RE: Maximum voltage of a toroid

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: "Derek Woodroffe" <tesla@xxxxxxxxxxxxxxx>


Antonio,

Thanks for your response.

>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

So from the above then (excuse my poor maths)

V(kv)=3*exp( ( log(R)+log(r) ) /2 ) where R & r are in mm, is a better
approximation?

Derek