Re: Breakdown voltages of toroids

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Original poster: "Dr. Resonance" <resonance-at-jvlnet-dot-com> 


Van de Graaff spheres in the 14, 24, and 30 inch size using 30% smaller
electrodes as the ground terminal, usually break down at 26.5 kV/cm.  With
equal sized electrodes we measured a consistent 27-28 kV/cm.


Dr. Resonance

Resonance Research Corporation
E11870 Shadylane Rd.
Baraboo   WI   53913

 > > > 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
 >
 >
 >
 >