The high voltage high energy capacitors store the charge until the voltage is high enough to break down the air in a high voltage spark gap. As the spark gap breaks down it conducts the high voltage charge directly in the high voltage inductor coil which forms the primary circuit of the high voltage Tesla coils. The high voltage charges rush back and forth between the high voltage capacitor and the high voltage inductor coil. The speed of this oscillation depends on the physical geometry of the high voltage capacitor and high voltage inductor coil. Typical high frequency operating values for a high voltage Tesla coil resonance transformer are in the range of 20 KHZ through 1 MHZ. Most medium size demonstration Tesla coil resonance transformers operate in the 100 KHZ through 500 KHZ range.
    Nikola Tesla, using his newly developed high voltage Tesla coil resonance transformers, delivered an astounding lecture before the American Institute of Electrical Engineers on May 16, 1888. Tesla, using his special high frequency high voltage Tesla coil resonance transformers impressed both the electrical engineers in attendance and also many Wall street investors who now wanted to invest in Tesla's high voltage power distribution systems.
    It is not clear exactly when the Tesla coil resonance transformer was actually developed by Nikola Tesla because he did not publish on a regular basis, but it is though the Tesla coil resonance transformers were developed around 1880. Tesla patented the idea of high voltage high frequency tuned electrical circuits a few years later. Tesla's friend, George Westinghouse, purchased many of Tesla's patent rights and began manufacturing these high voltage polyphase electrical power distribution systems.
    Tesla noted his large Tesla coil resonance transformers were producing high voltage high energy electrical charge in excess of 4,000,000 Volts, These huge lightning like sparks were rapidly becoming a fire hazard and Tesla decided to move his large Tesla coil resonance transformers to Colorado Springs, Colorado, where he would have more room for his high voltage high frequency experiments.
    Nikola Tesla arrived at Colorado Springs, Colorado, on May 18, 1899, and immediately began building a massive high voltage laboratory with an extremely large Tesla coil resonance transformer measuring over 52 feet in diameter. A large fence surrounded the Tesla coil with the sign, "Keep Out - Great Danger".
    Tesla constructed many Tesla coil resonance transformers in his lab and discovered the concept of tuned electrical circuits. A separate and smaller Tesla coil resonance transformer that is tuned to the same high frequency as the large high voltage Tesla coil resonance transformer will actually "receive" electrical energy from the massive Tesla coil which acts as a "transmitter" of wireless electrical energy. Tesla was later nominated for but declined the Nobel Prize in Physics for his experiments with tuned circuits using his large high voltage high frequency Tesla coil resonance transformers. Nikola Tesla first logged these observations into his diary on July 3, 1899. This information was later used to confirm his patent for radio which he received posthumously in 1946, 3 years after his death.
    Tesla coils / resonance transformers linger on today as the high voltage transformers found in most computer CRT's. Tesla coils are used by dental surgeons to painlessly cut gum tissue in their treatment of gum disease. Hospital surgeons use modified high frequency Tesla coil generators to cauterize blood vessels during surgery thus preventing excessive bleeding. Every large television set has a Tesla coil resonance transformer called a flyback transformer which provides the high voltage necessary to operate the picture tube.

This information taken mostly from: Resonance Research Corporation which has a great public museum called the Theater-Of-Science" which is worth the visit.
    Also, there are great pictures of Tesla and his work and his labortories at: The TWP Nikola Tesla Photo Archive. Currently, they have a great mission to preserve and restore Tesla's original Wardenclyffe Project in New York. Please check them out and help if you can.

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