Re: Measuring Streamer characteristics

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

Original poster: "Paul Nicholson" <paul-at-abelian.demon.co.uk> 

Steve Connor wrote:
 > So I don't see how a model that says
 > "X ohms per foot" can be correct.

I agree - we'd expect the effective load resistance to
fall as the streamers grow.

Here's a different standard to use for load impedance.

This is based on the idea that a properly working
coil (whatever its dimensions) should be loaded down to
some low value of Q factor by the streamer load.

If we specify a desired loaded Q factor, we can give
the load resistance in terms of the characteristic
impedance of the resonator, ie

   Rl = load resistance = Ql * Zo

where Ql is the loaded Q, and Zo = sqrt( L/C), with L and
C being the equivalent reactances for the resonator.

If Ql falls down to as low as around 6 as a result of
streamer growth, the loading is such that the remaining
stored energy of the resonator is dumped into the load
in only around one more cycle.  Therefore we might conclude
that 6 is about the lowest it will ever go.

Thus it would make sense to test TC models with a load
resistance of 6 * Zo to exercise the case of maximum
streamer loading.  (Whether that degree of loading is
actually achieved in the real coil depends of course on
lots of factors such as toroid size, bang energy, BPS, ...)

So much for the resistance, what about a parallel
capacitance to represent the charge stored in the streamers?

Perhaps the simplest way to estimate a load capacitance
is to assume that the streamers reduce the resonant
frequency by some percentage.   A nominal value for
heavy loading might be, say, 10% reduction of frequency
which would be achieved by around 25% increase in the
total effective capacitance.

As a worked example, my CW coil has L = 84mH and C = 55pF
so Zo = sqrt(84e-3/55e-12) = 40k ohms.  A heavy streamer
loading would therefore load the thing to around 6 * 40k,
or 240k ohms.   The parallel load capacitance would be
around 0.25 * 55pF = 14pF.

Using this rule of thumb is sure to give you a reasonably
realistic load model appropriate to the size of the system.

If we apply this recipe to one of Terry's coils [tfltr45],
we have L=70mH, C=40pF, so Zo=42k. Then the load model is
252k || 10pF.

A figure of 1pF per foot of streamer is a reasonable order
of magnitude for an estimate of charge storage.  Terry might
expect a couple of 5 foot streamers.
--
Paul Nicholson
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