Third harmonic YAG laser, Q Switched, of the fairly short pulse kind.
0.1J in 10ns is a fairly high peak power level, 10MW peak, 1W average unless I have dropped a decimal somewhere? Might be some pulse compression involved to get the peak power level?
NOT going to be cheap.
Coherent are a likely vendor for a (probably) optically pumped YAG, but I also wonder about exceminer lasers as possibly a cheaper short UV pulse source, got issues of their own, but might be worth a look.
Another thought is N2 gas lasers, might struggle with the PRF but they are fairly cheap as these things go, and have copious peak power in the UV.