On the theory of propagation of chain nuclear reaction

Chain nuclear reaction is studied in diffusion approximation. Multiplicating medium in the form of a long cylinder is considered. The propagation velocity of nuclear reaction is obtained in the overcritical regime. It is given by the formula analogues to that for slow burning and in the simplest case is proportional to the square root of the product of diffusion and multiplication coefficients divided by the neutron lifetime. The phenomenological nonlinear model, restricting the exponential growth of neutron density in the chain reaction, is considered. It is shown, that there exists a large interval of time, in which the expression for the velocity of the reaction propagation, obtained in the linear approximation, remains valid. It is also shown, that at very large times the regime of multiplication is replaced by the ordinary diffusion regime