Old CRT monitor or TV is a great source of electronic components that can be used in DYI constructions. One of them is a flyback transformer that can provide 10-30kV output. The input voltage can be in a range from a couple of volts to over a dozen of volts, power consumption is a couple of watts. In my construction input voltage is 9V, power consumption is 5W.
A flyback transformer is driven by one or two transistors that should be also extracted from the same TV or monitor, those are high voltage transistors, that are hard to substitute and if bought separably can be expensive.
Waring! The device uses high voltage that can lead to injury or death when used inappropriately. Don't touch it when power is on.
Waring! The device produces small amount of UV rays and X rays, don't look into the arc for a long period of time.
Waring! The device produces an arc that can ignite surrounding objects, don't use it near to flammable substances.
The electronic circuit
When current flows though L2 (Q1 is opened) then flyback transformer collects energy (as the magnetic field). When current stops flows (Q2 is closed) magnetic energy transforms into electric energy. Q1 opens and closes periodically because it's base is driven by a generator made from R1, R2 and L1.