New FAQ - What are Cusps and what kind does a Polywell Have?

[Roger]

The second, IMHO.

And it might make a wonderful graphic to illustrate what cusps are where....

[KitemanSA]

If I have two toroidal magnets positioned along the same axis of rotation, then the fields need to be of opposite sense to get a line cusp in the gap between their coils. In one case "same sense", in the other "opposite sense". In BOTH cases, the current in the parallel conductors are running in opposite directions. It is the single descriptor that I can find that works al the time. Do you have a better one?

First off, I'm not sure what you mean by "toroidal." Are you just talking about a wound electromagnet? Also, can't you create a cusp between permanent magnets?

I mean "toroidal" exactly as WB7 has toroidal magnets. And yes I mean electromagnets. As to permanent magnet systems having cusps, I have no idea. I suspect so, but I an not currently interested in them. But I will include the term electromagnet. Thank you for that one.

But I think what's most confusing about that portion of the definition is that it doesn't mention electromagnetism. That definition would also apply to two straight copper wires side by side, carrying current in opposite directions but obviously not generating a cusp. This will probably be confusing to people trying to understand the FAQ.

Two straight wires side by side do form electromagnets and I guess that technically, the space between them would be a line cusp; a mighty weak one, but a line cusp none-the-less. Can anyone show me info to falsify that?

It's probably easiest to talk in terms of magnetic polarity, which people generally understand (i.e. "a line cusp is formed by the meeting of N-N or S-S fields"). Positionality is probably something we can leave to the experts.

I tried. I truly did; but I just couldn't come up with a simple one that couldn't be misconstrued. I guess I will just have to put in graphics. If anyone has access to some good, simple graphics that show point, line, funny cusps, I'd appreciate seeing them. I think I will have to use a simple graphic of a cuboctahedron if I can't find something else.

[KitemanSA]

The second, IMHO.

Aren't these two graphics the two that Indrek and KCDodd did a while back? I was under the impression that in both the analyses they used square plan-form magnets turned the WRONG WAY. If you look carefully, the red on the sphere is quite square, and the faint light blue line on the green bag is also square. I think that neither is all that good. I would LOVE to see a bag analysis like the second but with more realistic magnet forms!

Anyone one have that bag-analysis routine for mathematica? The routine is free. MSimon posted a link to it about a month ago. Unfortunately, it requires Mathematica to run which costs two arms and a leg... unless you are a student. Any students on line? Do you have or are you willing to install Mathematica and the bag program?

[Aero]

Has anyone who knows what is needed, looked at the capabilities of Maxima? It runs a lot of Mathematica code and it is free. I've used Maxima a little bit and I was impressed. But then, I'm easily impressed.

[Roger]

I would LOVE to see a bag analysis like the second but with more realistic magnet forms!

2nd that.

[icarus]

KitemanSA:

I was under the impression that in both the analyses they used square plan-form magnets turned the WRONG WAY.

Your impressions are all turned the WRONG WAY. Indrek and I used an analysis with circular (toroidal) electromagnets. The cubic projection of lines of low magnetic field onto the sphere are exactly how you would see them, IF the plasma would be spherical. This is a simple geometric consequence of projecting a cube (the faces that the polywell magnets lie upon) onto a sphere.

The plasma was assumed to be spherical and made so using method of images ... read this document here, (slowly I might suggest)

http://www.mare.ee/indrek/ephi/images.pdf

As far as I know, kcdodd;s simulations were for circular toroidal electromagnets (close to the physical ones) and the plasma ball had infinitesimal current loops tangential to it's surface and allowed to relax until beta=1 ... i.e. internal pressure balanced field strength at the surface (current in loops goes to zero, I think).

Other octohedrons, cuboctohedrons ...and etc should make equally easy to achieve projections onto spherical plasmas.... someone just has to be bothered to code it up (I can throw the maths at it if anyone wants to do the code) .... maths is fun, i only program when paid.

[Art Carlson]

Art, this is not exactly so but only mostly, it's a rule of thumb of vectors you are using, in actuality MHD stability in general has to do with gradients and curvatures of the surfaces of scalar magnetic field strength, not just curvature of vector field lines.

Yes, MHD modes are a bit more complex than I suggested. That is why transport in tokamaks even after all these years and CPU-hrs is not yet fully understood. (But they've gotten impressively close.) Still, the curvature is the major factor. If I recall correctly, it is the only factor that determines the linear stability of short-wavelength MHD modes in a plasma with a sharp-boundary. And it is a major selling point of the polywell. If you could figure out how to build a polywell with a convex plasma, then you would be required to show that it is still stable, or that the unstable modes will not be deleterious. If you keep the boundary concave, I'm willing to take it on faith.

So a big question remaining for me is does the wiffle-ball look more like this

[a colorful ball]

or this??

[a spikey alien]

Although the proponents sometimes contradict themselves, the spikey version corresponds closer to what they claim, and - in a rare convergence - to the way I think it must work. The beach ball version, at least, is not consistent with a sharp-boundary, beta = 1 plasma in equilibrium. The alien is.

[Art Carlson]

Hrm. Well, maybe Rick will let us know at some point.

Whatever he tells us, I hope it doesn't violate Maxwell's equations.

I bet it violates local quasineutrality, though.

How? By being tiny, by having low density, or by having humongous electric potentials? Those are the only three options that Maxwell's equations (in this case Gauss's Law) allow. (Vacuum tubes do it by going to small densities.)

(Is this a non sequitor, or is there a connection between MHD stability and quasi-neutrality that I am not aware of?)

[MSimon]

How? By being tiny, by having low density, or by having humongous electric potentials? Those are the only three options that Maxwell's equations (in this case Gauss's Law) allow. (Vacuum tubes do it by going to small densities.)

With HF (below 30 MHz) tubes in the MW range I'd say the densities are getting near to Polywell ranges. At least in terms of power.

[TallDave]

Kiteman,

Two straight wires side by side do form electromagnets and I guess that technically, the space between them would be a line cusp; a mighty weak one, but a line cusp none-the-less. Can anyone show me info to falsify that?

Technically, maybe, practically, no. Plus it omits the possibility of permanent magnets.

I tried. I truly did; but I just couldn't come up with a simple one that couldn't be misconstrued. I guess I will just have to put in graphics. If anyone has access to some good, simple graphics that show point, line, funny cusps, I'd appreciate seeing them. I think I will have to use a simple graphic of a cuboctahedron if I can't find something else.

Graphics would probably help.

I think a FAQ doesn't necessarily have to be completely immune to misinterpretation, it mostly just has to be simple enough to help the layperson understand what's going on. I think most people can understand than when you push together two bar magnets N><N the magnetic fields butt up against each other.

[Art Carlson]

How? By being tiny, by having low density, or by having humongous electric potentials? Those are the only three options that Maxwell's equations (in this case Gauss's Law) allow. (Vacuum tubes do it by going to small densities.)

With HF (below 30 MHz) tubes in the MW range I'd say the densities are getting near to Polywell ranges. At least in terms of power.

Not sure what you mean here. You're not suggesting that vacuum tubes violate Guass's Law, are you?

[MSimon]

How? By being tiny, by having low density, or by having humongous electric potentials? Those are the only three options that Maxwell's equations (in this case Gauss's Law) allow. (Vacuum tubes do it by going to small densities.)

With HF (below 30 MHz) tubes in the MW range I'd say the densities are getting near to Polywell ranges. At least in terms of power.

Not sure what you mean here. You're not suggesting that vacuum tubes violate Guass's Law, are you?

No. Just that if you made one 10X as large (linear dimensions) you could pump 100 MW through it continuously.

[TallDave]

Whatever he tells us, I hope it doesn't violate Maxwell's equations.

I bet it violates local quasineutrality, though.

How? By being tiny, by having low density, or by having humongous electric potentials? Those are the only three options that Maxwell's equations (in this case Gauss's Law) allow. (Vacuum tubes do it by going to small densities.)

The last one, I think. Potentials can be huge across the system but smaller locally. Heck, that's pretty much what a well is.

(Is this a non sequitor, or is there a connection between MHD stability and quasi-neutrality that I am not aware of?)

I have a (somewhat hazy) notion that the shape of the plasma is influenced by the fact the plasma is nonambipolar and has an edge region where electrons dominate.

EDIT: Ah, the redoubtable icarus beat me to it:

The second result above includes no calculation for the additional pressure forces due to the electrostatic attraction between the electron layer on the plasma surface and the MaGrid.

Very nice pictures btw, thanks for sharing. Stay careful near the Sun.

[Art Carlson]

I bet it violates local quasineutrality, though.

How? By being tiny, by having low density, or by having humongous electric potentials? Those are the only three options that Maxwell's equations (in this case Gauss's Law) allow. (Vacuum tubes do it by going to small densities.)

The last one, I think. Potentials can be huge across the system but smaller locally. Heck, that's pretty much what a well is.

I'm not sure whether we're talking about current experiments of a hypothetical power reactor. If we take a small experiment, with a plasma ball of 10 cm radius, an average energy of 10 keV, and a 0.1 T field, we can calculate the potential if the charge density due to electrons and ions differs by 10%. The field pressure, and therefore the plasma pressure (assuming beta = 1), is (0.1 T)^2/(2*4pi*1e-7 H/m) = (4e3 Pa). That makes for a particle density of roughly (4e3 Pa)/(3*(1.6e-19 J/eV)*(1e4 eV)) = (8e17 m^-3). If half of that's electrons, then 10% of the charge density is 0.5*0.1*(1.6e-19 Cb)*(8e17 m^-3) = (6e-3 Cb/m^3). The potential difference between the center of the sphere and the edge is (0.1 m)^2*(6e-3 Cb/m^3)/(6*8.85e-12 F/m) = 1 MV. Of course, for a reactor, the result would be several orders of magnitude larger. I guess that's a consistent position, if you honestly think Rick Nebel is going to be claiming MV potentials in his machine.

[Art Carlson]

The second result above includes no calculation for the additional pressure forces due to the electrostatic attraction between the electron layer on the plasma surface and the MaGrid.

How much of a contribution does this electrostatic attraction make? Interestingly, it will be largest exactly where the MaGrid magnetic field is pushing back hardest, due to conformal MaGrid cans, orthogonality of conjugate harmonic B and E fields and etc.

The net electrostatic force on a quasi-neutral plasma isn't very big. You can calculate an equivalent (negative) pressure from 0.5*epsilon_0*E^2. For 100 kV/m, for example, this works out to 0.04 Pa. To get this pressure with magnetic fields you only need a few mT.