magrid configuration brainstorming

[rjaypeters]

Topologically, the closest coil configuration to a spherized Tombo is a tetrahedron which has terrible confinement (according to happyjack27). Let's be careful about loving the spherized Tombo too much before a simulation gives an idea about performance.

I take that back, there is a closer analog, hanelyp's winged octahedron*:



Which was simulated:
viewtopic.php?t=2720&postdays=0&postorder=asc&start=270

Allegedly performed pretty well. Now we just need to think: did the "wings" help the confinement performance, hurt or are they irrelevant?

* Although I don't have a better name for it, I mildly object to something with the equivalent of four physical coils and four virtual coils being called an octahedron, I do see the reasons for doing so in this case.

[KitemanSA]

The line cusps you need to worry about are the one diagonally through the metal of corners where the coils split and merge.

Except there is a transverse field inside the Magrid that protects that portion of the casing.

[rjaypeters]

The more I look at these, the hanelyp "winged" octahedron and the "single-coil" octahedron:

The more convinced I am the close approaches of each set of four coils of the winged are exactly like the "throats" of the quadruple coil extensions of the single coil.

After the close approach and the throats, the winged close approaches diverge, but they do so at the same angle and the single-coil extensions maintain their distance until the chamber wall. I submit charged particles will exhibit mostly the same behavior in both situations.

WRT to the exit of particles between the coil close approaches, I didn't see many of them in the winged simulation. Have to look again.

[rjaypeters]

I give you another rhombicosidodecahedron, the geometric shape that doesn't stop giving. The triangles have been eliminated, again, but this time with torii.



Forty-two coils total, thirty "squares" (in blue) with twelve "pentagons." 0.15m coil diameter, near zero close approach between coils.

[imaginatium]

The more I look at these, the hanelyp "winged" octahedron and the "single-coil" octahedron:

The more convinced I am the close approaches of each set of four coils of the winged are exactly like the "throats" of the quadruple coil extensions of the single coil.

After the close approach and the throats, the winged close approaches diverge, but they do so at the same angle and the single-coil extensions maintain their distance until the chamber wall. I submit charged particles will exhibit mostly the same behavior in both situations.

WRT to the exit of particles between the coil close approaches, I didn't see many of them in the winged simulation. Have to look again.

Actually if you spherize the inner edges on the hanlyp and bent the support pipise on the spherized octahedron 45˚ each way, they would be almost identical, I doubt that the back edges on the hanlyp improve containment much.

[KitemanSA]

I give you another rhombicosidodecahedron, the geometric shape that doesn't stop giving. The triangles have been eliminated, again, but this time with torii.
....
Forty-two coils total, thirty "squares" (in blue) with twelve "pentagons." 0.15m coil diameter, near zero close approach between coils.

You show red and blue torii. I hope they are all still the same polarity or this will be a seive. And by the way, the triangles are still there between each close approach of three torii.

[rjaypeters]

What I mean is the rhombicosidodecahedron has 20 triangular faces, 30 square faces and 12 pentagonal faces. Using some geometry, I turned these different shapes of faces into their complementary shapes (but still triangles, squares and pentagons) with only the corners touching*:



Further developments ensued until I decided to eliminate the torii sited on the triangular faces by expanding the torii sited on the square faces. The consequences are the "triangles" disappear, the "pentagons" get a lot smaller and there are only 42 torii. I've changed the colors to match the previous picture.



If you can correct in your mind for the different view (and colors), you can see this configuration is the straight-legged cousin of the previous.



With the torii, there aren't any funny narrow isosceles triangles and no three-pointed close-approaches.

*For comparison go look at the wiki entry for the rhombicosidodecahedron where the corners and edges of the faces touch each other.

[seedload]

The Tombo (in this early single-coil) example, has the current flowing around the core in a single orientation.

The Tombo arranges the coil to create four "virtual" coils.

One coil shaped like baseball stitching (Page 5).

[rjaypeters]

One coil shaped like baseball stitching (Page 5).

I'm not sure what you mean, but the baseball idea has been looked at...

viewtopic.php?t=2649&postdays=0&postorder=asc&start=135

See my post: Fri Nov 05, 2010 10:07 pm...

and generally found wanting.

[rjaypeters]

Take a dodecahedron and operate on it in a variety of ways and you encounter something that looks a lot like a geodesic dome:



I ought to know because I went back and created a geodesic sphere that is the close cousin.

But before that, I saw a close array of seven hexagons and I knew I had gone beyond the Platonic and Archimedean solids, but for a single-coil, it's kind of fun. I don't know what the technical name is, but I like it.

[rjaypeters]

"False" geodesic:



"Real" geodesic:



"False" and "Real" overlay:



The real geodesic pipes are laid on top of a sphere, the false only approximates one.

[happyjack27]

how about take that idea to the extreme and just have an iterated triangular mesh, like so:

http://www.flickr.com/photos/57764189@N05/5526912258/

sort of a "micro-grid".

(forgive the very sloppy drawing)

3 layers of wires (or tubbing), 1 layer per orientation. if not the magrid, this could maybe replace the faraday cage as a secondary magrid.

it's a 2-d structure though. wrapping it to a cylinder is easy enough, but i don't know how you'd wrap it to a sphere.

[rjaypeters]

Your idea for this style of geodesic sphere (I think):





I have appointments this p.m., so this is quick and dirty. Briefly, there are three coils in each of six linear projections onto six progressively smaller concentric spheres. I'll show pictures to explain later.

I haven't thought about current directions for each of the coils.

[happyjack27]

no. i mean a triangular grid tiling of the surfaces of say an octahedron, (edit: cuboctahedron,) tetrakis hexahedron, or a disdyakis dodecahedron. really any regular polyhedron with 4/6 edge vertices.

then blow that out like a balloon so its spherical.

what you show is more like a trihexagonal tiling.

(edit) speaking of which... i found this interesting.

[rjaypeters]

One coil "polar-arrayed" (twenty-four rings separated by fifteen degrees) around a sphere:



Situations:

Even thes few coils run into each other.

The poles have large openings. We can increase the inclination of the coils with respect to the equatorial plane; if we do, we might need more coils. Viz 75 degree inclination with 12 coils separated by 30 degrees:



Also, thinking about the current direction, we will need "lines of latitude" coils; again the poles will pose problems because the density near the poles.

Finally, the tiniest triangles near the poles (they are the ones I have examined because they are triangles without the lines of latitude included) don't have two of the currents running in the right directions.