The only safe way to produce 12Kv DC is with a switch mode power supply where a high frequency oscillator is stepped up to the required voltage in a Ferrite cored transformer, because of the high frequency, the transformer is a fraction of the physical size of one designed for 50 or 60Hz. The output is rectified and filtered. Whilst such power supplies can be designed for high currents, for 12Kv the current available would be milliamps, plenty for the purpose described.
Cathode Ray tube TV used a somewhat similar system by using the high voltage produced by the flyback pulse, that is at the end of each line, the spot had to "flyback"to the start of the next line and this back EMF was stepped up in the line output transformer which operated at 15,625Hz on our system and 15,750 on the American NTSC system.
These days we find small switch mode power supplies in all manner of everyday items from battery/mains shavers, to downlight and fluorescent fittings to flat screen TV's. They are far cheaper to produce than linear power supplies containing a wound transformer operating at mains frequency. Even though toroidal transformers are commonly used in linear supplies and they are wound on ingenious machines, they are far more costly than circuit boards that are produced and fully populated so fast that it makes one feel dizzy watching!
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