When we wanted a 5kV capacitor tester we build a fixed freq (6kHz), fixed on time (20%) flyback converter using an ETD59 core & bobbin, the mosfet was a 500/600V type, 20A, The input was a bench power supply 0-30V @ 3A max, we designed the flyback transformer with 6 outputs, you could use 10 output windings, each one rectified by 2 x 1kV fast diodes, and a 33nF 1kV cap, and all in series so the 1kV o/p's add to give 10kV in your case.
The turns ratio on the transformer (ETD59) was 12T pri to 50T on the sec's, such that when the fet is on and impressing 30V on the primary, the secondaries develop 125V, so 1125v on the diodes, when the thing flies back (fet off) there is 1kV on the sec's and 240V plus the initial spike (hence the 500v part) on the primary.
Thus you can use the bench psu to vary the o/p volts by varying from 0-30V to the flyback power circuit (you can vary the flyback freq and on time too for more/less power).
6kHz is good because you can hear when it is ON - a good safety feature..!!!
All windings were done with double insulated teflon wire to get the required insulation rating needed, and plenty of mylar tape..!
I advise caution as it is easy to get a lot of volts this way although the power is limited by the current limit of the bench psu (we set it to 1.5A)
Good luck...!