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Re: Directions for tesla coil research

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

Jim's comments cut to the heart of the matter:  The question is,
what is the relative significance of topload voltage and topload
charge in determining streamer performance?

We know that we need enough voltage so that the surface field
gradient reaches the 26kV/cm needed for streamer formation, and we
know that the subsequent length, quantity, and brightness of the
streamers depends on having a sufficient reservoir of stored charge

The toroid size establishes a trade-off between topload voltage and
stored charge - a bigger topload means more stored charge but at a
lower voltage.  For a given coil and power supply, there is
presumably a topload size that will maximise the streamer performance
by hitting just the right balance between volts and charge.  We don't
have a recipe to determine that optimum.

My comments:

> 1) ...arbitrary waveform generator...very tight coupling... 

So the topload sees the coil as a constant voltage supply, with
a controlled waveform.  One way to achieve this might be to run
CW at VHF into a quarter wave line transformer, stepping a few
hundred watts up to a few 10's kV, then rectify.  Amplitude modulate
the VHF exciter to determine waveshape.  Work with small toploads
to obtain results with lower voltages and charges.

> 1a) How much does the Cself of the secondary contribute to the
> spark growth, or is it safe to assume that Ctop is all that really
> matters

I think that Qtop is the thing that really matters. Most of that
charge will be putting Vtop across Ctop, and a proportion, 10% or so,
will be putting voltage across the topload-coil distributed
capacitance.  Both can be drawn upon quickly, ie in the nS timescales
of streamer formation.  How much charge can be drawn from the coil
depends on the response of the top of the coil to a falling step
transient applied to the top.  This could and has been measured,
eg on Electrum, I believe, and it could also be modelled although
AFAIK it hasn't.  To calculate it, we would first have to know how
sharp the step transient was, in other words, in what sort of time
scale the topload voltage is pulled down.  Roughly speaking, it
would take a quarter-cycle of f1/4 to drain all the charge from the
coil, a quarter-cycle of f3/4 to drain a third of the charge, and
a quarter-cycle of fn/4 to drain 1/nth of the coil's stored charge,
where fn is the resonant frequency of the n/4 wave resonance.  That
statement assumes uniform distribution of available charge along the
coil, which is roughly the case when n > a few.  If streamer
formation occurs in 10nS, that is 250 times shorter than a quarter
wave of a 100kHz system, so I guess we could only draw 1/250th of
the coil's stored charge.

> 2) What's the minimum size for a highly instrumented system?  

Too small and we suffer perturbation by instrumentation. Too big
and it is expensive, unwieldy, and dangerous. Choice would depend
on the particular experiment. Probe effects can be allowed for in
the calculations to some extent, but ultimately with a very small
coil, measurement of the small discharge currents would approach
the instrument noise level.  I'd say use the biggest system that
you can manage, but at the lowest power level possible for the expt.

> 3) Could one build a suitable means to measure the actual
> spark/leader current

A large toroid connected to a small sphere, with a fibre-optic
current sensor in between.  Some distance apart so that their E
fields can be considered separate.  The size of the small sphere
clamps the voltage to that which gives 26kV/cm at its surface, and
the size of the toroid controls the available stored charge.  Thus
the two variables: charge and voltage, can be altered independently.

What's that barrage balloon floating above the shed - Ah that's my
intermediate charge reservoir :)

> 4) High speed photography and recording.

Results could be obtained with a total light receiver, eg a photo-
diode or a few, suitably masked/collimated.  Then correlated with
the measured current entering and leaving the topload.

Overall, I think the topics raised by Jim are well considered, and
that investigations into the relative importance of charge and
voltage could deliver some very useful info for coilers.  It is an
area which is very difficult to model from first principles and is
thus a good candidate for empirical work.  Data drawn from
measurements could be used to produce very practical formulae or
tables that coilers could refer to when choosing a toroid.
Paul Nicholson