscillations to be more uniform? In other words, I am wondering whether a plasma sphere that doesn't fully collapse would be more stable. My thinking behind this is that the ions generally want to conform to the driven, in-phase oscillations of the potential well, but every time they approach too small of a target, the dramatic increase in random interactions would ruin that homogenizing of ion momentum with each pass through the cathode. This may simply be a property that is unavoidable, as any field strong enough to induce fusion will inevitably cause this repulsion (excluding electron injection).

The main problem I found when thinking about this is that if you have any sort of spinning spherical shell of ions, the ions located closer to the points on the surface that intersect the axis will have significantly less angular momentum about the rotational axis. This is sort of the idea I was thinking about in relation to the hairy ball theorem, where you can't really have a net velocity of ions moving about the surface of a sphere without having those static nodes in the vector field. You could potentially try to induce some kind of flat ring which increases and dramatically decreases in radius with an oscillating potential, though I am assuming that the massive energy required to force the ring into a smaller radius would just leave us back where we started, and it has probably already been attempted anyway.

That's why I was considering the whole toroidal oscillating plasma sphere idea; while electrostatic oscillating plasma spheres have 3 spatial dimensions of possible distribution blurring from uniform states due to random elastic interactions, would interactions which cause a change in ion momenta along the tangential direction of a torus be canceled out by similar interactions adjacent to it along the ring? This is what I meant by 'compression force;' interactions of ions traveling perpendicular to the center line with trajectories that are not perfectly aligned may interact elastically and each have new, opposing components of momentum along the tangent line which are equal in magnitude. In other words, the momentum of the system is conserved, but each individual particle may have an increase or decrease in its angular momentum after this interaction. And any net torque or change in angular momentum would simply accelerate or decelerate the ring of particles as a whole. So if we have ions along the surface of this oscillating torus, would one dimension of their motion be forced by the adjacent ion densities to be relatively constrained, leaving only 2 dimensions to worry about, ie. a planar cross-section of the torus? Not to mention, the presence of angular momentum might help to limit two-stream instabilities if electron injection is used.

Of course, easier said than done. I don't even want to think about the electromagnetic configurations required for something like this. I know it is possible in current tokamak setups to actually shape the plasma with poloidal magnets, perhaps even in a variable or oscillatory way, but there are definitely a tremendous amount of things to consider with such convoluted dynamic fields. I have no idea if any of this would even be remotely beneficial, and there are definitely many, many more probable ideas for greater fusion efficiency that would likely be far more viable and have been modeled with actual calculations by people who are qualified to work on this stuff. Still, always good to wonder about crazy ideas! At the very worst you end up reading a few more papers and learning a little bit more. Can't wait to explore all of this in greater depth, this is an incredible field with so many interesting puzzles! Thanks for all the help.

Also, about the SR stuff: I didn't even realize Tokamaks weren't relativistic, I guess I just assumed they would be without really thinking simply because it looks like a particle collider (I wonder if the sprinkles on a donut travel with relativistic velocities!), without even thinking that the velocities necessary for fusion in a tokamak would be on a similar order of magnitude to the ones in an IEC. That's definitely quite a large misapprehension, my apologies and thanks for the correction!

Hope that helps give a little more detail into my thoughts, and again thank you so much for taking the time to reply!

John Auerbach

[Frank Sanns]

Macroscopic oscillations, no matter how strong, do nearly nothing at the atomic level. Coulomb forces skyrocket long before you can get within fusion distances. It is still a game of terribly poor statistics to get fusion to occur.

[Richard Hull]

Tokamaks aim at obtaining 100% confinement of a near or perfectly neutral thermal plasma. The ion energies are hoped in this instance to be all at or near the same energy. (fusion energy). Due to the fuels used the average fuel ion velocity is often far below the ion velocities and fusion energies possible in the fusor operating near 40kv applied.

The Tokamak just bangs hard at increasing the fusion probabilities due to uniform fuel ion velocities found in an ideal neutral plasma. The fusor, being a non-neutral plasma device contains ion velocities all over the place from non-fusing neutrals to super hot deuterons itching to fuse and without any form of ideal electrostatic inertial confinement. (Fuel at fusion energy is all over the place in a fusor with only a hint at some kind of confinement.) Still, it does fusion....Just not very well.

Richard Hull