The start point would be zero voltage on the topload and a bang is
starting to ring up. One would integrate the RF current flowing into the
topload and compute the accumulated charge and voltage on the topload
using its capacitance (with no streamer loading present) and the time
step used in the program. The voltage would increase (in a sinusoidal
way) until the breakout voltage was reached. Any current flowing into
the topload after breakout occurs would result in excess charge going
into the streamer channel.
All sounds fine so far ;) Antonio's simulation code could easily do that.
If one could estimate the channel size needed to absorb the excess
charge perhaps using ambient temp and pressure, one could estimate the
added capacitance this presented to the topload.
Here's where it starts to get tricky. I thought of one possible simple way
to do it. In chemistry handbooks you can find ionization energies for
nitrogen and oxygen, ie so many kJ to ionise one mole of the stuff. Or
maybe (since you're dealing in charge) you could use the Faraday constant,
that says it takes 96500 (iirc) coulombs to singly ionise one mole of
anything. Also you know one mole of any gas is about 22 litres at STP or
whatever. So you could estimate what volume of gas gets ionized by a given
amount of charge, and make some assumptions about how it's distributed
(sphere, cone, fractal, whatever) to get a surface area and hence a
capacitance.
Possible problems with the Faraday constant approach- It doesn't take
impact ionisation into account (one loose electron- so one quantum of
charge- can ionize several atoms) nor account for the fact that current
might flow through previously ionized gas rather than creating fresh ions.
I don't know enough about the physics of atmospheric pressure discharges
to visualise how that would affect the result.