Talk-Polywell.org

Are there simulations of more rather than fewer faces?

How about lower order, such as tetrahedral?
Is containment sacrificed for lower orders?
If not, then wouldn't this be a less complex and lower cost approach?

-Bill

bcolias wrote:How about lower order, such as tetrahedral?
Is containment sacrificed for lower orders?
If not, then wouldn't this be a less complex and lower cost approach?

-Bill

Tetrahedral might be problematic since it does not have opposing faces.

MSimon wrote:

bcolias wrote:How about lower order, such as tetrahedral?
Is containment sacrificed for lower orders?
If not, then wouldn't this be a less complex and lower cost approach?

-Bill

Tetrahedral might be problematic since it does not have opposing faces.

Hmm. I think he means because it doesn't have an even number of faces at each vertex. An octahedron doesn't have opposing faces either but DOES have an even number of faces at each vertex. An octahedron should work.
A rectified tetrahedron would work too, but a rectified tetrahedron IS an octahedron, so...

KitemanSA wrote:

MSimon wrote:

bcolias wrote:How about lower order, such as tetrahedral?
Is containment sacrificed for lower orders?
If not, then wouldn't this be a less complex and lower cost approach?

-Bill

Tetrahedral might be problematic since it does not have opposing faces.

Hmm. I think he means because it doesn't have an even number of faces at each vertex. An octahedron doesn't have opposing faces either but DOES have an even number of faces at each vertex. An octahedron should work.
A rectified tetrahedron would work too, but a rectified tetrahedron IS an octahedron, so...

Octahedrons do have opposing faces:

http://www.scienceu.com/geometry/facts/ ... /octa.html

MSimon wrote:
Octahedrons do have opposing faces:

http://www.scienceu.com/geometry/facts/ ... /octa.html

Again, hmm. They have faces across the center from each other. The fields on said faces would not oppose. So I guess we can both be right!
It is the only such polyhedron of which I am aware.

Why are opposing faces needed?
Should each vertex have an even number of faces touching?

bcolias wrote:Why are opposing faces needed?
Should each vertex have an even number of faces touching?

Opposing M-Simons's way, I am not sure. Opposing my way, they are not.

What is fundamental to a Polywell is to have an even number of "faces" (i.e. field regions) around each vertex. Only in this manner can all the MaGrid elements be protected from impingement by electrons. And even with this condition, there are "funny" cusps which will leak electrons to whatever in in the way of the funny cusp. So it seems that what is actually needed is a MaGrid that has an even number of faces around the vertex but a hole AT the vertex. I hve taken to calling this configuration the "X" cusp. It started off as the "Holey X" cusp but I dropped the "holey" part.

KitemanSA wrote:

MSimon wrote:
Octahedrons do have opposing faces:

http://www.scienceu.com/geometry/facts/ ... /octa.html

Again, hmm. They have faces across the center from each other. The fields on said faces would not oppose. So I guess we can both be right!
It is the only such polyhedron of which I am aware.

Why not? After all the set up is for all North (or South if you prefer) Poles Facing in.

MSimon wrote: Why not? After all the set up is for all North (or South if you prefer) Poles Facing in.

Nope. With the rectified cube (aka cuboctohedron) it is set up for the "real" coils to be all in and the "virtual" coils to be all out, or vice versa. The plain octohedron would not have virtual coils but alternating real coils. There need to be as many ins as outs at each vertex for this thing to work. At least I haven't seen anything to contradict that. I acknoledge that WB6 and WB7 were not as clean a representative of the Polywell concept as DrB wanted, but they work after a fashion with more losses than desired.

Having thought about it a bit, it MAY be possible for the octohedron to be designed with only "real" coils facing in (or vice versa), but then the opposite faces would not each have coils. This would be a machine with four triangular coils. Possibly neat, but probably not too spherical. If the coils were made with spherical geometry triangles, rather than plane geometry triangles, maybe the wiffleball would still be adequately spherical. Hmmm!

KitemanSA wrote:

MSimon wrote: Why not? After all the set up is for all North (or South if you prefer) Poles Facing in.

Nope. With the rectified cube (aka cuboctohedron) it is set up for the "real" coils to be all in and the "virtual" coils to be all out, or vice versa. The plain octohedron would not have virtual coils but alternating real coils. There need to be as many ins as outs at each vertex for this thing to work. At least I haven't seen anything to contradict that. I acknoledge that WB6 and WB7 were not as clean a representative of the Polywell concept as DrB wanted, but they work after a fashion with more losses than desired.

Having thought about it a bit, it MAY be possible for the octohedron to be designed with only "real" coils facing in (or vice versa), but then the opposite faces would not each have coils. This would be a machine with four triangular coils. Possibly neat, but probably not too spherical. If the coils were made with spherical geometry triangles, rather than plane geometry triangles, maybe the wiffleball would still be adequately spherical. Hmmm!

The octahedron and the cube are duals of each other. As are the icosahedron and dodecahedron.

The current "cube" set up can be thought of as a truncated octahedron.

I have never accepted the conventional wisdom around here re: the alternating polarity of real coils in the octahedron. I never made an issue of it though. Perhaps we could go through it again and see if that really is a requirement.

BTW I think leaving out opposing coils is going to create a rather large hole in the confinement baring much stronger magnets.

Let me start with a question:

How do you get a null field in the center without opposing fields of the same polarity?

MSimon wrote:Let me start with a question:

How do you get a null field in the center without opposing fields of the same polarity?

By having 4 sets of them crossing in the middle.

KitemanSA wrote:

MSimon wrote:Let me start with a question:

How do you get a null field in the center without opposing fields of the same polarity?

By having 4 sets of them crossing in the middle.

Superposition says that will not work. Only opposing fields will exclude the field from the center.

What is fundamental to a Polywell is to have an even number of "faces" (i.e. field regions) around each vertex. Only in this manner can all the MaGrid elements be protected from impingement by electrons.

All that is required to protect the grid is a strong enough magnetic field that is conformal to the coil cases.

I have been thinking about the requirement for an even number of faces meeting at every vertex and I don't see why that is a requirement. Opposing faces makes sense to get a null in the center of the machine. But the number of faces meeting at a vertex? I can't see why that is a requirement.

I think the real rule is - all faces must have an opposing face. Which means an even number of faces. The simplest platonic solid that meets that requirement is the cube. And the cube has an odd number of faces meeting at every vertex. Its dual - the octahedron - has an even number of faces at every vertex. Both solids have opposing faces.