Re: Breakdown voltages of toroids

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

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

Hi Antonio,

Tesla list wrote:

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

Yes, but also note that North plotted actual breakdown performance of 
spheres as the separation distance changed. All of the sizes at 1cm apart 
broke down at 22kV/cm and to quote North, "which isn't 30kV/cm, but it's 
close". But yes, this is the average field strength across the separation. 
On Figure 7-5, he shows the 25cm spheres at 40cm separation had an average 
field strength of 8.9kV/cm.

> > 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.

Can you explain? I didn't write it, but I assume a rule is being broken here.

>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.

Yes, that's where I've pulled in Jim's equation. I'm simply solving for Vb 
from a known Eb (via Norths maxE equations).

>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.

Super!

Take care,
Bart