X-ray,
Has no effect on the device, except that (eventually) the total dose will accumulate, and the Vt of the devices will begin to shift, and eventually, the device will fail.
This is unlike a CCD, which may register 'hits' and display noise.
Only neutrons, or protons, with LET of 1 Mev have enough energy to create charge clouds, and change bits:
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Contact your local Xilinx FAE to find out about X-Ray dose (how long it can "take it.").
At some dose level, that usage becomes ITAR restricted (people use stuff this hard to build nuclear bombs, or operate in the presence of nuclear explosions) so you will no longer be able to buy, or use, such parts, unless the US State Department permits you to do so.
I suspect for your application, our commercial parts are more that "hard" enough.
X-rays, after all, are just photons, and they just do not pack enough energy to affect even the MGTs in our parts, and certainly do not affect the logic and memory.
Austin