## Different polyhedra require different strength magnets

Discuss the technical details of an "open source" community-driven design of a polywell reactor.

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KitemanSA
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charliem wrote:
KitemanSA wrote:... the main feature of a Polywell is that there are an even number of faces (pairs of opposite polarity) around each vertex. The faces may be either all real, or half real and half virtual. But always two or more pairs of fields.
Have to admit that I still fail to see the meaning of that.

In a cube, cuboctahedron, or dodecahedron I can only picture 3 faces touching each corner (or vertex), neither 2 nor 4, so... what am I missing?

And what exactly means "of opposite polarity"?

May he have meant edge instead of vertex?
In a cube or dodecahedron, you are correct, which is why neither will make a polywell. You need to truncate them; truncate them till the cuts meet in the center of the original edge. Then you have a cuboctahedron (if you start with a cube).
This is a cuboctahedron.
At each vertex (golden ball) there are 4 faces, two red and two yellow. Take the red to be the toroids and the yellows to be the triangular faces between and you have the classic WB6.
Clear now?

TallDave
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I am not quite sure what you mean by "the middle" here. Opposing faces are not required. Most folks think that if there is a "north in" magnet on one face, there needs to be an "north in" on the opposing side of the poyhedron, thru the center of the volume (reactor). This is not so. All that needs to happen is that there is a vector sum to zero at the center of the reactor.
The "middle" is the line cusp between opposing fields. Fields that don't oppose won't have a cusp, they'll have a field that falls to zero in the middle between them because they cancel out.

Am I missing something here? That doesn't sound like it can confine anything.

KitemanSA
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TallDave wrote:
I wrote:I am not quite sure what you mean by "the middle" here. Opposing faces are not required. Most folks think that if there is a "north in" magnet on one face, there needs to be an "north in" on the opposing side of the polyhedron, thru the center of the volume (reactor). This is not so. All that needs to happen is that there is a vector sum to zero at the center of the reactor.
The "middle" is the line cusp between opposing fields.
Ahh. Adjacent fields of the same polarity? The line-like cusps occur when two fields of the same polarity (e.g., north in) are adjacent but not touching. This was not the subject of my original post. I was talking about fields on OPPOSITE faces with the same polarity (e.g., north in).
TallDave wrote:Fields that don't oppose won't have a cusp, they'll have a field that falls to zero in the middle between them because they cancel out.
Not so, in general, unless we are using the words differently again. If you have two equal polarity fields side by side (red beside red in the graphic above), they either become one big field if they are touching, or they have a small area between them to allow the opposite polarity to complete the field line circuit. That opposite field is squeezed strongly and is the cusp. Fields of opposite polarity (red beside yellow) that are adjacent will result in a STRONG tangential field that makes a wonderful reflector.
TallDave wrote:Am I missing something here? That doesn't sound like it can confine anything.
It is not the field, but the tangential component of the field that confines. And the line like cusp that exists between the toriodal magnets has no tangential component over a long span. This is a poor confinement mechanism. This is also why Dr. B. wanted to replace the toroids with square plan-form magnets (with rounded corners so they don't touch at the vertices) to make the line like cusps as short as possible.

Besides, it is really the charge on the magrid that confines. The magnets just... "herd" the electrons a bit.

MSimon
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KitemanSA,

You are assuming Dr. B missed the obvious. I don't think so. More likely there is a hole in your argument.
Engineering is the art of making what you want from what you can get at a profit.

KitemanSA
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Away with your subtleness MSimon, tell me direct!

What do you think I am saying that is incorrect?

charliem
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Kitemansa,

Thanks. Much clearer now.

Then, if I get it right, any arrangement made with toroidal coils covering the surface of a virtual sphere would meet THIS criteria, correct? (3 or more coils, equal or different in size, their fields all north in, or all south in).

tombo
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What happen to the field between unlike faces? Wouldn't it gradually fall to zero at the middle where the two sides cancel? That would mean no cusp and no confinement.
The B field direction changes (in to out) at the conductor, where the electric current is and where the B field strength is highest ie. along the polygon edges.
IIRC
The electric potential on the Magrid confines the electrons by pulling them back into the device whenever they travel outside the surface of the polygon (which acts as a coarse Faraday cage).
The B field's job is to deflect the electrons to keep them from colliding with the conductor until they get to that location.
[Oh, I see Kiteman pointed this out already.]
And Dr.B. didn't really like the round magnets. He wanted a rounded corner square plan-form magnet for the cuboctahedron. But round is so much easier to make, in most peoples minds.
But, most people are not coil designers. Consider the shapes of the coils in the alternator in your car. Far from round. Far from planar.
3D thinking is essential.
3 or more coils
Actually 4 or more I think are required to enclose a volume in 3 space.
It is not the field, but the tangential component of the field that confines.
You keep saying this and it makes a certain intuitive sense, but I don't trust my intuition when considering plasma behavior.
Is this requirement mentioned by Bussard or other sources?
IIRC Charged particles orbit B lines as they move along them (parallel). The orbiting generates its own tangential component. So a radial B field could confine also. (mirror mode)
Also, an electron orbiting a tangential B field line is moving toward the magrid half the time and away half the time. Then, the E field drift moves it across the B field lines toward the positive magrid.
This would happen when it is close enough to the conductor that the local geometry overwhelms the further away coarse approximation of a Faraday cage. That would be when it is close enough that the portion of its "sky" filled by the nearby conductor is larger than the portion of its "sky" fill by all the other conductors together.
-Tom Boydston-
"If we knew what we were doing, it wouldn’t be called research, would it?" ~Albert Einstein

MSimon
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KitemanSA wrote:Away with your subtleness MSimon, tell me direct!

What do you think I am saying that is incorrect?
It is hard to follow your argument with your oversized picture messing up the formatting on my computer.
Engineering is the art of making what you want from what you can get at a profit.

TallDave
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Hrm. Let's take the simplest picture for my poor imaging cortex: two coils opposite each other (not at right angles). If one is S and the other is N, the field between would fall to zero at the middle because they cancel. If they are N:N or S:S, they meet and butt up against each other, forming a line cusp.

That's my understanding, and I thought it was why Bussard's machines all had N-N and S-S.
Besides, it is really the charge on the magrid that confines. The magnets just... "herd" the electrons a bit.
I'm with you here. The electrons want to get to the Magrid, the magnets keep pushing them sideways. The purpose of the magnetic shielding is to stifle the flow from gun to Magrid sufficiently that we get wells and hopefully Q>1.

KitemanSA
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charliem wrote:Then, if I get it right, any arrangement made with toroidal coils covering the surface of a virtual sphere would meet THIS criteria, correct? (3 or more coils, equal or different in size, their fields all north in, or all south in).
Hmm. That is an excellent question. It may be the case, but I am not sure.

I know that all the rectified Platonic solids work.

My problem with your suggestion is that toroids side-by-side produce line-like cusps which Dr. B. didn't seem to like. However, if the toroids could be replaced by regular polygons, that may be true. I just don't know if it is possible with anything except the rectified Platonic solids.

KitemanSA
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MSimon wrote:
KitemanSA wrote:Away with your subtleness MSimon, tell me direct!

What do you think I am saying that is incorrect?
It is hard to follow your argument with your oversized picture messing up the formatting on my computer.
So sorry. Do you know how to make a picture show up smaller? I just used an existing wiki-image and that is the size it happened. Are there imbeddable commands in phpBB that will allow sizing the image?

Besides that, how am I wrong?

MSimon
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KitemanSA wrote:
MSimon wrote:
KitemanSA wrote:Away with your subtleness MSimon, tell me direct!

What do you think I am saying that is incorrect?
It is hard to follow your argument with your oversized picture messing up the formatting on my computer.
So sorry. Do you know how to make a picture show up smaller? I just used an existing wiki-image and that is the size it happened. Are there imbeddable commands in phpBB that will allow sizing the image?

Besides that, how am I wrong?
You can use "Paint" to resize it. Then you put it up on photobucket or flickr and do the usual linkage.

I'm having trouble following your argument with the left right scrolling. I'll let you know where I think your error is once the formatting is right.

And unfortunately AFAIK you cant resize with the board's software.
Engineering is the art of making what you want from what you can get at a profit.

KitemanSA
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TallDave wrote:Hrm. Let's take the simplest picture for my poor imaging cortex: two coils opposite each other (not at right angles). If one is S and the other is N, the field between would fall to zero at the middle because they cancel. If they are N:N or S:S, they meet and butt up against each other, forming a line cusp.

That's my understanding, and I thought it was why Bussard's machines all had N-N and S-S.
Let us try to be specific.
IF I have two toroidal magnets placed one above the other about their mutual vertical axis of symmetry (e.g., as on the bottom and top surfaces of a cube): and, IF their polarity is arranged so that both had north pointing UP: the field would flow thru the two with little loss of strength along that axis and there would be no cusps except the point cusps at the center of each toroid. IF on the other hand, they had norths or souths facing each other, there would be no field at the center and there would be a line cusp all the way around the perpendicular mid-plane of the figure (the horizontal plane half way up the cube). God I hate English for technical descriptions!

The machines that Dr.B. built were all cube based, so the North facing in on both faces on opposite sides of the cube is how it would work out. But his patent, IIRC, showed an octahdral reactor wherein the opposite faces would NOT be the same polarity facing in.

Thru my time here, I have seen this condition (opposite faces with the same polarity facing in) being called "opposing fields". By this I have taken it to mean, the north pushes against the north, or vice versa. This condition is NOT necessary for the Polywell to work. A cube based Polywell will have one, but a rectified tet (aka an octahedron) will not. However, the field at the center of the reactor for both the rect-cube and the rect-tet will vectorally sum to zero, assuming equal strength coils.

Now do you get it?

KitemanSA
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MSimon wrote: 1. You can use "Paint" to resize it. Then you put it up on photobucket or flickr and do the usual linkage.

2. I'm having trouble following your argument with the left right scrolling. I'll let you know where I think your error is once the formatting is right.

3. And unfortunately AFAIK you cant resize with the board's software.
Red text added to MSimon's quote.
1. Too much pain going that way. I guess oversize pictures are here to stay.

2. Try copying the post into Word or another such program so you can resize the picture and adjust the margins as stuff so you don't have to scroll left right.

3. Oh well.

I wish Joe would allow downloading here. If it is just a matter of \$ I can provide some support for computer resources.

I don't believe there is a hole in my argument, since all I an arguing is geometry.

TallDave
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IF on the other hand, they had norths or souths facing each other, there would be no field at the center
Isn't that a problem?
But his patent, IIRC, showed an octahdral reactor wherein the opposite faces would NOT be the same polarity facing in.
...
I know that all the rectified Platonic solids work.
http://en.wikipedia.org/wiki/Polywell
If the configuration is looked at as solenoids on the faces of a polyhedron, then the polyhedron chosen must have an even number of faces at each vertex, so that the polarity of the solenoids can alternate. Infinitely many polyhedra satisfy this property, for instance all antiprisms, 2n-agonal bipyramids, and all rectified (fully truncated) polyhedra. As can be seen in the picture, WB-6 is a cuboctahedron. Bussard's planned WB-8 would be an icosidodecahedron.
I'm not sure this is actually correct. An earlier version said:
The name Polywell is a portmanteau of "polyhedron" and "potential well." The applicable polyhedra are those which have an even number of faces at each vertex, so that the poles of the solenoids can alternate. While many polyhedra satisfy this property - all 2n-agonal bipyramids for instance - the need for high symmetry limits the machine design to the three quasiregular polyhedra. The magnetic field produced is the dual polyhedron of the machine. As can be seen in the picture, WB-6 is a cuboctahedron, with one set of solenoids on the square faces, and virtual solenoids of opposite polarity on the triangular faces, producing a rhombic dodecahedral magnetic field. Bussard's unbuilt WB-8 would be an icosidodecahedron producing a rhombic triacontahedral magnetic field; it is unclear whether the driven faces would be the triangles or the pentagons.

The dodec model I've seen (from Tom's ISDC ppt) doesn't follow this, iirc. It's actually built from decagons on the faces of a dodec.