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Resonant Frequency??

Hi All

We are trying to make a Tesla coil using up to 4 - 15kV 30mA neon sign
transformers.  We were planning on using an archimedes spiral with about 20
turns, with a spacing of 3/8" using 3/16" refrigeration copper tubing.  This
would give an inductance value of 152.26 uH.

For 120 mA power supply at 15kV, using a 25.46 nF reso-cap, the frequency
would be 80827.8 Hz.
Is this way to low?

For our secondary, we were planning on using a 8" diamater piece of PVC pipe
with 1600 turns of 24AWG The secondary inductance is 93944.95 uH and the
self-capacitance is 15.69 pF.  WIth a toroid that is about 25 pF, the
resonant frequency is around about 81398.91 Hz.  We would match these by
adjusting toroid capacitance and or primary tap.

Is there anything majorly wrong with this?

We also don't quite understand how the primary circuit works.  How does the
voltage build up accross the capacitor to jump the spark gap and oscillate
with the primary inductor?
Also, will a given cap value resonate with any value inductor only changing
the frequency?

Thanks in advance.

Alan Williams