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Attn: Rich, Bert & Terry- Growing large arcs?

I remember numerous posts about the physics of streamer generation and
formation recently and I was hoping for one (or all) of you experts to
comment on the following.
I believe plasma physics is more challenging than rocket science. So don't
feel I expect you to write a book, just give me a specific case in the
context of your favorite Tesla oil! And if my reasoning process is flawed,
please comment!

Purpose: Grow a large (+) spark, and define relation between:

* Breakout E-field intensity - Electrode radius & initiating voltage
* Electrode Voltage vs Current vs. Arc length vs. Arc growth velocity
* Arc dia. (result of electrode geometry/curvature radius)
Lets assume 10cm radius, what arc dia from a hot spot?
* Arc power dissapation/unit length
The rate energy is dissipated per length of arc. Divided into initiating
energy and sustaining power
* Arc resistance, capacitance and inductance increase/unit length
I would assume distributed L and C would be calculated as for a conductor.
But I need to know the arc diameter, and 'fuzzyness' estimate?
* Arc prop velocity
Lets say for 2 cases.
1. A fixed charge source, like a large capacitive torroid
2. A current source, for a curve that show current into an electrode (AC or
DC, and with frequency effects) vs. arc growth velocity

Lets say a large transformer is connected to a large bridge rectifier and
filter cap, and generates a large ionizing voltage, for the purpose of
generating (what else?) a large spark. Lets assume the initiating electrode
is positive, for minimum required energy.

My purpose is, to understand why no one has put a thyratron bridge rectifier
on the output of their TC, to generate enormous sparks. Or have they? A
professor once described a giant spark, over 100' long. It was confined to a
straight channel with E-field shaping electrodes, and required an immense
trasformer to continously source current to grow the arc. He said the arc
grew as long as current was applied (at ever increasing potential).

So how much current? What initiating voltage? What electrode diameter? What
arc velocity and diameter? Whats the L, R, & C of the arc per distance &
time? No doubt you've read of that experiment?