some questions

[TallDave]

Imagine a polywell with two ion species and purely radial velocities. All collisions will be in the center of the machine, so they won't create any angular momentum. They will, however, change the radial velocities. For example, if the mass difference is very large, the heavy particle will be slowed down a bit and the light particle will bounce back with a little extra energy. When we follow these particles back out to the edge, we will find that they have a spread of radial velocities but still no azimuthal velocity. Collisions at the edge will tend to isotropize the distribution. Viola, reverse annealing!

It's an interesting thought experiment.

I assume we're thinking about p-B11 here. I suppose the larger ones are also going to have more force on them due to their larger charge, if I'm remembering how this works. I wonder if we would end up with two concentric edge regions, one dominated by p and one by B11.

I'll have to defer to Chacon et al, though. I'm told Luis didn't believe upscatter was a real issue in this kind of device.

[D Tibbets]

Imagine a polywell with two ion species and purely radial velocities. All collisions will be in the center of the machine, so they won't create any angular momentum. They will, however, change the radial velocities. For example, if the mass difference is very large, the heavy particle will be slowed down a bit and the light particle will bounce back with a little extra energy. When we follow these particles back out to the edge, we will find that they have a spread of radial velocities but still no azimuthal velocity. Collisions at the edge will tend to isotropize the distribution. Viola, reverse annealing!

Reading your post again, it occurs to me that you are confining the ions to purely radial velocities, no angular velocity allowed anywhere. With different mass ions (like deuteruim and Helium3) the rear ending or front ending collisons on the way out would do as you say, but once the ions turned around and the same reactions were occuring on the way in, wouldn't the process reverse itself so that the net result would be a wash? Of course, this presupposes that the ions interact only with other ions on the same inward or outward bound leg. Once bidirectional interactions, different turn around heights due to the different inertias, etc. are concidered things would get alot more complicated. I don't have any idea what the net effect might be on radial scattering. I would still expect the upper scattering to be limited somewhat by the increased likelyhood of these ions escaping the system.


Dan Tibbets

[Art Carlson]

My point is just that whether or not the explanation given for annealing is correct, it is not robust. I mean, there is not a simple argument that says it has to be that, and I was easily able to construct an argument suggesting that it might be just the other way around. You can't solve the problem on the back of an envelope, and even doing some heavy duty modeling, you still have the opportunity to make assumptions that may not be justified.

As a case in point, I have argued vigorously that the polywell is a spikey thing, nothing close to a sphere, and that it has to be that way to be MHD stable. For that reason, I expect ions to gain hefty amounts of angular momentum not from collisions in the central region, but from electrostatic forces near the edge. Your model may give you annealing, but if you put in the wrong geometry to simplify your equations, you will get the wrong answer.

[TallDave]

As a case in point, I have argued vigorously that the polywell is a spikey thing, nothing close to a sphere, and that it has to be that way to be MHD stable.

I still like Bussard's picture: spiky at low beta, round at high beta.

I guess I'd be surprised if the electron motion on the field lines could make the system MHD unstable.

[Art Carlson]

As a case in point, I have argued vigorously that the polywell is a spikey thing, nothing close to a sphere, and that it has to be that way to be MHD stable.

I still like Bussard's picture: spiky at low beta, round at high beta.

I guess I'd be surprised if the electron motion on the field lines could make the system MHD unstable.

You've got to have some spikes because of the cusps, even if you manage to find an arrangement of the magnet coils that, unlike Bussard's, makes large sections of the surface convex.

Have a look at elementary MHD stability theory. You'll be surprised.

[icarus]

TallDave:

I still like Bussard's picture: spiky at low beta, round at high beta.

How do you justify this position?

We have some basic simulations that show a spherical inclusion in the magnetic field will have a non-uniform magnetic field over it's surface, i.e. the magnetic field looks like the contours on this ...



and a beta=1 surface looks like this ... (i'm assuming beta=1 is high beta in your reckoning?)


The beta=1 surface shown has the electron kinetic pressure balancing the magnetic field pressure, i.e. the field is at equilibrium here. So unless you can come up with some additional force that has a distribution that looks exactly like the contours shown on the sphere and acts in the same direction, i.e. against the magnetic field, it must be spiky.

But if you know of some other additional force, I'm listening and I can put it into the simulation. Magnetic surface tension?, electrostatic attraction?, electron-plasma surface tension?

[KitemanSA]

Folks,
DrB. acknowledged that the beta=1 field from the WB-6 would be quasi-spherical at best and stated several times that he wanted to create small scale Polywells that were less quasi, more spherical. Sure would help settling this question.

On a related issue, regarding the bag graphic above, would someone PLEASE clarify this issue once and for all. Did kcdodd do the bag analysis or did icarus? If kcdodd, was the coil round or square?

PLEASE, I know you are both viewing this forum on occasion, set this issue to rest.

Thank you.

[TallDave]

You've got to have some spikes because of the cusps, even if you manage to find an arrangement of the magnet coils that, unlike Bussard's, makes large sections of the surface convex.

That leaves a lot of room in which the plasma could be very round with tiny spikes, or very spiky with little roundness.

Have a look at elementary MHD stability theory. You'll be surprised.

I suspect Bussard was more than a little aware of the issue, as he mentions it repeatedly. In fact, he states explicitly that it sets a limit on expansion:

Beyond this point excess electron density will be
driven out beyond the beta = one limit; the field will have
expanded as far as it can within MHD stability limits.

So what we have is a model where the field is deformed, to the limit of MHD stability. How round is that? Maybe Rick will tell us.

Another way to look at this might be to ask: at what electron pressure would a magnetic mirror lose MHD stability, and what would it look like at that point?

icarus,

It's a nice simulation, but as you say, basic. I'm guessing EMC2 has something more elaborate and dynamic (i.e., recirculation, transport loss, injection, etc). Also, there's some question of how different the ion geometry looks as compared to the electrons.

Kiteman's point is a good one too: we know Bussard was looking at higher-order polyhedra for a reactor, specifically a dodec which he believed would give the device 3-5x better performance. That would of course give us a more spherical field arrangement.

So all in all I think there's enough wiggle (wiffle?) room that we can't rule out an edge annealing effect in a roughly spherical ion distribution.

[icarus]

TallDave:

It's a nice simulation, but as you say, basic. I'm guessing EMC2 has something more elaborate and dynamic (i.e., recirculation, transport loss, injection, etc). Also, there's some question of how different the ion geometry looks as compared to the electrons.

So basically speaking, to answer my question you can't justify your feeling that the plasma is spherical and not spikey ... except that EMC2 maybe has a better simulation that includes as yet unidentified forces that will alter the basic magneto-static solution from spikey to spherical ... none of the effects you referred to (recirculation, transport losses, injection) could provide additional force to alter the plasma shape that I'm aware of. (An appeal to a gagged authority).

I agree the ions may not form the same geometry to the electrons and this question is key to IMO, just to note that I am referring to the electron plasma when speaking of beta=1.

So all in all I think there's enough wiggle (wiffle?) room that we can't rule out an edge annealing effect in a roughly spherical ion distribution.

Maybe wiggle room on the spherical ion cloud, granted but you'll have to get past Art on that one I'd imagine. Electrons not so.

More magnets make more spherical (less cubical and smaller lumps) but also more spikes. All these "DrB said so" appeals to authority (passed away now) make me uncomfortable. He struck me as a man who took nothing from authority.

[TallDave]

So basically speaking, to answer my question you can't justify your feeling that the plasma is spherical and not spikey ...

It's more a question of how spiky, and how spherical vs. how quasi-, and it also depends if we're talking about truncubes or dodecs. But no, I don't have the EMC2 simulations or the WB data, nor am I in a position to replicate them (though I do believe they exist), so I can't prove it. OTOH, I haven't seen anything to convince me it's so nonspherical we couldn't have a roughly spherical ion distribution in a reactor, such that Chacon's paper has some real-world relevance.

Have you run a simulation like this for a dodec? I suspect it's considerably more spherical. The Valencia cartoon is probably an idealized concept, like the initial magnets of zero cross-section, but the dodec should be closer to ideal than a truncube.

none of the effects you referred to (recirculation, transport losses, injection) could provide additional force to alter the plasma shape that I'm aware of.

Well, all those things involve electrons moving, as opposed to the static picture. Are the forces everywhere exactly the same regardless of where the electrons are going? I haven't tried to model it, maybe it really makes no difference. If you want I could try harder to poke holes in the picture, but I think we already agreed it was basic. And of course a dodec would look different.

(An appeal to a gagged authority).

Hey, I'd like to see the EMC2 simulations as much as anyone. It's frustrating.

All these "DrB said so" appeals to authority (passed away now) make me uncomfortable. He struck me as a man who took nothing from authority.

Not really. It would be odd, not to mention practically impossible, to argue over Bussard's theories without citing him. But I make no claim that Bussard was infallible, or even so expert we should take his statements on faith, I only note that the experimental evidence I've seen has tended to argue he was right. The WB effect, which is the heart of the Polywell concept, has been verified by Nebel, so I'm giving Bussard's version of the wiffleball geometry the benefit of the doubt until I see something convincing. It seems unreasonable to do otherwise.

[chrismb]

The beta=1 surface shown has the electron kinetic pressure balancing the magnetic field pressure, i.e. the field is at equilibrium here.

Lovely pictures. Maybe someone's got equivalent ones of tokamaks showing perfect, well-defined fields without turbulence. Tokamaks should work as well then, so long as we can get a smooth-looking picture out of the simulations...

....errr......

On the subject of 'gagged' research, has anyone simply written to the US Navy to ask how much they are prepared to allow EMC2 to release such information, and/or if they [the Navy] have already released all the information they know themselves? I don't actually see why they'd object, seeing as it is now 20 years down the line and such information still might not've even reached their possession. The Head Chop might even like folks asking after the work, so as to pull out useful information about this work he's commissioned that he might otherwise be unenlightened to himself.

[icarus]

TallDave:

Hey, I'd like to see the EMC2 simulations as much as anyone. It's frustrating.

Frankly, I don't think the EMC2 simulations will show much of anything that anybody else couldn't figure out with a desktop and some code. They have been concentrating on experiments so maybe they can put some better empirical fudge-factors to keep the models somewhat physical ... but I don't recall them making any claim to any new theory or equation sets (solvers) for better simulations??

Have you run a simulation like this for a dodec? I suspect it's considerably more spherical. The Valencia cartoon is probably an idealized concept, like the initial magnets of zero cross-section, but the dodec should be closer to ideal than a truncube.

Working up to that in my spare time. The Valencia "sketch" was indeed a cartoon methinks.

The WB effect, which is the heart of the Polywell concept, has been verified by Nebel, so I'm giving Bussard's version of the wiffleball geometry the benefit of the doubt until I see something convincing

Actually I think nebel confirmed "wiffleball-like confinement" NOT that the geometry of the electron plasma is spherical. I asked him the geometry question directly and got no answer, so either it is classified or he just doesn't want to answer.

I think Polywell has many merits, you might count me as an advocate, but I think tying the Polywell into the WiffleBall concept so strongly ("at the heart of it") without it have simply explainable theoretical basis (let alone analytical or numerical) is going to doom Polywell if it doesn't work out like they say ..... just saying.

Hmmm, just thought of an electrostatic effect that might yield an appreciable surface tension at the interface ..... where's my pencil?

[Roger]

We know that on the scale of WB-6&7, we got wiffleball/MaGrid, the mag field lines got squeezed.....

Is it reasonable to think that as power is turned up.. more squeezing occurs?

I could see those mountain tops getting pushed down right quick.

[TallDave]

The big difference imho is EMC2 had something like a dozen or so actual WB machines to experiment with over nearly two decades, while writing code to simulate what they were seeing. No one else has any WB machines, afaik, and very few people had ever heard of Polywell before 2007.

The WB effect is the key because confinement is the major challenge in IEC (temp being relatively easy) and we get better density since we operate at high beta. Rick said at one point without WB "we can kiss our behinds goodbye." Whether we like it or not, this poorly understood (by us, anyway) phenomenon is the heart of the concept.

Actually I think nebel confirmed "wiffleball-like confinement" NOT that the geometry of the electron plasma is spherical.

Yep. I don't think they had the eq to measure that. I'm not sure how spherical it would be for a truncube anyway.

[icarus]

Dave:

The WB effect is the key because confinement is the major challenge in IEC (temp being relatively easy) and we get better density since we operate at high beta. Rick said at one point without WB "we can kiss our behinds goodbye." Whether we like it or not, this poorly understood (by us, anyway) phenomenon is the heart of the concept.

Poorly defined is probably more correct than poorly understood. Without a satisfactory definition, understanding is a nonsensical notion.

Actually, the key is confinement, period. WB, at this stage, is a hand-wavvy argument as to how Polywell achieves confinement, call me sceptical.

I think, and have a reasoned, physical argument for why, the orthogonal E and B fields arising from the conformal cans ensures Polywell can be made to have good electron confinement .... however sphericity for focusing the ions adequately for fusion is another matter.