Re: Spheres on toroids

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> 

Tesla list wrote:

 > Original poster: Bart Anderson <classi6-at-classictesla-dot-com>

 > I used Antonio's Inca program to play with the toroid_sphere case. Take a
 > look at the Efield plot.
 > http://www.classictesla-dot-com/temp/toroid_sphere.jpg
 >
 > Max field is at the predominantly blue area of the toroid (where streamers
 > will breakout). But what I find interesting is the how the sphere has moved
 > the toroid max field downward on the toroid. Wonder if that's a problem? I
 > guess the toroid affects the sphere similarly.

Yes, the sphere repels the charges in the toroid. It's not difficult to
find a sphere size that results in identical maximum fields at the
sphere and at the toroid. With larger spheres, breakout will be at the
toroid. With smaller spheres, at the sphere. The height of the sphere
above the toroid has influence too, as well as the aspect ratio of the
toroid.

I have not implemented a cylinder with nonuniform voltage, required
for the modelling of a Tesla coil secondary. But it's possible to
assemble below the terminal a series of cylinders with specified
voltages. In the limit each can have just one ring.

I have made some updates in the Inca (ICCDTR) program:
- The maximum electric field can be adjusted, if you don't like 30
kV/cm.
- I have included some exact calculations:
- Exact maximum electric field at the surface of a toroid, and the
   exact (ideal) breakdown voltage. It can generate a table with exact
   capacitances and breakdown voltages.
- Exact potential around a toroid, and the exact electric field at the
   central plane (to be later extended to all space).
- Exact maximum electric field and ideal breakdown voltage for a
   two-spheres spark gap, with different spheres.
The exact calculations are useful to test the precision of the numerical
calculations. The exact solutions for potential and electric field for
a toroid are somewhat badly conditioned numerically. The precision that
can be obtained is not as good as with capacitances, specially in the
case of the surface field.

A Linux version is in the works, as I have already found how to use
Kylix.

Antonio Carlos M. de Queiroz