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Mr. Fusion
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Spherical Standing Waves
October 6, 2002 — 21:09

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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