A classic Tesla coil consists of two inductive-capacitive (LC) oscillators, loosely coupled to one another. An LC oscillator has two main components, an inductor (which has inductance, L measured in Henrys) and a capacitor (with capacitance C measured in Farads). An inductor converts an electrical current (symbol I, measured in Amperes) into a magnetic field (symbol B, measured in Tesla [yes, named in honor of Nikola Tesla]), or a magnetic field into a current. Inductors are formed from electrical conductors wound into coils. Capacitors consist of two or more conductors separated by an insulator. A capacitor converts current into an electric field (symbol V, measured in Volts) or an electric field into current. Both magnetic fields and electric fields are forms of stored energy (symbol U, measured in Joules). When a charged capacitor (U=CV2/2) is connected to an inductor an electric current will flow from the capacitor through the inductor creating a magnetic field (U=LI2/2). When the electric field in the capacitor is exhausted the current stops and the magnetic field collapses. As the magnetic field collapses, it induces a current to flow in the inductor in the opposite direction to the original current. This new current charges the capacitor, creating a new electric field, equal but opposite to the original field. As long as the inductor and capacitor are connected the energy in the system will oscillate between the magnetic field and the electric field as the current constantly reverses. The rate (symbol [Greek nu], cycles per second or Hertz) at which the system oscillates is given by (the square root of 1/LC)/2pi. One full cycle of oscillation is shown in the drawing below. In the real world the oscillation will eventually damp out due to resistive losses in the conductors (the energy will be dissipated as heat).In a Tesla coil, the two inductors share the same axis and are located close to one another. In this manner the magnetic field produced by one inductor can generate a current in the other. The schematic below shows the basic components of a Tesla coil. The primary oscillator consists of a flat spiral inductor with only a few turns, a capacitor, a voltage source to charge the capacitor and a switch to connect the capacitor to the inductor. The secondary oscillator contains a large, tightly wound inductor with many turns and a capacitor formed by the earth on one end (the base) and an output terminal (usually a sphere or toroid) on the other.
While the switch is open, a low current (limited by the source) flows through the primary inductor, charging the capacitor. When the switch is closed a much higher current flows from the capacitor through the primary inductor. The resulting magnetic field induces a corresponding current in the secondary. Because the secondary contains many more turns than the primary a very high electric field is established in the secondary capacitor. The output of a Tesla coil is maximized when two conditions are met. First, both the primary and secondary must oscillate at the same frequency. And secondly, the total length of conductor in the secondary must be equal to one quarter of the oscillator's wave length. Wave length (Greek lambda, in meters) is equal to the speed of light (300,000,000 meters per second) divided by the frequency of the oscillator.
Tesla coils differ in the type of switch used, the physical size of the components and the input voltage. Automotive ignition coils typically have a twelve volt input and are switched by a distributor, with moving contacts. They provide an output of 15-20,000 volts. Television fly-back transformers produce lower outputs but usually have 120 volt inputs and are switched by transistors or, in very old sets, vacuum tubes. The classic Tesla coil is switched by a spark gap. In this case, the primary circuit is known as a tank circuit. In its simplest form, the spark gap switch has two conductors separated by an air gap. When the electric field stored in the capacitor reaches a level sufficient to ionize the air within the gap a highly conductive plasma is formed, effectively closing the switch. Spark gap switched coils operate with inputs of about 5-20,000 volts and produce outputs of 100,000 to several million volts. For the spark gap to be effective, it must be able to open rapidly after the primary oscillation has damped out, in order that the capacitor may recharge. This is achieved by several methods, all of which amount to ways of cooling and dissipating the hot plasma formed during conduction. The simple gap can switch a few hundred watts of input power. Forced air cooling of the gap and, or using a number of gaps in series can increase power handling to several thousand watts. Higher power levels usually require a rotary gap, which mechanically moves gap electrodes rapidly into and out of conduction range. I should note here that even at input power levels of a thousand watts, the instantaneous power levels during gap firing can reach a million watts or more.