The principle of operation of a Jacob’s ladder is straightforward: A plasma arc is hot and prefers to take paths of least resistance. The hot air made by the spark is more conductive than ordinary air, and so as it rises away from the plasma, it creates a moving conductive channel. This phenomenon is responsible for the “arc” shape of high voltage sparks between terminals, as the spark starts out straight and then bends upwards due to air heating.
If two long, parallel rails are used as electrodes, then the arc will actually travel up them. Generally the rails form a sharp “V” shape, as the rising hot air allows longer arcs to be drawn:
In my Jacob’s ladder, I used a high-wattage Neon Sign Transformer(NST) as a voltage source. Much to the dismay of everyone else using my power gird, the NST takes 120V, 3A wall power and transforms it into a 12,000 V, .03A output signal. Note that conservation of energy holds true– Power = Voltage x Current results in roughly 360W for either side of the transformer. But the high voltage end is much more effective at breaking down air (at the cost of amperage, which affects brightness and loudness of a spark), and so it readily ionizes the air between the rails to start the arc. It is extremely important to have straight, rigid rails– I used two cheap, non-anodized aluminum bars I found at Home Depot (anodization makes the surface of the bars resistive, which is undesirable here).
If our atmosphere consisted of other gases, it actually would be possible to make a Jacob’s Ladder using wall power. All materials are electrical insulators at very low voltages, but once a certain threshold voltage is reached, they break down and begin to conduct. We see this occurring in the air every time lightning strikes– the voltage in the cloud finally becomes high enough to turn the air into a conductor. Copper, due to the relative freedom of its electrons to move about, will gladly allow even modest voltages to create currents, and so we call it a conductor because at most working voltages it acts as such.
Generally speaking, we refer to gases in their conducting states (such as the current-carrying air between the rails of the Jacob’s Ladder) as plasma. The tendency of an insulator to conduct at high enough voltages is quantified by its dielectric constant (k), which determines how readily it breaks down compared to a pure vacuum (which has k = 1). For example, paper has a dielectric constant of 4, which means that making current travel through paper requires roughly 4 times the voltage it would take to make current travel through the same thickness of vacuum. The process by which a dielectric(a word synonymous with “insulator”) turns into a conductor is dielectric breakdown. Lightning and the spark of the Jacob’s Ladder are both cases of dielectric breakdown in air.
Once the arc goes out, the rails need once again to build up enough voltage to bridge the gap at the bottom of the ladder and start a new arc—but once this arc starts, it is easy to maintain. In high-energy circuits, dielectric breakdown usually occurs in solid materials, like glass or plastic, where the heat of the spark is usually sufficient to burn a permanent path through the dielectric. This means that, even once a spark goes out, current is stil able to pass through the path of the original spark, causing damage to the circuit. If this effect occurred in air, then thunderstorms would tend to generate single lightning bolts, which would last for hours while the storm transferred all its excess charge to the ground. Instead, when a bolt of lightning forms, the air molecules it ionizes are quickly replaced by other molecules that drift into their places, preventing the arc from carving a permanent path to the ground and thus limiting the life of the lightning bolt.