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I think that this is enough muddling for tonight.
There is never enough muddling for my taste. :^)

Lumped circuit models always work for a fixed frequency, but 
they don't work over a large frequency range.

These large secondaries have all kinds of distributed capacitance
between turns and layers and very complicated mutual inductance
between turns and layers of the windings.

Another distributed coil example: your Tesla secondary. Can only
be treated as a lumped circuit if you stay in some small frequency

Very interesting though, Jim.
I did not see any self resonance in any of my measurments. Perhaps
the core or some other effect kills the Q of the bare coil...

-Ed Harris