It takes a threshold amount of current in a Tesla coil arc to be 'suitably' bright. This may involve subtleties such as the depth of ionization of atmospheric gas molecules. When lightening strikes, the electromotive force (emf or voltage) has become high enough to rip valence electrons out of the nitrogen & oxygen gas molecules in the atmosphere from 'there to there' so to speak. These electrons constitute current flow. A neutral atom of nitrogen has 7 protons (+charge) in the nucleus and 7 electrons (-charge) orbiting the nucleus (oxygen atom has +8 and -8). But gases are diatomic meaning molecules of gas have two atoms each, N2, O2 etc. So a neutral molecule of nitrogen has 14 electrons and protrons, neutral oxygen has 16 protrons and electrons.
When one or more electrons are ripped from a molecule it has an imbalance in (±) charges and therefore becomes a 4th state of matter - plasma. Plasma, ionized molecules plus free electrons, in an electric field will accelerate in opposite directions. Since a nitrogen ion is very much heavier (~51,200 times) than an electron, the electrons do most of the moving. The free electron will accelerate to high speed before crashing into another molecule of gas and knocking out more electrons and maybe be captured by that molecule. When an electron is captured by an ion it gives up accumulated kinetic energy which energy is seen as Tesla Coil arc light.
Power is the product of voltage times current. The TC builders goal is to produce a 'long impressive looking' arc. Since a bright arc requires a certain minimum current, the input power required to make TC arcs is more or less proportional to the desired arc length for given coil efficiency. The power input required may be about 35 watts per inch of desired arc length. Also see chart of spark length vs voltage; the correlation is not linear. Another nice feature about Variacs, they are robust and have high output watts/Lb. I run a 3 Amp variac at 5 Amp for a minute at a time with no harm to the above SS Tesla Coil.
There are many possible methods to power a solid state Tesla Coil. A Simple one that works fairly well is to employ a variac. A variac is a transformer with but a single winding. The winding is wrapped around a toroidal shaped core and the insulation is removed (by the Mfr) on one end of the torus cylinder. The winding is usually tapped at about 86% of the full winding. A shaft, coaxial to the axis of the torus, is fitted with a radial arm and carbon brush. The brush wipes the bare coil winding as the shaft is turned. When primary power (120 vac, 60 Hz) is applied across the 86% tap and the ground end of the variac, the full coil will develop about 140 vac (step up). The voltage on the wiper will range from zero to 140 vac as the shaft makes a full excursion. Shorting the output of a powered up Variac transformer will invoke the proverbial smoke test! (unlike a current limited NST). Variacs are made in 120 to 240 vac input (and higher, even 3-Phase devices can be had). 120 vac is the input of choice for my money to keep from having to use very high voltage switching transistors (Mosfets or IGBTs), more about transistors next.
Solid state power transistors have limitations on how fast they can turn ON and OFF maybe 20 to 200 nS). The solid state Tesla primary driver therefore will have a maximum operating frequency beyond which yields diminishing returns. The transistors operate in what is called 'switching mode'. The advantage in switching is that the transistors are either 'hard-ON=low_power_dissipation' or 'hard-OFF=zero_power_dissipation'. When hard-ON, they dissipate minimum power because high forward current is associated with very low forward voltage drop across the device. Huge amounts of power can be controlled in 'switch mode'. The 'be careful' news is that during both turn-ON and turn-OFF the power spikes to a very high value for a period related to the transistor turn-ON and turn-OFF time. During this period a power spike developed by 1/2 the peak current times 1/2 the peak voltage occurs. These 'turn-ON' and turn-OFF' spikes occur once each cycle. As the switch-mode operating frequency is pushed up, a higher and higher portion of the cycle time is spent in the very high power dissipation ON-OFF regime. Selection of transistor characteristics becomes important: for speed, for current capacity, and for voltage withstand when turned off.
In this mode two transistors work like a child's 'see-saw' with each child contributing to his half of the cycle. The 1st ½ cycle is handled by one transistor and the 2ND half by the other transistor. The primary is wound as a continuous coil with a center tap in the middle. The center tap is excited with (variac controlled, rectified) dc voltage. The ends of the coil are alternatively grounded by the two transistors. In this way current is made to alternately traverse the coil producing a north then south magnetic polarity at some frequency (secondary resonant frequency).
The TC secondary is a single layer coil wound on an insulating cylindrical form. The coil can be wound to within 1/2" to 3/4" inch of the end to permit mounting end baffles for structurally support; Use nylon screws. The coil should be close wound with formex or formvar insulated magnet wire. I spray the finished coil with glossy polyurethane (available in aerosol cans). Spinning the coil in a lathe or coil machine until the polyurethane gets tacky is helpful preventing 'runs'. Wire from B&S-23 to B&S-30 gage works.
Secondary coil resonant frequency will be affected coil turns, coil diameter, and winding length. Coil resonance from 60-90 kHz is functional. Included in next paragraph is an Equation for inductance from Inductance Calculations P-153 by Frederick W. Grover ISBN: 0-87664-557-0. Grover has a variable(r)=(diam/len) from a lookup table. I generated an algorithm that closely approximates the (F) value that is based on r=(D/L). This is need to complete the inductance computation. Grover uses a lookup chart for (F) given (r). Design the secondary coil to resonate at 60 to 90 KHz max with the chosen HV terminal capacitance.
Inductance: (uH)=0.00254*F*D*N2 Where: (F) is Table Lookup or algorithm; (D) is the mean coil winding diameter (IN); and N is the number of turns (usually 800-3000). My (F) algorithm is: (F)=9.785*(D/L)*(1-(D/L)).33 for use in the inductance Equation. The coil is wound with ~3896 turns of 29 gage (0.0114",0.0128" insulated) wire. The wound length is 50 inches (5093 ft of wire) that weighs 2.01 Lbs. The coil resistance at ambient temperature is about 399 ohms and resonates at 84 kHz. The secondary self-capacitance is about 12.7 pF and the HV terminal adds another 6 pF. The inductance computes to 181,700 uH. See TC_Coil_Equations for sizing of various TC components. The lead at the bottom end of the coil needs to be brought out to connect to ground; a suitably long ¼-20 screw through the bottom baffle centerline can be used to support the secondary coil and ground the winding. A wing-nut works nice; permits easy removal of the secondary for safe transport.
The primary is wound as a continuous coil with a center tap in the middle. The center tap is excited with (variac controlled) dc voltage. The ends of the coil are alternatively grounded by the two transistors. The primary coil shape is best as cylindrical. The physical size of the P-Coil and number of turns determines inductance. One concern on P-coil inductance is that the inductive reactance be high enough to not develop coil current when operating without the secondary installed. There are no resonant frequency concerns for the primary coil of a solid state Tesla coil.