Tom,
May I point out that a Tesla coil is an "antenna" that does not
conform
to Maxwells laws with respect to the adherance to the LC ratio.
The LC ratio is out of balance such that the capacitor is not
of the correct size to store and then return the imposed energy from
the inductive heavy coil which is visually seen as resulting in a
spark.
Regards
Art

Huh...

tesla coils follow all of Maxwells equations quite nicely. Paul
Nicholson did some very nice analysis on this a few years back,
published at a link previously posted.

They're two coupled LC resonant circuits, with the coupling adjusted to
around k=0.2. There are higher order systems with 3 or more resonators,
as well (called Magnifiers in the TC world)

The challenge in spark making is choosing appropriate operating
parameters (coupling, radius of curvature, topload capacitance, etc.) to
optimally promote spark growth.