The Arc starts from the narrowest point and ionizes and heats the air causing it to rise. This ionized air forms the path of least resistance. As it risees the arc follows along. When the ionized air reaches the top of the electrodes and continues to rise, the arc becomes too long for the voltage and breaks up . After the acrc breaks up at the top , the electrode voltage rises again. Another arcs forms at the narrowest point.

The video above describes how to make such a device using an electronic circuit known as Mazzilli ZVS flyback driver. You can download schematic diagram at the link below. It consists of two or four power Mosfet transistors (e.g.IRF530, IRFP240,irfz44,P65NF06 or similar) and several additional components that form a relaxation oscillator called Royer Oscillator , named after its inventor. The primary contains five windings of insulated wire with a diameter of 2.5mm^2 wound on the ferrite core of a flyback transformer from an old CRT monitor or TV.

The flyback trafo secondary is connected  with the rods bent so one point near the bottom of the wires is very close (1/4" to 1/2"). The arc will strike at the closest part, then the heat will make it rise.
   The device is powered by 12V Power Supply from old Server Computer.The power supply must provide a minimum 10 Ampers of current.

     Please note: A traveling-arc device is very dangerous. The spark can burn through paper and plastic and start fires. Contact with the high-voltage conductors can be lethal even if the high voltage power supply originates from a battery.