1. The Gas Centrifuge
2. A modern power reactor has a design burn-up of about 53 MWd/kg and uses 4.4% enriched fuel. About one third of the thermal energy is successfully converted to electricity. 53 MWd/kg/3 = 17.7 MWe-days/kg. At 90% capacity factor, a 1 GWe reactor would use (1000 MWe x 365days x 90% / 17.7 MW(e)d/kg) = 18.6 tons. A less modern reactor operating at lower burn-ups (say, 41 MWd/kg) would require about 24 metric tons. The separative work required to produce enriched fuel is based on a value function: V(e) = (2e-1)ln[e/(1-e)]. The total SWUs required per kilogram is V(ep)-V(et)-Fx[V(ef)-V(et)], where the subscripts p, f, t represent product, feed, and tails respectively; and F is the mass of feed per kilogram, given by (ep-et)/(ef-et). For a kilogram of 4.5% product, assuming natural uranium feed (ef = 0.000711), 0.32% tails (et = 0.00032), 10.7 kg of feed is required, and 6.0 SWUs. For 18.6 metric tons, this is 110,000 SWUs
3. For 1 kg of HEU, the amount of natural uranium needed is F = (ep-et)/(ef-et) = 236kg and SWU/yr = 190/yr at a tail concentration of 0.32%. For 25 kg of HEU, the amount of material required for a first generation implosion bomb, the amount of natural uranium needed is 5900 kg and the number of SWUs required are 4750/yr. If Pakistani P-2s are employed with a capacity of 5 SWUs a year, one would need about 1,000 centrifuges. The number of centrifuges will go down by about 70% if the clandestine facility is fed 4.4% enriched uranium as feed for 25 kg of HEU output. For a feed of 4.4% enriched uranium and a tail concentration of 0.32%, the number of SWUs required for 25 kg of 90% enriched uranium is 1,500. This would require 300 P-2 centrifuges. This number will drop further to about 160 centrifuges if the tail concentration is allowed to increase to 2% at the clandestine facility. This increase of the tail concentration would come at an expense of an increased feed requirement. Hence if the tail concentration increases to 2%, the amount of 4.4% enriched uranium feed needed for 25 kg of HEU will be 917 kg as opposed to 547 kg for 0.32% tail concentration