Correct Oznog, A Tesla coil does not produce a static charge. My take on the question was what alot people want to do with a Van der Graaf generator, throw a big spark at a grounded object.
my bad
At the risk of offending, by which I in no way mean to do, why not ask for ideas on making a home made electro-static precipitator, or air cleaner.
We all could have got there in one step.
Thanks, just me 2 cents worth.
The voltage multiplier circuits used in these devices must be very carefully constructed, often you will need voltages in the range of 8 to 10 thousand volts to create a suitably effective grid charge. The capacitors are easily available, bu the rectifiers are going to be expensive.
try a search for voltage doublers or Villard cascade / multiplier , similar to what's used in TV flyback circuits for the CRT circuits.