A question about higher order polyhedra.

[icarus]

Kiteman said:

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.

I think the loss "factor" was line cusps 1.5:1 to point cusps. So yes, I agree any geometric changes that reduce losses of that nature are a gain, for the same cusp gyroradii of course. But first you'd have to calculate that the same reduction in loss could not be achieved cheaper/faster/better by decreasing the line cusp gyroradius with a stronger B-field.

[charliem]

I imagine constructing a coil/torus "..." and resting it against the corner. "..." This coil's current would be parallel to that pseudo-loop.

There is at least one problem with that configuration. If you lay two parallel conductors, both carrying current in the same direction, there is a region between them where the magnetic field is null.

The same applies if you put another coil above or inside one of the corners of a WB6/7 like cube machine, at least for some segments. That'd ruin confinement.

And there is another issue, deforming the magnetic fields could mean that the coils cant be made conformal to them anymore, increasing electron losses.

[MSimon]

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.

What kind of help do you want? I think you are doing fine so far.

[KitemanSA]

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.

What kind of help do you want? I think you are doing fine so far.

I have repeatedly asked that a sticky topic be created to reference the FAQ and placed in each of the groups in the Technical Forum. So far, no such luck. A sticky with the Subject FAQ and the URL in the body would let folks know about it.

[KitemanSA]

Kiteman said:

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.

I think the loss "factor" was line cusps 1.5:1 to point cusps. So yes, I agree any geometric changes that reduce losses of that nature are a gain, for the same cusp gyroradii of course. But first you'd have to calculate that the same reduction in loss could not be achieved cheaper/faster/better by decreasing the line cusp gyroradius with a stronger B-field.

I have to admit, we are getting out of my field (heck, we've been out) but my recollection is that there was a length of the line cusp factor in there too. So if the effective radius of the point cusp hole is R, the the loss factor would be 1.5F*L/R given F=Factor(loss) for the point cusp. Thus even relatively short line cusps dominate the loss factor. I remember seeing the equation, but I am not sure where.

[KitemanSA]

I imagine constructing a coil/torus "..." and resting it against the corner. "..." This coil's current would be parallel to that pseudo-loop.

There is at least one problem with that configuration. If you lay two parallel conductors, both carrying current in the same direction, there is a region between them where the magnetic field is null.

The same applies if you put another coil above or inside one of the corners of a WB6/7 like cube machine, at least for some segments. That'd ruin confinement.

And there is another issue, deforming the magnetic fields could mean that the coils cant be made conformal to them anymore, increasing electron losses.

By this logic, the fact that the toroidal coils have more than one conductor in their can ruins confinement. This is obviously not the case. It is not the field nulls between magnets, it is the tangential field the electrons see inside the machine that define confinement.

Likewise, the conformation of the casing doesn't matter once the magnet cross section is smaller that the standoff needed to reflect what one wants reflected. No? Perhaps the mantra needs to be "No metal thru the wiffleball"; not "conformal casings".

[charliem]

I imagine constructing a coil/torus "..." and resting it against the corner. "..." This coil's current would be parallel to that pseudo-loop.

That'd ruin confinement.

... deforming the magnetic fields could mean that the coils cant be made conformal to them

By this logic, the fact that the toroidal coils have more than one conductor in their can ruins confinement. This is obviously not the case. It is not the field nulls between magnets, it is the tangential field the electrons see inside the machine that define confinement.

Likewise, the conformation of the casing doesn't matter once the magnet cross section is smaller that the standoff needed to reflect what one wants reflected. No? Perhaps the mantra needs to be "No metal thru the wiffleball"; not "conformal casings".

Ok, I see I failed to explain myself clearly. Let me try again.

You agree that if you place an extra coil inside or near a corner of the cube (opposite N-S orientation to the 6 main ones), then it will deform the field so that it gets stronger in some places and weaker somewhere else. Then the question that remains is if you can think of a configuration where the lowered field regions are shielded with other of enhanced (or at least not diminished) field. No trivial thing to achieve.

If you put an extra coil inside a corner, that would deforme the funny cusp creating a point cusp in its center (an enhancement, good thing), but also weaking the field in the line cusps between the primary magnets, that is WIDENING them (not so good).

And if we put the coils outside the corners then they'll "push" from the magnetic field lines created by the primary coils, and in doing so expanding the funny cusp mouth (very bad thing), and still weaking the field near the casings (and making easier for the E-field to get the electrons to the metal).

About "no metal thru the wiffleball": Its not just about the wiffleball not contacting with any metal structure, the ideal situation is that no metal in the magrid is unshielded from electrons; that includes its interior (where the wiffleball is supposed to form), but ALSO the cusp regions, AND even its exterior surfaces. Any metal of the magnets casings unprotected with a powerful enough B-field will suck electrons, because of the E-field.

A simulation with graphics could make all this much more evident... or disprove my intuition ...

[KitemanSA]

You agree that if you place an extra coil inside or near a corner of the cube (opposite N-S orientation to the 6 main ones), then it will deform the field so that it gets stronger in some places and weaker somewhere else.

Actually, I am not sure it would in fact have to get weaker anywhere. By turning the virtual coil real, it may just even things up and make the fields stronger.

Then the question that remains is if you can think of a configuration where the lowered field regions are shielded with other of enhanced (or at least not diminished) field. No trivial thing to achieve.

I can’t help but feel that what we want to achieve, after the plasma has inflated the waffle ball, is as spherical a wiffleball as possible with as small a total cusp area as possible. I agree with what I think DrB said which is the quasi truncated cube format is NOT it.

If you put an extra coil inside a corner, that would deforme the funny cusp creating a point cusp in its center (an enhancement, good thing), but also weaking the field in the line cusps between the primary magnets, that is WIDENING them (not so good).

Ok. It seems we have a disagreement here on terminology. The funny cusps are NOT at the corners of the cube. At the corners are the point cusps from the virtual out magnets. The things you call line cusps are where the funny cusps SHOULD be if the system were the true Polywell DrB stated that he wanted. But we are agreed that placing a magnet at the corner can be a good thing.

Re the “line” cusps, replacing the virtual magnet with a real one may “widen” the cusp, but it can also make it MUCH shorter. It is an area issue, and line cusps (according to DrB) are the dominant loss mechanism. He wanted to eliminate them in favor of funny cusps which had a very small area of null field.

I suspect you are currently locked into thinking the magnet must necessarily be toroidal. I don’t agree. I think it would be better to be triangular.

The other question is just exactly what you mean by “inside” a corner. I envision it to be at the same spherical standoff as the prime coils.

And if we put the coils outside the corners then they'll "push" from the magnetic field lines created by the primary coils, and in doing so expanding the funny cusp mouth (very bad thing), and still weaking the field near the casings (and making easier for the E-field to get the electrons to the metal).

IBID re terminology. And I don’t understand what you mean by “push” but I disagree that it would grow the corner cusp. The fields will all be of proper sense to shrink ALL cusps.

About "no metal thru the wiffleball": Its not just about the wiffleball not contacting with any metal structure, the ideal situation is that no metal in the magrid is unshielded from electrons; that includes its interior (where the wiffleball is supposed to form), but ALSO the cusp regions, AND even its exterior surfaces. Any metal of the magnets casings unprotected with a powerful enough B-field will suck electrons, because of the E-field.

Here we go with language again. To me, the wiffleball is the definition of that surface in space where the electrons cannot pass. Like the true waffle ball it has the inside surface, which is where most folks seem to stop thinking, but it also has a part of the surface that transits outward to an outer surface, thereby making holes (cusps) and continues across an outside surface (which in this case looks nothing like a wiffleball!). No metal should cross that surface, the wiffleball, unless it is remote enough from the cusps that the electrons have been returned thru the cusp by the electrostatic potential.

A simulation with graphics could make all this much more evident... or disprove my intuition ...

Tell you what, give me ~$5000 so I can buy the necessary software and I will do the sim. And a juicy one back at ya!

Actually, the software is free, but it requires Wolfram Mathematica which is not

[charliem]

Ok. It seems we have a disagreement here on terminology. The funny cusps are NOT at the corners of the cube. At the corners are the point cusps from the virtual out magnets. The things you call line cusps are where the funny cusps SHOULD be if the system were the true Polywell DrB stated that he wanted. But we are agreed that placing a magnet at the corner can be a good thing.

The other question is just exactly what you mean by "inside" a corner. I envision it to be at the same spherical standoff as the prime coils.

Maybe we should try to standarize terminology somewhere, having to agree definitions each time is soooooo tiresome . Here are my own:

1) In a polywell there are 6 point cusps, one at the center of each face, and 8 funny cusps at the corners. Funny because of their shape, a three pointed sun (not a star because of its fat nucleus). The line cusps are just the prolongation of the funny cusp spokes.

2) Wiffle-ball is the boundary of the magnetic field inside the magrid.

3) For "inside the corner" I meant that the new coils geometrical center are at the same distance from the polywell center than the main ones, and their perimeter rest on the same spherical surface.

Re the "line" cusps, replacing the virtual magnet with a real one may "widen"; the cusp, but it can also make it MUCH shorter. It is an area issue, and line cusps (according to DrB) are the dominant loss mechanism. He wanted to eliminate them in favor of funny cusps which had a very small area of null field.

It's an area issue, I concur, but if you widen and shorten a line/funny cusp it is not clear whether the total area is decreased or increased.

And by the way, if I'm not mistaken, in WB6/7 there where no areas of null field anywhere outside the wiffle-ball, not even in the cusps.

You agree that if you place an extra coil inside or near a corner of the cube (opposite N-S orientation to the 6 main ones), then it will deform the field so that it gets stronger in some places and weaker somewhere else.

Actually, I am not sure it would in fact have to get weaker anywhere. By turning the virtual coil real, it may just even things up and make the fields stronger.

As long as the new coils orientation is opposite to the main ones there has to be some places where the field is diminished, unless you make them with the exact shape and size of the virtual coils, and then why put more coils when improving the main ones would be easier.

I can't help but feel that what we want to achieve, after the plasma has inflated the waffle ball, is as spherical a wiffleball as possible with as small a total cusp area as possible.

I agree, although I'd add another condition, that the B-field is strong enough. I sense that many people tend to think about magnetic fields only in terms of field lines, and that is misleading, field lines give you vector, but not magnitude. You have to think in terms of shape AND strength.

A cusp area as small as possible is good, but weakening the field in some places to get it doesn't look so good. Why not position the new coils with the same N-S orientation that the main. If the 14 of them where, for example, North to the center, then the new coils would add their inbound flux to the wiffle-ball, and that increased flux could only exit between coils, both increasing field strength and decreasing cusps total area, and even enhancing wiffle-ball sphericity (creating something like the cuboctahedron someone mentioned).

[hanelyp]

Just threw this together.

Shown is the 3 faces of a 'cube' polywell adjacent to a virtual coil, and an extra coil over the virtual coil. Is this the configuration we're talking about?

I'm thinking that the overlapping field from the outer octahedral set might reduce the cusps between kissing coils towards a point cusp configuration.
[/list]

[KitemanSA]

Good question. I think we have ten people with twenty different ideas about what is being talked about.

After I stopped being TOTALLY confused about what the original poster had asked, I was thinking the capping magnet was much smaller and would kiss the three main magnets. I had also suggested that the capping magnet should be closer to triangular to improve it even more. Eventually, we get back to the bow-legger square-planform real-real setup that tombo graphed so beautifully before.

[MSimon]

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.

What kind of help do you want? I think you are doing fine so far.

I have repeatedly asked that a sticky topic be created to reference the FAQ and placed in each of the groups in the Technical Forum. So far, no such luck. A sticky with the Subject FAQ and the URL in the body would let folks know about it.

Lay it out exactly how you want it and I will post it.

[VernonNemitz]

To hanelyp, the diagram is mostly what I had in mind, but the corner coil doesn't need to be that large.

To KitemanSA, one reason I've mentioned an octahedron more than once, for the facet coils, is because there are 4 facets at each corner instead of 3. That means a round corner coil is a better shape for an octahedron corner than any other polyhedron for a Polywell (except the icosahedron which has five facets connecting at each corner).

Regarding weak spots in the overall magnetic field, I'm pretty sure it is well established that the weak spots are the centers of the facets and the corners. So, if the facets have appropriately strong magnet coils, and the corners are enhanced with real coils, then any place not covered (the nubbin zone, for example) doesn't really matter; that place was not a weak spot in the first place, and will not become weak just because we added extra magnetism.

[charliem]

I'm pretty sure it is well established that the weak spots are the centers of the facets and the corners.

Regarding the workings of polywell very few thing are well stablished yet, and I don't think that's one of them. The little info we have about WB7 results may suggest otherwise, if not, why the declared intention of changing the design of the "nubbins"?

[VernonNemitz]

why the declared intention of changing the design of the "nubbins"?

No such thing. I did not know what the nubbins were, when I started writing about the corners. So, I'm talking about affecting the magnetic fields at the corners, and the actual nubbins are completely out of that picture.