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Re: Lower secondary cself => better performance?

Original poster: "Dr. Duncan Cadd by way of Terry Fritz <twftesla-at-uswest-dot-net>" <dunckx-at-freeuk-dot-com>

Hi All!

>Thus, selecting the optimum h/d ratio and using the smallest possible
>coil length, along with the smallest possible topload, is the advice
>I would give to achieve the maximum output voltage for a given input

I agree.  It's classical intermediate frequency transformer theory.
However, I have done much thinking over this last year and am no
longer persuaded that the potential difference across the secondary
coil is the bit which is important.  This simply is a measure of the
amount of energy needed to stick a given charge (or number of
electrons) on a given top load or capacitance.

>However, the experienced coilers on this list all seem to advocate
>using the largest possible topload, reporting that performance
>improves as the toroid size is increased.

This is what got me thinking in the first place, because to start with
I simply could not reconcile the idea of IFT theory with larger
capacitors apparently giving higher voltage outputs.  It seemed on the
face of it impossible.  I started off on the track that a larger load
helps quenching and thus efficiency, and doubtless there is some truth
in that, but I still couldn't satisfy myself that this was the real
reason why the sparks got bigger with the topload size.

>Why should this be?  There must be some other factor(s) which in
>practice are more important than energy storage considerations.

I began to wonder about the physics of charging isolated electrodes
and concluded that the basic process has to be the same for Tesla
coils as for Van de Graaf generators.  The volts there in a VDG accrue
through an increase in charge, physically transported as it were and
almost mechanically dumped on the topload.

When it comes down to it, what are sparks made of?  At the lowest
level, it's charge i.e. electrons added or electrons taken away.  In
air at STP it's either positive or negative ions (no free electrons in
air, leastways not for long).  No charge = no spark.

>The conditions for obtaining efficient primary circuit operation and
>an optimum coupling to the secondary may demand a larger topload.
>The effective inductance Les of the secondary coil does increase as
>topload is applied, and it could be that an over-sized (from the
>of view of energy storage) toroid is of benefit by enabling use of a
>higher primary L/C ratio and a lower f1, both of which may lead to
>greater primary efficiency. Also there is the matter of obtaining an
>optimum power-transferring impedance match between the toroid and the
>breakout loading, and it may be the case that a large toroid provides
>the appropriate shunt matching - the optimisation is then for power
>transfer rather than top voltage.

That's what I started to think but after considering VDGs began to
reason that, whilst this does indeed matter, there is something far
more important going on.

I concluded that since 0,5 CpriVpri^2 = 0,5 CsecVsec^2 = 0,5 qsec^2
/Csec that as the secondary capacitance increases, so does the free
charge qsec on the top electrode for a given bang size and that it is
the electric field
established by the total charge on the topload which is
important, rather than the work done to put it there - if the
capacitance is increased, the same work puts more electrons on the
electrode (or removes them).  As the number of electrons increases
(decreases), so does the field due to them.

Of course there is a certain amount of scientific semantics here
because the charge, capacitance and voltage are all inter-related.
Maybe it ought to be expressed in terms of "wave equations" of the
Tesla secondary ;-)  Some kind of expression of its characteristics as
a whole, rather than a lumped system.  Eigenvalues, Green functions or
I-know-not-what.  I rather like what Antonio wrote:

"Streamers, maybe except for an initial forming transient, become part
of the whole system."

It seems that the charge on the secondary topload can easily establish
a larger electric field than the potential difference across the coil
if the top capacitance is increased.

Example.  One joule bang size.  Looking at the field at one metre
distance and at the topload surface:

Top capacitance 30pF.  Pd across coil 258kV.  Charge 7,7uC.  Electric
field at one metre = q / 4.pi.Eo.r^2 = 69kV /m.  If topload is
spherical, diameter = 54cm.  Field at the surface = 950kV/m.  No
spark. If topload is toroidal with a minor radius of 7,5cm, field at
the surface = 12,3MV/m.  Spark!

Top capacitance 100pF.  Pd across coil 141kV.  Charge 14,1uC.
Electric field at one metre = 127kV /m.  If topload is spherical,
diameter = 1,80m.  Field at the surface = 157kV/m.  No spark.  If
topload is toroidal with a minor radius of 15cm, field at the surface
= 5,6MV/m.  Spark!

Top capacitance 250pF.  Pd across coil 89kV.  Charge 22,4uC.  Electric
field at one metre = 201kV /m.  (No point in calculating for a
spherical electrode.)  If topload is toroidal with a minor radius of
30cm, field at the surface = 2,2MV/m.  Borderline.  A breakout point
may be needed.

These calcs assume 100% efficiency: 50% is probably more like it, in
which case they are for a 2J bang size.

Depending on the physical size, curvature of the topload, a field of
2-3MV/metre can easily be produced at the topload surface and hence
dielectric breakdown of air and hence a spark.  What I currently have
no means of doing is estimating the spark length from a knowledge of
the charge and radius of curvature of the electrode (and whatever else
might be relevant).  I suspect it will be some hideous integral
describing the energy required to move each electron/ion however far
it travels down the ion channel.  The further it travels, the less
energy remains, the sparks get thinner and peter out.

>Anyway, for what it's worth, those are my speculations on the

FWIW, my speculations are at:
and in other pages to a lesser extent.

I am not totally convinced by everything I have written there - it was
simply the best I could do at the time.  Especially Prof. Cotton's
derivation I may have misapplied as the RC time constant vs
oscillation frequency may well come into it.  But I would be
appreciative of your thoughts, you lot out there!

I'm currently trying to (mis)apply NEC2 to Skip's coil.  It has
sufficiently few turns to be barely modellable on my system, but first
results don't look too encouraging.  Think I need a Sun ;-)