Re: Resonance, and now magnifiers

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

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

Ed Phillips wrote:
 > I've always suspected the reason the top loading helps is that the
 > greater amount of energy stored when the streamers start.

Yes.  We often hear alternative suggestions involving choosing
the topload to achieve some kind of 'ideal' resonance condition
within the resonator itself.  But as Ed, Terry, and others have
said, the topload should be chosen with a view to optimising the
generation of streamers (at least for the intended application of
most TCs!)  Quite how to do that is anybody's guess - the general
idea seems to be 'large is good'.

 >  As for the impedance of the discharges themselves, I suspect
 > they're so low compared to the equivalent parallel losses of
 > the secondary that the "unloaded Q" of any decent design really
 > doesn't affect performance much.

Yes, the discharge loading will be high (assuming the topload is
doing its job properly) so would be seen as a low-ish impedance
shunting the topload to ground.  Perhaps the Q of the resonator
thus loaded would be down to 5 or 10 or 20, against an unloaded
Q of say 50 at least.   The efficiency of transfer of energy from
resonator to discharge is given by

  Eff = 100% * (Qunloaded - Qloaded)/Qunloaded

That means if the topload is not working right, loaded Q will be
higher than it need be, and you'll be heating up the coil instead
of the streamers.

Also, as Dr. Resonance wrote:

 > A large topload helps to reduce unwanted small resonances at
 > frequencies higher than the fundamental frequency.

Yes, perhaps in two distinct ways:
1) The large top-C pulls the 1/4 wave frequency way down from the
overtones, so perhaps reducing the proportion of energy going into
them.
2) The large top-C brings down the top end impedance at the overtone
frequencies, ie reducing the voltages but the stored energy in the
overtones stays the same.

I still wonder about the 'unwanted' part though.  Certainly as
Dr. Resonance goes on to say

 > Also, all resonances, however small or large, can begin "beating"
 > against each other and form small standing waves which can
 > interfere (destructive & constructive interference) with the
 > lower fundamental resonance.

We have lots of little standing waves and the beating between them
appears as a whole mess of little ripples and transients running
up and down the coil.  Their amplitudes, though small, can be
induced across small numbers of turns due to the short wavelengths.

 > These unwanted frequencies can produce unequal potentials
 > across the sec coil

The effect is seen in this animation

  http://www.abelian.demon.co.uk/tssp/cmod/jftt42a.grad.gif

showing the voltage gradients in one of John Freau's coils. At the
the start of the bang the initial excitation of overtones due to the
end-concentrated primary induction takes the form of a transient
which rapidly traverses the coil and reflects back and forth.

After a few lengths of the coil it has dispersed into a jangling
mess of incoherent overtone resonances.   You can see in John's coil
that this HF stuff has quite a few kV/cm to contribute to the overall
voltage gradient that the turns have to withstand.

So yes, unwanted I think in this respect.  But set against this is
the beneficial possibility that the HF currents may contribute to
heating of the breakout plasma.  Even though the voltage amplitudes
are relatively small at the topload, the low impedance could drive
a substantial bunch of charge rapidly back and forth through the
leaders with each half cycle of the high frequency oscillations.

Perhaps then, a balanced diet of for feeding TC discharges is a mix
of large low frequency voltage to push out the streamers plus some
high frequency stuff to keep the leader channels hot.  It might be
possible to look for this experimentally in a number of ways.

Well I'd better bring this thread on resonance to a close because
I've said all I can just about.  If I seem to labour a few things
it's because
a) It's interesting, if nothing else.
b) There's a few misapprehensions in circulation which may appear
fairly innocent and perhaps subtle to many coilers, but which can
result in some individuals wasting a lot of time on futilities.
c) Someone was asking about ideas for experiments and research a
while back.  In the last few years there's been a lot of talk and
modelling and speculation about the HF behaviour of TCs.  But no
one has really got to grips with the experimental/practical side
of observing, testing, refuting, exploiting, etc.

A summary of some specific open practical questions:-
1) Do HF overtones have any bearing on racing arcs?
2) Is there any beneficial discharge heating effect from HF currents?
3) Can magnifier overtones be tuned into contributing to output
voltage and efficiency?
4) Can overtones be tuned to match drive harmonics in the CW TC,
and is there anything to gain?

We just don't even know whether any of this overtone stuff matters
at all.  If some reliable experimenter could just answer that
question, at least we'd know whether to stop thinking about it and
do something else instead.
--
Paul Nicholson,
Manchester, UK.
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