On the theory of propagation of chain nuclear reaction

Chain nuclear reaction is studied in diffusion approximation. Multiplicatin g medium in the form of a long cylinder is considered. The propagation velo city of nuclear reaction is obtained in the overcritical regime. It is give n by the formula analogues to that for slow burning and in the simplest cas e is proportional to the square root of the product of diffusion and multip lication 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 i nterval of time, in which the expression for the velocity of the reaction p ropagation, obtained in the linear approximation, remains valid. It is also shown, that at very large times the regime of multiplication is replaced b y the ordinary diffusion regime. (C) 1999 Elsevier Science B.V. All rights reserved.