Anyone have a better explaination for Magnetic Mirrors?

[krenshala]

hanelyp,

Yes - over the weekend I talked with a physicist and he corrected me on a few points. I plan to get the correct motions explained out.

As I understand it, (1) the mirror is due to denser fields, NOT curved fields and (2) curved fields do create a “drift force” which pushes the particle away from the center.

I had these muddled together.

I sort of wish you had left your original post (three up from this) as it was in case your original input plus the correct helped others understand where they were misunderstanding how it works. There are times where reading someone else's understanding and subsequent change of information makes things clearer for me. Of course, I can also see where only listing the 'correct' information can be less confusing as well.

[mattman]

I sort of wish you had left your original post (three up from this) as it was in case your original input plus the correct helped others understand where they were misunderstanding how it works. There are times where reading someone else's understanding and subsequent change of information makes things clearer for me. Of course, I can also see where only listing the 'correct' information can be less confusing as well.

hanelyp,

Yes - over the weekend I talked with a physicist and he corrected me on a few points. I plan to get the correct motions explained out.

As I understand it, (1) the mirror is due to denser fields, NOT curved fields and (2) curved fields do create a “drift force” which pushes the particle away from the center.

I had these muddled together.

I sort of wish you had left your original post (three up from this) as it was in case your original input plus the correct helped others understand where they were misunderstanding how it works. There are times where reading someone else's understanding and subsequent change of information makes things clearer for me. Of course, I can also see where only listing the 'correct' information can be less confusing as well.

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Ok, Here is what was up:

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The fields are curved. The curvature causes there to be particle to experience reverse acceleration.



This acceleration reduces the forward motion causing the rotations to get tighter together. When rotations are 90 to the field line the particle reverses motion.



The geometry to look at is the biconic cusp. This is caused when two a-like poles are place together.



The biconic cusp was first simulated in 1961 (“The Motion of a Charged Particle near a Zero Field Point”). They found 3 types of particles: stable, erratic and a transition. They called these particles adiabatic, non-adiabatic and a transition.



This work formed the basis of the 2011 Sydney paper. Dr. Khachan extended this work to fit the cusps inside a polywell. Unfortunately the cusps in Polywells are NOT biconic.

[TheRadicalModerate]

I asked this question a while back and didn't get a very satisfactory answer: Doesn't a genuine, rectified, truncated cube, with opposite-polarity coils on the triangular faces, get rid of the funny cusps?

Right now, you get funny (biconic, triconic--pick a name) cusps because the 3 coils that meet at each vertex of the cube all have the same polarity, so the dipole field of each coil gets squished on the outside by the other coils, but there's always a null pointing directly out of the vertex. OK so far?

Now, by analogy, let's look at a two-dimensional version of the problem, namely a quadrupole magnet. Fresh from wikimedia, here's what the B-field looks like:



Note that in this case, there are no funny cusps. Because each coil has the opposite polarity of its neighbor, the fields of each dipole cancel between them but add together at the "tops" and "bottoms" of each pair of dipoles. So, in 2 dimensions, there are only dipole point cusps through the center of each coil.

Now, you can't do this in 3 dimensions with a cube, because each dipole can't have the opposite polarity of all its neighbors, but you **can** do it with a truncated cube. Furthermore, if you rectify the cube:



...then there are no line cusps at all.

I think somebody argued last time that the open corners of the WB5+ machines acted like virtual anti-poles, but I don't buy that. Those virtual anti-poles don't seal off the corners, while real anti-poles on the triangular facets do. Seems to me that such a machine has **nothing** but point cusps in the center of each coil.

What am I missing? This is obviously a more expensive machine to make (it's got 14 coils instead of 6) but shouldn't this dramatically reduce electron losses?

[hanelyp]

In the idealized rectified cube polywell, with zero thickness conductors, you get funny cusps at the vertexes of zero size. With real thickness conductors the funny cusp expands, like the X-cusp proposal that's come up here, except with material over the cusp.

If you offset the triangle face coils radially rather than superimpose them on the square face coils, you still get a cusp at the vertexes, but I'm thinking closer to a point cusp.

[KitemanSA]

I asked this question a while back and didn't get a very satisfactory answer: Doesn't a genuine, rectified, truncated cube, with opposite-polarity coils on the triangular faces, get rid of the funny cusps?

Right now, you get funny (biconic, triconic--pick a name) cusps because the 3 coils that meet at each vertex of the cube all have the same polarity, so the dipole field of each coil gets squished on the outside by the other coils, but there's always a null pointing directly out of the vertex. OK so far?

No. You have a misunderstanding of the funny cusp. A funny cusp occurs where there are 4 or more even number of alternating fields meeting at one point. Given your cube-octahedron graphic, the funny cusps are where the little golden balls are. At the centers of all the red and yellow faces are point cusps.

[TheRadicalModerate]

No. You have a misunderstanding of the funny cusp. A funny cusp occurs where there are 4 or more even number of alternating fields meeting at one point. Given your cube-octahedron graphic, the funny cusps are where the little golden balls are. At the centers of all the red and yellow faces are point cusps.

OK, I can almost see that. Thanks.