Re: Racing Spark Prediction

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>

Dimitry wrote:

> secondary, say 72cm long ....  let H:D ratio would be 4:1
> 1565 turns ... 0.46mm enamelled copper wire

> A ten turn primary at 20kV ... not flat but solenoidal primary
> 15cm hight, OD is 28cm only, so you would have only 5cm of
> clearance

I confirmed Dimitry's calculations by modelling the above
with the tssp simulator.  I added a topload and groundplane and
aligned the bottom of the two coils, so the thing looks like

   http://www.abelian.demon.co.uk/tmp/fd1.plan.gif

The dual resonator mode frequencies came out to be 74.7kHz and
102.8kHz, so giving an effective k of 0.309.

(Dimitry got 0.307, calculated from the 'dc' mutual inductance
 and self inductances, whereas tssp first computes the normal
 modes of the structure, then calculates k from their ratio.
 Nice that we get the same answer.)

The terminal V/I waveforms (spanning 2.5 beats) are

   http://www.abelian.demon.co.uk/tmp/fd1.wave.gif

and a secondary V/I animation (spanning 1 beat) is in

   http://www.abelian.demon.co.uk/tmp/fd1.anim.gif

Dimitry calculated the vertical voltage gradient due to
transformer action alone by considering the distribution of
mutual inductance.  When we look at the instantaneous voltage
gradients we find the max vertical gradient briefly reaches
26kV/cm as seen in the voltage gradient animation

   http://www.abelian.demon.co.uk/tmp/fd1.grad.gif

and is generally peaking at around 20kV/cm.   This is a little
higher than Dimitry's estimation because we have some higher
overtone content which is flicking the gradients up higher than
you would get with just the fundamental modes.

When we add the radial voltage gradient, the combined stress is
totally excessive, as might be expected with the solenoid primary
being so close and reaching so far up the coil.  But it's clear
that even with this outrageous primary, the secondary volts/turn
due to induction by the primary is barely enough - by itself - to
produce vertical breakdown.

--
Paul Nicholson
Manchester, UK.
--