Re: VdG sphere

[John Denker <jsd@MONMOUTH.COM>]

At 04:47 PM 11/22/00 -0500, Bob Sciamanda wrote:
> > Am wondering what kind of voltage i can get from a 16" or 20" sphere ?
...
> For a given R, V is limited by E, which in turn is limited by corona
> discharge into the air.  This maximum E value depends on atmospheric
> conditions, but as an example:
>
> using E = 500,000 Volts per meter (a crude guess), and R = 0.5 meter gives
>
> V= 0.25kV.

1) When I do that multiplication, I get 250 kV or 0.25 MV.

2) A so-called 16" sphere is probably a 16" diameter.  The radius is then
more like 0.2 meter.  That gives a V of "only" 100 kV.

3) Using 500,000 V/m as the breakdown field of dry air is
questionable.  Conventional values are more like 3,000,000 V/m.  For low
pressures and/or small gaps (mm or less) it could be even higher, according
to the Paschen formula
  http://home.earthlink.net/~jimlux/hv/paschen.htm
see also
  http://home.earthlink.net/~jimlux/hv/hvmain.htm
  http://home.earthlink.net/~jimlux/hv/corona.htm

A rough "dimensional analysis" of the physics suggests even higher
numbers:  a typical ionization voltage (1 volt) divided by a typical mean
free path (.05 micron).

For large gaps (appropriate for VdGs) I'm not 100% sure how to think about it.
Possibly the Townsend mechanism isn't the whole story.

================

ON THE OTHER HAND... the voltage on a home-made VdG is not simply
determined by the nominal radius of the dome.
  *) One must also worry about leakage (not to mention breakdown) through
the belt and the supporting structures -- especially if there is nonzero
humidity.
  *) Asperities on the dome can make a big difference.  At some point you
care about the radius of the asperity, not the nominal radius of the dome.
  *) Et cetera.