Slowing Down and Diffusion of Neutrons

As a consequence of the undermoderated lattice of thie N-Beactor, the fast to-themal flux ratio Is quite large relative to that of existing, overmodera. ted Bisnford reactors As an lUustratlon of this difference, the ratio of fast flux to thermal flux Is estimated to be 2.50 at N (compared to 1 08 at a K reactor). 

This enhances the production of plutonium in the reactor and also makes the lattice fall-safe (from a reactivity standpoint) upon loss of water. 

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The appropriate time-dependent differential equations for the com-bined-slowing-down diffusion theory may be obtained by recognizing that the time rate of change of the neutron density is given by the difference between the rates of disappearance and appearance of neutrons from sinks and sources. Thus we write... 

The first two chapters serve as an introduction to the basic physics of the atom and the nucleus and to nuclear fission and the nuclear chain reaction. Chapter 3 deals with the fundamentals of nuclear reactor theory, covering neutron slowing down and the spatial dependence of the neutron flux in the reactor, based on the solution of the diffusion equations. The chapter includes a major section on reactor kinetics and control, including temperature and void coefficients and xenon poisoning effects in power reactors. Chapter 4 describes various aspects of fuel management and fuel cycles, while Chapter 5 considers materials problems for fuel and other constituents of the reactor. The processes of heat generation and removal are covered in Chapter 6. 

While 8 is somewhat greater than 1, both p and / are somewhat smaller than 1. Therefore, for approximate calculations, epf can be set 1. The fission factor rj varies appreciably with the energy of the neutrons, as shown in Fig. 11.4 for The neutron losses in a reactor of finite dimensions can be taken into account approximately by the sum L +1 , where Ls is the mean slowing-down length of the fission neutrons in the moderator and L the mean diffusion length in the fuel-moderator mixture. For a spherical reactor of radius R the approximate relation is... 

There are two particularly simple problems in connection with the energy distribution of neutrons which are present in a medium of finite temperature. In the first problem the slowing down is uniform throughout the entire space which is itself uniformly filled with the slowing down material. In this case the neutron distribution is evidently the same all over space. In the second problem the neutrons enter a half space from one side with uniform intensity and diffuse into it. The question in this case is the density distribution of neutrons at large distances from the boundary plane of the half space and the exponential relaxation length of the neutron density. We shall be interested only in the first problem. 

In these, r = InE/Eo is the logarithm of the energy of the neutron in units of the thermal energy Eq. The q r) is the number of neutrons per imit volmne in unit r range, multiplied with their velocity no is the density of thermal neutrons, multiplied with their velocity. D and Dq are the diffusion constants (divided by the velocity) for fast and thermal neutrons the former is a function of r. 5 is the slowing down per imit volmne. So is the value of S for thermal energies, i.e., r = 0,... 

In these Ut is the density of thermal neutrons multiplied by their velocity, q t) is proportional to the slowing down density t is the age of neutrons, to the age of thermal neutrons, k the multiplication constant, Kf the reciprocal diffusion length of thermal neutrons in the mixture. The above equations were derived by Fermi on the assumption that the number of collisions which a fission neutron suffers before it becomes thermal is the same for all neutrons and that the distance between two collisions is also a well-defined quantity depending only on the energy. 

In FIG. 18, A, B, and C represent individual particles of material containing natural uranium, but it is to be distinctly understood that. the entire chain may take place in one body, two bodies, or three, as shown, because of 60 the fact that the neutrons during the slowing down process are diffusing over random paths throughout the entire composite mass of ffie slurry, and are not nec sarily passing directly from one uranous body to the next adjacent body. The factor n represents any fixed number of neu-65 irons. 

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