Tesla coil circuits were used commercially in spark-gap radio transmitters for wireless telegraphy until the 1920s,[1][4] and in medical equipment such as electrotherapy and violet ray devices.

A Tesla coil is a radio frequency oscillator that drives an air-core double-tuned resonant transformer to produce high voltages at low currents.

The primary coil (L1) consisting of a relatively few turns of heavy copper wire or tubing, is connected to a capacitor (C1) through the spark gap (SG).

[7][8] The secondary coil (L2) consists of many turns (hundreds to thousands) of fine wire on a hollow cylindrical form inside the primary.

The peculiar design of the coil is dictated by the need to achieve low resistive energy losses (high Q factor) at high frequencies,[9] which results in the largest secondary voltages: The output circuit can have two forms: The circuit operates in a rapidly repeating cycle in which the supply transformer (T) charges the primary capacitor (C1) up, which then discharges in a spark through the spark gap, creating a brief pulse of oscillating current in the primary circuit which excites a high oscillating voltage across the secondary:[10][12][15][19] This entire cycle takes place very rapidly, the oscillations dying out in a time of the order of a millisecond.

If the supply transformer has inadequate short-circuit inductance, radio frequency chokes are placed in its secondary leads to block the RF current.

Although the "toroid" increases the secondary capacitance, which tends to reduce the peak voltage, its main effect is that its large-diameter curved surface reduces the potential gradient (electric field) at the high-voltage terminal; it functions similarly to a corona ring, increasing the voltage threshold at which air discharges such as corona and brush discharges occur.

[37][36] Resonant circuits using Leyden jars were invented beginning in 1826 by Felix Savary, Joseph Henry, William Thomson, and Oliver Lodge.

[42][43] and first publicly demonstrated it May 20, 1891, in his lecture "Experiments with Alternate Currents of Very High Frequency and Their Application to Methods of Artificial Illumination" before the American Institute of Electrical Engineers at Columbia College, New York.

Earlier oil-insulated Tesla coils needed large and long insulators at their high-voltage terminals to prevent discharge in air.

Since the transmission line operates at relatively high RF voltages, it is typically made of 1" diameter metal tubing to reduce corona losses.

An electronic feedback circuit is usually used to adaptively synchronize the primary oscillator to the growing resonance in the secondary, and this is the only tuning consideration beyond the initial choice of a reasonable top-load.

A large Tesla coil of more modern design often operates at very high peak power levels, up to many megawatts (millions of watts, equivalent to thousands of horsepower).

Tuning can then be adjusted so as to achieve the longest streamers at a given power level, corresponding to a frequency match between the primary and secondary coil.

The resonant frequency of the secondary can be difficult to determine except by using a GDO or other experimental method, whereas the physical properties of the primary more closely represent lumped approximations of RF tank design.

Although the space charge regions around the toroid are invisible, they play a profound role in the appearance and location of Tesla coil discharges.

As the secondary coil's energy (and output voltage) continue to increase, larger pulses of displacement current further ionize and heat the air at the point of initial breakdown.

When the switch closes, energy is transferred from the primary LC circuit to the resonator where the voltage rings up over a short period of time up culminating in the electrical discharge.

In a spark gap Tesla coil, the primary-to-secondary energy transfer process happens repetitively at typical pulsing rates of 50–500 times per second, depending on the frequency of the input line voltage.

Today, although small Tesla coils are used as leak detectors in scientific high-vacuum systems[5] and igniters in arc welders,[48] their main use is entertainment and educational displays.

[49] Since they are simple enough for an amateur to make, Tesla coils are a popular student science fair project, and are homemade by a large worldwide community of hobbyists.

Scientists working with high-vacuum systems test for the presence of tiny pin holes in the apparatus (especially a newly blown piece of glassware) using high-voltage discharges produced by a small handheld Tesla coil.

In 2016, Rice University scientists used the field of a Tesla coil to remotely align tiny carbon nanotubes into a circuit, a process they dubbed "teslaphoresis".

Teachers and hobbyists demonstrating small Tesla coils often impress their audience by touching the high-voltage terminal or allowing the streamer arcs to pass through their body.

[65] Even a small Tesla coil produces many times the electrical energy necessary to stop the heart, if the frequency happens to be low enough to cause ventricular fibrillation.

Carefully controlled Tesla coil currents, applied directly to the skin by electrodes, were used in the early 20th century for deep body tissue heating in the medical field of longwave diathermy.

[59] Particularly if it passes through narrow structures such as blood vessels or joints it may raise the local tissue temperature to hyperthermic levels, "cooking" internal organs or causing other injuries.

[68] Even low power Tesla coils could exceed these limits, and it is generally impossible to determine the threshold current where bodily injury begins.

An erroneous explanation for the absence of electric shock that has persisted among Tesla coil hobbyists is that the high-frequency currents travel through the body close to the surface, and thus do not penetrate to vital organs or nerves, due to an electromagnetic phenomenon called skin effect.

[77][57][76] In the medical therapy called longwave diathermy, carefully controlled RF current of Tesla frequencies was used for decades for deep tissue warming, including heating internal organs such as the lungs.