Different polyhedra require different strength magnets

[KitemanSA]

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?

No. It is what WB6 and 7 have, so I don't think it is a problem.

But his patent, IIRC, showed an octahdral reactor wherein the opposite faces would NOT be the same polarity facing in.

Thanks for the link below. Via said link, the patent shows the octahedron as Figure 4 and the cuboctahedron as Figure 8. So I guess they are both there.

... 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.

Yup, and would have had some doozies of line cusps. They should have been pentagons with rounded corners.

The only small scale machine work remaining, which can yet give further improvements in performance, is test of one or two WB-6-scale devices but with “square“ or polygonal coils aligned approximately (but slightly offset on the main faces) along the edges of the vertices of the polyhedron. If this is built around a truncated dodecahedron, near-optimum performance is expected; about 3-5 times better than WB-6.

From which I take that the "square" coils would go with the cuboctahdron, which has square and triangular faces, and equivalently, pentagonal faces would be used on the rectified dodecahedron (the icosododecahedron), which has pentagonal and triangular faces. Of course he may have ment triangular, but I don't think so.

Remaining Small-Scale Experiments
Design, building and parametric testing of WB-7 and WB-8, the final two true polyhedral coil systems, with spaced angular corners, to reduce “funny cusp“ losses at the not-quite-touching points, and yet provide very high B fields with conformal coil surfaces.

True Polyhedral, which I take to mean squares for the rect-cube and pentagons for the rect-dodec.

[MSimon]

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.

You know as moderator I must say I don't like your attitude. Too much trouble to make it easy for other users is not in the spirit of this place.

I have eliminated pictures (while leaving a link to them) for similar problems.

In fact I fix long urls all the time. Perhaps you would care to reconsider.

I'm a real stickler on the formatting thing. Left right scrolling ruins the flow.

[MSimon]

Let us suppose you have a cube plan coil that looks like this (polarity given is to the center) top view.

Code: Select all

 

                       N
                     S   S
                       N

What is the polarity of the top and bottom coils?

I think the field cancels between the coils - i.e. the cusps losses get worse. Or think of it this way - instead of the line cusp fields squeezing they cancel.

[blaisepascal]

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.

I don't know offhand about the planned WB-8 icosidodecahedron, but otherwise it's correct.

One key with seeing the WB-6/7/8/8.1 configuration as a "cuboctahedron" is recognizing that there are two fundamentally different types of "solenoids" present in the device. One type, the "physical" solenoid is obvious: they are the 6 stainless steel donuts that you see looking at the device. In each of them, there are large electric currents circulating clockwise around them when viewed from outside the device, so that all the North ends are pointed at the center.

The other type, the "virtual" solenoids aren't as obvious: Around each of the 8 vertices of the cube, there are three large currents from the three adjacent physical solenoids forming a triangle (a very curvy triangle, but a triangle) with the currents going counterclockwise when viewed from the outside. Since all the physics cares about is a circulating current around the axis of the solenoid, doing it in three unconnected segments is perfectly fine, and you get a solenoid without a coil.

The appearance of the WB-6/7/8/8.1 is cubic, with six coils on the faces of the cube, but the underlying physics is cuboctahedral, with inward pointing (physical) solenoids on the 6 square faces and outward pointing (virtual) solenoids on the 8 triangular faces. The vertices of the cuboctahedron are at the 12 points where the physical coils come close to touching. Around each of these twelve points are 4 solenoids, two pointing in, two pointing out, alternating. This arrangement, of alternating inward and outward solenoids is the key to Bussard's design for the polywell.

If you put an inward-pointing coil on all the faces of any polyhedron, preferably such that the coils touched just the midpoint of each edge, you'll get the critical aspects of the polywell. If the polyhedron is spherically symmetric, so will the polywell. With circular coils, you'll have portions of coils on adjacent faces nearly parallel with antiparallel currents, which causes a "line cusp" between them. With polygonal coils such that the coils come close at the corners of the coils rather than the sides, the size of the line cusps is reduced.

[KitemanSA]

I don't know offhand about the planned WB-8 icosidodecahedron, but otherwise it's correct.

The only small scale machine work remaining, which can yet give further improvements in performance, is test of one or two WB-6-scale devices but with “square“ or polygonal coils aligned approximately (but slightly offset on the main faces) along the edges of the vertices of the polyhedron. If this is built around a truncated dodecahedron, near-optimum performance is expected; about 3-5 times better than WB-6.

A fully truncated (rectified) dodecahedron is an icosadodecahedron. QED.

One key with seeing the WB-6/7/8/8.1 configuration as a "cuboctahedron" is recognizing that there are two fundamentally different types of "solenoids" present in the device. One type, the "physical" solenoid is obvious: they are the 6 stainless steel donuts that you see looking at the device. In each of them, there are large electric currents circulating clockwise around them when viewed from outside the device, so that all the North ends are pointed at the center.

The other type, the "virtual" solenoids aren't as obvious: Around each of the 8 vertices of the cube, there are three large currents from the three adjacent physical solenoids forming a triangle (a very curvy triangle, but a triangle) with the currents going counterclockwise when viewed from the outside. Since all the physics cares about is a circulating current around the axis of the solenoid, doing it in three unconnected segments is perfectly fine, and you get a solenoid without a coil.

The appearance of the WB-6/7/8/8.1 is cubic, with six coils on the faces of the cube, but the underlying physics is cuboctahedral, with inward pointing (physical) solenoids on the 6 square faces and outward pointing (virtual) solenoids on the 8 triangular faces. The vertices of the cuboctahedron are at the 12 points where the physical coils come close to touching. Around each of these twelve points are 4 solenoids, two pointing in, two pointing out, alternating. This arrangement, of alternating inward and outward solenoids is the key to Bussard's design for the polywell.

If you put an inward-pointing coil on all the faces of any polyhedron, preferably such that the coils touched just the midpoint of each edge, you'll get the critical aspects of the polywell. If the polyhedron is spherically symmetric, so will the polywell. With circular coils, you'll have portions of coils on adjacent faces nearly parallel with antiparallel currents, which causes a "line cusp" between them. With polygonal coils such that the coils come close at the corners of the coils rather than the sides, the size of the line cusps is reduced.

Yeah. What you said. Well stated.
BUT, it would work with 4 "physical" and 4 "virtual" coils too. In which case the basic shape would not be a cuboctahedron, but simply an octahedron, aka a rectified tetrahedron.

[KitemanSA]

Let us suppose you have a cube plan coil that looks like this (polarity given is to the center) top view.

Code: Select all

                       N
                     S   S
                       N

What is the polarity of the top and bottom coils?

Hunh? I am not sure what you are asking. If this is a plan view, (i.e. a "top view") then it seems you have two "south in" coils facing in from the left and right and two north in from the front and back and you haven't shown a top or bottom coil. You have me totally confused.

I think the field cancels between the coils - i.e. the cusps losses get worse. Or think of it this way - instead of the line cusp fields squeezing they cancel.

Again, you have me totally confused. What has that to do with what I said?
Let me try your way.
Horizontal slice thru typical WB6:

Code: Select all

                       N
                     N   N
                       N

But it is actually more like this when looked via a canted slice:

Code: Select all

                    S N S
                    N   N
                    S N S

Opposite faces the same inward polarity, N vs N, S vs. S where the Norths are the real coils and the souths are virtual. But that is not important. The Ns and Ss alternate around each vertex, and the vector sum in the center is zero.
But it can also be this way:

Code: Select all

                      N  
                    S   S
                    N   N
                      S  

Opposite faces have opposite inward polarity, N vs S, S vs. N where the Norths are the real coils and the souths are virtual. But that is not important. The Ns and Ss STILL alternate around each vertex, and the vector sum in the center is STILL zero. (please note that the figure is supposed to represent a 6 pointed star. The rectified tetrahedron is kind of like this except in 3D rather than 2D.

[blaisepascal]

A fully truncated (rectified) dodecahedron is an icosadodecahedron. QED.

I knew that an icosadodecahedron was a rectified dodecahedron, I just wasn't sure if WB-8 was planned to have that topology.

One key with seeing the WB-6/7/8/8.1 configuration as a "cuboctahedron" is recognizing that there are two fundamentally different types of "solenoids" present in the device. One type, the "physical" solenoid is obvious: they are the 6 stainless steel donuts that you see looking at the device. In each of them, there are large electric currents circulating clockwise around them when viewed from outside the device, so that all the North ends are pointed at the center.

The other type, the "virtual" solenoids aren't as obvious: Around each of the 8 vertices of the cube, there are three large currents from the three adjacent physical solenoids forming a triangle (a very curvy triangle, but a triangle) with the currents going counterclockwise when viewed from the outside. Since all the physics cares about is a circulating current around the axis of the solenoid, doing it in three unconnected segments is perfectly fine, and you get a solenoid without a coil.

The appearance of the WB-6/7/8/8.1 is cubic, with six coils on the faces of the cube, but the underlying physics is cuboctahedral, with inward pointing (physical) solenoids on the 6 square faces and outward pointing (virtual) solenoids on the 8 triangular faces. The vertices of the cuboctahedron are at the 12 points where the physical coils come close to touching. Around each of these twelve points are 4 solenoids, two pointing in, two pointing out, alternating. This arrangement, of alternating inward and outward solenoids is the key to Bussard's design for the polywell.

If you put an inward-pointing coil on all the faces of any polyhedron, preferably such that the coils touched just the midpoint of each edge, you'll get the critical aspects of the polywell. If the polyhedron is spherically symmetric, so will the polywell. With circular coils, you'll have portions of coils on adjacent faces nearly parallel with antiparallel currents, which causes a "line cusp" between them. With polygonal coils such that the coils come close at the corners of the coils rather than the sides, the size of the line cusps is reduced.

Yeah. What you said. Well stated.

Is there anyway that this (or someone else's rendition) could end up in a FAQ? It seems to be a frequent issue that comes up, even among folks who've been here a long time.

BUT, it would work with 4 "physical" and 4 "virtual" coils too. In which case the basic shape would not be a cuboctahedron, but simply an octahedron, aka a rectified tetrahedron.

Exactly. The main problem is that if you talk about octahedron geometry, someone's going to infer (incorrectly) that you want 8 coils, and you are back to cuboctahedron geometry.

What might be interesting for experimental purposes is that it was mentioned that the family of 2n anti-prisms have the appropriate properties. The number of physical coils would be n+1, and wouldn't all be the same size. It might be easier to build, in terms of supporting the coils. I suspect that the symmetry would be sufficiently non-spherical such that it wouldn't work for a polywell reactor. If n=3 it should be all right, but would the field at the center for n>3 be zero? I dunno.

[KitemanSA]

I knew that an icosadodecahedron was a rectified dodecahedron, I just wasn't sure if WB-8 was planned to have that topology.

Well, now you know.

Please check the FAQ linked in the first sticky topic in each of the technical fora. See where you think your description would best serve and we'll get it inserted. (All the links go to the same wiki.)

Thanks.

[blaisepascal]

I knew that an icosadodecahedron was a rectified dodecahedron, I just wasn't sure if WB-8 was planned to have that topology.

Well, now you know.

Please check the FAQ linked in the first sticky topic in each of the technical fora. See where you think your description would best serve and we'll get it inserted. (All the links go to the same wiki.)

Thanks.

I get:

Polywell Wiki Faq has a problem

Sorry! This site is experiencing technical difficulties.

Try waiting a few minutes and reloading.

(Can't contact the database server: Access denied for user 'ohiovr2'@'localhost' (using password: YES) (localhost))

[MSimon]

It seems to me that you need opposite faces facing each other (not a tetrahedron) in order to facilitate internal oscillations (face to face).

I believe those internal oscillations are an essential feature.

I have studied Dr. B's engineering and it is rather elegant given his assumptions. It is hard for me to believe that if there was an advantage in the geometry you suggest that he would have missed it.

[KitemanSA]

Blaise....
That bites! It was working yesterday.

I hope Ohiovr hasn't taken his ball and gone home!

[TallDave]

TallDave wrote:
I wrote:
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?
No. It is what WB6 and 7 have, so I don't think it is a problem.

I thought the whole point of this was that it's not what WB-6 and WB-7 have. Are you saying WB-6 and WB-7 don't have N:N and S:S? Why would we be arguing over whether it's necessary if we already aren't doing it?

Are you saying you don't get a field null between N:S? It seems intuitively obvious there should be, but maybe I'm missing something.

EDIT: I do remember Rick said they went over WB-7 and there weren't any field nulls. (Which you would expect with anything like WB confinement.)

[KitemanSA]

It seems to me that you need opposite faces facing each other (not a tetrahedron) in order to facilitate internal oscillations (face to face).

I believe those internal oscillations are an essential feature.

I have studied Dr. B's engineering and it is rather elegant given his assumptions. It is hard for me to believe that if there was an advantage in the geometry you suggest that he would have missed it.

He didn't miss it. It was the first configuration in his first patent on the subject. I was just saying that it isn't REQUIRED. Dr. B. seemed to like the idea of MORE faces for MORE sphericity, not less. But that doesn't mean it wouldn't work.

As to "internal oscillations", why wouldn't the rect-tet oscillate? It has a number of north-ins and north outs like every other polywell. Each Polywell would need to oscillate in a different mode. The rect-tet mode may be anti-symmetric vice symmetric, but that isn't necessarily a problem. No data = speculation. I'm done with this, I think.

[TallDave]

The other type, the "virtual" solenoids aren't as obvious: Around each of the 8 vertices of the cube, there are three large currents from the three adjacent physical solenoids forming a triangle (a very curvy triangle, but a triangle) with the currents going counterclockwise when viewed from the outside. Since all the physics cares about is a circulating current around the axis of the solenoid, doing it in three unconnected segments is perfectly fine, and you get a solenoid without a coil.

Yes, that's interesting. I saw it suggested in there somewhere that you could also (in theory) wire the virtual solenoids instead.

The appearance of the WB-6/7/8/8.1 is cubic, with six coils on the faces of the cube, but the underlying physics is cuboctahedral, with inward pointing (physical) solenoids on the 6 square faces and outward pointing (virtual) solenoids on the 8 triangular faces. The vertices of the cuboctahedron are at the 12 points where the physical coils come close to touching. Around each of these twelve points are 4 solenoids, two pointing in, two pointing out, alternating. This arrangement, of alternating inward and outward solenoids is the key to Bussard's design for the polywell.

Yes, having trouble visualizing that, but it sounds like it makes sense. Is there a picture of this floating around anywhere? Too much to hope I expect.

[blaisepascal]

I thought the whole point of this was that it's not what WB-6 and WB-7 have. Are you saying WB-6 and WB-7 don't have N:N and S:S? Why would we be arguing over whether it's necessary if we already aren't doing it?

Let's be very clear here: when I'm discussing N and S configurations, I'm talking about which pole is direct into the polywell towards the center of the device. I believe KitemanSA is doing likewise. If we aren't using the same convention, then we will just horribly confuse each other. For instance, if we have two solenoids sharing the x axis, one at x=-1 with N pointing in the x+ direction and one at x=1 with N pointing in the x- direction, I would call both solenoids N solenoids, and that configuration as N:N. If both were pointing in the x+ direction, I'd call it N:S.

WB-6/7 have 6 N's and 8 S's in a cuboctahedron configuration. With a cuboctahedron it's the case that each of the N's have a diametrically opposed N, and each of the S's have a diametrically opposed S. If you want, you could call that three N:N and four S:S pairs, but I wouldn't. There is enough interference from the other 12 solenoids that any solenoid in a pair would barely see it's partner.

But the geometry for a polywell does not require N:N and S:S "pairs". If you use an octahedral configuration, which would have 4 N's and 4 S's, the N's would be diametrically opposed to the S's (in an N:S configuration). Yet because of the symmetry of the coil arrangement there would be a null field in the center of the device.

Are you saying you don't get a field null between N:S? It seems intuitively obvious there should be, but maybe I'm missing something.

In the example of two solenoids on the x axis, if they are both pointing in (an N:N configuration), you do get a field null at the origin. However, if they are both pointing in the same direction (an N:S configuration) then physically they act the same as one long solenoid. The field of one continues through the other, and they both reinforce each other. There is no field null, and the resulting field is twice as strong as it would be for each solenoid alone.