Cusp Ion Plug

[chrismb]

Does this help?

Indeed. Positively enlightening! (into the thoughts of Dr Bussard)

I'll have to chew over the numerical implcations for the assumptions he's making there. I must say I find it surprising that his essential conclusions are the ions won't be thermalised into a Maxwellian state according to various residence times. I don't really think that could be possible because you would still get a population of ions diffusing in phase space into those areas of the distribution that he thinks would be excluded states. However, that being said, I have read papers (and of confirmatory measurements) that suggest the distribution in a thermonuclear plasma isn't Maxwellian either but more like a N^1/8 distrubution -i.e. Maxwellian-like but a bit narrower about the mode. Sounds like a rather similar conclusion...

More significantly to my reading of it, though, is that he discusses ion thermal distribution and electron distribution and thermalisaion, but he doesn't seem to touch on the thermalisation mechanisms between ions and electrons. He appears to be generally disregarding ambipolar diffusion within the device. Am I misreading that??

[chrismb]

I've never really bought into the argument that Polywell would be "a sphere - but with holes in it". It would be, I rather think, a ball with spiky bits. They are all, and one of the whole, the same thing. Looking at it that way you suddenly find yourself with a set of much simpler questions - what happens at the termination of the spiky bits? The nature of 'the cusps' then becomes somewhat irrelevant.

I do not see why the electrons wouldn't migrate and be 'held' in the same topology, even if there is the claimed radial polarisation that goes on. If the sought-after central polarisation occurs in a stable fashion, I would then suppose that the higher electron density would simply be a facimile of this spikey ball, and the spikes of increased electron density would run up into the cusps.

This is good. Go on.

Well, if I was to be told that "a shape" of plasma (of as-yet undefined topology) could be so configured that by controlled injection of electrons and ions into that shape that you could create a charge gradient towards its centre, then I can't really say that isn't possible. And I guess this is where the idea of Polywell springs. However, if you view that shape as being incomplete with holes, you're now struggling with whatever boundary conditions those represent. Both in terms of the added complexity of the problem, and also for the unlikeliness of big discontinuities in such a plasma, it would seem reasonable to suggest that whatever shape the magnetic fields impose on this shape, that the basic structure of a core of differential charge exists throuough that "shape". The shape is clearly going to be a ball with spikes, what seems to have been a point of argument is that the spikes have a fundamentally different structure. Maybe they would be just the same - a spike with a central core of higher negative charge, just like the sphere.

Ambipolar diffusion would mean that this effect would diminuish the further away you are along a spike, from the source of the constant ion/electron injections. The only questions left, in that case, are; how long does a spike need to be so that it is 'neutral plasma' at its end interacts as a sheath structure when in contact with a surface, and whether the losses across that sheath are tolerable to the operation of the device. As mentioned elsewhere, the 'fast' electrons at the end of the spikes (those that exceed the Bohm velocity on account of their own energy) would self-expel themselves whilst there is also a constant loss of ions of a very regular and preditable energy (Bohm velocity + system pd, presumably?). The pd of the wall might even be managed to optimise the behaviour.

At this point, you'd only have to feed in the lost ions and replacements for the high energy electrons. However, if this is all you fed in, a further question arises; does the charge gradient remain?

So far it sounds like I'm being rather helpful to Polywell theory. But, as always, I have to drop a small bombshell somewhere: If a charge gradient structure can be maintained in a plasma 'shape' by electron/ion injections, then why use a Polywell shape? Why not just use a mirror scheme with two cusps? And if you don't need the cusps at all to maintain this process, then why not use a toroidal shape?

[alexjrgreen]

How does the positive charge on the magrid affect how the spikes behave?


Apparently a polyhedral configuration has better confinement than the mirror scheme with two cusps:

"Spherical Multipole Magnets for Plasma Research", Sadowsky, M.,
Rev.Sci.Instrum. 40 (1969) 1545

"Electrostatic and Electromagnetic High-Temperature Plasma Traps", Lavrent'ev, O.A.,
Conference Proceedings, Electrostatic and Electromagnetic Confinement of Plasmas and the Phenomenology of Relativistic Electron Beams,
Ann. N.Y. Acad. Sci., 251 (1975) 152-178

[alexjrgreen]

More significantly to my reading of it, though, is that he discusses ion thermal distribution and electron distribution and thermalisaion, but he doesn't seem to touch on the thermalisation mechanisms between ions and electrons.

Rick says the energy transfer between the electrons and the ions happens through collective mechanisms. On a different occasion he strongly implied that the discussion was ignoring inertia.

He appears to be generally disregarding ambipolar diffusion within the device. Am I misreading that??

Rick says the device doesn't exhibit ambipolar behaviour.

Not wanting to rely on such a shameless appeal to authority , I'd want to simulate it and see.

[TallDave]

I think it's a mistake to assume local quasineutrality only ends at the wall. It's also possible it ends at the cusps, which therefore eject electrons because the electron drive is injecting them. This seems more likely given the limited amount we know about the WB machine results.

I didn't assume the cusp plasma must be quasi-neutral. I calculated it. .

I've already said why I think your calculation was flawed. You are free to assume your calculation was correct, of course.

Of course, if you have a solid surface, quasi-neutrality can break down in the last Debye length. There is no reason for it to freak down in the middle of nowhere

The cusps aren't the middle of nowhere, they're the top of the well and the transition area between regions of vastly different electron density. If the plasma has to push out 10MW of electrons, it seems reasonable to expect quasineutrality to break down in the bottleneck.

[TallDave]

The shape is clearly going to be a ball with spikes, what seems to have been a point of argument is that the spikes have a fundamentally different structure. Maybe they would be just the same - a spike with a central core of higher negative charge, just like the sphere.

Yes, that seems like it would work. That would plug the cusps for electrons, and ion losses would be minimal because few upscatter far enough to be pulled out.

Keep in mind too, the opposing ends of the cusps look significantly different, both in terms of electron density and field geometry.

But, as always, I have to drop a small bombshell somewhere: If a charge gradient structure can be maintained in a plasma 'shape' by electron/ion injections, then why use a Polywell shape? Why not just use a mirror scheme with two cusps? And if you don't need the cusps at all to maintain this process, then why not use a toroidal shape?

It would be better for confinement, but have problems for the same reason stars would have problems working as toroids: you need a shape that focuses the confining force to a point (i.e., a sphere, or at least a quasi-sphere).

There's a long discussion here somewhere about "toroidal Polywells" and their problems.

[TallDave]

Rick says the device doesn't exhibit ambipolar behaviour.

Not wanting to rely on such a shameless appeal to authority , I'd want to simulate it and see.

I think on that score you don't have to trust Rick. We're shoving 10MW of electrons into the plasma. They have to go somewhere.

TallDave wrote:
Maybe we can borrow EMC2's PIC code.

Of course, I'm pretty sure I already know what that looks like...

Why don't you post your version? It might inspire others...

Well, I think we can infer certain things about what the EMC2 simulations look like from the statements of Nebel and Bussard. OTOH, I don't really trust the simulations too far anyway, so I'm about 1e20 times more interested in the WB-8 results.

Really, arguing over whether the WB effect actually happens is a sideshow that's already moot for the people with the data (and anyone willing to make reasonable inferences from the continued funding). The unknown that will make or break Polywell is how the WB effect scales with B and R.

[TallDave]

re. Debeye quote - was that from Valencia paper - to me, all it suggests is we have a confined plasma under some effective pressure (and turbulence).

Sorry, I didn't mean to be overly cryptic. That's actually from the paper linked earlier in the thread.

I thought it was interesting because Bussard puts an upper limit on the densities for the ion behavior he talks about, and to compare to some other estimates of Debye length that have been tossed around, which I think have been calculated differently.

[Art Carlson]

I think it's a mistake to assume local quasineutrality only ends at the wall. It's also possible it ends at the cusps, which therefore eject electrons because the electron drive is injecting them. This seems more likely given the limited amount we know about the WB machine results.

I didn't assume the cusp plasma must be quasi-neutral. I calculated it. .

I've already said why I think your calculation was flawed. You are free to assume your calculation was correct, of course.

Are you referring to this post? I didn't respond to it at the time because I couldn't identify any content. Things you mention that you seem to think qualify as "flaws in the calculation" are

• cusp plugging oscillations,
• WB field geometry, and
• the force driving the non-ambipolar losses in a Polywell.

If there is some physics content behind these phrases that you would like me to understand, you will have to elaborate.

Of course, if you have a solid surface, quasi-neutrality can break down in the last Debye length. There is no reason for it to freak down in the middle of nowhere

The cusps aren't the middle of nowhere, they're the top of the well and the transition area between regions of vastly different electron density. If the plasma has to push out 10MW of electrons, it seems reasonable to expect quasineutrality to break down in the bottleneck.

The sheath equation (about which I happen to know a great deal) only applies at a wall because you can have a discontinuity in the electric field there. In free space you would have to continue integrating the equation, which would result in astronomical potentials.

[Art Carlson]

The shape is clearly going to be a ball with spikes, what seems to have been a point of argument is that the spikes have a fundamentally different structure. Maybe they would be just the same - a spike with a central core of higher negative charge, just like the sphere.

Yes, that seems like it would work. That would plug the cusps for electrons, and ion losses would be minimal because few upscatter far enough to be pulled out.

Nonsense. You can't plug a hose with water. And where there are enough electrons to make a negative potential, the ions don't need to upscatter to go there.

[KitemanSA]

Did we ever get a page of those together?

It does help to agree on the meaning of words.

Yes.
The first or second sticky at the front of each of the history, technical, and design fora give you a link to the Polywell FAQ wiki.

Please review and comment at your leasure.

Thanks.

[KitemanSA]

(btw - re 'RECIRCULATE' - shouldnt we mention 'possibility'/opportunity of recirulation between cusps, outside the magrid, supposing suitably configured container -

Please review and comment on the definition here: http://www.ohiovr.com/polywell-faq/inde ... =Main_Page

[D Tibbets]

I think it's a mistake to assume local quasineutrality only ends at the wall. It's also possible it ends at the cusps, which therefore eject electrons because the electron drive is injecting them. This seems more likely given the limited amount we know about the WB machine results.

I didn't assume the cusp plasma must be quasi-neutral. I calculated it. Of course, if you have a solid surface, quasi-neutrality can break down in the last Debye length. There is no reason for it to freak down in the middle of nowhere.

Is it truely nowhere? I suspect that a double layer might exist at the level where the positive charge on the magrid becomes visible to the charged particles. What effect this would have is beyond me.

http://en.wikipedia.org/wiki/Double_layer_(plasma)

Dan Tibbets

[TallDave]

Are you referring to this post? I didn't respond to it at the time because I couldn't identify any content. Things you mention that you seem to think qualify as "flaws in the calculation" are
cusp plugging oscillations,
WB field geometry, and
the force driving the non-ambipolar losses in a Polywell.
If there is some physics content behind these phrases that you would like me to understand, you will have to elaborate.

If they don't qualify as flaws maybe you can tell me why (or I can dismiss your calculation as irrelevant, you can dismiss my objections, and we can just make faces at each other until we get some data). Electrons oscillate in the cusps, plugging them from electron losses and leading to much smaller densities at one end than the other. Since we know there is a force pushing 10MW of electrons out of the plasma and there's a parabolic well pulling ions toward the middle, how do you account for these in the balance of potentials at the cusp (i.e. why aren't far more electrons leaving than ions)? Why can't there be some potential that doesn't draw in massive numbers of ions due to a combination of the well, the magnetic field, and screening?

The WB geometry means electrons and ions have a difficult path to get out. Just because a potential exists doesn't mean particles are getting to the bottom of it -- e.g., the Magrid is the bottom of the well for electrons but they tend to fly around it due to the magnetic field.

Nonsense. You can't plug a hose with water.

Sure you can. Get a really long hose and put one end on top of a 10-story building. Now try to push water out of it from the bottom. What's pushing back?

And where there are enough electrons to make a negative potential, the ions don't need to upscatter to go there.

That depends on how much energy they need to get somewhere where the potential from the cusp-plug is bigger than the one they see going to the center of the Polywell. And how often they tend to get knocked away by the magnetic field into a region where the pull of the well is stronger before they get out of a cusp. And how big the potential is inside a cusp where electron density is dropping by a factor of 10,000.

[D Tibbets]

I've never really bought into the argument that Polywell would be "a sphere - but with holes in it". It would be, I rather think, a ball with spiky bits. They are all, and one of the whole, the same thing. Looking at it that way you suddenly find yourself with a set of much simpler questions - what happens at the termination of the spiky bits? The nature of 'the cusps' then becomes somewhat irrelevant.

I do not see why the electrons wouldn't migrate and be 'held' in the same topology, even if there is the claimed radial polarisation that goes on. If the sought-after central polarisation occurs in a stable fashion, I would then suppose that the higher electron density would simply be a facimile of this spikey ball, and the spikes of increased electron density would run up into the cusps.

I have a diferent picture. So long as the electrons have sufficient energy to bounce off the WB surface, the magnetic field serves as much as a wall that reflects the electrons as a barrior that limits outward motion. As such, any electron that hits this wall at any angle other than almost parellel will bounce off at an angle that will then intercept a wall on the next lobe or side of the WB. Even electrons in the throat of a cusp might be reflected back towards the the center after a few bounces. The point where an electron could enter the cusp and penitrate deep enough to only (or mostly) have bounces that carries it deeper into the cusp could be concidered the 'hole'. I speculate that the non spherical- lobular strutucture of the WB border may occasionally have an advantage over a more spherical geometry with imaginary shap bordered holes, at least to the extent that the hole size is equivalent to a tighter deeper portion of the cusp as opposed to the region where the shoulder of the cusp begins.
Or another way of saying it is that the real Wiffleball withs some conical shape to the hole entrances way not suffer to much in comparison to an idealized Wiffleball with sharp cutout holes. I believe this is a more wordy discription of what alexjrgreen said.



Dan Tibbets