I caught a pretty well done 2 hour documentary on atomic bomb history yesterday on the local PBS station. In it, they go over the paths taken for design of the first bombs, including the Thin Man Pu239 based gun design. After Segrè found the spontaneous fission rate from the reactor-produced Pu was much too high (from Pu240 contamination), that design was abandoned.
It is stated by one of the speakers in the documentary (might have been Rhodes) that such a design is "impossible" (not "was impossible"), implying that it's not feasible at all.
I did a quick back-o-the-envelope calculation as follows (I'm a mathematics guy, not a physicist, hence the question...):
Taking the ~60Kg U235 of the Little Boy, and 3*10^-4 neutrons/gram-second, ~18 neutrons/sec.
Guessing at (since it won't be as efficient as implosion) 2.5X the 6Kg mass of the Fat Man Pu239 to be used in the hypothetical gun and 0.022 neutrons/gram-second, ~330 neutrons/sec.
Taking the insertion time as 1 millisecond (which I assume could be improved with current technology), I get ~0.018 and ~0.33 neutrons/ms average for U235 mass and Pu239 mass respectively.
Assuming Poisson distribution of arrivals, I end up with ~0.98 and ~0.72 probabilities of no stray neutrons during assembly for U235 mass and Pu239 mass respectively.
While that shows a much higher possibility of a fizzle in that latter, it seems far from "impossible".
My question: Given a sufficient mass of "pure" Pu239 (say cyclotron produced, or whatever the current state-of-the-art might be to produce it), and current state-of-the-art technologies to accelerate a projectile, is such a design really impossible (cost of Pu production, efficiency, practicality aside). As in, could an actual high-yield device (as opposed to a fizzle-yield) be produced?