Stochastic Theory of Neutron Transport

Abstract: A stochastic neutron transport theory, in which we consider the probability PN(r, t,uΩ） that the neutron densities Ni(i=1, 2, …, n) emerge in the phase space point (r, uiΩi) at time t respectively, was given by means of the probability theory, and a set of non-linear integral-differential equations for the probability generating functions Fn(r, t, uΩ, S) was derived. The equation for one-order moment F1/S1 under some approximation is just the Boltzman equation for the average neutron number. One-velocity neutron stochastic theory with isotropic scatting was applied to a point model. An approximate solution for the generating function and the equations for moments of the probability distribution and their solutions were derived. It is shown that in a supercritical system, at t→∞, the probability appearing finite neutrons is zero, P_N=0 (0＜^_N＜∞), in other words, the system has no or infinite neutrons. A formula for standard deviation shows that the fluctuation of neutron number in the near critical (0＜λ<1) system should be paid our attention when the fluctuation of initial neutron numberξ0 is larger and the initial neutron average number N0 is not large enough, or neutron source Q is weaker.