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Yeah....the Allies were not interested in genocide.
Systematic genocide, no. Hammering away ruthlessly at Axis powers without regard to casualties until they surrender...it would be most interesting to know if the attitudes so demonstrated OTL against Japan would in fact have prevailed against a land of white people who look like the dominant sector of the USA and Britain.
Meanwhile and much much more to the point in such a TL...are we in ASB here? Checking, no, we are in After 1900. Plausibility constraints apply. Discussion of delivery methods is interesting but if all that has been accomplished with good fortune in the MP is to advance the time scale "a year," then the supply of available A-bombs is strictly limited!
The USA was not yet able to churn them out like so much cotton candy. The biggest constraint is the supply of suitably weapons grade fissionable materials. The options are to use plutonium, which does not occur in significant amounts in natural ores, and must be transmuted into being from more common fissionable isotopes in a nuclear reactor then chemically isolated. Or, to use Uranium-235, which does occur in nature, but in really tiny concentrations versus the commoner and less easily fissioned isotope U-238. I suppose a suitable fission pile might also produce enhanced numbers of -235 nuclei via transmutation but no one ever talks about that, either it doesn't happen or it is not cost-effective versus other options. What was done OTL was to separate it by various ways and means that use the slight relative mass difference between the isotopes which otherwise behave identically chemically.
Both processes are quite slow, especially when you are setting them up for the first time and have to learn a certain amount by trial and error. MP had all the money thrown at it the project runners wanted, and the USA had resources to spare despite heavy war mobilization, so IIRC 3 methods of U-235 concentration were explored and each put into action on a serious production scale, while the fourth route of creating and stockpiling suitable plutonium isotope mixes via generating them by transmutation in a uranium-based fission pile was also adopted. The outcome was that both methods yielded a slow trickle of accumulation. We have some nuclear experts on site, my personal Bat-Signal goes out to
@asnys, author of fine materials based on knowledge of nuclear processes and the history of their development.
Since Uncle Sugar funded MP lavishly and the world's greatest scientists and engineers were heavily recruited for it, I find it implausible to argue they could have proceeded much faster. With hindsight we know of mistakes made and wrong paths pursued but it is not clear, if we imagine the directors blessed with uncanny intuition and hunches, whether shutting down the less productive options and throwing all saved resources at the in-retrospect most cost-effective options would have accelerated getting results or not. Two parallel things are going on--one, the mindless drip drip drip of accumulating stocks of weapons grade fissionables at a snail's pace. Building more facilities presumably would accelerate that but experts on the history of the project might point out constraints on that. Let's presume that in fact doubling the existing plants would indeed double the pace, and that the cost of doing so is something like the square of the ratio of outcomes, and to offset that drawback that managers have intuition or guesses or sheer chance happenstance decisions are made that raise the ratio of the most effective methods so overall we don't have to double total plant acreage and associated costs to get double production, because they have stumbled into the best methods available. It would not be realistic for 100 percent to go into the best; they are finding their way blindly and have to try everything, but it might be fair if the relative share of the best methods is doubled versus OTL. Do the research to finger which possible method in the wartime '40s was in fact the best, figure the earliest date it gets started and push that back a little, raise the level of investment in it until it is up to twice OTL and after that calculate on the nonlinear rising costs of increasing all forms of production until the OTL rates are surpassed by one year as of springtime 1944. This means that, provided you can show that the additional bulk budget for all MP stuff can be covered and sustained, the mass of materials to produce suitable bomb cores is available by then and not a year later.
That's one hurdle--the other is, the design teams worked right up into the spring of '45 and indeed kept puttering about trying to improve things from a far less than optimal state--well, presumably to the present day! They too would need uncanny intuition and luck in experimentation to arrive at workable bomb designs a year before they did OTL.
Nuclear fission is a messy process and tends to gross inefficiency in plain fission bombs, because one needs two halves of a critical mass/density combination kept separate enough not to trigger a fizzle yield dud blast, then somehow the criticality is raised enough for a major amount of fission to take place, but unfortunately when only a fraction of the mass that could theoretically be split has actually done so, the heat released by the partial fission is enough to blow the rest of the perfectly useful core materials to the four winds. That is, fission bomb making starts out very inefficient! To practically make one bomb, you need large multiples of the mass that will actually undergo fission to make that fraction do its job. It might be otherwise with more advanced designs, but we are conceding enough to match OTL performance a year earlier. So, the amount of fissile materials needed is far greater than that that will actually be fissioning.
This is why the early bombs were so damned big.
I see conflicting reports on the number of bombs the USA could have had by the end of 1945 OTL had they persisted; OTL it was just a handful of completed articles. Others say that the plans for Operation Olympic, the invasion of the Japanese Home Islands, relied on a couple dozen being available. I think the major factor explaining this discrepancy is gross confusion in the minds of the actual planners, overoptimism about what would in fact be available, mitigated just a little by the assumption that if use of a couple bombs did not drive Japan into surrender than the USA would double down on production facilities and increase their performance considerably versus OTL--but I think it would be impossible to have as many as some say MacArthur's invasion plans called for to use during it. There could also be confusion about what those plans actually were.
Overall, I think if the MP status on April 1, 1944 were exactly that of OTL April 1, 1945, this means that subsequent production will be maybe twice as fast as OTL, maximum. I want to say ten bombs built by New Year's Eve 1944. One at least went for a vital test shot.
With 9 bombs in hand, the most gung-ho version of FDR would not be able to do as some have advised and simply pulverize the Reich into glowing dust overnight, not if Skippy the ASB were to personally appear with two dozen Bomb delivery capability versions of the B-29 complete with manuals and blueprints and hand them in person to Leslie Groves.
The A-bomb, in the timeframe '44-45, cannot be used to simply flatten Germany; targets must be chosen either to inflict maximum damage, logistical being the prime target; or for terror value in demoralizing the Germans.