When was the earliest research of using plasma as a source for X-ray carried out? And by whom?

Answer 1

That would be a Z-pinch or the related plasma focus. I think Marshal Rosenbluth, then at Los Alamos built the first Z-pinch for the purposes of fusion research. I'm not sure who first used them (with high Z gas) for x-ray production. The oldest report I have on Z-pinches is LANL report LA-2030 from 1956 "Stability of the Pinch" by Rosenbluth. Check out their web site to see if you can track it down.