Uses a Femtosecond IR laser pulsed into an atmosphere of He. Helium atoms when given a 1.6KeV pulse of energy respond in turn by producing a wide range of outputs including those into the 11.7nm range. Ultrahard UV. Technically Soft X-rays start around 10nm. 11.7nm is pretty darned close to Xray output. (I think I have oversimplified the process somewhat), but you get the idea.
There you have it. I bet you the laser they're using is a Femtosecond Sapphire as well.