(Pre-Wiffle) B-Field From Cubic Magrid

TheRadicalModerate · Post by **TheRadicalModerate** » Fri May 25, 2012 5:16 am

I realized today that I don't understand why the Magrid B-field has line cusps between the coils. The point cusps through the center of the coils I understand, but I've been looking at the classic field lines of a quadrupole magnetic field, and it doesn't have cusps between its current loops.

I've been assuming that the quadrupole is a reasonable 2D model for the Magrid, and when you add the pair of loops to the top and bottom, you get essentially the dual of the cube, i.e. an octahedron with the sides squished a bit.

But then there are no line cusps between current loops after diamagnetic inflation is complete.

What am I missing? And where are the line cusps?

KitemanSA · Post by **KitemanSA** » Fri May 25, 2012 11:28 am

If I understand you correctly, what you are missing is that the 4 equatorial magnets are NOT a quadrapole which implies alternate in-out-in-out. The Polywell has 6 (six) "in" magnets and no "out" EXCEPT that the eight quasi-traingular gaps (corners of the cube) are virtual "out" magnets. Since the adjacent magnets point in, the field also exits between the coils where they get close. That location between the coils is the like-like cusp.

Does that help?

TheRadicalModerate · Post by **TheRadicalModerate** » Fri May 25, 2012 4:54 pm

Yes, I realized that that was my problem at about 2:00 in the morning.

So does that mean that there's a line cusp that extends along each edge of the cube?

So that explains Bussard's comment about needing an even vertex configuration. But I notice that there's been a lot of talk about dodecahedrons, and they don't solve the problem either (vertex config is 5.5.5 vs. the cube's 3.3.3--both odd).

So I think I understand why the truncated cube (cuboctahedron) comes up. Even though it's not a platonic solid, its vertex configuration is even: 4.3.4.3. You can now have all faces that share an edge have opposite polarity, with opposite faces being parallel to each other. But that means that the radius of the current loops isn't the same on the square faces as it is on the triangular faces. (For edge length E, Rsquare=.5E, Rtriangle=.43E) I'd assume that you'd use the shorter radius for all loops? The cusps would still be evenly spaced, right? And the shape of the B-field would then be the dual of the truncated cube, a rhombododecahedron with only point cusps.

The other alternative is to use an octahedron (vertex config = 3.3.3.3), but now you run into the problem that opposite faces aren't parallel to each other. Does this matter if you have a trap with only point cusps? The dual of an octahedron is a cube, which would seem like a promising B-field shape...

I assume that the reason none of these was attempted was simply cost, in that the current loop magnets were too expensive?

krenshala · Post by **krenshala** » Fri May 25, 2012 6:08 pm

The dodecahedron does have the correct orientation as described by Dr. B.

Also, the octahedron does have parallel facings. It has four pair of parallel faces, while a cube only has three pair (and the dodec has six pair).

TheRadicalModerate · Post by **TheRadicalModerate** » Fri May 25, 2012 7:23 pm

krenshala wrote:The dodecahedron does have the correct orientation as described by Dr. B.

Also, the octahedron does have parallel facings. It has four pair of parallel faces, while a cube only has three pair (and the dodec has six pair).

You're right about the octahedron (so why doesn't polywell use that?), but you can't have a dodec and have the poles point in opposite directions for any pair of faces that share an edge. Try it!

The real question, I guess, is why you wouldn't want alternating poles if you could have them (you obviously can't with a cube). When all the poles face in, there have to be edge cusps. When they alternate, then the field lines between neighbors add in superposition and you get a smooth B-field between neighboring point cusps.

No doubt I'm missing something...

KitemanSA · Post by **KitemanSA** » Fri May 25, 2012 9:39 pm

Folks, the Polywell does not use either a cube or a dodecahedron. It used a truncated (best truncated to being rectified) version of them. For the WB6/8 that is desired to be a cubeoctahedron. For the dodec, it is actually desired to be an icosadodecahedron.

Check out the Polywell FAQ. The link is available at the top of this forum. Sometimes bozos sabotage it and it takes a while to restore. But if it is working it has some goodbasic info.

TheRadicalModerate · Post by **TheRadicalModerate** » Fri May 25, 2012 10:15 pm

KitemanSA wrote:The Polywell has 6 (six) "in" magnets and no "out" EXCEPT that the eight quasi-traingular gaps (corners of the cube) are virtual "out" magnets.

I guess I still have two questions:

1) All the WB pictures show cubes that are truncated by virtue of the magnets being circular, but the truncated cube is far from rectified. Why isn't it rectified?

2) Why wouldn't the proper config be to have real, non-virtual "out" magnets in the rectified triangles?

BTW, the FAQ has stuff on cusps, funny and otherwise, but I didn't see any place where it talked much about the actual geometry and polarity of the magnets.

hanelyp · Post by **hanelyp** » Sat May 26, 2012 1:31 am

The polarity is simple, all real magnets have a like pole towards the inside, leaving all virtual magnets to have the opposite pole towards the inside.

The line like, or "funny", cusps are between pairs of real magnets where they approach closest. Equivalently, where adjacent virtual magnets meet.

Having a second set of real magnet matching the virtual magnets from the first set has a problem, reversed polarity at the funny cusps, canceling the magnetic field there.

The shape of the magnets, at least on WB-6 and WB-7, is round because that shape is easier to produce. Another shape will likely prove more optimal.

ladajo · Post by **ladajo** » Sat May 26, 2012 1:42 am

The coil form is also about being able to make a conformal can that shapes to the fields. Can't have any field lines crossing metal.

D Tibbets · Post by **D Tibbets** » Sat May 26, 2012 2:37 am

ladajo wrote:The coil form is also about being able to make a conformal can that shapes to the fields. Can't have any field lines crossing metal.

The round or possibly even oval shaped minor radius is different from the gross shape of the coil. It could be a curved vertex(?) cube of triangle, etc.

As for rectified. I may be wrong but in this incidence I interpret the question to be why isn't the coils smaller so that the edge regions/ cusps are ~ the same area as the center point cusps. This isn't required, so long as the opposite cusp is symmetrical. The corner cusp has some point like characteristics, but there are still three line cusps radiating out from the corner. Making these cusp areas smaller by having the coil close to the corner compensates for this and my impression is that the corner cusp leakage (cusp area) is perhaps ~ 1/2 of the face point cusp losses. This is a design element that can be modified, perhaps for the better by using more complicated shaped coils (like square) and perhaps rotating the vertex.

I can add that alternating the coil current in adjacent magnets does not give a symetrical cusp geometry and behaves much different from the Polywell

Dan Tibbets

D Tibbets · Post by **D Tibbets** » Sat May 26, 2012 2:38 am

ladajo wrote:The coil form is also about being able to make a conformal can that shapes to the fields. Can't have any field lines crossing metal.

The round or possibly even oval shaped minor radius is different from the gross shape of the coil. It could be a curved vertex(?) cube or triangle, etc.

As for rectified. I may be wrong but in this incidence I interpret the question to be why isn't the coils a smaller so that the edge regions/ cusps are ~ the same area of the center point cusps. This isn't required, so long as the opposite cusp is symmetrical. The corner cusp has some point like characteristics, but there are still three line cusps radiating out from the corner. Making these cusp areas by having the coil close to the corner compensates for this and my impression is that the corner cusp leakage (cusp area)is perhaps ! 1/2 of the point cusp losses. This is a design element that can be modified, perhaps for the better by using more complicated shaped coils (like square) and perhaps rotating the vertex.

I can add that alternating the coil current in adjacent magnets does not give a symmetrical cusp geometry and behaves much different from the Polywell.

Dan Tibbets

KitemanSA · Post by **KitemanSA** » Sat May 26, 2012 5:02 pm

[/quote]

TheRadicalModerate wrote:
KitemanSA wrote:The Polywell has 6 (six) "in" magnets and no "out" EXCEPT that the eight quasi-traingular gaps (corners of the cube) are virtual "out" magnets.
I guess I still have two questions:

1) All the WB pictures show cubes that are truncated by virtue of the magnets being circular, but the truncated cube is far from rectified. Why isn't it rectified?

. If you read Dr. B's Valencia paper, he wanted to build a more exact rectified cubeoctahedron by building a "WB7" with square plan form magnets. That is still to be done.[/quote]

mvanwink5 · Post by **mvanwink5** » Sat May 26, 2012 7:41 pm

KitemanSA,
Optimizing for leaking cusps might not be an issue requiring geometry efforts if confinement is excellent as reported by EMC2. Just a thought. On the other hand, increasing the number of coils keeps the practical B fields maximized thus taking advantage of B^4 scaling (smaller diameter coils have higher B fields), with the detracting cost of more supports (which might be required anyway with high strength B fields).

Best regards

KitemanSA · Post by **KitemanSA** » Sat May 26, 2012 9:22 pm

mvanwink5 wrote:KitemanSA,
Optimizing for leaking cusps might not be an issue requiring geometry efforts if confinement is excellent as reported by EMC2. Just a thought.

True, but Dr. B seemed to think there would be a significant improvement, so who am I to argue? Could "excellent" be bettered?

mvanwink5 · Post by **mvanwink5** » Sat May 26, 2012 11:26 pm

Dr. Bussard unfortunately did not have the advantage of confinement data at .8T and his data at .1T was thin (he didn't really get to see WB-7 and 7.1, right?). Further, what will confinement look like at higher fields? But, it is good to keep an open mind either way.
Best regards