I will not describe in detail what it is Jacob's ladder. The images and
video below can describe it much better :). It consists of two high voltage electrodes, on which an arc gradually
climbs from the bottom up, then goes out and is immediately re-ignited at the bottom. It is still
repeated with a frequency of about 0.2 - 10 Hz. In my case, the electrodes
have distance between each other 0.5 - 1 cm at the bottom and 3-4 cm at the top. Their height is 14 cm. Their shape is
seen at the pictures.
This device must have a high voltage power supply powerful enough (10kV and at least hundreds of watts of power). The simplest option is to use a neon sign transformer. However, if none is available, a switching HV power supply can be used as a source of high voltage. It's a simple Half Bridge, the same as in induction heating. The output is connected to two HV transformers from TVs (originally designed for use with multiplier), which give each about 5 - 6kV, so 10 - 12kV in series. PRIMARIES are rewound and each have about 50 turns. (Reducing number of turns can increase the output voltage, but there is the risk of secondary breakdown.) Protective bulb in my case 100W + 200W in parallel. Transistors have small heatsink from ATX supply. Potentiometer is set to operating frequency about 18 - 30 kHz (set to the best effect).