This schematic diagram represents the Tesla coil distilled to its essence. A cursory examination will reveal that it consists of a spark-excited LC tank circuit magnetically coupled to an un-terminated resonator. L1 and L2 form a simple resonant, air-core transformer. High voltage current from any convenient supply is applied in parallel with the spark gap SG1. When the charge on capacitor C1 reaches the breakdown potential of SG1, the spark gap arcs violently, switching immense current through L1 at astonishing speed. (Spark gaps are still among the fastest electrical switches known to science).
With an electric arc established across SG1, the current surges rapidly between L1 and C1 at a fixed frequency determined by their respective values. The resulting intense magnetic field surrounding L1 couples some of the tank circuit energy to L2, exciting it to oscillation as well. The powerful oscillations developed in L2 cause very high potentials to develop at the un-terminated end, resulting in the formation of lightning-like electrical discharges into the air as well as to any nearby objects. At some point, power transfer to L2 steals so much energy from the tank circuit that the arc across SG1 can no longer be sustained. The extinguishing of the arc is called quenching, and marks the end of a charge/discharge cycle. This cycle can be a single pulse, or a series of charge/discharge cycles up to as many as several hundred per second, depending on the current available from the high voltage supply. If the train of charge/discharge cycles is fast enough, the Tesla coil appears to the eye to produce a steady output of electrical discharge, although it is actually a pulsed device.