Re: what determines if breakout will occur?

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

Original poster: "Paul Nicholson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

Laurence Davis wrote:

...some really good questions.  Hoping in vain that someone else
would attempt answers, I'll try...

> is it merely a factor of the toroid size compared to top
> terminal voltage?  

For breakout to occur, we think that the voltage on the topload
must be sufficient for the E-field strength at some point on
the surface to reach the value 26kV/cm. Breakout would begin at
that point. 

For a 13"x4" toroid that would be around 260kV, a 24"x6" gives
380kV, and 30"x9" gives 590kV.

You need to make sure that you have sufficient bang energy, net of
a guess at RF efficiency, to charge up the coil and topload's
effective shunt capacitance to reach this voltage.  And then some,
because these figures are just for the onset of breakout - you
need to have a whole load more charge on the way in order to 
develop the breakout into long streamers.  Coils that I've
studied data on seem to fire with two or three times the bang
energy needed to reach breakout.
 
> does frequency effect breakout voltage?

Yes, the above applies only above several 10's of kHz, I believe.
At low frequencies or DC, the threshold field is a little higher,
30kV/cm.  The values are affected significantly by air density,
and therefore by temperature and pressure.  I'm not sure what
happens at frequencies a lot higher than TC's use.

> as in AIR has RF dissipation factor

No, not the same thing.  Air is very low dissipation.  The
crucial thing is how far an electron can accelerate through the
E-field before it hits a gas atom.  If it can fall far enough, it
gains enough energy to ionise the atom, releasing more electrons,
which in turn accelerate, etc, creating the avalanche that becomes
the breakout.

> for example: a 6 six sphere will breakout at above 80kv.  

If you meant a 6cm diameter sphere, I make that 76.9kV to
reach breakout. 

> so if you have a breakout using said sphere, your output voltage
> is at least 80kv.

I think that's a safe bet, but take it as a rough figure because
things like air density, surface roughness, risetime, the presence
of the coil beneath distorting the field, and limited amount of
stored charge all make some difference.  Much experimental work
is called for here.

> even though surrounding surfaces and EM field affect breakout 
> (right?) would that still be a close enough approximation?

If the topload is in reasonably free space.  Judge that by 
estimating how much the top capacitance varies as objects are
moved up to the coil.  Estimate this in turn by the change in Fres.

Eg your 6cm sphere atop a 3cm diam coil, 27cm long, over a 2 metre
circular ground plane, breakout rises a little to 80.2kV.

Would it be worth tabulating toroid breakout voltages?  If so I'll
make up a table for common sizes.

Hope that helps.
--
Paul Nicholson
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