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High voltage boost converter help

I want to build a small machine for electrospinning various materials into fiber. For this I need the capability of reaching very high voltages and I need it to be variable. The voltage I will need to reach will be anywhere from 1kv-20kv.

I've got an HP 6268B DC power supply but it tops out at 40v DC. What would my options be for being able to step this voltage up into a range that would be usable for me?

I was thinking winding a transformer for this to just directly multiply the voltage but I'm not sure if this would be unsafe or if it may damage my power supply or something.
 
Referencing:

ElectroSpinz_Doris.jpg


DC High Voltage very low current . . . almost electrostatic rated .
I'm seeing the spin source cup at far left top corner and its feed over made by tubing and the central target slab of Teflon /or/ Nylon /or/ HDPE /or/ Delrin that would seem to have a central internal conductor that is making the other HV connection or ground connection,
Then the filament is electrostatically attracted out of the Taylor cone stylus orifice and continuously shoots across and impacts against the slab and then falls and accumulates as a pile at the base.
There is a like set up at the right side for a duplicate operating unit.
The small size of the power supplies cases suggests of a TV fly back type of supply . . . . with a mere 13 " tube sets transformer being able to best those voltage and current requirements.
Thus agreeing with the use of your power supply to feed power to a transistor driver of that flyback HV transformer.
Just GOOGLE up auto ignition coil drivers, but you will then be driving the primary winding of a TV flyback transformer.
Its secondary winding then puts out rectified 13,000 + VDC.

( OOPSIES . . . .just now noticed that Sir Bertus-es-es-es final HOT link gave just about a million different flyback driver circuit options. )

The rest of the story . . . . . repeat of . . .
https://en.wikipedia.org/wiki/Electrospinning

.
 
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Use a series resonant converter, I made one many years ago at 100KHz and 150KV DC at 1 A for a X-ray machine.
Unitrode now TI had a lovely chip to control it simple to use. Part No now forgotten sorry.
 

@bertus The high voltage side needs to be DC. Thank you all who have replied so far I'm reading about the flyback transformers right now.

I really should have added a bit more information in that original post, my bad.
 
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