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New secondary

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

I have a new secondary 3" in diameter, 10 7/8" high, and wound with 440 turns
of 24 SWG enamelled copper wire.

Calculations (Wheeler s and Medhurst s) suggest self-resonance at circa

The max inductance of my present primary (flat spiral) has been calculated at
21.321368 uH which will require circa 3.017 nF to 2.217 nF to resonate between
600 kHz and 700 kHz but this will require more charging current from the HV
transformer (an ignition coil)or less frequent firing of the spark gap.
Alternatively a higher inductance primary will have to be used to match the
secondary using the existing capacitor (530pF) but is this wise considering
that inductors are usually more lossy than capacitors?

What is best -bigger cap or bigger primary? Or a compromise?