Different polyhedra require different strength magnets

Discuss the technical details of an "open source" community-driven design of a polywell reactor.

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MSimon
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Post by MSimon »

blaisepascal wrote:
KitemanSA wrote: AHA!!! That is how you do it! Thank you blaisepascal.

Unh, how did you find the URL?

I first used the firebug extension in Firefox to examine the html which displayed the image on the wikipedia page, and copy/pasted the image URL.

Then I noticed that when I right-clicked on the image, Firefox had a "Copy Image Location" option, which did exactly what I wanted.
Netscape 9.0 has the same feature. (yeah - I know - I'm totally retro. And some day I'm going to have to give it up.)
Engineering is the art of making what you want from what you can get at a profit.

KitemanSA
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Post by KitemanSA »

MSimon wrote:If you see a left/right scroll bar added the link is too long. The picture too big. etc.
I find it odd that yours was causing a scroll bar to appear. My monitor at the office is oriented portrait vs the usual landscape, and so is rather narrower than most, and I was NOT getting a scroll bar. Tres-strange!

KitemanSA
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Post by KitemanSA »

TallDave wrote:
Kiteman wrote:WB6,7 have N:N across the cube.
Magnets across the cube from each other aren't relevant to the question of confinement.
Some people, MSimon (and me) among them, believe they are and some such people have stated that the rect-tet (octahedron) won't work because the magnets across the core are NOT N:N or S:S. I was merely disagreeing that the rect-tet was non-viable for that reason.
The reason I believe they are relevant is that the formation of the wiffle ball depends on it (I think).
TallDave wrote:
A stand alone N:S configureation (two and only two coils) would NOT have a null field between the magnets. The field would be almost as strong at the point midway between coils as it was in the middle of each coil.
This is what I'm not clear about. Intuitively I would expect a particle at the center line between them to feel cancelling effects, because the forces are equal and push in opposite directions (and I remember someone claiming that here a year or so ago). Nor do I see how you get an increase in force at the center (surely this must fall with distance). Is there an equation that describes this behavior?
Picture in your mind the analogy that the coil is a fan. The air flow (field lines) enters into the fan (coil) from the back (South) and flows out the front (North). If you place one fan in front of the other so they are facing the same direction, the air flows thru one, across the gap with little or no reduction in speed, and then thru the other. If the fans are facing towards each other, the air flows thru them both, in opposite directions, and collides in the middle where it stops. At the very center of the N:N fan configuration, there is no flow (field) at the very center between the fans (coils). Now???
TallDave wrote:I've dug around a little, but all I've found is descriptions of a magnetic bottle (which requires N:N or S:S).

It's not a terribly esoteric problem, so you'd think a definitive source would be relatively easy to find.
I have found that the more basic the issue, the harder it is to find in simple form on the internet. Maybe it is just me. :(
By the way, if you follow the wikipedia Polywell reference to Dr. B.'s first patent, the N:N configuration is shown graphically as "Prior Art". Maybe I should cut that out and paste it into the FAQ, if it ever comes back.

KitemanSA
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Post by KitemanSA »

TallDave wrote: We have all these places along the line edges of the cube where magnetic fields run into each other. Aren't they butting against each other and making cusps?
YES!!! At least if they are both red per Blaise's graphics (truncated cube vs rectified cube). But that is NOT the subject of this discussion. The subject has been the coils on OPPOSITE faces of the polyhedron. (Not sibe by side, but FACE TO FACE.)

Some folks have maintained that the opposite faces MUST be N:N (or S:S) for the polywell to work. I disagree. As long as the "even numbers of faces around a vertex" rule is maintained (with equal strength, symmetric rectified Platonic polyhedra, a previous given) the field in the center will be null, and the wiffleball will grow. It is a vector summation thing. IMHO.

KitemanSA
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Post by KitemanSA »

MSimon wrote:
blaisepascal wrote:
KitemanSA wrote: AHA!!! That is how you do it! Thank you blaisepascal.

Unh, how did you find the URL?
I first used the firebug extension in Firefox to examine the html which displayed the image on the wikipedia page, and copy/pasted the image URL.

Then I noticed that when I right-clicked on the image, Firefox had a "Copy Image Location" option, which did exactly what I wanted.
Netscape 9.0 has the same feature. (yeah - I know - I'm totally retro. And some day I'm going to have to give it up.)
I looked and looked and found out something. For those like me who are still stuck with IE, an older version, you can actually find the image location (laboriously) via the View>Source option. In the wiki page of interest, figure out about where in the page the image is, also look for some distinguishing text, the go to View>Source. "Find" the text in the right place and look for what seems to be the correct image. It is a major pain, but it is possible. Does anyone know if the newer IEs have the "Copy Image Location" option like Firefox? Might be a reason to update.

TallDave
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Post by TallDave »

Some people, MSimon (and me) among them, believe they are and some such people have stated that the rect-tet (octahedron) won't work because the magnets across the core are NOT N:N or S:S. I was merely disagreeing that the rect-tet was non-viable for that reason.
I just mean they don't form a cusp.
But that is NOT the subject of this discussion.
Well, that was certainly my point. LOL No wonder this has been confusing.

As you said earlier, this is hard without pictures. This would be much easier if I could hook a chip into my visual cortex and upload a nice 3-d image of what I meant.
Some folks have maintained that the opposite faces MUST be N:N (or S:S) for the polywell to work. I disagree. As long as the "even numbers of faces around a vertex" rule is maintained (with equal strength, symmetric rectified Platonic polyhedra, a previous given) the field in the center will be null, and the wiffleball will grow. It is a vector summation thing. IMHO.
I thought this was just another way of saying you need alternating solenoids (but that was when I thought you were talking about coils opposite each other within a face). But I wonder if there are actually geometric solutions that do both.

blaisepascal
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Post by blaisepascal »

TallDave wrote:Sure. Now turn one 180 degrees and place it next to the other. Is there a null at the center between them? Or do they make one big magnetic field that an electron bounces off of as though it were one big coil?
It gets... complicated and hard to visualize.

Magnetic field lines never end and they don't cross; they are (directed) loops. Around a straight conductor with a flowing current, they form circular rings. Bend that conductor into loop, and they bunch together in the center and spread out around the outside. Put more loops, or higher current (effectively the same thing), and you get more field lines through the loop, for a stronger field. (The density of the field lines is proportional to the field strength.) Any straight line which isn't straight through the bore will cross many field lines.

If you put two solenoids side by side, look at where the field lines can go. They have to remain loops. They can't cross. If two solenoids are side by side with N pointing in the same direction, the field lines coming out of the bores along the shared side can't curve far away from the solenoids to form a loop because of the other field lines going in the same direction, so they end up curving close and tight to the solenoids, forming a strong field going the other way between the solenoids. In this case, there is a plane, equidistant from both solenoids, in which no field lines cross and all close field lines are directed anti-parallel to the ones in the bore.

If two solenoids are side by side with N pointing in opposite directions, the field lines emerging from the bores along the shared side have an easy way to form a loop: just go back through the other solenoid! As such, you have a significant portion of the magnetic field lines passing through both solenoids in a closed loop, and virtually no magnetic field actually between the two solenoids. In this case, there is a plane, equidistant from both solenoids, in which all field lines which cross it are perpendicular to it.

As for electron confinement, the key is that electrons are deflected when they cross field lines, not when they travel parallel to them. In the situation above (two equal solenoids side by side with bores parallel to and equidistant from the x axis) an electron in the plane equidistant to the two solenoids would not cross any field lines when approaching two solenoids with N pointing in the same direction and would see no deflection. In the other case, an electron travelling in that plane would cross a metric buttload of field lines when approaching two solenoids with N pointing in opposite directions and would see a lot of deflection before it got close to the area between solenoids where there is little to no actual field.
We have all these places along the line edges of the cube where magnetic fields run into each other. Aren't they butting against each other and making cusps?
Yes, they are! As you have gathered, that's not good. If you have adjacent solenoids who's bores are both pointing in the same direction, you'll get planes between them with no deflection. Typically, we think of a surface containing the polywell, and these planes intersect the surface along lines, so we call them "line cusps", and they are a loss mechanism. They are an artifact of the shape and design of the coils. If the coils on the WB-6/7 were square instead of round (and mounted corner-to-corner, like the square faces of a cuboctahedron) then the line cusps would be greatly reduced or eliminated.

Another set of cusps are along the bores of the solenoids, where you have strong field lines going directly parallel to the radius from the center and thus no deflection. We call these "point cusps", and they are less of a concern than the line cusps because they are generally smaller (a point instead of a line).

There's also something called a "funny cusp", but I'm not 100% sure what that is.

blaisepascal
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Post by blaisepascal »

TallDave wrote:
Some people, MSimon (and me) among them, believe they are and some such people have stated that the rect-tet (octahedron) won't work because the magnets across the core are NOT N:N or S:S. I was merely disagreeing that the rect-tet was non-viable for that reason.
I just mean they don't form a cusp.
Well, the directly opposite faces don't form a cusp...

Using KitemanSA's fan analogy, imagine a plywood octahedron with fans mounted on each face, 4 configured to blow in, 4 configured to blow out, such that no two adjacent fans were configured to blow in the same direction. When all 8 fans are turned on, imagine the airflows. What's going to happen to a floating dust mite in the very center? It will be blown in 4 symmetrically spaced directions by the fans blowing in, such that overall there will be no net force blowing it one way or the other. It will be sucked in 4 symmetrically spaced directions blowing out, such that overall there will be no net force sucking it one way or the other. The end result is that there is no net force, and thus no air flow directly through the center -- even though directly opposing fans appear to be blowing straight through.
I thought this was just another way of saying you need alternating solenoids (but that was when I thought you were talking about coils opposite each other within a face). But I wonder if there are actually geometric solutions that do both.
What do you mean by "coils oppose each other within a face"?

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Post by KitemanSA »

blaisepascal wrote: If the coils on the WB-6/7 were square instead of round (and mounted corner-to-corner, like the square faces of a cuboctahedron) then the line cusps would be greatly reduced or eliminated.

Another set of cusps are along the bores of the solenoids, where you have strong field lines going directly parallel to the radius from the center and thus no deflection. We call these "point cusps", and they are less of a concern than the line cusps because they are generally smaller (a point instead of a line).

There's also something called a "funny cusp", but I'm not 100% sure what that is.
You basically answered your own question. If the coils are perfectly square and meet at the vertices ( and the virtual triangles do too) the point where they meet will have NO field and is the funny cusp. In other words, when that line cusp shrinks to a point, that is a funny cusp. It looks like a point cusp, but since the coils touch at that point, all the electrons leaving that cusp would be lost to the coil sheath.

There is yet another cusp I call the X-cusp which is similar to the funny cusp but has no metal there. If the square and triangular coils (all real this time) have rounded corners, the effect is very like a funny cusp, but the hole is devoid of metal. This is another reason I like an "all real" magnet configuration. This image by tombo shows the X cusp. If there were NOT a hole at each vertex, they would be funny cusps.

Image
Sure is a pretty system!

KitemanSA
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Post by KitemanSA »

Ok, now THAT is odd. The picture ain't very big, but I still get a scroll bar! What gives?

blaisepascal
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Post by blaisepascal »

KitemanSA wrote: You basically answered your own question. If the coils are perfectly square and meet at the vertices ( and the virtual triangles do too) the point where they meet will have NO field and is the funny cusp. In other words, when that line cusp shrinks to a point, that is a funny cusp. It looks like a point cusp, but since the coils touch at that point, all the electrons leaving that cusp would be lost to the coil sheath.
That's what I had thought, but I also though I recall Dr. Bussard initially talking about observed "funny cusps" in the WB-6, possibly in the place where the line cusps intersected, not at the midpoint of the line cusps. Certainly, with it's truncated-cube configuration, the WB-6 shouldn't have had funny cusps as you describe, as it has no proper vertices with alternating fields around it.

There is yet another cusp I call the X-cusp which is similar to the funny cusp but has no metal there. If the square and triangular coils (all real this time) have rounded corners, the effect is very like a funny cusp, but the hole is devoid of metal. This is another reason I like an "all real" magnet configuration. This image by tombo shows the X cusp. If there were NOT a hole at each vertex, they would be funny cusps.
I don't think the presence or absence of metal at the cuboctahedral vertices change the real nature of the cusp; certain loss mechanisms, yes, but not the nature of the cusp (which is on the surface of the wiffleball, after all). If a funny cusp is how you describe above, then I think your X-cusp is really a funny cusp.

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Post by TallDave »

There's also something called a "funny cusp", but I'm not 100% sure what that is.
Zero field over zero radius at the corners. It was what an early observer called Bussard's theoretical design, which had idealized zero-radius coils.
Finally, in terms of practical limitations it was noted that the basic physics concept
presumes magnet coils of near-zero physical cross-section, which touch at acute to right
angles at the corners of the polyhedral-vertex boundaries on which they are supposed to
lie. This has always given a “funny cusp” at such touching corners, which has been noted
as having essentially zero tangential radius, although it also has zero B field. However,
with realistic coils of finite dimensions (i.e. the coil cross-sections are a not insignificant
fraction of the machine or coil major radius) this “funny cusp” expands to involve a
rectangular region bounded by the dimensions/size of the coil containers. This
rectangular region will have competing fields at 90 degree intervals, thus will act as an
unshielded area for electron losses from the machine drive. The fractional size of this
unshielded area is always found (from magnet design studies using real conductors) to be
in the range of 0.01-0.1 of the total surface area of the coil containers. Since unshielded
fractional areas above 1E-5 to 1E-4 are untenable, this effect gives losses that are ca.
1000x too large for useful fusion output.
8. The only way to avoid this, with coils of realistic finite size, using realistic conductors
(e.g. superconductors) is to space the coils a distance from each other, as described in (3),
above, so that NO B fields intersect the coil container metal surfaces, but rather the field
lines flow in parallel between the spacing at these corners.

KitemanSA
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Post by KitemanSA »

blaisepascal wrote:
KitemanSA wrote: You basically answered your own question. If the coils are perfectly square and meet at the vertices ( and the virtual triangles do too) the point where they meet will have NO field and is the funny cusp. In other words, when that line cusp shrinks to a point, that is a funny cusp. It looks like a point cusp, but since the coils touch at that point, all the electrons leaving that cusp would be lost to the coil sheath.
That's what I had thought, but I also though I recall Dr. Bussard initially talking about observed "funny cusps" in the WB-6, possibly in the place where the line cusps intersected, not at the midpoint of the line cusps.
You are observant. Dr. B. called that same point by both terms, "funny cusp" and "line-like cusp". I suppose if you want to be technical (and I usually do), the round coils don't ACTUALLY produce a line cusp because they are not ACTUALLY parallel but produce a very NARROW virtual field face, but they don't actually produce a funny cusp either. So what are ya gonna do?.
blaisepascal wrote:
There is yet another cusp I call the X-cusp which is similar to the funny cusp but has no metal there. If the square and triangular coils (all real this time) have rounded corners, the effect is very like a funny cusp, but the hole is devoid of metal. This is another reason I like an "all real" magnet configuration. This image by tombo shows the X cusp. If there were NOT a hole at each vertex, they would be funny cusps.
I don't think the presence or absence of metal at the cuboctahedral vertices change the real nature of the cusp; certain loss mechanisms, yes, but not the nature of the cusp (which is on the surface of the wiffleball, after all). If a funny cusp is how you describe above, then I think your X-cusp is really a funny cusp.
I agree, it is not the presence or absence of metal that makes it an X cusp, it is the fact that the coilss don't ACTUALLY meet at the vertex. But you are also correct in that from the inside of the machine, the funny and the X cusps look effectively identical. I just distinguish the two because way too many people just don't get the funny cusp and when they do they automatically think it is no good because of the metal. but I guess the best distinction is that the funny cusp is a mathematical artifact while the X cusp is buildable.

tombo
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Post by tombo »

Kiteman,
One concern I have with the X-cusp is that it looks like a classic setup to display the Magnetic Reconnection phenomenon.
http://en.wikipedia.org/wiki/Reconnection
AIUI: Magnetic Reconnection losses breach containment and dissipate energy much faster than theory says it should.

Have you considered this already?
Am I barking up the wrong tree?
-Tom Boydston-
"If we knew what we were doing, it wouldn’t be called research, would it?" ~Albert Einstein

KitemanSA
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Post by KitemanSA »

tombo wrote:Kiteman,
One concern I have with the X-cusp is that it looks like a classic setup to display the Magnetic Reconnection phenomenon.
http://en.wikipedia.org/wiki/Reconnection
AIUI: Magnetic Reconnection losses breach containment and dissipate energy much faster than theory says it should.

Have you considered this already?
Am I barking up the wrong tree?
Have I considered: no.
Are you barking: I wish I knew enough to answer that! From the link (prelim scan) this seems to be a self-generated field kind of issue rather than a coil generated field issue. The containment breach seems to be the "plasma flowing along field lines that get all twisted up in the plasma and allow the plasma to leak out of the field flow" kind or thing. I guess. Maybe.

I will have to read it in again, probably several times, to begin to make sense of it! :oops:

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