Half-cycles (total energy transfer)

The number of half cycles at the resonant frequency required to transfer all of the energy in the tank circuit to the secondary, not including losses. Because of voltage stress limitations causing a low coupling ratio (k), most Tesla coils will fall in a range of 4 to 8 half cycles to ideally transfer the total energy in the tank. Gap losses will affect the time of energy transfer. This is easy to understand when considering the total energy will partially dissipate into producing the desired spark output, partially dissipate in the sparkgap, and a few other losses elsewhere. Any energy dissipating in the gap is less energy available for spark output.

Reference the image below and note the half cycles between t0 > t1, t1 > t2, etc. You may have heard the terms 1st notch quenching, 2nd notch quenching, etc. These so called "notches" are seen in the primary and secondary voltage and current envelopes. Ideally, we want to quench by the 1st primary notch, trapping all the energy in the secondary, and then dissipating that energy as output sparks. In reality, some of the energy remains in the secondary following an output spark event. The energy then travels back across the gap to the tank circuit. If sufficient energy resides in the tank circuit, the gap will continue conducting and transfer all the energy back to the secondary. This process will repeat until there is insufficient energy to keep the gap conducting. Note that after each notch (primary or secondary), the amplitude decreases. This is due to energy being consumed in either sparks or other losses.