Last
night I changed the SimIon model to use one electrode for the entire cage and
received much better agreement with the five fold symmetry. In the
previous model, each of the great circles was a separate electrode. I know
this was bone headed, as they are all at the same potential, but I won't go into
the reasons why this came about. The extra bonus is that the field
calculation is about half as long. Only two electrodes, not 7. <heh>
I can be silly at times.
In any event, on the left is the field contours of the new model. Unlike the previous model, the icosahedral symmetry is obvious... Which makes the model a far better analysis model!
It's
clear that a lot of the chaos I saw in the previous model was a Tiffin phantasm
of the way the equations were solved. Which is pretty good news.
On the right is the electron
trajectories resulting from injecting electrons in one of the pentagon faces.
The view is the same isometric vantage point as the
above field image. The
injection point is just inside the actual radius of the cage. The energy
of the electrons is 7.71 keV, directed along the X axis. The potential
contours are nice and smooth and regular. I believe that I'll have to have
some directional focusing to capture the majority of the electrons, but a simple
Pierce reflector should be sufficient to focus the beam. It's the
direction that's hard to get accurate without deflectors.
The injection energy is 10 keV or less in the pentagon faces, and that means the electron guns will be a lot simpler to construct. I also found that the ideal grids that SimIon allows will give a reasonable approximation of the virtual grid formed by the electrons. Too ideal... But it's a good first approximation.
What's nice to have confirmed is that it doesn't take much of a change in momentum to push the electrons into the right contour. For example, a difference 10's of volts on a base of 7,000 is enough to shift the electron's trajectory into reverse. The addition of the magnetic array should add just the right kicks to keep these beasts caged for a significant number of orbits before becoming power losses.
On to the magnets.
Nice :)