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Re: Frequency splitting (fwd)



---------- Forwarded message ----------
Date: Mon, 20 Aug 2007 15:25:51 -0500
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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