Re: Maximum voltage of a toroid

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: "Antonio Carlos M. de Queiroz" <acmdq@xxxxxxxxxx>

Tesla list wrote:
> Original poster: "Derek Woodroffe" <tesla@xxxxxxxxxxxxxxx>
> Re Maximum voltage breakout from a toroid..
>     Take a look at
> http://www.roffesoft.co.uk/tesla/calcs/toroidcalc.htm
>     That calculator uses 3*Diam = breakout in Kv. Where diameter is the
> minor diameter of your toroid in mm
>
>     This was extracted from a site on VDG's and assumes a maximum
> electric field of 3Mv/M also take a look at
>     http://www.coe.ufrj.br/~acmq/myvdg.html from Antonio Carlos M. de
> Queiroz although it deals with DC from a VDG I don't see why its not
> applicable for a torroid before breakout..

The breakout voltage from a toroid is not identical to the breakout
voltage from a sphere, and is not also simply related to one or
another of the two radii of curvature.
A table listing breakdown voltages (kV) for several toroids with major
radius R and minor radius r:

r/R   0.050   0.100   0.150   0.200   0.250   0.300   0.350   0.400   0.450
V/R  639.43  998.45 1261.10 1470.00 1644.57 1795.52 1929.30 2050.02 2160.33

Note that for a thin toroid (r/R=0.05) the breakdown voltage is
much larger than the value for a sphere of radius r (0.05 x 3000 = 150),
and that the value for the thickest possible toroid is smaller than
the value for a sphere with the major diameter (V/R = 2262.05 instead
of 3000).
Using the geometrical mean between r and R as the effective radius of
an equivalent sphere, reasonable values are found:

r/R   0.050   0.100   0.150   0.200   0.250   0.300   0.350   0.400   0.450
V/R  670.82  948.68 1161.90 1341.64 1500.00 1643.17 1774.82 1897.37 2012.46

Antonio Carlos M. de Queiroz