Computational Analysis of Signatures of Highly Enriched Uranium Produced by Centrifuge and Gaseous Diffusion

Different enrichment processes have been used historically to produce highly enriched uranium (HEU) for weapon purposes. The most relevant ones are the gaseous diffusion process and the gas centrifuge. The two exploit different physical principles to separate isotopes of different molecular weight. It could therefore be expected that HEU might carry an isotopic signature that is unique to the enrichment process used to produce the material. Multi-isotope enrichment cascades are generally modeled using the matched-abundance-ratio approach. In this paper, we will present comparisons of the isotopic signatures predicted in gas centrifuge cascades with those predicted in gaseous diffusion cascades by using a modified version of the matchedabundance-ratio cascade code, MSTAR, which accounts for the physical differences in the stage separation factors in the two processes. Additionally, we will present the methodology used by the modified code and discuss representative results for HEU produced from both natural and reprocessed uranium. We find that essentially complete knowledge of the enrichment technologies employed, of the cascade design, and of the mode of operation is required in order to make meaningful (quantitative) statements about expected HEU signatures. Introduction Uranium can be used as fuel for nuclear power reactors and for nuclear weapons. As uranium occurs in nature, it has three isotopes: 234 U, 235 U, and 238 U. The abundance of these isotopes is shown in Table 1. The isotope of interest for producing fission reactions is 235 U, and the uranium must be enriched in that isotope to ~ 3–5% for lightwater-cooled power reactors and to ~ 90% for weapons. There are a number of different ways of separating or enriching isotopes, but the two processes used for large-scale enrichment of uranium are gaseous diffusion and gas centrifuge. Uranium that has been used as fuel in a nuclear reactor, for example, in a plutonium production reactor, can be reprocessed and re-enriched in 235 U, but this irradiated uranium contains additional isotopes, which are produced by the nuclear reactions in the reactor. These isotopes include 232 U, 233 U, and 236 U, in addition to the 234 U already present. Understanding the unit separation factors for these minor isotopes is important in the enrichment of reprocessed uranium. Table 1. Isotopic concentrations of natural and Hanford-type irradiated uranium. 1 Natural Uranium Hanford-type RepU U-232 2.03E-10 at% U-233 3.58E-09 at% U-234 0.0055 at% 0.0053 at% U-235 0.7200 at% 0.6010 at% U-236 0.0186 at% The unit separation in gaseous diffusion is a function of the square root of the ratio of the molecular weights of the components being separated in contrast with the unit separation in a gas centrifuge, where it is a function of the difference of the molecular weights. 2 When analyzing cascades being fed reprocessed uranium for production of low enriched uranium (LEU, less than 20% 235 U), this distinction may be small, but in the case of producing HEU (greater than 20% 235 U), one might reasonably expect the two processes to produce rather different concentrations of the minor isotopes. For designing cascades for enriching multi-component mixtures of uranium, the difference in assays of minor isotopes may be of little importance. However, one might be interested in ascertaining how a particular sample of enriched material was produced. In that case, the minor isotopes might provide forensic signatures, which could identify the separation process or ultimately even the origin of the material. In this paper, we explore how the separation factors of minor isotopes may differ between gaseous diffusion and gas centrifuge, and we present example calculations of enriched LEU and HEU. For the mathematical and numerical analysis, the matched abundance ratio or M* (read M-star) cascade theory is used. This theory was first suggested by de la Garza. 3,4 Matched-Abundance-Ratio Cascades In a cascade separating a binary mixture, the assay of the desired isotope in the up-flowing stream from a stage is matched to the assay of the down-flowing stream from the stage above. This results in a no-mixing cascade or ideal cascade, which has the desirable feature of minimum inter-stage flow. In a multi-component mixture, the ideal cascade is generalized to a matched-abundance-ratio cascade, which will become an ideal cascade when the mixture is binary. Following Von Halle, 5 in a multi-component mixture of J components, let the k th component be designated the “key” component, and let the abundance ratio of each component be defined in terms of the key component by