magrid configuration brainstorming

Discuss how polywell fusion works; share theoretical questions and answers.

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ladajo
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Post by ladajo »

Intuitively, it would seem the fields would not merge where each half of the coils come together due to the bending away for the supports.

I keep trying to see it in my mind, but I think I need to put it on paper.

D Tibbets
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Post by D Tibbets »

I agree with ladajo, the faces would not be true point cusps. There would be a funny cusp extension into the gap. I'm still struggling to appreciate how much leakage there would be in these areas. The opposing fields are strongest so the cusp width would tight, which suggests there would not be much leakage, but Nebel's comments about nub heating suggests these funny cusp areas are a significant loss area.

As for how many limb extensions there are, keep in mind there will need to be considerable strength to hold the magrid in place. Without direct bridges/ nubs between the magnets, the support has to be from the vacuum vessel walls- long arm cantilevers(?). The more the merrier from a structural standpoint, and probably the less the merrier from a confinement standpoint.

Dan Tibbets
To error is human... and I'm very human.

Aero
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Post by Aero »

As I wrote earlier, intuition is not good enough to tell us what the magnetic fields look like around these "Nub" replacements. Would it be too difficult to calculate the magnetic field for this configuration? It should be very interesting, but that's intuition again - not good enough. It seems that the wiffleball should survive in this configuration but even that is a leap of faith.
Aero

rjaypeters
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Post by rjaypeters »

All supports quadruple:
Image Image
The +X and -X coils get split into four segments.
"Aqaba! By Land!" T. E. Lawrence

R. Peters

rjaypeters
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Post by rjaypeters »

I was working, doggedly, on the straight-segment rhombo...you know what I mean and noted how tiny the triangular coils were. A few geometric studies later et voila:

Image Image
No triangles at the price of small pentagons.

I particularly like (but probably not in a good way) the skinny triangular gaps between the squares and pentagons. A Friday Folly?
"Aqaba! By Land!" T. E. Lawrence

R. Peters

KitemanSA
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Post by KitemanSA »

???? MANY triangles!

rjaypeters
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Post by rjaypeters »

There were twenty triangles in the straight-sided rhombicosidodecahedron.

Count what you see here and multiply by two: Image
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hanelyp
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Post by hanelyp »

The star cusps where 3 square corners come together look leaky.

imaginatium
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Post by imaginatium »

ladajo wrote:Intuitively, it would seem the fields would not merge where each half of the coils come together due to the bending away for the supports.

I keep trying to see it in my mind, but I think I need to put it on paper.
You are right that they don't merge, but none of Bussards designs has merge either, every Pollywell has cusps that leak, hens Bussard called it a Wiffleball, not a Nerfball. The difference is where the cusps are, and how much do they leak.

Remember, cusps have to be viewed, as they appear from the center of the wiffleball. I crudly illustrate in the drawing below, that the only real line cusps, are only as wide as the nearest approaches, of the width of the cross section of the support pipes (the red area); not the width of 2 approaching faces. In the space in the center of the pipes, there would be an x cusp (the orange area). However, because this space is so small, there shouldn't be much leakage.
Image

Thats why I like the short segment, spherized octagon below. Since of the cusps are virtual, sharing the same pipe segments, all of the the larger line/x cusps, where the "real" coils approach, are eliminated.

Image[/img]

imaginatium
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Post by imaginatium »

rjaypeters wrote:Okay. I just like the single-coil, if it can be built...

Edit: I looked back and the spherized Tombo was never submitted for simulation. AFAIK it hasn't been simulated.

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.
Actually it is an octahedron, which is far better than a tetrahedron.

However, if you want a higher order polyhedron, how about a spherized triacontakaidihedron. Each of the faces of the octahedron divided into 4 faces. Here's another crude drawing, which should give you the general idea:
Image

rjaypeters
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Post by rjaypeters »

This: Imageis the octahedron. Eight coils with six "virtual" coils created in the gaps between the physical coils. The current seems to flow in the opposite sense of the current in the physical coils.

Don't be mislead by the orthogonal nature of the Tombo concept. Like the Tombo, the tetrahedron has four coils where the current flows in a particular orientation, counter-clockwise (in my imagination, yours may be reversed) around the outside of the core
Image and four "virtual" coils.

The Tombo (in this early single-coil) example, has the current flowing around the core in a single orientation.ImageThe Tombo arranges the coil to create four "virtual" coils.
"Aqaba! By Land!" T. E. Lawrence

R. Peters

rjaypeters
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Post by rjaypeters »

I don't think I've seen a triacontahedron before. Thanks for the heads-up. I'll think about it, but I'm not positive about it right now. I've already gone far beyond thirty-two faces, but we'll see.
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D Tibbets
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Post by D Tibbets »

imaginatium, I considered posting a similar drawing. There are actually two components to the corner cusps. The 'funny cusp' like linier portion, that then flares out to the point cusp like area. Since these corner point like portions are closer to the magnet cases, they would be smaller than the true point cusps of the faces( in most models). The question then becomes what is the sum of the two regions of these corner cusps. With a line like magnet these cusps would seem to have a significant advantage over point face cusps. But with magnets of real finite thickness the relationship becomes less pronounced.

Another factor which may also be very significant is the shape of the cusp throat as it narrows into the cusp. The Wiffleball effect pushes these throats out and flattens them to almost a flat surface (spherical towards the center). This is what effectively decreases the leakage. The cusp itself (where opposing magnet field lines are parallel to each other is not changed.
So what happens when the basic intersection of the opposing magnetic fields are curved away from the center. The cusp throats would seem to be steeper, but possibly longer (and thus not compressed outward to the swmaller diameter of the cusp throat, ie- the Wiffleball effect is not as pronounced). What I wonder about is how this different geometry (if real) will respond to the inflating Wiffleball effect.

If there is an effect, then it would be most significant with bowed (curved towards the center) magrids, or, as in the above examples, the magrids are actually curving away from the center at the corner regions. The first inward curvature may compromise the face centered point cusps, while the outward curvature may compromise the corner point/funny cusps.

There are a lot of compromising considerations. The increased thickness of the magnets will shrink the face centered point cusps, allow more windings and cooling, but it will also expose more magnet surface area to ExB transport losses (I think). Increased magnet numbers would also, improve the face centered point cusps, and increase sphericity. But this also translates into more magnet surface area exposed to ExB drift, and also more radiant energy (X=rays) exposure (and neutron exposure if using D-D fuel) . Having curved magrids may improve sphericity without as much magnet surface area exposed to radiant and possibly neutron fluxes. It also will decrease the total number of cusps, though losses may increase through some of them. Where the best balance may lie is open to interpretation without a good computer model or available truckloads of experimental data.

Bussard said that increased sphericity may improve performance by a factor of ~ 3-5X. I don't know if this was due to expected better confluence (central focus), lower cusp losses (because each face centered point cusp is smaller, and this more than compensates for the increased total cusp numbers), or a combination of both.

In the 2008 patent application, it is mentioned that losses through the cusps strongly dominates over losses due to ExB transport losses. If recirculation is good enough the difference in loss rates might be in the 10-100 range. If excellent recirculation can be achieved, then the loss ratio may approach one. Reading between the lines, this seems to suggest that at ~ WB6 characteristics, Bussard, etel expected that increasing the magnet surface area either through increased number of magnets or by making thicker magnets would not penalize much (through ExB transport (drift or diffusion are alternate terms)) compared to the gains. If recirculation can be optimized well enough, this may change. Considerations of cooling and direct conversion may also change the priorities some.

I might add that without any recirculation, the cusp losses would dominate over ExB, etc losses by a factor of ~ 1000 or more, even with Wiffleball formation. This illustrates the validity of those claims that the primary confinement of the Polywell is indeed dismal compared to closed confinement systems like LARGE Tokamaks. Recirculation redresses a portion of the difference, but still the confinement (energy confinement due to electron losses- the ions are decoupled from this aspect due to the excess electrons and resultant potential well) falls far short of what is needed at equal plasma densities. BUT, the Wiffleball effect also allows for confinement densities 100-1000 times greater than Tokamaks. As the fusion rate varies as the square of the density, this compensates very well for the much shorter confinement times (numbers I have used is ion dwell times to fusion of ~ 800 seconds in a Tokamak compared to ~ 1 millisecond in a Polywell). This also translates into much smaller sizes for the same power output. This is a considerable economic advantage for the Polywell. All of this, of course, depends on the Polywell working as advertised.

Sorry for the ramble, but everything is so intertwined , I often drift into the global aspects of the system.

Dan Tibbets

Dan Tibbets
To error is human... and I'm very human.

KitemanSA
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Post by KitemanSA »

rjaypeters wrote:This: ... is the octahedron. Eight coils with six "virtual" coils created in the gaps between the physical coils. The current seems to flow in the opposite sense of the current in the physical coils.
"This" is a cuboctahedron, (rectified cube / rectified octagon) just like WB6, except that what are virtual in the WB6 are real here, and vice versa.

It is possible to make an octagon Polywell, as you prove with your next image (eight faces, 4 real, 4 virtual).

D Tibbets
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Post by D Tibbets »

Related to my last post, this image illistrates the relative sizes of the face centered point cusps and the "corner cusps" in a WB 6 type arrangement. With the imaginary zero width line magnets, the face point cusps are relatively huge. But, as the real magnets thickness increases these cusps shrink and may even become near the size of the corner cusps. Of course this is a simple representation. The real situation depends on a number of factors, but this hopefully shows the gross relationship in 2 dimensions. The edge of the teal color represents where the B fields may be equal,
The 'funny type line cusps have a diameter dependent on the arbitrary separation distance of the magnets and cannot be smaller than the gyroradii (actually several gyroradii as the electrons are not purely monoenergetic, and to prevent several collisions of the electrons while transiting the cusp leading to electrons grounding on the magnet case due to ExB drift).

At one time I had the impression that the face point cusps leaked 3-4 times less than the corner cusps. If I did read this somewhere (I can't find a reference to this now) the illustration implies that I had it backward. The picture becomes more complex as you consider the ExB transport losses in these two types of cusps.

This illustration also leads to my opinion that the corner cusps are not strictly equivalent to point cusps, but are compound structures incorporating point and very narrow line cusp components.

Image

I should also point out that increasing the number of magnets would have a similar effect as increasing the thickness of the magnets, with a different set of trade-offs.



Dan Tibbets
To error is human... and I'm very human.

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