I posted the CAD repository, as it stands.

Certainly need some more work, so be kind in your criticism.

I’ve

also been thinking a bit about spherical standing waves. Something that

has confused me about Bussard’s

second patent has been the description of the

spherical standing waves.

He describes them as "quasi-hexagonal-conical cellular repetitive structures".

These are shown on the right in figure 5a (from the

patent illustrations). I think he may have the wrong model for

spherical standing waves.

I don’t even play a mathematician on TV, so this is one of those things that

I can’t say with complete confidence – be kind. I’m going to ask my friend Harlan

tomorrow if my understanding of this is correct (he is a PhD Mathematician who

just plays a memory management programmer on TV).

The

standing waves that are described in the patent are the result of coupling the

radial and transverse waves in the plasma. This is shown in

figures 4a and 4b (shown on the

left) in the patent illustrations.

Where I think Bussard had it wrong was in the description of the standing

waves as being quasi-hexagonal cells. My belief is

that you simply cannot subdivide a sphere with only hexagons – regular or

quasi-hexagonal. If I understand the process he’s describing correctly, the only possible

structures the standing waves can form are only the spherical polyhedra where

all the edges are the same, or all the edges are integer multiple of some

fundamental.

This pretty much limits the set of structures that can form from the waves

Bussard describes. In my never-ending information trawling on all things

spherical, I came across a very interesting

paper,

Nonlinear Standing

and Rotating Waves on the Sphere. I’m going to have to have Harlan

take a look at it before I can say whether this is really relevant… In

any event, the number of structures that can be formed by spherical standing

waves of the type Bussard describes would seem to be limited. And I don’t

think any of these structures can be formed completely by quasi-hexagonal cells.

If you have the gumption to read the

paper on nonlinear standing waves on the

sphere, take a gander at figure 7. Note that this is simply my fascinating

friend the

disdyakis triacontahedron.

So this is kind of interesting. The theory that I have is that the

types of standing waves formed can be strongly influenced by the circulation

patterns imposed by the magnetic fields containing the plasma. Note that

in inertial electrostatic confinement, the ions in the plasma are *not*

contained by magnetic fields. However in Bussard’s fusor based on magnetic

traps for electrons, there *is* a magnetic field which the ions will be

influenced by. As charged particles, they are going to move in specific

ways in reaction to the magnetic fields which are confining the electrons (which

are in turn confining the ions). I’m not sure about all the coupling of

the magnetic fields in a plasma, but I believe these magnetic fields should have

a strong statistical effect on the movement of ions in the core.

The upshot is that the spherical symmetry of the magnetic confinement field

in Bussard’s design should have major influence on the symmetry patterns formed

by the spherical standing waves. My theory is that the influence of the

electron magnetic containment fields should be so strong as to actually

determine the symmetry of the standing waves in the plasma core. In IEC

fusion devices which use spherical grids, my theory predicts the symmetry of the

standing waves is determined by the grid symmetry.

I have no idea if this is true, but it sure seems reasonable to me. I

have no idea as to how I’ll actually experimentally verify the symmetry of

standing waves. I actually have to start generating them first. If I

could penetrate the math of Christoph Gugg’s

interesting paper,

perhaps I would be closer to an answer. Certainly, talking to Harlan about

my understanding of the issues will at least provide a first approximation as to

whether I’m on a wild goose chase or not.

‘ta

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