A question about higher order polyhedra.

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

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VernonNemitz
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Some generic observations

Post by VernonNemitz »

First, a bit of history. In some of the older magnetic-confinement approaches, a "magnetic mirror" was to be used when the overall confinement zone was not a toroid. The cubical Polywell design of course is the equivalent of six magnetic mirrors (14 if you add the corners).

One thing about a magnetic mirror, in an older magnetic confinement design, is that it needs to be significantly stronger than the rest of the confiment field. Ways to do that of course involve increasing the ampere-turns of the mirror coil, but also simply decreasing the diameter of that coil can help, too.

It seems to me that since the Polywell approach needs a large volume surrounded by a bunch of magnetic mirrors, then the most logical way to achieve it is to incorporate a large number of facets. That is, a large cube means 6 large coils, with large diameters (and larger potential ion leakage through those centers than small-diameter coils). But a dodecahedron and especially an icosahedron can surround a significant volume with comparatively small-diameter coils. Imitating a soccer ball (or buckminsterfullerene) should be even better, in terms of mirroring ions back into a large volume.

I've seen the arguments posted about increased complexity. There's no doubt that increasing the size of the unit will be associated with increases in coil materiel. How that materiel is distributed, now...that is what these observations are about, regarding efficient ion mirroring. I'm willing to express the opinion that an increase in complexity (number of facets) here will be worth it.

TDPerk
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Ah ha!

Post by TDPerk »

VernonNemitz gets at what I was wondering about.

I recall (I think) a rule of thumb that larger T is easier with smaller size. I presumed from that that it would be easier to contain a given volume by having as may coils as possible...

...which doesn't mean the labyrinth of supports, plumbing, and electric leads that many coils would require is doable.

Would smaller radius of the individual coils plus higher T lead to mean "cusp" dimensions which are a smaller fraction of an electron gyro-radius, and would that improve the distribution of electrons radially from overall device center? (I'm thinking the more relatively high, steep, and dense a histogram of electron probability is, where the greater concentration is just in from the coils, and the more sphere-like that surface is, the better the confinement).


Yours, TDP, ml, msl, & pfpp
molon labe
montani semper liberi
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D Tibbets
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Post by D Tibbets »

Increasing the number of magnets was desirable in Bussards view. I understood it was primarily due to increased sphericity of the Wiffle ball. The above comments also points out the possible advantages of having stronger B fields because the distances from the magnet cores would be lessened. A near shere with thousands of magnets would presumably be the most efficient, but also the most difficult/ costly from an engeenering perspective. I think Bussard said he expected a 3-5 fold improvement in going from the cube to a dodecahedron(?). I speculate that the next higher polyhedron would possibly be a further 1.5 to 2 times better, the next ~0.5 better, etc. So there would be deminishing returns for more complex systems. Add to that the arguments some have presented that square or even trigular shaped coils might be better than round, and coils with curved faces might be better than the flat magnets. There are alot of variations that could be explored due to the apparent lack of a good computer model.

Add to that the possible variations in drive energies, pulsations, POPS type effects, fuels, mixtures, vacuum technology, energy conversion, space use, etc, etc. There is alot of work that could be persued by many groups if this technology was persued with passion ( ie- lots of money- all those displaced Tokamak labs need something to do, especially as the ITER project is running backwards). Of course all this is dependent on the system working well enough that there is enthusiasm for working around any hopefully temperary road blocks.


Dan Tibbets
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tombo
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Post by tombo »

IMO the structural loads get better with higher order polyhedra.
Consider the limiting case of a plane of coils.
The forces all balance out and there is no net mechanical load on the coils.
Near the limiting case with each coil covering a small solid angle (as seen from the center of the PW) there is only a slight net outward force on each coil.
Basically all that heavy structure holding 6 Sumo coils in place is divided up among all the smaller coils.
Lighter currents reduce complexity of the leads.
Yes there are more of the problematical "nubbins".
The big limit to the number of polyhedral faces is that the thickness of each coil remains the same due to the many layers of insulation and cooling passages. They can't be thinner because the inside and outside temperatures and heat flux from the reaction remain the same. We would get a little reduction due to the smaller cross section of the superconductor itself. But, that is a small fraction of the total cross section.
(Is there an echo in here? :wink: )
-Tom Boydston-
"If we knew what we were doing, it wouldn’t be called research, would it?" ~Albert Einstein

VernonNemitz
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nubbins?

Post by VernonNemitz »

I'm not sure what the word "nubbins" refers to, in this discussion. For the moment I make the guess that it refers to the vertices of the chosen polyhedra. Even if nubbins are something else, I do have something to say about the vertices, so....

But first, let me talk about the dodecahedron, which has 12 facets and 20 vertices. I want to focus on a section of the object, a 3-pentagon group, meeting at 1 corner.

Those 3 connected pentagons can APPROXIMATELY be "laid flat" on a piece of paper. So, take a piece of paper and draw 3 circles, to represent not pentagons, but the flows of current in 3 rings that would be used as 3 adjacent facets of a dodecahedral Polywell device.

Because we want the magnetic poles toward the center of the device to all be the same, through the facets, this means in the above drawing, the 3 circles can be given arrows all the same direction (choose clockwise OR counterclockwise, for all of them).

The single corner of our flattened pseudotripentagon, surrounded by the three circular flows, can now be examined. If you draw the arrows in just the right place on each circle (near the corner), you will see that the exact center of the corner is surrounded by a kind of circular flow.

Well, we all know here that the corner is where the magnetic field comes back out of the Polywell device, to complete its loop around/through any specified ring. It is quite logical that that drawing should reveal a pseudo-loop, at the corner. There is nothing wrong with building an actual ring at that corner, specifically to intensify that effect (and also to make the corner work better as a magnetic mirror).

Yes, I know this means that if we built a dodecahedral Polywell device, I'm saying "build 12 largish rings for the facets and 20 smaller rings for the corners". Or we could go octahedral, with 8 largish rings for the facets and 6 smaller rings for the corners. Or we could go icosahedral, with 20 largish rings for the facets and 12 smaller rings for the corners. Lots more complexity.

I'm sure there is a Law of Diminishing Returns in there somewhere, when it comes to building lots of rings to ensure the ions are always mirrored back into the core volume of the Polywell device. For the moment, I think that "recommending" the octrahedral version might be good enough (14 rings total). I'm hoping that a moderate increase in complexity, over the current cube, will lead to adequately greater ion confinement.
Last edited by VernonNemitz on Tue Jun 02, 2009 7:36 pm, edited 3 times in total.

KitemanSA
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Re: nubbins?

Post by KitemanSA »

VernonNemitz wrote:I'm not sure what the word "nubbins" refers to, in this discussion. For the moment I make the guess that it refers to the vertices of the chosen polyhedra. Even if nubbins are something else, I do have something to say about the vertices, so....

But first, let me talk about the dodecahedron, which has 12 facets and 20 vertices. I want to focus on a section of the object, a 3-pentagon group, meeting at 1 corner.
Please go back and read some background info. The Polywell only works if there are an even number of opposing fields at each vertex. This means that the dodec won't work. What is needed is a rectified dodec, aka an icosadodecahedron. This will have 12 pentagonal faces, 20 triangular faces, and a whole load of vertices, each with 4 fields. The four will be arranged North in-out-in-out around the vertex.
the "nubbin", aka nub, aka crossover, aka a lot of other things is the little piece that holds the magnets together in the WB6/7 design.

VernonNemitz
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Re: nubbins?

Post by VernonNemitz »

KitemanSA wrote: The Polywell only works if there are an even number of opposing fields at each vertex. This means that the dodec won't work.
??Can you be more specific about where to find that background info?
Certainly what you just wrote is not making sense to me. The current cube design only has 3 fields at each vertex (not an even number). The only polyhedron that has an even number at each vertex is the octahedron. Did you notice I focussed on the octahedron at the end of my last post?

MSimon
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Re: Ah ha!

Post by MSimon »

TDPerk wrote:VernonNemitz gets at what I was wondering about.

I recall (I think) a rule of thumb that larger T is easier with smaller size. I presumed from that that it would be easier to contain a given volume by having as may coils as possible...

...which doesn't mean the labyrinth of supports, plumbing, and electric leads that many coils would require is doable.

Would smaller radius of the individual coils plus higher T lead to mean "cusp" dimensions which are a smaller fraction of an electron gyro-radius, and would that improve the distribution of electrons radially from overall device center? (I'm thinking the more relatively high, steep, and dense a histogram of electron probability is, where the greater concentration is just in from the coils, and the more sphere-like that surface is, the better the confinement).

Yours, TDP, ml, msl, & pfpp
B field (with constant amp-turns) scales inversely with coil size up to the limit of the SCs.
Engineering is the art of making what you want from what you can get at a profit.

KitemanSA
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Re: nubbins?

Post by KitemanSA »

VernonNemitz wrote:
KitemanSA wrote: The Polywell only works if there are an even number of opposing fields at each vertex. This means that the dodec won't work.
??Can you be more specific about where to find that background info?
Certainly what you just wrote is not making sense to me. The current cube design only has 3 fields at each vertex (not an even number). The only polyhedron that has an even number at each vertex is the octahedron. Did you notice I focussed on the octahedron at the end of my last post?
I would start at wikipedia, then "askmar" and go from there. You may also want to read DrB's original patent, was referenced at wikipedia.
The "cube" does not have square coils, but round ones which leave big gapping holes at the vertex of the cube. Look closely and you will see that the holes look somewhat triangular. Admittedly, they are puckery triangles, but triangles none-the less. So in fact there are 6 round faces and 8 puckery triangle faces with two triangles and two circles meeting at each vertex (not well, but well enough to allow a demonstration). DrB wanted to make the round coils squarish and the triangles more triangular to make a more realistic "rectified cube" that is the true Polywell shape. A rectified cube is also called a cuboctahedron.

Remember, what makes the wiffle ball is the part of the field that is tangential to the spherical core, not the part that points toward it. What you want is NOT an all north in (can't happen) but a nice flow from North in to North out with little teeny holes at the cusps.

MSimon
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Post by MSimon »

I think the most important point is that the corner cusp fields are squished. The more squished (within the limit of 6 to 8 gyroradius separation between coils) the better.

Of course the more squished the smaller the gyroradius. Up to the limit of the fields at the coil faces - not to be confused with the coil container faces.

The engineering will be tricky.
Engineering is the art of making what you want from what you can get at a profit.

VernonNemitz
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Re: nubbins?

Post by VernonNemitz »

KitemanSA wrote: What you want is NOT an all north in (can't happen) but a nice flow from North in to North out with little teeny holes at the cusps.
Thanks for the reply. Please note in my other post I was not trying to say that if coils were added to the corners, their fields should be the same direction as the main facet fields. I talked about intensifying the existing flux direction at the corners, with the purpose of making better mirrors of those corners. (So, it if is all-North-in at the facets, then it would be all-North-OUT at the corners.) And it should be obvious that mismatched numbers is not a problem, if, for example, there were 8 largish facet coils and 6 smaller corner coils (a modified octahedral Polywell). After all, the current design is also unbalanced, with 6 facet coils and 0 corner coils.

icarus
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Post by icarus »

Cusp losses are said to scale proportionately to both gyroradii (at the cusp) and the total number of cusps (ref. rnebel).

Increasing either will increase cusp losses. More coils means more cusps does it not?

You'll have to put a up detailed analysis to show how more coils decrease gyroradii faster than the proportionate increase in cusp number to justify the complexity of more coils (cusps).

You too KitemanSA. Continuosly advocating for more coils but not one shred of calculation to prove the benefit, except "DrB said so".

KitemanSA
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Post by KitemanSA »

icarus wrote: Cusp losses are said to scale proportionately to both gyroradii (at the cusp) and the total number of cusps (ref. rnebel). Increasing either will increase cusp losses.
More coils means more cusps does it not?
My recollection is that looses are proportional to the cusp area, point cusps being MUCH smaller than line cusps. So getting rid of line cusps at the expense of more point cusps may be a good thing.
icarus wrote:You'll have to put a up detailed analysis to show how more coils decrease gyroradii faster than the proportionate increase in cusp number to justify the complexity of more coils (cusps).
There is more than one factor that effects performance. The primary "other" factor of which I am aware is sphericity. More magnets have been linked with better sphericity. If twice as many magnets yields twice as much loss, but 10x gain, it is a net positive. Lacking any data or the ablility to do a major field analysis with electron containment, I must fall back on DrB's expertice. When I hear someone pontificate in a manner that is contrary to his writings, I will question the pontificator.
icarus wrote:You too KitemanSA. Continuosly advocating for more coils but not one shred of calculation to prove the benefit, except "DrB said so".
I continuously advocate for designs that may achieve the improved sphericity that DrB stated he wanted to try. My current opinion as to how to GET that improved sphericity changes abruptly from day to day as I get more data and have new thoughts. Currently, I would truly like to see the bow-legged square plan-form cubeoctahedron tried. Same six magnets, but possibly better sphericity. Along that line, making said machine with the modified MPG format discussed earlier would allow the machine to be built without nubs, potentially reducing those losses too.

I would also have a concern with spending $20M to $40M on an intermediate sized machine without spending the $1M to check out the other two cases that DrB wanted. So sue me. I am curious.

VernonNemitz
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some parallelism

Post by VernonNemitz »

To icarus: In my 2:27pm message above, I wrote about adding coils for the corners, but I did not say much about how big they might be (other than they would obviously be smaller than the facet coils).

As I write this I'm looking at the "Talk-Polywell.org" logo, with its nice picture of the cubical Polywell. I can imagine mentally rotating the device so one of its corners faces me. Then I can imagine three lines radiating from the glowing central point through the bodies of the three coils that are adjacent to that corner. Each line intersects at the center of the minor radius of each coil/torus.

Together, the three intersection points suffice to define the size/circumference/diameter of a circle. I imagine constructing a coil/torus of that major diameter (pick an appropriate minor diameter), and resting it against the corner. Current flow in this coil is arranged so there will be magnetic attraction between its field and the field passing through that corner of the Polywell device. SEPARATOR nubbins might be needed, but not hold-in-place nubbins (except when power is off).

In my 2:27 post I described something I called a "pseudo-loop" of current, around the corner. This coil's current would be parallel to that pseudo-loop. This imagination of parallelism, for corner coils, can be extended to any other polyhedron.

KitemanSA
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Re: nubbins?

Post by KitemanSA »

VernonNemitz wrote:
KitemanSA wrote: What you want is NOT an all north in (can't happen) but a nice flow from North in to North out with little teeny holes at the cusps.
Thanks for the reply. Please note in my other post I was not trying to say that if coils were added to the corners, their fields should be the same direction as the main facet fields. I talked about intensifying the existing flux direction at the corners, with the purpose of making better mirrors of those corners. (So, it if is all-North-in at the facets, then it would be all-North-OUT at the corners.) And it should be obvious that mismatched numbers is not a problem, if, for example, there were 8 largish facet coils and 6 smaller corner coils (a modified octahedral Polywell). After all, the current design is also unbalanced, with 6 facet coils and 0 corner coils.
Got you, I think. In general, the triangular opening is known as a virtual coil because as you point out, all the currents along the triangle form an "out" field if the toruses make an "in". That language would have it that you want to make the virtual out coils real. With that understanding, I won't argue with you. Read thru the Optimize thread that is right next to this one today and you might find additional background.
Several of us are trying to put together a FAQ for this forum, but we are getting very little help from the admin. None-the-less, you may want to check out http://www.ohiovr.com/polywell-faq/inde ... =Main_Page.

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