Jim Kelley wrote:
Presumably there is a lower limit to the number of turns the coil would
have to have, or an upper limit to the pitch angle, in order to behave
as described - a helical sheath. Tesla coils usually have at least a
few hundred turns wound closely together, and often operate at
wavelengths considerably longer that 75 meters. One could easily argue
that 30 turns do not a Tesla coil make, in which case Eq. 32 would not
apply.

Dr. Corum says that it behaves as a helical sheath when
it is electrically longer than 15 degrees (0.04WL). The
frequency doesn't matter - just the electrical length.
Of course, it takes more turns at a lower frequency
since the reactance is proportional to frequency. Eq.
32 is not concerned with the number of turns, just that
the coil is electrically longer than 15 degrees and is
therefore outside the range for which the lumped-circuit
model is valid.

Note that the title of the paper is: "RF Coils,
Helical Resonators and Voltage Magnification
by Coherent Spatial Modes". "Tesla coil" does not
even appear in the title.

A Tesla coil can be 1/4WL self-resonant all by itself.
Thus, 30 turns could easily be a Tesla coil over a
certain range of HF frequencies.

Some Tesla coils have a top hat and are operated below
their 1/4WL self-resonant frequency.

In Dr. Corum's paper, take a look at "Figure 2, A
capacitively tuned distributed resonator" and tell
us how it differs from a 75m mobile antenna with a
top hat.

The 1/4WL self-resonant frequency for a 75m Texas
Bugcatcher coil has been measured at ~6.5 MHz where
it is known to be electrically 90 degrees long. Why
does anyone have a problem with it being electrically
40 degrees long on 4 MHz?

In "Fields and Waves ...", by Ramo and Whinnery, the
analysis of a helical sheath assumes an infinitely
long helical sheath for the purpose of eliminating
reflections. Does that ring a bell? Hint: The current
on a standing-wave antenna cannot be used to measure
phase shift or delay. Yet, that is exactly what w8ji
and w7el tried to do.

I once turned my 75m mobile Texas Bugcatcher system
into a Tesla coil. I had a latch to which I could
connect the top ball of the antenna when I needed
to lean it over for more clearence. I was at a hamfest
at night and had forgotten I had the antenna latched
down. I started transmitting and my friend told me
I was drawing a two-inch arc from the tip of my antenna
to the pickup body. It was indeed "Voltage Magnification
by Coherent Spatial Modes".

http://www.ttr.com/TELSIKS2001-MASTER-1.pdf
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com