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Mr. Fusion
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Field Simulation
April 12, 2003 — 17:36

got some time and dug into simulating the beast with SimIon. 
Click here to download the SimIon geometry
  Why was this hard?  Just figuring out the three
dimensional rotation matrices, that’s all.  Tedious, as the SimIon
reference frame is a right handed, and the reference frame I had from my cad
system is left handed.  Projection and a few sign changes later and I had
the icosidodecahedron cage modeled as an electrostatic potential array (shown on
the left).  Click on the image for the
full size image
.  It’s the standard 3D isometric viewpoint of the
icosi-grid as modeled in SimIon.


have only modeled the electrostatics.  I have yet to add the magnets to the
simulation.  I must say that you can see the symmetry bias quite clearly. 
First, SimIon represents 3 dimensional space via small cubes.  So the
icosi-grid structure has some significant aliasing.  Nothing really
horrible, but certainly noticeable.  It becomes even  more noticeable
when you plot the potential contours for the beast (shown
on the right
).  I know it’s a really complicated contour plot, but it
is using the same isometric view of the cage
shown above

The immediate thing that stands out from the field is the one great circle
that happens to lie on the Y-Z plane.  This is the only great circle
that lies on the icosi-grid which aligns with the 3 ordinal planes of the cubic
system of SimIon I might add.  Why am I even mentioning this?  Well,
technically, all 6 great circles that make up the icosidodecahedron are the same
great circle – just in 6 different orientations.  This should result in a
five fold symmetric figure – i.e. all 6 great circle’s should have identical
fields.  But such is not the case because all I have to divide up the space
with is cubes.  Cubes results in an aliasing of the space partition, and
thus the imposition of symmetries not in the original model.

<sigh>  That’s okay.  The simulation is far better than required to
do some serious engineering with, however!

BTW, the simulation took up 270 megabytes of grid memory alone!  It took
SimIon to calculate the potentials for the seven electrodes (six great circles
on the icosi-grid plus the spherical chamber ground) about an hour or so on my
1.7 GHz P4 laptop.  Non trivial calculation times.

Right now, the simulation is a solid ground potential spherical shell
surrounding the the icosi-cage electrode in the center of that sphere – held at
-30,000 volts potential.  To make this more accurate, I’ll need to poke the
holes in the sphere that approximate the actual geometry of the vacuum chamber. 
It will significantly change the field – that much is clear.  So it’s
necessary.  I can also try to rotate the entire icosi-cage before
calculating the fields, removing the aberration of the Y-Z great circle.

ran some electron trajectories using this set up, and they were very promising. 
As I said, more than good enough to do some real engineering.  On the right
is a view of one of the runs
Click on the picture for the full size picture.

The grid and vacuum chamber are not shown in the picture, but roughly the
same orientation is used as the previous graphics on this page.  The
electrons were shot into the open pentagram of the icosi-cage, sharing the
X-Axis of the model view.

What I was hoping to happen has indeed shown to work – at least in
simulation.  The electrons are shot into the icosi-cage with a potential of
15,429 volts.  As you can see, they actually penetrate to the center of the
cage and spin out – tracing the field
contours shown above
.  There was some question as to whether one could
really inject electrons into the negative potential inner grid.  Since the
grid is mostly empty space, there field isn’t uniform.  So only 15.5 kV is
needed to inject the electrons using an electron beam.

I found that if you inject the electrons on the same radius as the icosi-cage
– i.e. an electron emitter sitting right in the open pentagon at the same radius
of the cage, you can inject electrons with only 1.5 kV of potential. 
Pretty nifty – if true.  Far easier to build an electron gun that only
requires 10 keV or less.  And what I think I can show with more simulations
is that I can simply use the electron gun equivalent of a flood lamp – i.e. an
unfocused electron source.

This vastly simplifies the complexity of this hair brained idea I have.

What’s also interesting from the electron trajectories I have modeled so far
is the very nice spiraling and symmetric splitting around another axis. 
Obvious from looking at the field contours, and obvious in hindsight, but
pleasing to see none-the-less.  I think once I add the magnetic circuit of
the icosi-cage, I’ll have a very nice electron trap.  A very nice one

The magnets are going to alter the momentum of the electrons.  They
don’t provide a conservative force, rather an orthogonal force via the cross
product.  But the whole point of the icosi-cage is to provide an
advantageous geometry for making use of these cross-product forces.  The
way that I see the electron trajectories bouncing around, the addition of
magnets should be more than enough to push the electrons into a nice bouncing
orbit around the insides of the icosi-cage.

I did a few ion simulation runs, and they were pretty fun, too.  The
trajectories are much more chaotic.  The focusing of the beam is much more
important.  And I can’t effectively simulate the space charge of the
virtual grid of electrons…  Once I get the magnets in, and assuming that
the structure actually is an effective electron trap, I can simulate some of
that in SimIon.  I was thinking of using some point electrodes (pixels) to
simulate the space charge as well.  Hope that works.  Should provide a
good approximation…

In any event, it’ll be interesting to find out.  Next step is to add the
magnetic circuit and see if there is the effect I believe it will.

In more real news (as opposed to simulated news), I got the electro polished
cages back.  They’re absolutely gorgeous.  The stresses in the cages
have also evened out nicely, so they look very symmetric – not a lot of
irregularities.  Very nice.  I also built the ceramic insulator
standoffs.  I used the vacuum grade epoxy and constructed 9 of them. 
I need 10, but I only ordered enough parts for 10 and I broke one of the
cylindrical standoffs when I was trying to drill a venting hole.  Can’t
really drill fired ceramic without special equipment.  As the standoffs
have screw holes, and I epoxy’d a ceramic ball on top of one of these holes
(I’ll be posting pictures later), I may have a virtual leak situation. 
I’ll have to see.  Hope not.  The epoxy forms a tight seal… 
Fingers crossed.

I tried to come to grips with the wiring of the grid from the electrical feed
through.  Got a little bit ugly, but I think I may have a way to do it
simply.  We’ll see.  I have to drill out a hole on those electro
polished pieces of beauty…  Then I have to mount the insulators, then
mount the magnets.  Joy of joys.  The magnets are always fun to have
flying about :)  So, still lots to do.  Hopefully I’ll have more time

  • ar

    we seem to be of like mind

    July 10, 2008 — 13:26
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