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Re: Lumped vs. Helical Resonator

Greetings Coilers,
        Sorry for the delay in jumping in to this interesting thread, but
here goes:
        Jim Fosse wrote:
<snip>
>> "During the spark dwell time, the 
>>magnetic flux produced by the primary links the entire secondary.
>>Consequently the primary/secondary interplay of energy may be treated
>>by lumped circuit analysis". 
>
>I have to disagree (with) their statement for 3 reasons.
>
>Based on both yours and Richards prior post on Toroid coupling into
>the primary field, in which  you both stated that the coupling was
>nil. If the Toroid was NOT coupled into the primary field, then the
>top of the coil was not either (to any great extent)
        I agree that the toroid on top is little affected by the primary
coil.  Malcolm's experiment where he broke the loop of the toroid by placing
a gap in it, resulting in little effect, also supports this concept.
>
>Dr. Rzeszotarski's prior post on coupling indicated a decreasing
>coupling based on height above the primary. ( sorry, I seemed to have
>not saved that post:( so I can't quote exact numbers.
        The important point that I extracted from the coupling simulations
is that most of the energy is coupled into the bottom of the coil in a
conventional tesla coil.  The secondary does not behave like a uniformly
bathed inductor.  Having said this, I also feel that lumped circuit analysis
is probably a better model for the conventional tesla coil (but not a
magnifier) than the helical resonator model.  Yet, both aspects are observed
in an operating coil.

>Finally, If you visualize a single turn secondary with a volt meter
>attached, and slowly raise it up from the bottom of your TC secondary
>to the top of your TC secondary, you will get a decreasing induced
>voltage: almost NIL at the toroid position.
        This is true due to the rapid falloff in mutual inductance, as shown
in the simulations.  However, the standing waves produced on the helical
resonator demonstrate a voltage rise along the secondary which is nearly
sinusoidal in appearance.  The voltage is a minimum at the base, rising to a
maximum at the toroid in an approximate quarter wave sinusoidal fashion.
This is demonstrated experimentally in Duane Byland's text, where he wired
up a tesla coil secondary with multiple LED's every inch or so along the
secondary.  
        I also suggest that once the air ionizes and a spark breaks out, all
the above rules are out the window.  At that point,  The energy stored in
the toroid is "probably" being dumped out, so you want a big "C" on top to
make 1/2xCxVxV large.

>
>Treating the secondary as a lumped coupled inductor  ignores the
>transmission line effects. Treating it as a transmission line uses a
>LUMPED driving voltage. Either model ignores the effects of the other
>phenomenon. I am afraid that the TC secondary will have to be treated
>as an integrated equation combining both  transmission line segments
>and decreasingly coupled single turn inductor segments.
        I agree.  There is a simple solution, however.  Build a magnifier.
Then you can use helical resonator theory (at least until the spark breaks out).

>
>Unfortunately, until one of us begs, buys, or borrows a HV RF voltage
>probe to measure the TC output voltage, We may never know:( 
> Or until we can excite the interest of a good modeling mathematician,
>hey Dr. R.   ;)
        The interesting part of all of this to me is the influence the
toroid has on the proximity effects near the top of the coil.  This may be
due to a change in the voltage standing wave along the secondary, resulting
in a more linear voltage response, with reduced turn to turn proximity
effects due to the similarity of voltage between adjacent turns.  As one
experiments with toroids of different sizes and positions above the top turn
of the secondary, there is an optimal position whereby the secondary coil Q
is maximized.  This has been demonstrated by Malcolm in his experiments last
year, and by Richard Hull on one of his video tapes.  I have also observed
this with my system, (but have too much metal nearby to get a quantitative
measurement).
        Anyone have a good method for measuring high RF voltages?
Regards,
Mark S. Rzeszotarski, Ph.D.