Does a dodecahedron really meet Bussard's requirements?

[drmike]

We are all in total agreement because we are all talking about different things. I may very well have a sign wrong some place, that's why I asked
for things to be checked.

But single particle tracking doesn't help understand the full picture, it just gives clues. Plasma models give other clues. If all the clues appear in an experiment, then you have a good idea you know what you are doing. If what you expect to happen doesn't happen, then your models are wrong.

The math says there are exponential and oscillatory (imaginary exponential) solutions to the equations of motion. It may well be the conditions for exponentials never occur, but I don't a priory know that. Since the code shows a linear increase over time, it says that the exponential conditions are rare and the oscillatory are more common.

I won't say it's right, but until I see proof it's totally wrong I'm going to stick to my guns - the static condition appears to be unstable.

I'm not afraid to admit making a mistake - I just need it shoved in my face

[MSimon]

What do you mean by "static condition"?

[drmike]

DC B field and DC E field, with no electron guns, no current flow and no plasma.

I thought of another analogy. Again, I may well be wrong, but let's have fun hashing it out.

Take a satellite and pass it near a planet, then toss it near another planet, then toss it back at the first one. Every time it goes near a planet it gains energy - it is called gravity boost. NASA does it all the time to get to the outer planets with less fuel. Here's an example

On every pass near the MaGrid the electron gets a "gravity boost" because it is on a different path each time.

Counter argument!

[TallDave]

One of the major loss mechanisms Bussard claimed was electrons exiting via line cusps. He further said that it was not possible to eliminate these in a cube geometry machine because each vertex has three faces around it, and you don't want two faces to have the same pole. Fair enough, but a dodecahedron has 12 faces, each a pentagon, and each vertex also has three faces on it! Taking out my collection of platonic solids (yes, I used to play D&D), I notice that the only such that meets his stated requirement is the octahedron, which does indeed have four faces off every vertex. What am I missing here?

Here's Ligon's picture of the WB-8 truncated dodec (p24ish):

http://www.deanesmay.com/files/Inertial ... mpr[1].ppt

It's actually a collection of 10-sided planar shapes (decagons?). Each vertex appears to have 3 faces on it.

Does it matter, though? I thought those losses recirculated along the field lines.

[TallDave]

On every pass near the MaGrid the electron gets a "gravity boost" because it is on a different path each time.

Counter argument!

Hrmm, not sure that holds up. It has to be a velocity change relative to something else.

A slingshot maneuver around a planet changes a spacecraft's velocity relative to the Sun, even though it preserves the spacecraft's speed relative to the planet (as it must do, according to the law of conservation of energy).

http://en.wikipedia.org/wiki/Gravity_assist

[TallDave]

Here's Ligon's picture of the WB-8 truncated dodec (p24ish):

http://www.deanesmay.com/files/Inertial ... mpr[1].ppt

Interesting, this looks very different from a regular dodec.

http://en.wikipedia.org/wiki/Dodecahedron

Aha! Here we go:

http://en.wikipedia.org/wiki/Truncated_dodecahedron

60 vertices! Wow. Where's that supercomputer?

[scareduck]

Does it matter, though? I thought those losses recirculated along the field lines.

If it didn't matter, why did Bussard explicitly mention it in his Google video presentation?

[TallDave]

Does it matter, though? I thought those losses recirculated along the field lines.

If it didn't matter, why did Bussard explicitly mention it in his Google video presentation?

Possibly just to make the point that you can't make a closed (nonrecirculating) model of that shape. I seem to recall there were several major efforts along those lines.

[scareduck]

Here's the excerpt from the transcript of Bussard's Google Tech Talk:

The fundamental problem in constructing this device is making a good quasi-spherical magnetic field. We can’t tolerate the mirror losses at the equator that Livermore spent time and money on [emphasis mine]. We needed a magnetic field having only point cusps. If you put a north pole and north pole together, you get an enormous loss at the equator.

There is only one configuration that works, and that is the one that we patented. It is a configuration that is a polyhedron where the coils are all on the edges of the polyhedron, and the polyhedron has the property that there are an even number of faces around every vertex so that alternate faces are north, south, north, south, north, south.

If you look at the cube which constitutes the normal biconic cusp, it only has three faces around every vertex, so you have the line cusp problem. The only thing we could find to solve it is to make a system that is quasispherical with no magnetic monopole, so you have to do it from the surface, so you only have have point cusp losses.

This is what I keep coming back to: a dodecahedron has an odd number of faces off each vertex. It seems wholly inexplicable, then, that he would choose it if it didn't meet this requirement, or that he would bring this up if it were irrelevant.

[drmike]

Hrmm, not sure that holds up. It has to be a velocity change relative to something else.

What you guys are saying is that generating a plasma in a polywell using a microwave so that the electron energy is about ice cold guarantees no electrons will ever escape. Should be an easy enough experiment - I bet the confinement time is a lot shorter than "forever".

Back to electron fluid though - it will be totally different code and if I made a mistake in the single particle orbit hopefully I won't make the same one twice!

[MSimon]

What happens if you bias the outer "wall" slightly negative relative to the MAgrid?

[TallDave]

You know what, I think maybe we've (I've?) misunderstood what he meant by "vertex."

Look at the truncated cube, it has the same issue.

http://en.wikipedia.org/wiki/Truncated_cube

Maybe he just meant there was an even number of faces around every place that the surface polygons' edges diverged. That does seem to be the case for both the trunc cube and the trunc dodec.

-------------
This is interesting, too:

Under the auspices of the AEC's Project Sherwood, several other laboratories were also looking for practical methods of confining a fusion reaction to produce useful energy. Livermore chose to pursue the so-called magnetic mirror approach: magnetic fields would confine ionized gas or plasma within an open-ended cylindrical cavity

https://www.llnl.gov/str/Hacker.html

Magnetic fusion research at Livermore began to produce results by the mid-1970s. An experimental magnetic mirror machine (2XII-B) created a stably confined plasma at temperatures, densities, and times approximating those a power plant might need. Although not the most favored approach in the fusion research community, the magnetic mirror then stood second only to the tokamak concept of power generation through fusion. The AEC approved a large-scale scientific feasibility test of the magnetic mirror approach, the so-called Mirror Fusion Test Facility, but changing priorities scuttled the $350-million experiment, canceled in 1987 before ever operating and sold for scrap a decade later

Hey, all we want for Polywell is a measly $200M! That's like $150M in 1987 dollars.

[TallDave]

Maybe he just meant there was an even number of faces around every place that the surface polygons' edges diverged. That does seem to be the case for both the trunc cube and the trunc dodec.

You can see this wouldn't be true for other shapes:

http://en.wikipedia.org/wiki/Archimedean_solid

[TallDave]

And Bussard did call WB-6 a truncated cube, even though it's really a collection of circles arranged as the faces of a cube:

WB-6, 2005, R = 15 cm, B = 1.3 kG, E = 12.5 kV, clean recirc truncube with minimal
spaced corner interconnects, multi-turn, conformal can coils, uncooled, cap pulsed drive, Ie
to 2000 A, incorporated final detailed engineering design constraints

http://www.emc2fusion.org/QuikHstryOfPolyPgm0407.pdf

[drmike]

What happens if you bias the outer "wall" slightly negative relative to the MAgrid?

Theoretically it doesn't matter, since the outer wall is a sphere every point inside is at the same potential relative to the wall.

But you raise a good point - where is the bottom of the valley? The MaGrid E field peaks on the grid itself, and so does the B field. So the electron can't get to the bottom of the valley, but it can get closer on every pass. (Why? because the B field is perpendicular to the E field and as the electron falls towards the grid, the B field forces it to move perpendicular to that direction.)

So I've been arguing from the wrong place - the code does follow the math, but not the chunk of math I think it does.

In a real world, the grid has finite size and the electron will hit it. The regions of zero E field occur in the center of the MaGrid, but also it will be almost zero in the corners where 3 coils are near each other. The field will be pointing slightly outward as you go from center to cusp, then it will switch to slightly inward as you near a cusp, to highly inward as you go well past the cusp. This path never hits the peak E field, and it isn't until you get really close to a grid coil that you hit peak E field.

So there is a peak kinetic energy you can't get past - you just can't get there unless you hit the grid. The peak potential is the bottom of the hill for the electron, and B field prevents it from getting there. Unless it starts really close to the grid, but that's kind of what we want to prevent!

Looking at the electron path though, I wonder where the "recirculation" comes from? It's more like bouncing.