STATEMENT OF OBJECTIVES from RFP

[KitemanSA]

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?

Apparently not. It is the funny cusp that is at the vertex (of a true polyhedral MaGrid) and there should be NO line cusps. HOWEVER, because the vertex in WB6 and 7 doesn't really exist and is instead replaced by a quasi-edge, we get a quasi-line cusp. Make the quasi-edge more like a vertex (which I have been trying to do) and the quasi-line cusp becomes a funny cusp.

There are no field nulls except at the very center where the plasma lives.

Again, not so. With a true Polywell, there is a field null at each vertex. The only machines so far to achieve that were the MPGs, but they had a hunka matter in the way. I am trying to "free the funny cusp"!

(If you think I am wrong show me exactly where and why. Last time I looked at Indrek's models there were none.)

Indrek never actually modeled a true Polywell. He modeled WB 6 (or 7) IIRC.

The cusps are where the field lines are straight. (strong but straight)Actually more to the point (I think) where they are diverging.

Once again, not so. The cusps are where the field lines enter or leave the MaGrid. They can be the IN or OUT point cusps in the centers of the coils or virtual coils, they can be line cusps where the fields from two coils OF THE SAME POLARITY meet and squeeze out (or in) between them, or they can be the "Funny"cusps where there are both IN and OUT fields trying to squeeze past each other.

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.

Not getting this. "the center of 2 adjacent corners of the cube, the center of the edge connecting them" are the identical point, no? You have described two points which does not a plane make. What am I missing?

Now there is a set of (diverging) field lines on that surface. They are straight and they lie in a plane. (Due to symmetry)

Again, ???

Any electron (or ion) moving in that plane follows a field line to the wall.

Presuming an ion is headed toward a cusp from the center of the machine, if the ion has enough velocity to climb the potential well past the edge, then you are right, the hit the wall. But they usually don't have that much velocity. Any electron similarly headed exits the MaGrid, gets restrained by its potential, and returns thru the same hole or travels around to another one. Again, if it has too much velocity, it too will reach the wall, but it started at the same potential so there is very little loss there.

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.

Ok. I disagree.
I will steal a recent graphic and try to describe the situation as I understand it.

[KitemanSA]

Greetings,
Please excuse the truly crude graphics, but I hope it will get the idea across.

The top panel depicts (all-be-it poorly) a WB-7 like machine (non-conformal, but forgive me).
The coils (torii) of the WB-7 are placed symmetrically on the faces of a cube (obviously the red box).
Said coils (middle panel, pink!) can be approximated as being octohedra on a truncated cube. The point cusps are the light bluish dots in the middle of the octohedra, and the middle of the yellow triangles (not all shown). The black line is the quasi-line cusp. If there were no top coil, there would be no virtual coil (The aqua-marine triangle over the yellow) and the line cusp would extend effectively to infinity (cusp in an infinitely weak field!). Since the top coil IS there, the virtual coil comes into existance and does wierd things to the line cusp making it only quasi linear. The line cusp peters out starting at the vertex where the three coils meet.
Final panel. The coils can also be approximated as a diamond (rotated square) on a RECTIFIED cube (cuboctohedron). In this case, the virtual coils reach effectively to the vertex where 4 (FOUR) coils meet. The star in the middle there is the funny cusp.

Tell me now if I have this wrong!

[MSimon]

there should be NO line cusps.

Quite so. And if you can eliminate edges from the coils it might be possible to accomplish that.

My experience is that the understanding of the magnetic fields and how they function is the hardest part in understanding this design.

You really have to start with a current in a wire and THINK about the field. Then go to a coiled wire and THINK some more.

Then you should look at Indrek's field dwgs. And THINK some more.

[KitemanSA]

there should be NO line cusps.

Quite so. And if you can eliminate edges from the coils it might be possible to accomplish that.
...
You really have to ... THINK ... and THINK some more. And THINK some more.

Not pain no gain, hunh? I done thunk so had my brain hurts

[MSimon]

there should be NO line cusps.

Quite so. And if you can eliminate edges from the coils it might be possible to accomplish that.
...
You really have to ... THINK ... and THINK some more. And THINK some more.

Not pain no gain, hunh? I done thunk so had my brain hurts :)

I know what you mean. It is why so little thinking gets done. It physically hurts.

[blaisepascal]

Greetings,
Please excuse the truly crude graphics, but I hope it will get the idea across.

Truely crude graphics excused. They have one major advantage over the elegant graphics I was thinking of drawing: they exist. They also get your point across. Now we can discuss their accuracy.

Final panel. The coils can also be approximated as a diamond (rotated square) on a RECTIFIED cube (cuboctohedron). In this case, the virtual coils reach effectively to the vertex where 4 (FOUR) coils meet. The star in the middle there is the funny cusp.

Tell me now if I have this wrong!

Your diagrams and explanation matches my understanding, so I don't think you have it wrong.

[Art Carlson]

Working toward a common language: A "polyhedral magrid" (which Kiteman considers to be a "true" polywell) is a configuration of conductors with current flowing along the edges of a polyhedron, as opposed to current flowing in discrete coils as in all experiments to date. See Kiteman's third picture.

Agreed?

As Kiteman reminds us, there is (by symmetry) a field null at each vertex of a polyhedral magrid. Nebel has said this is a big bad and the reason that discrete, non-osculating (my six-bit word of the day) coils must be used. I would like to add that the line cusps (or semi-line cusps, or quasi-line cusps - time for another round of dictionary) forming the three-armed star in the middle of triangular faces do not go away. On the contrary, there are now four-armed stars of line cusps in the middle of the square faces, too.

This is a consequence of the fact that the magnetic field cannot have a component perpendicular to any plane of symmetry. We also know from Indrek's beautiful pictures some time back that the field lines are not simply radial, but -- umm, what did they look like?

[Torulf2]

Can this be a possible octahedral magrid?
http://farm4.static.flickr.com/3593/334 ... 74.jpg?v=0
I think this is the configuration for the mix reactor.
http://www.fpgeneration.com/

[KitemanSA]

Can this be a possible octahedral magrid?
http://farm4.static.flickr.com/3593/334 ... 74.jpg?v=0
I think this is the configuration for the mix reactor.
http://www.fpgeneration.com/

This is a bowed octohedron with sharp corners. The bowed may be good (I think so, but this is not my specialty) , the octohedron may be ok (I've suggested it in the past, but IBID) but I am pretty dang sure that the sharp corners put metal in the funny cusp which I think everyone agrees is a no-no.

[KitemanSA]

Working toward a common language: A "polyhedral magrid" (which Kiteman considers to be a "true" polywell) is a configuration of conductors with current flowing along the edges of a polyhedron, as opposed to current flowing in discrete coils as in all experiments to date. See Kiteman's third picture.
Agreed?

If you mean effectively that the MPG was a true polywell, yes, but it had kissing vertices. (Osculating indeed! How'd you like a punch in the osculator? That's a joke, son, a joke!) But the square plan-form cubeoctahedron and the pentagonal iscosedodec are also true Polywells because their coil members align between the vertices. But DrB seemed to think that keeping metal out of the funny cusp was important since he specified rounded corners.

As Kiteman reminds us, there is (by symmetry) a field null at each vertex of a polyhedral magrid. Nebel has said this is a big bad and the reason that discrete, non-osculating (my six-bit word of the day) coils must be used.

This is where I don't understand his logic. As long as there is no metal there, (and it is not too big) why should we care?

I would like to add that the line cusps (or semi-line cusps, or quasi-line cusps - time for another round of dictionary) forming the three-armed star in the middle of triangular faces do not go away. On the contrary, there are now four-armed stars of line cusps in the middle of the square faces, too.
This is a consequence of the fact that the magnetic field cannot have a component perpendicular to any plane of symmetry.

Which would suggest that there is an infinite armed line cusp in a circular coil since it has infinite planes of symmetry. There has got to be a limit to what actually leaks electrons; between what is actually a line cusp and what is merely a wrinkle in the wiffleball.

We also know from Indrek's beautiful pictures some time back that the field lines are not simply radial, but -- umm, what did they look like?

Neat as heck!

[icarus]

This is the field line diagram in the diagonal plane that intersects the edge and corner cusps.

[tombo]

As Kiteman reminds us, there is (by symmetry) a field null at each vertex

Only in the case of a mathematically sharp point at the vertex. With real world materials there must either be a chunk of metal there (not good), or there must be a gap between the coils DrB's solution. Zoom in and look closely at that gap. It can be modeled to a first approximation as 2 straight wires with opposite direction currents. This does not make a null. Moreover the direction of that field is the same as the 2 connected triangular(ish) regions. Null? NO. Cusp YES.
DrMike had some enlightening comments on this geometry some months back.

of a polyhedral magrid. Nebel has said this is a big bad

YES FIELD NULL VERY BAD

and the reason that discrete, non-osculating (my six-bit word of the day) coils must be used. I would like to add that the line cusps (or semi-line cusps, or quasi-line cusps - time for another round of dictionary)

I looked it up but how do you mean it to apply here? Do you just mean that the coils don't touch?

forming the three-armed star in the middle of triangular faces do not go away. On the contrary, there are now four-armed stars of line cusps in the middle of the square faces, too.

YES YES YES This is what i tried to say with too many words and maybe not enough of the right ones.

This is a consequence of the fact that the magnetic field cannot have a component perpendicular to any plane of symmetry. We also know from Indrek's beautiful pictures some time back that the field lines are not simply radial, but -- umm, what did they look like?

I liked the solar flare picture.

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.

Not getting this. "the center of 2 adjacent corners of the cube, the center of the edge connecting them" are the identical point, no? You have described two points which does not a plane make. What am I missing

It was late I was tired and mis-spoke(mis-wrote?)
The plane formed by 2 adjacent corners and the center of the cube.
I was emphasizing that the center of the edge between them is on that plane and is the location of the funny cusp.
Art said it better.

In fact all the line cusps and funny cusps are part of one connected cusp system.
Ok. I disagree.

Look here http://www.mare.ee/indrek/ephi/invwb/ball2.png Follow all the connected blue and light blue areas. Then look at what Art Said.

Kiteman I agree with your cube geometry and the location of the funny cusp.
Good enough graphics to do the job, that's all that matters. Sometimes fancier is distracting from the point.

[tombo]

Can this be a possible octahedral magrid?
http://farm4.static.flickr.com/3593/334 ... 74.jpg?v=0
I think this is the configuration for the mix reactor.
http://www.fpgeneration.com/

This is a bowed octohedron with sharp corners. The bowed may be good (I think so, but this is not my specialty) , the octohedron may be ok (I've suggested it in the past, but IBID) but I am pretty dang sure that the sharp corners put metal in the funny cusp which I think everyone agrees is a no-no.

It might work if they leave a hole there and your highway interchange idea works.
But, I don't have a warm fuzzy feeling about the sharp corners.
I have no problem with the octahedron. I think it meets all of the explicit criteria (of the polyhedron patent) if not some assumed ones.
(I did not take the time just now to reread it. Looks like I'm getting no drawing done tonight. I have a bunch that I want to do.)

[KitemanSA]

of a polyhedral magrid. Nebel has said this is a big bad

YES FIELD NULL VERY BAD.

WHY? As long as there is no metal there, why is it such a big bad? Can it be any bigger a bad than a line cusp with a nub in the middle?

[KitemanSA]

It might work if they leave a hole there and your highway interchange idea works.

Their unit doesn't need a "highway interchange". They have discrete coils, each feeding its own corner. Interesting concept. SIMPLE, elegant, and with slightly rounded corners, it may even work. I am jealous. Oh, and with rounded corners they may actuially be able to build it!

Such discrete coils would be a fall-back position for the bowed CubOctahedron (CO) too. Theirs would have 8 standard coils, the OC woiuld have 6 "square" and 8 "triangular" coils and a more complex piping design.