A question about higher order polyhedra.

[MSimon]

Suppose higher order Polyhedra with all their added complication, expense, and additional failure points can improve electron confinement by a factor of five.

We can get the same effect by increasing magnet strength by 50%. If we only gain a factor of three a 30% increase in magnet strength will do.

Now if we were limited by the possible field strength of SC magnets it might be a good idea. But that is not the case. Rick is proposing 10 T magnets. Experimental physics is already using 20 T SC magnets. And 100 T is the ultimate - for now.

So we get the same effect of the complications and the added material costs of higher order polyhedra by just making the magnets stronger. That seems to me to be the better route.

[pfrit]

Suppose higher order Polyhedra with all their added complication, expense, and additional failure points can improve electron confinement by a factor of five.

We can get the same effect by increasing magnet strength by 50%. If we only gain a factor of three a 30% increase in magnet strength will do.

Now if we were limited by the possible field strength of SC magnets it might be a good idea. But that is not the case. Rick is proposing 10 T magnets. Experimental physics is already using 20 T SC magnets. And 100 T is the ultimate - for now.

So we get the same effect of the complications and the added material costs of higher order polyhedra by just making the magnets stronger. That seems to me to be the better route.

I would guess that would depend on the cost of the magnets. Are 3T magnets significantly cheaper than 4.5T magnets? It goes without saying that 3 3T magnets are likely much cheaper than 1 9T magnet. If the relative costs are small, then in a perfect, government payrolled, world you would do both. And the current record for SC magnets is 26.8T (though though the record for a hybrid is 45T and the record for non-destructive pulse magnets is 90T). The strongest field ever acheived was 850T in a destructive pulse magnet. That is beside the point as the "cheap" SC magnets top out at 15T. To go higher, you need expensive, hard to wind materials or hyrids which would probably not work (size issue).
If I had to guesstimate, the most cost effective route would be to go to the edge of commonly used magnets (3T) and then, after testing, increase the number of magnets. When they start rolling out the 9-10 T MRIs, I would then increase the strength of the magnets again. I would not think it would be worthwhile changing the strength and type of magnets while at the same time changing the geometry of the system. Too many things could go wrong at the same time.

[KitemanSA]

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.

Superposition says it WILL work. There are 4 opposing fields meeting in the middle. They cancel.
Saying it anouther way, the each pair of opposing faces make a north-in north-out line. There are 4 of these pairs. The pairs cross in opposition at the center. Thus they cancel.

[KitemanSA]

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

True.

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

Almost true. If the current set-up were actually a rectified cube it would also be a rectified octahedron. They are known as a cuboctahedron. So the rectified octahedron will work. The thing is, an UNtruncated octahedron will also work. It is the only Platonic solid that will, as far as I am aware.

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.

If you accept that each vertex must have an even number of faces, alternating in field orientation, then alternating polarities fall out with the untruncated octahedron. Once truncated to rectifaction, the truncations become the virtual North out faces and all the real coils are the North-in faces (or vice versa). The only distinction would be that the rectified Octohedron would have 8 real triangular faces and 6 virtual square faces, while the rectified cube would have 6 real square faces...

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

The real and virtual fields would be identical to the real-in/real-out fields if the real magnets of the real/virtual set-up had all the strands of the real in/out setup. You would have half as many magnets with twice as many strands each. Same fields, close enough. Of course there may still be be big holes, but but they would occur in either set-up.

[KitemanSA]

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.

You have it backwards. The octahedron will work without opposing faces because there are opposing sets of faces that accomplish the same thing.

FOLKS, come on. You will ALWAYS have an even number of fields at a vertex. There are only two polarities so there will always be an even number of fields. Put two North outs side by side and they become one larger field. The question is whether there are an even number of coil segments to go with them. If there are, they can all be protected by the appropriate field. If there are not, one of the coils segments is going to have a field exiting thru it rather than spanning across it. Not protected!

[KitemanSA]

Suppose higher order Polyhedra with all their added complication, expense, and additional failure points can improve electron confinement by a factor of five.

We can get the same effect by increasing magnet strength by 50%. If we only gain a factor of three a 30% increase in magnet strength will do.

Bigger fields mean bigger, heavier magnets, and sometimes space and weight is important. A 50% stronger magnet implies a 50% heavier magnet, and I would prefer NOT to have to haul that around in my launch vehicle, nor in my submarine, nor on my surface ship... At this point, the improved sphericity MaGrids need to be built and tested to find out how to design properly. Without them we are FORCED to design in ignorance. that can be expensive. And what if it turns out that the better sphericity gives us 10x not 5x. We need to find out!

Do we need to find out FIRST? No, probably not. But we need to find out before going to full scale. Heck, that 3x may turn out be the difference between getting the money for full scale and not getting it.

[MSimon]

I would guess that would depend on the cost of the magnets. Are 3T magnets significantly cheaper than 4.5T magnets?

It is not just the cost of the magnets. There is also support structure. A more complicated machine. More points of failure. More instrumentation. More safety system. etc.

Since the 3T magnets are currently in series production they will definitely be cheaper than individually produced 4.5 T magnets.

However, if the BFR concept is workable what ever magnets are used will go into series production. So the question is not what to do for an experimental machine. The question is: what is optimum for production.

It escapes me at the moment which but either ITER or the LHC use 20 T magnets.

The 100T number is theoretical - 0 deg K. Jc typically goes up at lower temps. Now of course 0K is not practical except in experiments. Still. It may be cheaper to lower the operating temps of the SC coils vs. a more complicated machine.

In addition SC tech has not reached its limit. I expect improvements as time goes on.

Now I have not run the numbers so this is just a gedanken experiment. Something to think about. In fact there is no way to accurately run the numbers without sending out the two different machines for quotes.

===

The current machine is based on all N poles facing in. If you mix N and S poles facing in the machine may not work according to what has been researched so far. The currents would definitely circulate differently.

[MSimon]

Bigger fields mean bigger, heavier magnets, and sometimes space and weight is important.

Not if you lower the SC coil operating temps.

Space is less important than it is at lower field strength since above around .35 T ions no longer impinge on the coils. Operating at 3 T or above ought to allow you a larger projected area fraction than the original 20% contemplated.

[MSimon]

A 50% stronger magnet implies a 50% heavier magnet.

Vs twice as many magnets?

[MSimon]

You have it backwards. The octahedron will work without opposing faces because there are opposing sets of faces that accomplish the same thing.

The octa does have opposing faces. At least if you trust the link I provided. You can rotate the octa and see the opposing faces.

BTW where I said double the number of magnets I was thinking dodec. But let us take the octa vs cube 8/6 = 1.33... At least for terrestrial machines I think the advantage still goes to the cube. Even if you need more mass.

KISS is still a valid engineering principle.

[MSimon]

And what if it turns out that the better sphericity gives us 10x not 5x. We need to find out!

Dr. B. estimated a 3X to 5X improvement. But as you point out - the proof is in the pudding. If you get 10X then the field equivalent is 1.77X. i.e. 75% stronger. B^4 helps a lot.

[KitemanSA]

Bigger fields mean bigger, heavier magnets, and sometimes space and weight is important.

Not if you lower the SC coil operating temps.

Space is less important than it is at lower field strength since above around .35 T ions no longer impinge on the coils. Operating at 3 T or above ought to allow you a larger projected area fraction than the original 20% contemplated.

Please, apples to apples, one thing at a time! The question is, given a magnet condtion, is it better to improve the sphericity or to increase the strength. Until we know what the improvement is, and what the actual need is, we can't just assume that we can just make the system with stronger magnets and be ok.

[KitemanSA]

A 50% stronger magnet implies a 50% heavier magnet.

Vs twice as many magnets?

Again, apples to apples please!. For a given initial magnet configuration, what is the trade-off between sphericity and magnetic power. With the same size core (thus magnet for the cube), increasing the power by 50% means effectively 50% more windings and 50% more weight. Going to higher order Polyhedra means the individual magnets are smaller for the same field strength, and thus lighter, though there will be more of them. What the trade-offs will be is undefined as yet because we don't know the effects of improved sphericity design.

[KitemanSA]

You have it backwards. The octahedron will work without opposing faces because there are opposing sets of faces that accomplish the same thing.

The octa does have opposing faces. At least if you trust the link I provided. You can rotate the octa and see the opposing faces.

True, there is a face opposite each and every face of an octa. But with an UNtruncated octa polywell, the magnet on one face will be the opposite polatity of the one on the opposite face. If one is North in, the other will be North out. They don't become "opposed fileds" (both N-in) until you use the rectified octa.

BTW where I said double the number of magnets I was thinking dodec. But let us take the octa vs cube 8/6 = 1.33... At least for terrestrial machines I think the advantage still goes to the cube. Even if you need more mass.

KISS is still a valid engineering principle.

I don't argue that a larger system or stronger magnet isn't potentially the right answer some times. And if KISS is your operative principle, a 4 magnet bow-legged octa may be the most cost effective unit possible. I just don't like things written as if it is a forgone conclusion that a toroidal magnet faced cube is necessarily the best design. Ain't necessarily so!

[KitemanSA]

And what if it turns out that the better sphericity gives us 10x not 5x. We need to find out!

Dr. B. estimated a 3X to 5X improvement. But as you point out - the proof is in the pudding. If you get 10X then the field equivalent is 1.77X. i.e. 75% stronger. B^4 helps a lot.

Yup, with 75% more weight... Without the data, we CAN'T know. Eventually, it is just not practical to ASSUME we can improve the field strength. Material science has limits too. Show me the trade-off. Show me the DATA!

By the by, DrB assumed straight legged coils aligned between the vertices. It may be that spherically "bow legged" coils would improve that even more. Data, where's the DATA!