# Re: Racing Spark Prediction

```Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>

Referring back to the secondary voltage gradient animation of
the hypothetical helical primary system,

note the initial transient travelling up the coil.  It bounces
off the top end and returns to the base, and it is when this
transient echo washes against the base that we obtain the
highest vertical voltage gradient.  This is how the higher
overtone content caused by the concentrated coupling geometry
appears in the time domain.  Interesting how it does more
damage on the rebound - it arrives just in time to meet a
rising quarter cycle of primary current which is of the
correct polarity to add to the arriving transient voltage.

For comparison with the high-k helical primary model, I ran a
conventional primary, normal-k version. The primary was chosen
to have the same L as the helical so same bang energy and Fres.

http://www.abelian.demon.co.uk/tmp/fd2.plan.gif

Mode frequencies are now 80.7kHz and 93.4kHz giving k = 0.145

Waveforms, secondary V/I and voltage gradient animations:-

http://www.abelian.demon.co.uk/tmp/fd2.wave.gif
http://www.abelian.demon.co.uk/tmp/fd2.anim.gif

In this system, that initial transient is less pronounced,
(ie less overtone content) but still present.  The waveforms
are much cleaner, especially the base current, without those
overtones.  This system reaches the same peak topvolts and peak
primary current, but this time the highest vertical voltage

Note that in both these systems, if you just calculated the kV/cm
based on expected peak topvolts divided by length, you would
expect 15kV/cm.  With the transient effects of the concentrated
primary induction taken account of, the peaks are 26kV/cm and
20kV/cm in the two systems.  The helical primary system has
transient ripples of up to 11kV/cm on top of the smooth underlying
1/4 wave resonance, whereas the flat primary version only has
ripples of around 5kV/cm gradient.  Not only that but the
slower buildup of the 1/4 wave pedestal gives time for the
transients to decay and scatter.

In these models the top voltage is peaking at over a megavolt,
which in practice would not be achieved because the surface
field at the rim of the topload reaches 26kV/cm when the toroid
voltage gets to 350kV or thereabouts.  Breakout would occur and we
expect some degree of voltage clamping to hinder further rise.

The sudden onset of non-linearity due to breakout would be expected
to launch a transient into the coil from the topload, possibly a
series of them if breakout is advancing in rapid steps.  These will
add to the V/turn along the secondary as they reverberate back and
forth.  Therefore we can't assume that the limiting of topvolts by
breakout also limits the V/turn occuring in the secondary.

Q: Is it the case that, in a high-k system, the rapidly rising
voltage causes breakout to occur in fewer but larger steps,
compared with a low-k system in which a more gentle rise to
the same voltage gives time for a larger number of smaller
breakout advances, and hence presumably a larger number of
smaller amplitude transients sent into the coil?

Q: Do racing arcs only occur in coincidence with topload breakout?

at times on that helical primary system.  Is that enough to
produce breakdown?  What would be a suitable 'never exceed'
vertical gradient limit to design to?  The flat primary system
reaches 20kV/cm, so not vastly less even though we have halved
the coupling.

Q: Are we in a position yet to capture and study topvolts waveforms
during breakout?
--
Paul Nicholson
Manchester, UK.
--

```