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What it takes to get big sparks?

I have been contemplating the whole issue of what factors most influence
the length and size of the sparks from a tesla coil and have some ideas
which I'm going to throw out for discussion.

Starting with some assumptions:

1) The actual spark develops very quickly if there is a suitable low
impedance source. The leader moves very very fast, essentially running its
entire length in a microsecond or thereabouts.

2) The charge for the spark comes almost exclusively from the top load. The
inductive impedance of the secondary coil is so high (when considered in a
time frame of a microsecond) that any sort of stored energy in the coil
isn't going to get there in time (except of course, for the current already
flowing from the inductor into the capacitor as the top load voltage is
rising).

3) As the spark develops, it is essentially a capacitor that has increasing
capacitance (because it is getting bigger) and is charging at the same
time, as well as heating the air up.  This means that current is flowing
through this "spark capacitor".

I asked myself, where is the other connection of this capacitor?

I think it is the ground (and the surroundings, etc.).

And, because we are talking fast time scales here (microseconds, again),
the inductance of any sort of wire connection from the bottom of the coil
to the "ground" means that the coil can't really supply any appreciable
current while the spark is forming.

So then, what we have is an inductor (the secondary) which charges a
capacitor (the top load working against the ground). That capacitor then
breaks down (i.e. a leader forms) and discharges into the spark. The actual
spark formation is almost independent of the secondary inductor because the
current required to develop the spark is much higher than that coming from
the inductor to the capacitor.

This is why big top loads help make big sparks. And it is also why good
grounds make big sparks.  Interestingly, though, the nature of the ground
is important. Of course, it has to be low impedance at the coil's basic
operating frequency (otherwise, the secondary can't charge the top
load/ground capacitor fast enough). Given the high inductance of most
secondaries (milliHenries) compared to the inductance of even thin wires
that are several feet long (microhenries), from this standpoint, it doesn't
matter how you connect the base of the coil to the "ground".

However, once that "capacitor" is charged, and it starts to discharge (into
the spark), you want the capacitor to be low inductance. The top load is
pretty low inductance (it is physically small) and resistance (it is
metal), but what about that ground? How low impedance is that ground?
Remember, at this time, what we are really looking at is one capacitor
charging another through a resistance and inductance.

  So, I think what you want is a suitably conductive sheet to operate your
coil on top of. It doesn't have to be solid, but it does have to have low
resistance per square, and, also important, low inductance per square (i.e.
I don't think one long wire running around would really do it). It can be
insulated because it is part of a capacitor with mostly air dielectric, and
adding a thin layer of anything won't make any difference. It should be big
enough that it can supply enough charge to keep the spark going... I would
suggest that it should be big enough so that increasing its size by some
increment doesn't increase the capacitance to the top load by more than
5-10%. This probably isn't all that big.  For a big sheet which has low
inductance, the propagation velocity of the charge is going to be a
significant fraction of c (1 ft/nSec), and assuming you want your capacitor
to be able to discharge in something on the order of 10-100 nSec, making it
bigger than 20-30 ft isn't going to buy you much.

Thinking about how the field from the top load is distributed, in fact, I'd
hazard a guess that you should work against a disk of radius equal to the
height of the top load above the disk, or maybe, twice that.

Comments, thoughts, etc.....