Transformerless TC-Excited Capacitive Transformer?

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Jolyon Vater Cox by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jolyon-at-vatercox.freeserve.co.uk>

Is it worthwhile to consider using the directly-coupled Transformerless TC 
to excite a Capacitive Transformer TC.
I am thinking of a system where the topload of the "transformerless" part 
of the circuit is replaced with the influence ring of the subsequent 
"capacitive transformer" section, as in diagram below.


                        (=====)
                           |
                           |
                           L3
  +----+---C1---+---L2---) L3 (
  |    |        |          L3
PSU    SG      L1         |
  |    |        |          |
  +----+--------+----------+

its lumped elements would be:-

----+---C1---+---L2---+---C3---+----+
     |        |        |        |    |
     SG       L1       C2      L3   C4
     |        |       |        |    |
----+--------+--------+--------+----+

The output of a transformerless TC would be tuned with an influence plane 
(C2) of adequate capacitance to give a moderate Av on the first section.

The presence of inductor L2 would raise the voltage on the ring above that 
which is possible with an ordinary capacitive transformer with C1 and L1 by 
the resonant effect.
The increased voltage would then be further boosted by the capacitive 
transformer section C2,C3,L3 and C4 to give a maximum voltage across L3 and 
the parasitic capacitance,C4.

What are the mathematics of the above circuit- are they basically the same 
as for the capacitively-coupled Magnifier?
would it be possible to connect a transformerless TC to a capacitive 
transformer using the normal formulae to get an enhanced hybrid of the two?