STATEMENT OF OBJECTIVES from RFP

Discuss how polywell fusion works; share theoretical questions and answers.

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KitemanSA
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Post by KitemanSA »

MSimon wrote: Indrek is a he.
Thank you.
MSimon wrote: He is on to other things.
Is anyone else on this forum able to do those analyses?

Anyone??

Hello o o o .

blaisepascal
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Post by blaisepascal »

KitemanSA wrote:
blaisepascal wrote:On the other hand, the octahedron alone has the important all-even-vertex property that allows the polywell to work. Two-coloring the octahedron yields 4 faces of one color, 4 faces of the other color, but opposite faces of the octahedron will have different colors.
Good catch!! And I've been pushing an octohedron myself. :oops:
Personally, I think the symmetry of the situation would make an octahedral polywell theoretically possible (but probably not ideal), even with opposite faces of of differing color.

Of the geometries being considered (essentialy, rectified platonic solids) the octahedron is the only exception to the idea that opposite faces will have the same color. But that's only three geometries: octahedron, cuboctahedron, and icosidodecahedron. I haven't looked in detail at the other Archemedian solids with the even-vertex property, the rhombicuboctahedron and the rhombicosidodecahedron. Nor have I looked in detail at the Catalan solids with that property, the tetrakis hexahedron, the disdyakis dodecahedron, and the disdyakis triacontrahedron.

I doubt they'd make good polywells, but they've got great names.

TallDave
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Post by TallDave »

It's interesting, I've seen WB-6 called a truncube, rectified cube, and cuboctahedron. Of course they're all close to the same thing, it's just a question of how you expand the truncated corners.

Tom Ligon's fancy WB-100 graphic for the space conference was a truncated dodec.

http://en.wikipedia.org/wiki/Truncated_dodecahedron

Could the requirement to have same-polarity sides facing have to do with balancing the forces between coils? With a bunch of 5-10T magnets, that seems like it would be a large engineering concern. If you've got a coil casing being pulled one direction while being pushed the same direction from the other side, that's a hell of a lot of force on whatever holds the whole thing together.

TallDave
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Post by TallDave »

If there is an "out" coil directly in front of the "in" coil, (read North and South if you wish) the field just continues through the second coil and you get a longer coil. There is no line cusp between them, but they sure as heck don't cancel.
Here's what I don't like about this, and maybe someone can explain why it's wrong.

Hold two identical bar magnets, N facing S, and put a piece of iron in the exact middle between them. Which way does it go? Well, it goes nowhere; the forces cancel so there is no force on the iron. Isn't that what's going to happen to an electron, too? It seems like it should go streaming through instead of being diverted at right angles to the coils.

Now, you can do the same thing with the magnets with same polarities facing, but the fields don't cancel there, they butt up against each other, forming a line cusp, and only the tiny area directly between them has no field.

KitemanSA
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Post by KitemanSA »

TallDave wrote: Tom Ligon's fancy WB-100 graphic for the space conference was a truncated dodec.
Should have been rectified rather than just truncated IMHO.
TallDave wrote:Could the requirement to have same-polarity sides facing have to do with balancing the forces between coils?
Where do you find this "requirement"?
TallDave wrote:With a bunch of 5-10T magnets, that seems like it would be a large engineering concern. If you've got a coil casing being pulled one direction while being pushed the same direction from the other side, that's a hell of a lot of force on whatever holds the whole thing together.
Sounds like a benefit, though not a requirement.

blaisepascal
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Post by blaisepascal »

TallDave wrote:It's interesting, I've seen WB-6 called a truncube, rectified cube, and cuboctahedron. Of course they're all close to the same thing, it's just a question of how you expand the truncated corners.
A cuboctahedron and a rectified cube are the same thing, and is the same thing as a rectified octahedron. The process of "rectification" for a polyhedron is done by finding the midpoint of each edge and using those points as the new vertex set. By construction, each vertex of a rectified polyhedron is of degree 4. The original vertices and edges are completely eliminated in rectification.

Usually, "truncated" doesn't extend to the point of completely eliminating the original edges, but just introduces new edges. A traditional soccer ball (consisting of 12 pentagons and 20 hexagons) is a truncated icosahedron, not a rectified icosahedron). If a polyhedron is truncated, but not to the point of rectification, then all the vertices will be of degree 3, which is unsuitable for a polywell.
Tom Ligon's fancy WB-100 graphic for the space conference was a truncated dodec.

http://en.wikipedia.org/wiki/Truncated_dodecahedron
I believe you are wrong, as the truncated dodecahedron pictured on that page has odd degreed vertices, and thus are unsuitable for a polywell according to Dr. Bussard's writing.

However, placing 12 coils in a dodecahedral structure will create an icosidodecahedron polywell, with 12 physical coils and 20 virtual coils. An icosidodecahedron is equivalent to a rectified dodecahedron or a rectified icosahedron.
Could the requirement to have same-polarity sides facing have to do with balancing the forces between coils? With a bunch of 5-10T magnets, that seems like it would be a large engineering concern. If you've got a coil casing being pulled one direction while being pushed the same direction from the other side, that's a hell of a lot of force on whatever holds the whole thing together.
I don't believe there is such a requirement, except for potential engineering issues like you state. But even then, the symmetry of the situation tends to balance forces out.

Let's look at it this way... For simplicity, symmetry, and minimization of coils, we've really only been looking at models based on rectified platonic solids. The WB-6/7 design uses 6 coils to generate a cuboctahedral polywell, and the proposed dodecahedral WB-100 uses 12 coils to generate an icosidodecahedral polywell. That uses 2 of the 5 platonic solids. In general, a rectified platonic solid is the same as its rectified dual platonic -- rectified cube and rectified octahedron are cuboctahedrons, for example. So there's no major differences in geometry for 6 and 8 coils, or 12 and 20 coils.

that leaves 4 coils, in a tetrahedral pattern. A rectified tetrahedron is an octahedron. Unlike the 6, 8, 12, or 20 coil situations, a physical coil in a 4 coil polywell is opposite a virtual coil. So this would be exactly the situation where a N pole is directly facing an S pole. But it is also facing 3 other N poles which are symmetrically distributed off-axis. The net force from the 3 N poles is axial.

KitemanSA
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Post by KitemanSA »

TallDave wrote: Hold two identical bar magnets, N facing S, and put a piece of iron in the exact middle between them. Which way does it go? Well, it goes nowhere; the forces cancel so there is no force on the iron. Isn't that what's going to happen to an electron, too? It seems like it should go streaming through instead of being diverted at right angles to the coils.
It will, except for the gyro-motion. When it reaches the end (the second coil) it will try to transit the point cusp there and will either make it or be reflected back depending on how far away from the axis it is and how tight the pinch. No?
TallDave wrote:Now, you can do the same thing with the magnets with same polarities facing, but the fields don't cancel there, they butt up against each other, forming a line cusp, and only the tiny area directly between them has no field.
The cusps got field! Heaps o tight field. (Except for the "funny cusp".) An electron headed outward from the axis along the plane of symmetry toward the line cusps may be gyratin like mad due to the field, but if the lines keep heading out straight, it'll just follow them out, just like an electron on the axis in the first example, unless the pinch is too tight. Or do I have to re-think this entire thing?

KitemanSA
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Post by KitemanSA »

blaisepascal wrote:
TallDave wrote: Tom Ligon's fancy WB-100 graphic for the space conference was a truncated dodec.
http://en.wikipedia.org/wiki/Truncated_dodecahedron
I believe you are wrong, as the truncated dodecahedron pictured on that page has odd degreed vertices, and thus are unsuitable for a polywell according to Dr. Bussard's writing.
As a matter of fact, you are both correct. The graphic in Tom Ligon's ISDC presentation did use decagonal coils instead of pentagonal, which would have produce strong line cusps between the adjacent sides of the decagons, and probably wouldn't have been as good a Polywell as one would want. But man is it PURDY!

I'd love to see the equivalent graphic with bowed pentagonal plan form magnets. That should be fine art!

blaisepascal
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Post by blaisepascal »

KitemanSA wrote:]As a matter of fact, you are both correct. The graphic in Tom Ligon's ISDC presentation did use decagonal coils instead of pentagonal, which would have produce strong line cusps between the adjacent sides of the decagons, and probably wouldn't have been as good a Polywell as one would want. But man is it PURDY!

I wasn't able to find Tom Ligon's presentation easily. Do you have a link to it?

I'd love to see the equivalent graphic with bowed pentagonal plan form magnets. That should be fine art!
Indeed.

TallDave
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Post by TallDave »

Blaise,

Heh, I originally mentioned the icosidodecahedron in the earlier post, then took it out when I realized it was substantially different than Ligon's truncated dodec (unlike the truncube/cuboctahedron).

http://en.wikipedia.org/wiki/Icosidodecahedron
I wasn't able to find Tom Ligon's presentation easily. Do you have a link to it?
Here's a link. It's the little PPT icon on bottom right, p24.
I believe you are wrong, as the truncated dodecahedron pictured on that page has odd degreed vertices
I'm not sure what you mean by this. Can you cite a reference for Bussard on that, or explain why this matters? My understanding was it just needed an even number of sides at a vertex.

blaisepascal
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Post by blaisepascal »

TallDave wrote:Here's a link. It's the little PPT icon on bottom right, p24.
Thanks.
I believe you are wrong, as the truncated dodecahedron pictured on that page has odd degreed vertices
I'm not sure what you mean by this. Can you cite a reference for Bussard on that, or explain why this matters? My understanding was it just needed an even number of sides at a vertex.
I believe we are in agreement. The "degree" of a vertex is the number of edges incident at that vertex. Equivalently, it's the number of faces meeting at that vertex. Bussard said that for polywell to work adjacent faces on the polyhedron had to have opposing magnetic fields (i.e., N adjacent to S, not N adjacent to N or S adjacent to S). In order for that to work, the faces around each vertex had to be alternating N/S. Therefore there can't be an odd number of faces around each vertex. Therefore, all vertices have to be of even degree.

The octahedron, cuboctahedron, and icosadodecahedron all have vertices of degree 4 and are worthy of consideration for polywell design. Any rectified polyhedron will have vertices of degree 4 and would also qualify. Truncated, but not rectified, polyhedra have all vertices of degree 3, and therefore wouldn't qualify. There are other Archimedian and Catalan solids which also have the "all vertices of even degree" property and thus would qualify.

The WB-6/7 machines both used circular toroidal coils arranged on the faces of a cube, yielding a cuboctahedral polywell structure with somewhat distorted virtual coils -- concave polygons, not regular polygons. I am uncertain how much this distortion affected the polywell. Proposed in this forum are next-experiment machines which use coils which are square (with rounded corners) in plan-form (but field-conformal in cross-section), which would yield planar equilateral triangular virtual coils. The overall shape would look more like the underlying cuboctahedron than the current WB-6/7 design.

Is there any remaining uncertain point of potential disagreement?

Art Carlson
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no equivalence between real coils and virtual coils

Post by Art Carlson »

Discussing the problem in terms of polyhedra that have vertices of an even degree is elegant, but a bit beside the point. If the magnetic coils are really laid along the edges of a polyhedron, then the vertices will be field nulls and leak like sieves. I think we agreed that the coils cannot touch, so there is no equivalence between real coils and virtual coils.

KitemanSA
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Re: no equivalence between real coils and virtual coils

Post by KitemanSA »

Art Carlson wrote:Discussing the problem in terms of polyhedra that have vertices of an even degree is elegant, but a bit beside the point. If the magnetic coils are really laid along the edges of a polyhedron, then the vertices will be field nulls and leak like sieves.
Right, and that field null is called the "funny cusp". As long as there is nothing in the way of said FC, Recirc (a.k.a.) oscillation of the electrons should prevent excessive losses.
Art Carlson wrote:I think we agreed that the coils cannot touch, so there is no equivalence between real coils and virtual coils.
Not sure what you are driving at here unless you mean that with a pair of real and a pair of virtual coils, you will get a modifed line cusp that is related in length to the area over which the two real coils parallel each other. The shorter the span, the shorter the cusp.

TallDave
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Post by TallDave »

OK thanks Blaise, that makes more sense. I thought you were talking about the degree of the angles.

tombo
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Post by tombo »

Opposite coils facing same poles inward create structural forces pushing the coils apart.
Opposite coils facing different poles inward create structural forces pulling the coils together.
Same magnitude force for the structural people to deal with, just different directions.
Which is better structurally? That depends on the details of any particular structure. For example if the coils are attracting the mounts to the shell are in tension. Bad for ceramic but very good for buckling.

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As I understand it.
There are 3 kinds of cusps in cubical 6 coil polywell.
Point cusp located in the center of each face.
Line cusp located at each vertex.
Funny cusp located in the center of each edge. (where the coils are closest)
Are we all on the same page here?

There are no field nulls except at the very center where the plasma lives.
(If you think I am wrong show me exactly where and why. Last time I looked at Indrek's models there were none.)
The cusps are where the field lines are straight. (strong but straight)
Actually more to the point (I think) where they are diverging.

Consider the plane surface defined by the center of 2 adjacent corners of the cube, the center of the edge connecting them and the center of the cube.
Now there is a set of (diverging) field lines on that surface. They are straight and they lie in a plane. (Due to symmetry) Any electron (or ion) moving in that plane follows a field line to the wall.

I contend that this whole surface (and beyond) is a cusp that includes the funny cusp which is just a portion in the center of it and both line cusps at the cube corners.
In fact all the line cusps and funny cusps are part of one connected cusp system.
-Tom Boydston-
"If we knew what we were doing, it wouldn’t be called research, would it?" ~Albert Einstein

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