Two More Coils?
Two More Coils?
Would it be worth the cost to buy two more coils and related hardware and set up an octahedral polywell, call it WB7.5?
If data are consistent with theory, then four more coils could take the WB7 to WB8.
How much would it cost for the coils and hardware? Heck, it may be worth it just to get the data without so many restrictions.
If data are consistent with theory, then four more coils could take the WB7 to WB8.
How much would it cost for the coils and hardware? Heck, it may be worth it just to get the data without so many restrictions.
I think you can put any number of coils around a center and have the field go to zero in the exact center (or if you get fancy, a couple of places). You don't have spherical symmetry though unless you have 4, 6 or 12 coils.
How important that is remains unknown. My initial feeling was that symmetry is really important, but really, it is only important in the sense that it simplifies the math and enables understanding a lot faster.
If ball lightning is any guide, you don't need any coils. But nobody understands that either!
How important that is remains unknown. My initial feeling was that symmetry is really important, but really, it is only important in the sense that it simplifies the math and enables understanding a lot faster.
If ball lightning is any guide, you don't need any coils. But nobody understands that either!
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The main things which Dr. B. stated was necessary for the core polyhedron for a polywell are:drmike wrote:I think you can put any number of coils around a center and have the field go to zero in the exact center (or if you get fancy, a couple of places). You don't have spherical symmetry though unless you have 4, 6 or 12 coils.
1. A high degree of spherical symmetry, and
2. Polyhedron vertices which have an even number of edges.
The first gets you the symmetry, the second assures that the faces of the polyhedron can be 2-colored -- each face is either N or S, and adjacent faces are different.
The edges surrounding an N-labeled face correspond to a coil in the polywell, and the edges surrounding an S-labeled face correspond to segments of several coils in the polywell.
An easy way to get appropriate polyhedra is to take normally very symmetric polyhedra which might not have the second property and "rectify" it -- truncate each vertex to the midpoint of each edge, yielding a resultant polyhedron which has as many faces as the original had faces and vertices, as many vertices as the original had edges, and as many edges needed to make the Euler characteristic V-E+F = 2. Any convex polyhedron can be rectified, and any rectified polyhedron has vertices of order 4, with new and original faces alternating around each vertex. Rectified convex polyhedrons are exactly what you need for a polywell.
Rectified convex polyhedrons are also exactly what you get if you make a polywell by putting a coil on each face of a polyhedron. The center of each original face corresponds to what we've been calling a "center cusp", the center of each new face corresponds to what we've been calling a "corner cusp", and the vertex of the rectified polyhedron corresponds to what we've been calling an "edge cusp" or a "line cusp".
The platonic solids are a good example of very symmetric polyhedra, and work well for this.
A tetrahedron (V=4,F=4,E=6) rectifies into an octahedron (V=6,F=8,E=12). So with 4 coils you get a polywell with octahedral symmetry.
A cube (V=8, F=6, E=12) rectifies into a "cuboctahedron", which has V=12, F=14, E=24. Six of the faces are square, eight are triangular. Six coils in a cube gives you a WB-7, which has cuboctahedral symmetry.
A cube and an octahedron are dual of each other -- you get from the other by replacing vertices with faces or vice versa. Dual polyhedra rectify to the same polyhedra, so a rectified octahedron is also a cuboctahedron. So with eight coils you also get a polywell with cuboctahedral symmetry, not so different than from a six-coil polywell.
A dodecahedron has V=20, F=12, and E=30. Rectifying it gives a structure called an Icosidodecahedron, which has V=30, F=32, and E=60.
It is a different structure than a cuboctahedron, and is a reasonable alternative to investigate. It has 12 pentagonal faces and 20 triangular faces, and only takes 12 coils to investigate.
An icosahedron has V=12, F=20, and E=30, and is the dual to the dodecahedron. Rectification also yields an icosidodecahedron. You can make one with 20 coils.
While there are some differences between the two cubocahedral arrangements due to the fact that the coils are not square/triangular but are round (and similar for the differences between the to icosidodecahedral arrangements), it is unlikely that, big picture wise, the difference is sufficient to make one significantly better or worse than the other. Comparing 6 v 8 coils, or 12 v 20 coils is probably best done after we know the answer to "will it work?"
A "buckyball" is a highly symmetric shape, corresponding to a truncated icosahedron. It doesn't have property 2 above, but a rectified truncated icosahedron would. But then we quickly run into issues of diminishing returns: A rectified truncated icosahedral polywell would require 32 coils, likely of two different sizes. Compared to a 6-coil "cube" or a 12-coil "dodecahedron", I doubt the improvement would justify the complexity.
Wouldn't using the toruses on the faces of a rectified octahedron provide slightly more radius and slightly more sphericity providing a substantial amount of increased capacity with little increase in funding?blaisepascal wrote:The main things which Dr. B. stated was necessary for the core polyhedron for a polywell are:
1. A high degree of spherical symmetry, and
2. Polyhedron vertices which have an even number of edges.
...
A tetrahedron (V=4,F=4,E=6) rectifies into an octahedron (V=6,F=8,E=12). So with 4 coils you get a polywell with octahedral symmetry.
A cube (V=8, F=6, E=12) rectifies into a "cuboctahedron", which has V=12, F=14, E=24. Six of the faces are square, eight are triangular. Six coils in a cube gives you a WB-7, which has cuboctahedral symmetry.
A cube and an octahedron are dual of each other -- you get from the other by replacing vertices with faces or vice versa. Dual polyhedra rectify to the same polyhedra, so a rectified octahedron is also a cuboctahedron. So with eight coils you also get a polywell with cuboctahedral symmetry, not so different than from a six-coil polywell.
Just a thought.
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It would also provide larger "corner cusps", making it easer for contained electrons to escape.KitemanSA wrote:Wouldn't using the toruses on the faces of a rectified octahedron provide slightly more radius and slightly more sphericity providing a substantial amount of increased capacity with little increase in funding?blaisepascal wrote:The main things which Dr. B. stated was necessary for the core polyhedron for a polywell are:
1. A high degree of spherical symmetry, and
2. Polyhedron vertices which have an even number of edges.
...
A tetrahedron (V=4,F=4,E=6) rectifies into an octahedron (V=6,F=8,E=12). So with 4 coils you get a polywell with octahedral symmetry.
A cube (V=8, F=6, E=12) rectifies into a "cuboctahedron", which has V=12, F=14, E=24. Six of the faces are square, eight are triangular. Six coils in a cube gives you a WB-7, which has cuboctahedral symmetry.
A cube and an octahedron are dual of each other -- you get from the other by replacing vertices with faces or vice versa. Dual polyhedra rectify to the same polyhedra, so a rectified octahedron is also a cuboctahedron. So with eight coils you also get a polywell with cuboctahedral symmetry, not so different than from a six-coil polywell.
Just a thought.
Since the underlying geometry of the setup is the same (rectified cube = rectified octahedron), it probably won't change the sphericity.
Escape? I thought they just tried to escape but were retained and reinserted by the + charge on the magrid; and that this applied to ALL the cusps, corner, center, line, etc.blaisepascal wrote:It would also provide larger "corner cusps", making it easer for contained electrons to escape.KitemanSA wrote:Wouldn't using the toruses on the faces of a rectified octahedron provide slightly more radius and slightly more sphericity providing a substantial amount of increased capacity with little increase in funding?
Just a thought.
Since the underlying geometry of the setup is the same (rectified cube = rectified octahedron), it probably won't change the sphericity.
I can't help thinking that more coils = better sphericity.
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Not all that get out the cusps make it back in. Some have enough energy to hit the walls, the coils, etc. These have to be replaced.KitemanSA wrote:Escape? I thought they just tried to escape but were retained and reinserted by the + charge on the magrid; and that this applied to ALL the cusps, corner, center, line, etc.blaisepascal wrote:It would also provide larger "corner cusps", making it easer for contained electrons to escape.KitemanSA wrote:Wouldn't using the toruses on the faces of a rectified octahedron provide slightly more radius and slightly more sphericity providing a substantial amount of increased capacity with little increase in funding?
Just a thought.
Since the underlying geometry of the setup is the same (rectified cube = rectified octahedron), it probably won't change the sphericity.
I can't help thinking that more coils = better sphericity.
The cusp "losses" have been a point of confusion.
The electrons that go out the cusps do mostly recirculate back in, but you need confinement sufficient to establish a 1000:1 or better ratio of electron density inside the device versus outside (the Gmj factor, more or less) to achieve conditions useful for fusion.
The truncated dodec makes this ratio 3-5 times better, in theory:
The electrons that go out the cusps do mostly recirculate back in, but you need confinement sufficient to establish a 1000:1 or better ratio of electron density inside the device versus outside (the Gmj factor, more or less) to achieve conditions useful for fusion.
The truncated dodec makes this ratio 3-5 times better, in theory:
The only small scale machine work remaining, which can yet give further improvements in performance, is test of one or two WB-6-scale devices but with “square“ or polygonal coils aligned approximately (but slightly offset on the main faces) along the edges of the vertices of the polyhedron. If this is built around a truncated dodecahedron, near-optimum performance is expected; about 3-5 times better than WB-6, This is somewhat like a combination of MPG-1,2/WB-6, and it must also be run in the puff-gas/cap-discharge mode (as for WB-4,6) to reach useful conditions. This will also incorporate another feature found useful, that is to go to a higher order polyhedron, in order to retain good Child- Langmuir extraction by the machine itself (which is more straightforward than relying on stand-alone e-guns for the cusp-axis, very-high-B-field environment), while not giving excessive electrostatic droop in the well edges. These small scale tests are discussed further, below.
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1) Design, building and parametric testing of WB- 7 and WB-8, the final two true polyhedral coil systems, with spaced angular corners, to reduce “funny cusp“ losses at the not-quite-touching points, and yet provide very high B fields with conformal coil surfaces. These would be topologically similar to the original WB-2 and PZLx-1, but without their excessive unshielded surface losses, and with pure conformal coils and small intercept fractions. These latter can be achieved by appropriate spacing between the corner junctions (typically several gyro radii at the central field strength between adjacent coils) to allow free circulation of electrons and B fields through the “funny cusp“ regions, without direct B field line impact on or intersection with the coils themselves.
These should be tested best in an external vacuum system, with capacitor-driven power supply for the electron injection drive, and be driven to fusion conditions for a period of several tens of milliseconds. If these achieve true minimal losses (as derived from WB-6 results), electron trapping factors of Gmj > 5,000 will be achieved and thus yield significant fusion output, because of the very low loss design configuration of these machines. To achieve this will require both high e- drive currents (see above re secondary ion-driven sources), and controllable, pulsed, neutral gas input to the machine interior.
If there is ever a real push to start working toward a dodec, then intermediate steps, (cube, octahedron) should be attempted along the way. Take delivery of the first 6 coils, check out the cube. Take delivery of two more, check out the octahedron. Accept the last four, run the dodec. Two points define a line, three define a curve.
Might be worth it.
Might be worth it.
You just have to keep scaling up the vacuum chamber, or start with a large enough chamber to fit all the coils for the dodec. If you can afford the vacuum pumps up front, it'd make sense to do all those experiments. But the larger the volume, the higher the cost of your pumps and other equipment.
From the scientific perspective, it'd be great! More experiments are always better.
From the scientific perspective, it'd be great! More experiments are always better.