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Re: Maximum voltage of a toroid



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