http://www.bugman123.com/Tesla/Tesla.html

A Tesla coil is a high voltage transformer with an air core. The primary and secondary coils each have inductance and capacitance so they function as an LC circuit with its own resonant frequency. The primary capacitance comes from a capacitor that discharges across the spark gap when the voltage is high enough. The secondary capacitance comes from the coil itself and the sphere or toroid at the top. When both circuits have the same resonance frequency, the oscillations efficiently contribute to the induced voltage.

This Tesla coil was designed to run on a 900 Watt neon transformer. Unfortunately, all I had was a 240 Watt neon transformer, which was still enough to generate 175,000 Volts with streamers up to 18" long. It cost about $50 to build (not including the transformer).