Tesla List wrote:

> The current problem is that the professor mentoring my project DOESN'T
> BELIEVE my new TC will require 20 kW of power!

I would not like this too... Seems as something hugely inefficient.
But if you are using a primary capacitor of 0.1 uF and 800 BPS,
charged to 22360 Volts, this is really the power that you need
P=0.5*C*Vin^2*f=0.5*0.1e-6*22360^2*800=20000 Watts...
Of REAL power, losses not included. But this you know.

> - how to show relationship between coil size and needed power (to get some
> decent performance)?

You must have enough voltage for breakout (I calculate about 620 kV
in your case, what is probably enough), and after this any increase
in break rate results in more impressive performance. Other more
experienced "coilers" may give you better advice on this. 

Your problems appears to be the rather large capacitances, what require
a large amount of energy per break (0.5*C*V^2=25 J), and the
high break rate. Note that a single spark from that large top terminal
fully charged is well within the fatal range (>10 J).

> - how to show were the power is dissipated and that it's not simply
> reactive?

At each break, all the energy stored in the primary capacitor is
dissipated, as sparks/streamers in the secondary, in the primary
spark gap, in resistive losses, irradiated, etc. Nothing returns
to the power supply. You will have reactive power too, added to
the real 20 KW, depending on how you build the power supply.

Antonio Carlos M. de Queiroz