ABSTRACT A one-group diffusion equation coupled with slightly simplified burn-up equations is investigated for a burn-up drift wave problem, which is concerned with the recently developed concept of a so-called CANDLE reactor. By neglecting radioactive processes this one-dimensional system is integrable and a permanent plane solitary wave with an arbitrary amplitude exists for a suitable fuel composition. Theoretically, by adjusting the initial transverse fuel distribution, a 3-D permanent solitary wave pattern with a conventional transverse buckling shape can be also obtained. Key Words : Diffusion model, burn-up equations, one group, solitary wave solution, multi-dimension. 1 INTRODUCTION In ICENES 1996 Teller, Ishikawa and Wood proposed an interesting concept of a self controlled nuclear fission reactor [1], in which a nuclear breeding and burning wave is ignited and propagates slowly in the core axial direction. Natural thorium and uranium fuel can be used for this type of reactor and no fuel enrichment and reprocessing are needed. It can be designed for a long operation duration and a high fuel burn-up. Since the burning mechanism and the geometry of this reactor are similar to those of a candle, it is sometimes called
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