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Mr. Fusion
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Ranting Like a Madman
September 30, 2002 — 4:45

Well, the nice folks at Duniway are correcting mistakes due to my naiveté. 
These guys must be saints – or seasoned old vacuum engineers – to put up with
me.  But it looks like I’ll have the 12"x18" glass bell jar (and cage, ‘natch)
the TOPS was originally slated with.  <sigh>  I really love the
current Aluminum beast.  It’s like an Olympic size swimming pool of out
gassing source, though.  I’m also upgrading the backing rotary vane pump
for the TOPS.  It came with a Trivac D4-B, which is really meant for the
lower flow 151 turbo pump.  Since I now have the 361 turbo pump, I really
need the equivalent of the Trivac D16-B. 

I fired up the TOPS again yesterday and realized the convection gauge at the
fore pump input wasn’t plugged in correctly – read 0 all the time, so I should
have figured it out earlier.  So I got that sensor firmly attached and
pumped the system down.  At 40 microns chamber pressure, the pressure at
the fore pump was about 7 millitorr.  I’ll have to work things out, but
I’ll bet the system will behave much better with a larger capacity pump. 
I’ll bet the smaller glass bell jar volume, as well as the superior out gassing
properties of glass, will make a huger difference than a new pump will. 
But I want to get to 10-7 torr, so I mine as well take care of the
whole shebang in one huge pain in the ASCII for Duniway (sorry guys).

Mental note.  Big vacuum volumes are reasonably hard to come by at the
bottom of a gravity well.  Be conservative in your designs and thankful for
what you can produce.

I also graciously accepted a change of plans regarding a magnetic cage based
on the dodecahedron.  The fatal flaw was that the resulting magnetic field
configuration has edge cusps along all of the edges.  <double sigh>. 
But every idiocy has a silver lining.  I am even more impressed with the
usefulness of point cusps in multi pole magnetic field geometries.  Aha
experiences are cool.


So now I’m going
to use a geometry based on the
cuboctahedron
which are used for
Bussard’s patent examples.  The shape is easy to construct.  This polyhedron does not have
5 fold symmetry
But that’s okay.  The reason I want to experiment with 5 fold symmetry is
because of Bussard’s

second patent
.  In

Inertial Collisional Containment
(ICC), Bussard takes advantage of
collisions and creates standing waves of ions which focus the ions into fusion
producing collisions even better than the electrostatic field does.  This
means less gain required in the system (i.e. the number of times electrons and
ions recirculate in the system before they become a power loss).


Anyways,
the upshot is that while the cuboctahedron forms very nice point cusps, I think
the 15 great circles of the icosahedron (5 fold symmetry) form a very
interesting magnetic trap.  The
disdyakis
triacontahedron
, which is the polyhedron formed by the intersections of
these great circles, seems to obey the conditions set forth by Bussard for
polyhedral point cusp magnetic traps – i.e. that every point cusp vertex is
surrounded by an even number of faces.

My belief is that you can just wind the 15 great circles with wire and the
resulting magnetic field will provide the most spherically symmetrical field you
can make.  It’s a really odd result that this shape is (unproved, as of
yet) the most symmetrical
way of dividing up the surface of a sphere1.  After this, you require
pyramids, which make a different class of polyhedra.  Not easy to wind
coils with and most likely of little use.

In the design of the fusion chamber (don’t worry, I’ll be posting my design
specifications soon), Bussard provided a model for generating ion acoustic waves
in a plasma sphere.  When you think about that, it’s an amazingly cool leap
of logic Bussard made.  It’s obvious when you read it, but it’s an
extraordinary leap of intuition.  I believe by taking advantage of the
cells that may be formed with five fold symmetric magnetic traps perhaps we can
decrease the gain required by the fusion chamber, decreasing power losses
significantly in the process.

If you imagine that each of the tetrahedron formed by the 120 triangles and
the center point of the polyhedron are formed from ion acoustic waves in the
same way that the hexagonal structures that Bussard describes, my theory is that
these tetrahedrons are far more effective at channeling ions into collision in
the center of the chamber than the hexagonal cones.  We’ll see when I get
data from that experiment (some day).

Anyways, the upshot is that five fold symmetries tend to torque down on the
space where the middle sphere used to be.  Note that the icosahedron is
simply the same 12 spheres around the center sphere of the cuboctahedron with
that center sphere removed.  It’s a polarized compression of equilibrium. 
Organizing the collision statistical behavior for the fuel ions on five fold
symmetry may yield surprising power amplification configurations.  Again,
we’ll see.

But I digress.


If you place ring magnets in all the faces of the cuboctahedron, alternating
N/S along the faces, you end up with only point cusps at all the vertexes of
the polyhedron.  If you look at figure 1c
from Bussard’s
patent
, you can see what a 2 dimensional cross section of the field looks
like.  Basically, it’s a cone.  A good picture to have is 12 ice cream
cones surrounding a sphere in the center.  The cones form a magnetic field
point cusp.  Electrons which have just the right momentum can escape the
magnetic trap the cuboctahedron forms.  The point cusp is similar to these
ice cream cones.  If the electron is aimed just right, it’ll bounce out the
hole at the end of the ice cream cone like a BB.  You can see a dramatic
form of this in the Aurora Borealis (northern lights).  High energy,
charged particles come streaming down the point cusps formed by the earth’s
magnetic field, slamming into the high atmosphere.  Now you can see why I
think the operation of fusors is
beautiful
, not just a cool physics project.

A point that Buckminster Fuller keeps bringing up is that there is no zero
size vertex.  In Fuller’s synergetic geometry, lines have width and
thickness as well as extent.  A vertex, which is commonly represented to us
as a dimensionless point, is simply the crossing of two lines.  As the
lines have volume, so do their intersections.  In fact, Fuller’s geometry
goes even further noting that nothing really intersects.  So points can be
modeled by overlapping and woven line intersections – kind of like an
intersection of pieces of yarn, rather than the way vertexes are generally
portrayed. 

Why is this remotely relevant to the price of tea in China?  Well, we
don’t have any perfect "lines" and "points" in reality – i.e. everything we can
construct LEAKS.  The best we can approximate of what we call geometry
is a leaky sieve compared to the ideal of mathematics as we currently model
things with.  We can only make the hole smaller, we can’t get rid of
them entirely.  So the engineering problem is how to strategically arrange
the minimal number of holes.  You want the statistics to work for
you, rather than against you.

So any ways, the model I have in my head at this point is that you can, to
some degree of approximation, treat the electrons you inject into a magnetic
trap as a gas.  The goal is to reduce the leakage – from a statistical
point of view – of the electrons from the magnetic trap.  The use of point
cusps significantly reduces the power leak of electrons out of the trap.  A
point is smaller than a whole edge.

While point cusps provide better reduction of power loss, I think we may
actually be able do better than this, by taking advantage of particle scattering
in the plasma.  Like Bussard’s use of ion-ion and ion-electron collisions,
we may be able to produced tighter weaves of the polyhedral nets, limiting the
the leaks of the system.  One thing that has been driven home to me in my
research into the wacky realm of plasma and fusion is the problem with
collisions.  Ideally, you don’t want the ions and electrons to be bouncing
off each other, scattering in unpredictable ways.  As Bussard points out, when particles collide they can shift energies.  One of
the frustrating things a particle can do is shift magnetic field lines and climb
out of containment and hit the walls.  These are very "hot" particles –
i.e. they have 10’s and 100’s of thousands of
electron
volts
of energy.  Joules by any other name still smack just as bad, and
there is no solid structure that we know of that can hold a fusion plasma.

Clearly, avoiding the walls of the containment chamber with these beasts is
something critical for a fusion machine.

As summarized in Bussard’s patent, there are various ways of keeping this
super "hot" state of matter confined long enough to fuse elements together. 
Farnsworth’s original Fusor (as it is known)
patent
uses electrostatic forces to keep the hot ions contained. 
Hirsch and Meeks improved on this design. 
Bussard, as I’ve mentioned seems to have
improved
on this design by eliminating the inner electrode grid by injecting high energy
electrons into a magnetic trap.

I think this is a
stroke of brilliance.  Basically, he’s still containing the fusion fuel
ions (i.e. Deuterium, Tritium, Helium 3, etc) with electrostatic forces –
electrons – which are in turn confined by magnetic fields.  Unlike, say, a
spheromak
or tokamak, in fusors the ions
aren’t contained purely by magnetic fields.  The ions in the plasma are
positively charged, so they are attracted to the electrons – and vice-versa of
course.  So by creating a highly negative charge, you can keep ions
confined in the center of a sphere long enough so that, statistically, they
smash together so hard that they fuse into a new element and perhaps produce
neutrons in the process.  In any event, the fusion products are extremely
high energy (temperature) particles and escape the fusor’s confinement center. 
The reason Bussard’s device gets away with this is that it’s much easier to
confine electrons with magnetic fields than it is confining the ions with
magnetic fields.


Figure
9
, from Bussard’s
patent, is
the canonical view of the device I’m trying to put together.  In this
figure, he shows two electron injectors and two ion injectors (955, 980 and 910,
970 respectively in figure 9).  My goal is to get just one electron
injector and later add an ion injector.  Right now, it’s going to cost me
an arm and two legs to buy just a moderate powered commercial electron gun
commercially (from, say Kimball Physics).  Ion
guns are even more expensive.


However,
from my thinking, I don’t really require a really precise beam.  I think
with reasonably simple setup, I should be able to get a moderately focused beam
I can inject into the magnetic trap.  However, there are always catches. 
One of the things that make it much easier to build these ion and electron guns
is that their only purpose is to axially inject charged particles into the
magnetic containment grid.

As you can see from figure 5a
of the patent,  all the action takes place along the axes of the magnetic
field formed by the face.  This is extremely convenient, as magnetic fields
can be used to focus and direct charged particles along the magnetic axis of the
faces of the fusion chamber.  Thus, one would have to work really hard to
get electrons that start out directed down the magnetic axis of a face to go
anywhere but down the center of this magnetic field. 
The magnetic fields I’m using are approximately 3800

gauss
.  While not 15
teslas,
like they are building for
some
fusion magnets
, these are still extremely powerful magnetic fields. 
The upshot is that the containment chamber faces provide perfectly adequate
focusing magnets for the charged particle beams.  All you have to do is
point the electrons in the general vicinity of the center of the face and they
"fall" straight down, radially into the center of the fusion chamber.

Very cool.



I recently bought the

CD collection
of the famous "Amateur Scientist" columns from Scientific
American.  Kids, if you’re reading this, have your parents buy this
wonderful item.  Just about everything in this fantastic series is still
valid today and contains incredible amounts of useful techniques, mechanisms and
a host of ideas.  Maybe it will seem dated to you children of the web, but
when I discovered the "Amateur Scientist" in seventh grade, it was like a breath
of heaven.  You budding physics nerds will find a lot of fun stuff to read
and dream about building – electron microscopes, particle accelerators, dye
based lasers, mass spectrometers, ruling engines….  The list is amazing. 
Anyways, I digress.


I
vividly remember reading and re-reading the column about a bunch of high school
students who had built an
electron microscope
.  The
electron gun
is simply a hot cathode (just a tungsten filament) which emits
the electrons which are then accelerated towards the positively charged anode
cylinder.  They use a solenoid magnet, axially, as the
objective
lens
of the electron microscope.  The magnets formed by the faces of
the fusion chamber form ready made lens.  As the magnet fields in my fusion
device are produced from permanent magnets, I won’t be able to do any focusing
with these.  It could well turn out that I need another means of focusing
the beams to compensate for the huge magnetic lens of the cuboctahedron face
field.  But I’m not anticipating it.

In the
world I want to live in, there will be little need to compensate for this and I
can build trivial ion and electron guns that won’t require
finite element analysis
to get correct.  I’m operating on the principal that the technology
required to achieve modest results should be pretty low, and allow "close
enough" approximation and be tolerant of some jury rigging by an amateur.

Well, that’s it for tonight.  Hopefully the nice people at Duniway will
get back to me with good news about my vacuum system Snafus.  In the
meantime, I’m going forward with doing AutoDesk Inventor construction of the
chamber as well as the ion and electron guns.  I’m going to use a 5
centimeter radius instead of my original 10 centimeter radius fusion
chamber.  Bussard puts the lower limit on the radius of the devices he
describes at 10 centimeters in order to get multiple gain factors.  But I’m
sure that I have a lot to learn about this stuff before I even get to the point
of worrying about such things.  Making it smaller will have some beneficial
effects – magnets are smaller for one thing – and I think I can weld up the grid
pretty easily.

I’m going to start transferring the base plate of the TOPS into Inventor so I
can start doing placement.  One thing that has become crystal clear to me
is the incredible value advanced CAD programs have.  It’s really hard to do
these things right.  Something that reading about all the other amateur’s
(spectacular) fusors makes clear is the reason why vacuum engineers get paid so
much money.  This kind of machining is non-trivial (ask Richard Hull) and
requires pretty reasonable skills.  Unless you have the budget of a silicon
valley startup (and even then…) these skills are hard won.  But that’s
part of the fun of doing this kind of hacking.  In essence, the systems are
pretty simple.  Building the instrumentation and control devices aren’t
hard – conceptually.  Doing this all at vacuums of 10-7 – 10-10,
with 10’s of kilovolts of energy, with explosive gasses, is pretty hard.

That’s what grad students are for, I guess.

Footnotes:

1. Croft, Hallard T., Falconer, Kenneth J., and Guy, Richard
K. Unsolved Problems in Geometry. New York: Springer-Verlag, 1991

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