Re: Lower secondary cself => better performance?

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

Original poster: "Bert Hickman by way of Terry Fritz <twftesla-at-uswest-dot-net>" <bert.hickman-at-aquila-dot-net>

Duncan, Paul, and Gary,

I agree with most of Gary and Duncan's reasoning. There's fairly strong
empirical AND theoretical support for using as large a topload as
possible as long as the terminal voltage remains sufficient to cause
initial streamer formation ("breakout"). However, for a fixed bang size,
increasing the topload capacitance reduces the maximum output voltage,
so a larger diameter toroid may also require a smaller Radius of
Curvature (ROC) to ensure that initial breakout still occurs at the
appropriate point on resonator ring-up (more below). (BTW, for those who
are very seriously interested in gaining a better understanding of
streamer formation and propagation, undoubtedly one of the most valuable
in-print publications on this topic is "Spark Discharge" by E. M.
Bazelyan and Y. P Raizer (CRC Press, 1998, 320pp, ISBN 0-8493-2868-3 -
$105 from Borders On-Line - cheap it is not... superb it is...). I'll
try to provide a Readers Digest Condensed (and considerably less
technical) summary.  

Under the right conditions, an initial streamer transforms itself into a
high current channel, called a leader, which very rapidly propagates to
a distance which is governed by the amount of charge that is
_immediately_ available from the top terminal. The leader provides a
conductive path for charge to be injected from the top terminal
into surrounding regions of lower potential in a sudden surge of
[ampere-level] displacement current. Charge residing in the internal
capacitance of the resonator does not significantly impact the
length of this step. Even though the more correct term for the streamers
we see is probably "leaders", I'll continue to use "streamers" to be
consistent with discussions on this list. Because of the physics
involved, initial breakout is achieved at a lower voltage for a positive
voltage excursion than for a negative one. And, once the initial
streamer begins propagating, if the topload voltage can be made to rise
at an appropriate rate, the leader can continue to propagate
indefinitely. Both conditions can be met (at least for a while) in a
Tesla Coil with a properly sized topload.

As Gary and Duncan have surmised, charge flow is fundamental to the
streamer propagation process. Once initial breakout begins, the distance
that the initial streamer will travel (sometimes called the leader step
length) is a function of the _amount_ of charge that can be made
immediately available from a reservoir of charge. Because of the huge
amount of charge residing in a charged cloud, individual step length may
be hundreds of feet for a lightning leader, but for Tesla Coils, leader
length would be inches or feet. In a Tesla Coil, the larger the
available topload charge (Ctop*Vtop), the slower the rate of topload
voltage collapse as charge is "sucked out" via heavy displacement
currents flowing into a newly formed streamer, and the longer the "step"
becomes. Because of the high velocity of propagation (10^6 - 10^7 cm/sec
or more) and the short duration of mthe current pulses, charge residing
within the internal capacitance of the resonator is of limited utility
since the intervening inductance prevents large instantaneous currents
from being supplied directly to the streamer. 

In effect, during each step, an increment of charge is transferred from
topload C into the capacitance of the streamer through a lossy,
non-linear conductor (the plasma channel), forcing the topload voltage
to decrease. If the topload voltage collapses quickly (small Ctop),
further streamer growth is starved, prematurely ending propagation. A
"stiffer" reservoir of charge (i.e., a larger Ctop) provides a larger
slug of [take your pick: energy, charge, or current] necessary to
develop a longer, hotter conductive channel. Small topload C = short
step length. But wait, there's more...

If initial breakout occurred while energy was still being transferred
from the primary to the secondary, the topload voltage recovers as
additional potential energy is pumped into the topload capacitance and
topload voltage resumes its sinusoidal progression towards Vmax. Under
the rising potential, displacement current is again driven into the
channel capacitance, and the streamer can again propagate, further
extending the initial streamer. The increasing topload voltage
compensates for increasing voltage drop in the lengthening streamer
channel, so that a sufficient E-field (~30 kV/cm) can be maintained at
the streamer tip to advance ionization and add to streamer length. The
additional streamer growth further adds to streamer capacitance and in
increased displacement current in the streamer root. However,
propagation can't continue indefinitely, since conservation of energy
eventually limits the maximum voltage that can be achieved in the
system, and the process stops.

At least that's my interpretation of what's going on... :^)

-- Bert --
-- 
Bert Hickman
Stoneridge Engineering
Email:    bert.hickman-at-aquila-dot-net
Web Site: http://www.teslamania-dot-com


Tesla list wrote:
> 
> 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
> >energy.
> 
> 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
> point
> >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
> subject.
> 
> FWIW, my speculations are at:
> http://home.freeuk-dot-net/dunckx/wireless/scotty/scotty.html
> 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 ;-)
> 
> Dunckx