Time Dependence of the Slowing-Down and Diffusion Processes
In this chapter, we shall study the behavior of neutron fields with nonstationary sources. In doing so we shall round out our discussion of the diffusion and slowing-down processes and in particular prepare ourselves to understand those important methods of measurement that employ non-stationary sources (these methods will be discussed in Chapter 18). First we shall consider the time-dependent slowing-down process in the absence of diffusion, then the timedependent diffusion process in the absence of slowing down, and finally the spacetime distribution during moderation, though only in the age approximation. We shall almost always assume a very short pulse of neutrons as the source (S (t)~δ (t)). In practice, this is the most important case. Also, with suitable normalization the resulting (E, t) can be considered as the probability that a neutron produced at time zero has the energy E at time t. Thus the life history of an “ average “ neutron can be read directly from the solution Φ (E, t). If we integrate the time-dependent solution over all t, we must again find the result we obtained earlier for a stationary source. In Sec. 9.4, we shall consider, in addition, the case in which the neutron sources are periodic in time.
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