Re: Lumped vs. Helical Resonator
I was interested in Mark's detailed note on this subject.
There is model of the resonator that I think is remarkably accurate.
Clamp a 2 foot steel rule in a bench vise at one end so that the top
section is free. Distributed capacitance is represented by the mass
and inductance by the "springiness" (for want of a better term).
In a 2-coil system, you can get a feel for what the primary is
trying to do by waggling the ruler to 1/4 wave resonance at different
heights. It is hard to move at the bottom (low k) and matches better
to a stiff push (high Cp) whereas moving it further up (higher k) is
easy, but the primary needs to be able to swing much greater distances
(small cap). Damping the movement at the top of the ruler (sparks)
gives a feel for the degree of match required of the primary. You can
see where the voltage rises most (bend/unit length) and see why with
no terminal, the top inductance has little effect. You can also add a
terminal at the top (lump of mass) and note the amount of push needed
to move it. Note also the inductance near the top begins to be
effective (ruler bends more near the top). Also, you can see why the
Q rises as you add a terminal (up to a point) - you get more inertia.
Using the ruler as an extra coil effectively means waggling the
bench (resonating against ground a la Tesla).
On a related topic, I see no-one's risen to the challenge of
picking the best primary for my small system. I'll give it another
day or so. I should have stated that the transformer is 12kV 60mA
and also that I got nice 3 foot arcs with the configuration I chose
from the measurements (easily the best) and simple 2-gap system