Re: Breakdown voltages of toroids

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

Original poster: "Jim Lux" <jimlux-at-earthlink-dot-net> 

 > This is all better explained in a document by J R Lucas, 2001, Breakdown
of
 > Gaseous Insulation. Good read!
 > http://www.classictesla-dot-com/download/breakdown_gi.pdf


Actually, Lucas' book is not a bad read overall. and it's on the web.
Assuming we're both talking about the Lucas that's a professor in Sri Lanka?
I'll see if I can find the URL.
 > > > Your values assume Emax=30kV/cm. Why?
 > > > I'm assuming Paschens curve ideal?
 > >
 > >30 kV/cm is the usual value in normal conditions of temperature and
 > >pressure. I could add corrections for altitude and temperature.
 >
 > True, 30kV/cm is the normal field gradient or strength (at breakdown) in
 > uniform fields for small gaps on the order of 1cm. But for large gaps of
 > several meters can reduce down to 6kV/cm (reference J R Lucas). Paschen's
 > curve I think is where the 30kV/cm is pulled as just about every text I've
 > read references the curve, but the curve itself is for 1cm spacing at 1
 > atmosphere and 25 deg C for conductors of an infinite plane, parallel, and
 > perfectly smooth (as quoted from North). If this is case, we know in the
 > real world it will always be below 30kV/cm.


I think, also, we use 30kV/cm, because it's a nice round number that's
approximately correct, just like 70 (or 71) kv/inch.

Paschen's original paper actually is quite exhaustive in his range of
electrode sizes/spacings/pressures.
(Like a fool, though, I don't have the figures, just the paper... I had the
library get me the paper, but didn't think to ask if there were other figure
pages. Apparently, back in the 19th century, figures were published
separately from the text. )

 >
 > The text also notes that under constant atmospheric conditions, it is
 > experimentally found that the breakdown voltage of a uniform field gap amy
 > be expressed in the form:
 > V = A*d + B * sqrt(d)
 > where
 > d = gap spacing
 > and for air under normal conditions,
 > A = 24.4kV/cm
 > B = 6.29kV/cm^1/2
 >
 > At Jim Lux's website, the breakdown voltage is expressed as:
 > Vbreakdown = B * p * d / (C + ln( p * d))
 > http://home.earthlink-dot-net/~jimlux/hv/paschen.htm
 > <http://home.earthlink-dot-net/%7Ejimlux/hv/paschen.htm>

Which formula I probably got from Cobine or Naidu&Kamaraju...
 >
 > What I do is use Jim's equation for field strength and use it in North's
 > equation for Arc Voltage. Works very well I've found. If I were to use
 > Jim's arc voltage, it would hold well up until the gap spacing is 1/2 the
 > electrode diameter. At that point it takes a fairly steep climb.

When gap spacing starts to be a significant fraction of electrode diameter,
then the field is no longer "approximately uniform", which is what that
equation is for.