Fast reactor burnup and breeding calculation methodology

The computational analysis of the nuclear fuel cycle is reviewed with emphasis on conversion and breeding, especially in fast reactors. A review is presented of a methodology for describing breeding, conversion, long-term fuel logistics, and related subjects. This is derived from the mathematical description of the fuel cycle, presented in Part 1. Special results are calculated from the computational method and are presented in such a way that they directly suggest the methodology for the description of breeding reviewed in Part 2. The key ideas are the following: The 'accumulating fuel' concept in a 'reactor-fuel strain' comprises the fuel in an originally started reactor or fuel batch and all the excess bred material, including the fuel bred by this excess, in other reactors of the same type, etc. Fuel logistics are then described by the fuel multiplication in a strain, acting as a kernel, and by strain-introduction dates or rates. The mathematical simplicity of the time dependency of the fuel in a strain, m(t), allows the introduction of concepts such as transitory and asymptotic growth rates, breeding bonus, and delay times. The simplicity of the mathematics itself is exhibited by the fact that asymptotic growth-rate and fuel composition are just the solution of the characteristic equations of the differential equations describing the accumulation of the fuel in a strain. The characteristic equations have the form of an eigenvalue problem. The corresponding adjoint problem yields the 'isotopic breeding worths', that play in the fuel cycle area the same role as the reactivity worths in neutronics and safety analysis. The methodology can be directly extended to symbiotic and negative growth-rate systems. From the growth rate as primary concept, the doubling time and the breeding and conversion ratios are readily deduced. (author)