Re: Breakdown voltages of toroids

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

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

At 11:42 AM 12/17/2003 -0700, Tesla list wrote:
>Original poster: "Gerry Reynolds" <gerryreynolds-at-earthlink-dot-net>
>Hi Jim,
>
>If p*d is empirically derived,  doesn't one need to specify what the
>dimensions are?
>
>Gerry R

Paschen's original paper basically said that you can construct a relation like:

Vbreakdown = f(p*d)

(where p*d would be something like torr-cm)

and that, within some limits, you could trade p and d back and forth (i.e. 
if you doubled the gap and halved the pressure, the breakdown voltage would 
be the same)

There was no attempt to try and characterize f(x) in some real terms at the 
time, just to state that breakdown voltage is related to the product of 
pressure and distance (or, more accurately density and distance.. it might 
have been rho*d, and rho(density) looks like a p)

Paschen gives data for  sphere gaps with spheres of radius (0.25, 0.5, and 
1.0 cm), with gap lengths of 0.01 - 0.14 cm (which he calls short gaps) and 
0.1, 0.15, ..1.5cm (which he calls long gaps) (There's a lot of detail... 
the barometric pressure as 756 mm, average temperature of 15C, etc...

There's also a whole lot of work with the effects of temperature, humidity, 
etc. and data to try and relate his data to that of previous workers 
(Baille, Quinke, Czermak) and different seasons (im Winter, im Sommer)

The pressures were varied from 2cm to 75 cm of Hg (cm Q. in German 
(Quecksilber))

Finally he has tables that show that if delta*P (distance * P) is constant


Paschen also used several different gases (Luft (air), Wasserstoff 
(Hydrogen), and Kohlensaeure(CO2) , and showed that this feature was gas 
independent (for reasonable distances and pressures).  Not that the 
breakdown voltage is gas independent, or even that the shape of the 
function f(pd) was the same, but that, for a given breakdown voltage, the 
product of p and d is constant.

Later, a whole raft of empirical curve fitting was done, using pd as the 
independent variable and Vbreakdown a the dependent variable, with 
selection of the functions based on some rational physical basis (how it 
winds up being logs, etc.)




> > Original poster: "Jim Lux" <jimlux-at-earthlink-dot-net>
> >
> >  >  > 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.
> >
> >
> > Nope.. it's an empirical relation (and stated as such in my original
>source,
> > which, if I didn't credit it on the page, I will fix today), so not
>subject
> > to dimensional analysis.. basically, it attempts to fit to the usual
>Paschen
> > relation of Vbreak = f(pd), where the product of p*d is the independent
> > variable
> >
> >