How the coil works is quite simple :

-         The transformer loads the capacitor

-         As soon as the voltage at the sparkgap’s bounds is high enought, it is crossed by a spark; the circuit closes and the capacitor discharges trough the primary coil, thus creating a very high intensity power (more or less 150 A during the first oscillation period), oscillating at a very high frequency (more or less 300000Hz for our coil) as shown on the following graph.

This oscillation creates a powerful variable magnetic field that will induce a gigantic tension in the secondary coil.