Delighted to be of help in furthering anything I know about

Just had a lot of time to learn while being unable to work....now that I am able to work, i'll probably follow an inverse square law of knowledge haha
Here are some pointers, relating to the operation of these solid state devices.
Frequency, is partly dependent on the size of the tower, the gauge of wire used and the transistor. While spark gap operated, I would expect a solid state full scale version of Tesla's Wardenclyffe to have operated at only a few 10's of kHz, if indeed that high, there's always propagation to consider....which is rather odd, considering the speed of impulse transition through copper. But, there it is, tiny towers like my 'Walgreen' pills bottle design will run from 2MHz to 4MHz, a large Kacher may only run at 600KHz. That scaling extends into any such build and is of importance when considering step down methods for load devices. A slower operating speed doesn't necessarily correspond with more output per transistor firing, like a capacitive pump say. But, the larger Kacher's will use larger gauge wire and through which you can pass more operating current.
Lynxsteams's design is a Kacher/Tesla tower derivative and was why I mentioned using an AV plug and LED to see about wireless energy from the design. With your meters being affected Steve, it was a high pointer to wireless energy being present.
Every design has a 'sweet spot', a very highly defined exact point at which resonance is achieved, inductance is highest and the system runs optimally. It's got everything to do with tuning a radio - and there's no surprise there, it's Tesla's work and he invented radio.
Output ability scales with size of tower, but not linearly. We're taught that the bigger something is the more powerful it is. Car engines to rockets to even air conditioners. It doesn't really hold true with a Tesla tower/Kacher device. Everything is, instead, about capacitance and inductance interacting between the parts. When selecting what sort of Primary coil to use, capacitance between the coil strands will greatly affect the efficiency of that coil. The spacing is generally 1:2 or greater, with each turn separated by at least the width of the gauge of wire. Too large a gap between turns will again bring deficiency. As such, many designs can be used...including pyramidic shapes, flat pancake types and vertically spaced. Tesla used vertically spaced, outside of the main, thinner gauge Secondary. He designed conical towers later in life.
For a quick example...here I show a pyramidic Primary used, which encroaches on Walter Russell's work or Bashar coils. It's not a pretty Primary, but is capacitively correct and allows the levitated car headlights to be wirelessly powered - rather essential for any levitated object !
http://www.youtube.com/watch?v=nzNEUa4ZagwIt really is as simple to appreciate as a regular transformer - but they work so much differently, in regard to the final output from the often unconnected other end of the Secondary being able to emit energy.
One might picture a standard transformer with no connection to it's Secondary end. Imagine then, the transformer also had spacing between every turn of it's primary and no steel laminations on the outside. That picture is perhaps a way to view the Kacher design.
Ferrite might benefit a small tower, but capacitance changes of the Primary are highly preferable in anything over a few mm of Secondary width. Any tower design below approx 1/2" width will suffer capacitive issues and require ferrite to bring the design into the operating parameters of the transistor.
A good, workable, effective sizing, of gauge, diameter and more is what Woopy has built and used to great success over recent videos.
The use of an antenna on a collection section, is directly related to picking up the energy emitted, just like radio.
With reference to:
http://www.teslaradio.com/pages/wardenclyffe.htmHere are a few words, about the antenna function (which is often built as a 'topload' ring of aluminium tubing on top of conventional tall Tesla towers).
"the elevated capacitance in Colorado consisted of a relatively small sphere mounted on top of a tall and slender metal mast. In contrast, the Wardenclyffe elevated capacitance consisted of a large oblate spheroid mounted on top of an insulating wooden structure. In the 1914 patent the connection from the top of the extra coil to the elevated terminal is shown as a relatively short, large diameter metal cylinder. "
The function of the antenna is at least twofold. Without an antenna, breakout of the high voltage generated will manifest as the popular streamers of plasma, seen in Tesla tower demo videos. With a good tower design, voltages of around 6V are all that's needed for such plasma, when using high 30's gauge Secondary wire. Limiting that discharge is what the antenna is about. Instead, broadcast power is of much more use and the correct design of antenna section will greatly affect wireless range.
Here's a description from the above website, describing onlookers fascinations with the Wardenclyffe project:
"Local residents were aroused at night by startling lightning-like flashes, but no one knew exactly what the activities were at the plant because the whole operation was shrouded in secrecy.”
While spectacular, it is also reported that Tesla would disappear down under the tower on such occasions. You see, the design was failing to contain the energy - the lightning flashes were a hugely obvious sign that breakout was occurring and that severe attenuation of output power was manifesting in that escaping energy !