Re: Breakdown voltages of toroids

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

Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> 

Tesla list wrote:

 > Original poster: Bart Anderson <classi6-at-classictesla-dot-com>

 > 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

Ok. I will look.

 > 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).

I think that this would be the average electric field, the 30 kV/cm
is the maximum field anywhere that doesn't cause ionization of the
air.

 > 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.

Yes, but not by much. Note that North uses this value too.

 > 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

This dependency on the distance is very strange. Maybe this uniform gap
was not so uniform.

 > 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>

There is an apparent dimensional error in this formula. p*d doesn't look
adimensional.

 > I've made comparisons across a typical range of gap distances and both Jim
 > and Lucas follow each other well. Their both based on the Townsend affect
 > (as is Paschen's curve). The reason to pull in North is for the electrode
 > geometry.
 >
 > 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.
 >
 > Here's a plot showing actual, Jims, Lucas, and then with North's geometry.
 > http://www.classictesla-dot-com/temp/arccomp.gif

North's formula computes only the maximum electric field. To calculate
breakdown voltages, you must assume something about what is
the maximum allowable electric field. An independent problem.

I have now coded an exact series formula for the maximum electric
field between two spheres with different sizes and arbitrary voltages.
It agrees with my simulations very well, and also with North's formula
when the spheres are identical, exactly when the spheres are very
close or very distant, and with an error of about 1% when at distances
comparable to the radii of the spheres.

Antonio Carlos M. de Queiroz