If I'm inputting DC current because of the rectifier
indicates that you don't know much about simple electrical theory of circuits/devices. You are dealing with exceedingly dangerous and lethal devices when building a real fusor. You get no second chances if you make a mistake with an x-ray x-former nor radiation above 25 - 30 kV. You really must read all the related FAQ's and study these subjects like x-formers!
The x-former, and diodes will need to be under oil (especially when used for a fusor supply or for any high voltage work; not necessarily needed for testing at lower voltages (say, a few kV or under) and very low power draw); however,one does not just place a x-former in oil. There is a procedure so research that in this forum and learn about that subject.
Richard raises a good point - whether the x-former can output 10-20 ma at 20 kV. This will be determined by the rated x-former power. Exceeding its rated load can quickly burn out a x-former (another reason these are placed under oil; to help with heat load, besides helping to suppress voltage shorting between the HV secondary winding's.)
Be aware that diodes have to be rated to handle the max voltage and an AC voltage has a rated value and a peak value - your diodes must be rated for the peak, not average voltage. If this isn't clear, you need to read up on this subject as well. A ballast resistor for the x-former output is another issue you will need to know but not important yet; however, Richard covers that subject in detail in the FAQ's so do read that.
Also, as Richard said, get your He-3 detector working - that will educated you a great deal on high voltage systems (in the low kilo-voltage range) that is also low current. Once you get the He-3 detector going, calibrating it for background and signal is very useful. If you have funds to burn, possibly consider renting (for six months so have the detector working first!) a powerful (but legal and safe) polonium source. Combined with a very thin and small (!) sheet of beryllium (extremely toxic so know the safe handling and disposal of Be!) and one can have a safe and low flux neutron source to calibrate the detector. However, getting a bubble detector is the easiest (but these are a little pricey) way to calibrate a detector but that does require that one has a working fusor ... .
Consider getting some type of Geiger-counter to scan for x-ray issues around your chamber. A surplus unit (ancient CD units) that works (can be rather low cost) is all one needs. A uranium ore (small amount; Richard sells these) can be used to confirm proper operation. This need not be calibrate - just knowing roughly if there is an x-ray flux is what's critical. Shielding isn't very difficult; I use sheets of slate available from any home depot - extremely cheap, non-toxic (unlike lead), easy to cut (use an abrasive blade) and can be stacked/glued together to form thick enough shielding for any x-ray threat. Doesn't conduct so safe around high voltage.
From now on, post your questions in the appropriate section; this belongs in the High voltage forum.