Re: Corona breakout voltages?

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

Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz <twftesla-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>

Tesla list wrote:
 
> Original poster: "Terry Fritz" <twftesla-at-qwest-dot-net>

> There is this well known formula for corona of 3MV per meter of radius.  If
> I have a 1 meter radius sphere, I can but 3,000,000 volts on it before
> corona breaks out.

Ok. This formula applies in all situations where the charge density
at all the surfaces is uniform. Isolated balls and pairs of planes at 
small distance (capacitors).

> So I used to work on 375kV power lines, they were about 1 inch in diameter
> (0.0127m radius).  0.0127m radius suggest a corona voltage of 38,100 volts.
>  So at 10X that, those lines should have been glowing and streamering like
> crazy!!!  375kV was also an "RMS" voltage...

This is really funny, but what happens is that long straight wires
don't accumulate charge (the charge quickly escapes to the ends). 
Consider the case of a coaxial cable, with internal radius a and 
external radius b, with air dielectric. The maximum voltage that can 
be applied to the cable before the air breaks down can be calculated 
(see any book about electromagnetism) as:
Vmax=Emax*a*Ln(b/a)
where Emax is the 3e6 V/m limit. If the cable is reduced to a central
wire with the outer conductor far away (b->oo), Vmax goes to infinity
too, although more slowly.
The actual limit for a transmission line cable is somewhat different,
since a better model would be a wire over an infinite plane, and
there is the influence of adjacent cables with different voltages too.
In practice small irregularities in the wire cause corona breakout
before this limit, but the ideal case explains what happens. High
voltage doesn't necessarily mean high surface charge density or high
electric field.

> I am having trouble getting little spheres to corona at the voltage I think
> they should (seems to take far far higher voltage) and I think what ever
> held corona back on those high voltage power lines is also holding back
> corona in my sphere experiments.  Is the surrounding air just charged up
> and acts to reduce the e-field or something???

Once corona starts, it self-limits, increasing the effective radius
of the ball. The 3e6 V/m limit would apply for the first breakout
only.
 
> I am just wondeing if anyone has any insight into this or can tell me what
> I am missing in all this?

The fundamental point is that electric field is associated to charge, 
not to voltage.

Antonio Carlos M. de Queiroz