Elementary solutions of the kinetics equations. Chapter 4

The practical solution of almost all kinetics problems is complicated by the individual behaviour of the different groups of delayed neutrons. A numerical solution to a given problem is therefore normally sought by computer. We shall return to chapter 7 to the numerical methods generally used to solve the point-kinetics equation. However, in the case of some simplified problems, an analytic solution can be found. These elementary solutions are extremely useful in the understanding of reactor behaviour, and often allow the derivation of analytical relationships between basic parameters. Such analytical solutions can also serve to verify the numerical solutions. The analytical treatment presented in this chapter generally makes use of the simplified model introduced in the previous chapter. In this chapter, we shall study 'elementary' solutions, i.e., the response of the neutronic power p(t) to simple reactivity perturbations, such as a step change or a pulse. (author)