Re: Frequency splitting (fwd)

["Tesla list" <tesla@xxxxxxxxxx>]

---------- Forwarded message ----------
Date: Tue, 21 Aug 2007 13:50:41 -0500
From: Bert Hickman <bert.hickman@xxxxxxxxxx>
To: Tesla list <tesla@xxxxxxxxxx>
Subject: Re: Frequency splitting (fwd)

Hi Gary,

Thanks for the kind words. My responses (and speculations) are below.

Tesla list wrote:
> ---------- Forwarded message ----------
> Date: Tue, 21 Aug 2007 08:41:42 -0400
> From: "Lau, Gary" <Gary.Lau@xxxxxx>
> To: Tesla list <tesla@xxxxxxxxxx>
> Subject: RE: Frequency splitting (fwd)
> 
> Thank you Bert - I always look forward to and save your posts.  I wholly
> agree that there must be capacitance between the conductive plasma
> channel and the rest of the world, in the same way as there would if the
> arc is replaced with a piece of wire.
> 
> But if I may play the devil's advocate for a moment - I recall about a
> year ago when Terry and others were playing with streak cameras, the
> duration of arc luminosity was extremely brief.  Is the plasma
> "conductiveness" correlated with the luminosity?  

Channel luminosity corresponds to the current flowing through the 
channel at that instant. While there is some "afterglows" (from 
thermally excited nitrogen and oxygen species), an air spark behaves 
similar to a high pressure flash tube, and the bright flash pretty much 
directly correlates with the sudden movement of significant charge 
through the spark channel during stepwise propagation at the FAR end. 
What I found to be extremely interesting was that the above experiments 
also showed high current pulses in the reverse direction, as previously 
injected space charges were extracted back into the channel during 
subsequent topload voltage reversals.

> In other words, is the
> effective increase in Csec due to the plasma channel, in effect for the
> entire bang duration, for only for a few nanoseconds during each HF
> peak, or does it span bangs?  

Yes...  :^)

Spark growth (or the reignition of a partially cooled down channel from 
a previous bang), is accompanied by abrupt, large current pulses. Only 
after a hot, conductive channel has been created, can the comparatively 
lower RF displacement currents heat and maintain the channels.Current 
measurements through an already-established leader show high current 
spikes at (or near) terminal voltage peaks (corresponding to further 
spark propagation or reignition) superimposed on lower, pseudo 
steady-state RF displacement currents into/out of the leader 
capacitance.

Both of these effects were observed during direct streamer current 
measurements made by Greg Leyh on Electrum in 1997-98. For the benefit 
of newer coilers, the streamer current measurements were made while Greg 
was seated INSIDE the topload of his operating 130 KW coil...  =<:^O
http://www.lod.org/Projects/electrum/testing/pages/Leyh23pwr.html

A large topload capacitance permits larger chunks of charge to be 
instantly "on tap" to support initial spark propagation and initial 
formation of a hot leader. Once the leader has been formed, 
comparatively lower RF displacement currents will help to _keep_ it hot 
and conductive. The latter currents do not add to further spark growth, 
but only serve to make existing sparks fatter and hotter. In DRSSTC's, 
CW VTTC's and SSTC's, increasingly more power goes into maintaining the 
main channel. Although sparks become fatter and hotter, they stop 
growing once streamer loading begins to "clamp" the maximum HV output 
voltage.

Terry and Peter's experiments seem to show that the surrounding space 
charge regions not only absorb energy from, but can also supply energy 
back into the leader-streamer via "hard" discharges. Energy flow can be 
discontinuous (during nanosecond spark propagation or channel reignition 
events), or continuous (during simple RF displacement current flow 
through existing leaders). Although these nanosecond events can extract 
significant energy from the system, only the RF displacement currents 
will directly impact TC tuning.

The size of the topload capacitance limits the "stepping" distance a 
spark will propagate before the terminal voltage collapses to the point 
where further growth is killed. If the secondary is undergoing ring-up, 
a number of spark extending steps may occur before maximum terminal 
voltage is achieved. The mechanism (within a given bang) may be similar 
to stepped-leader growth in lightning, but on a much smaller scale. 
However, the effects of RF voltage reversals and residual space charge 
regions (from previous discharges) significantly complicate the overall 
picture... I suspect they further facilitate the development of long 
sparks.

I'm sure the answer is a great deal more
> complex than any one of those answers, but I have to wonder what the net
> effect would be if the channel capacitance were present for just a few
> nanoseconds per bang.
> 
> Thanks, Gary
> 

There's still a quite lot that is not known about just how Tesla Coil 
sparks form and grow, both within a bang and between bangs. As coils 
become increasingly sophisticated, even more surprises are uncovered. A 
simple problem it is NOT, but it sure is fun trying to figure out what 
it all means...  :^)

Bert

>> From: Bert Hickman <bert.hickman@xxxxxxxxxx>
>> To: Tesla list <tesla@xxxxxxxxxx>
>> Subject: Re: Frequency splitting (fwd)
>>
>> Tesla list wrote:
>>> ---------- Forwarded message ----------
>>> Date: Sun, 19 Aug 2007 15:22:28 -0400
>>> From: Jared Dwarshuis <jdwarshuis@xxxxxxxxx>
>> <snip>
>>>
>>> Commentaries:
>>>
>>>
>>>
>>> It has come to my attention that many experts on Pupman are now
> describing
>>> the plasma arc from the secondary capacitor  as having a
> capacitance. They
>>> are tuning coils as if the capacitance was really there.
>> One might reasonably ask where the currents flowing through the roots
>> Tesla Coil air discharges ultimately "go"? The answer is that, unless
>> these discharge actually complete an arc to ground, all of the current
>> flowing through the "root" of a TC air discharge is ultimately due to
>> capacitive charge transfer (i.e., displacement currents) since there
> is
>> no direct or resistive path to ground on the far end.
>>
>>   >
>>> There is no such capacitance in the arc. Capacitors do not increase
>>> capacitance when they arc out. Arcs do not have an ability to store
> charge.
>>> Arcs  do not have plates nor can they be described with a fixed
> geometry.
>> Unfortunately, you are artificially limiting the physical definition
> of
>> "capacitance". Any conductive object has the ability to store and
>> transfer charge. This includes toploads, a projecting length of wire
>> from a topload (the effects on tuning being easily measurable), or a
>> similar length Tesla Coil discharge springing from the topload.
>>
>> The easily visible part of a TC discharge is only part of the total
>> discharge. Most of the actual charge transfer process occurs at the
> far
>> ends of the sparks, in the dim bluish colored region just beyond the
>> leader tips. In this region, countless microscopic filamentary
> streamer
>> discharges busily transfer charge into, and out of, thin air - into
> and
>> out of the invisible "space charge" regions that form around Tesla
> Coil
>> sparks. The cumulative result of these filamentary streamer currents,
>> when combined through various leader branches, is a significant
>> (multi-ampere) displacement current that flows through the root of the
>> main channel.
>>
>> There are also voltage drops along the plasma paths from (nonlinear,
>> arc-like) channel resistances. Even though the discrete processes are
>> considerably more complex and operate across time scales spanning at
>> least 6 orders of magnitude, at a macroscopic level the channel can
>> simply be modeled (for most TC purposes) as a distributed resistance
> in
>> series with a distributed capacitance, each scaling with overall spark
>> length.
>>
>> In 2001, Terry Fritz measured an effective spark "load" of about
>> 220k/foot and 1.9 pF/foot. Although YMMV based on coil size and power
>> level, this seems to be in the ballpark for disruptive Tesla coils. A
>> similar degree of detuning can easily be measured (by attaching a
>> suitable length of wire from the toroid and using a signal generator
> to
>> find the loaded resonant frequency of the secondary (emulating the
>> effect of the capacitive loading by conductive plasma channels).
>>
>>>
>>> Nor can we describe an arc as having an appreciable inductance. The
> geometry
>>> is not much good for inductance.
>> I agree that path-associated inductance has little bearing on low
>> frequency behavior of the coil (i.e., TC tuning). However, leader path
>> inductance does limit the charge transfer rate between HV terminal and
>> streamer tips during the nanosecond-scale current events that
>> characterize actual streamer growth. More accurate dynamic models for
>> leaders and streamers do include include distributed inductance,
>> capacitance, and channel conductivity. Channel inductance also comes
>> into play during direct toroid-ground discharges.
>>
>>>
>>>
>>> Nope!;  you are altering C or C'  to make up for changes in
> frequency caused
>>> by dampening. (dampening from  the non linear resistance of the arc)
>>>
>>>
>>>
>>> Empirical corrections are wonderful, my hats off!  I am sure that a
> great
>>> deal of effort was involved in arriving at a useable correction
> factor. But
>>> there is no capacitance in the arc. There is only non linear
> resistance and
>>> perhaps a tiny bit of inductance.
>>>
>> OK... Let's assume that leaders are merely nonlinear resistances. What
>> is tied to the "other end" of the current path? How do you (otherwise)
>> account for multi-ampere air streamer currents on one, seemingly
> flowing
>> into thin air at the other end?
>>
>>>
>>>
>>> Jared Dwarshuis  August 07
>>>
>>>
>> The roles of pulsed charge transfers, displacement currents, and
>> streamer capacitance are included within the "streamer theory" of
> spark
>> propagation. The streamer model, originally developed in the 1930's,
> has
>> been experimentally verified and refined by countless researches in
> the
>> intervening years. It is now accepted by virtually all serious spark
>> researchers. The streamer model appears to apply to the formation and
>> growth of any long spark within a nonuniform field, not just sparks
> from
>> Tesla Coils. A couple of excellent resources that cover spark
>> propagation in much greater depth include "Spark Discharge" by
> Bazelian
>> and Raizer (ISBN 0849328683) or Gas Discharge Physics by Raizer (ISBN
>> 354019622). You can also find tons of information by searching the
>> literature for "streamer capacitance", "leader capacitance", or
>> "streamer model".
>>
>> Bert
>> --
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