Transverse buckling effects on solitary burn-up waves

A three-dimensional one-group diffusion model with explicit effects of burnup and feedback is studied for a so-called “candle reactor”. By a perturbation method the problem is reduced to a one-dimensional one, for which a solitary wave solution was obtained by van Dam (2000) [Self-stabilizing criticality waves. Annals of Nuclear Energy 27, 1505]. Therefore, such a travelling burn-up wave exists as well in the multi-dimensional problem, which has a solitary wave profile in the long axial direction and a buckling shape, as in usual reactors, in the smaller transverse direction. Two solutions are obtained and discussed: (i) a uniform drift-speed solution in the case of a burn-up parameter, i.e. the value of neutron fluence associated with the maximum of k∞, adapted to the transverse buckling; (ii) a nonuniform drift-speed solution for uniform burn-up parameters, where the contour lines of the wave pattern are distorted from symmetric ellipsis to sickle-shaped ones. The buckling effects on relationships of principal parameters are presented.