# Derivation of Simple Point Kinetics Equation

## Derivation of Simple Point Kinetics Equation

Let n(t) be the number of neutrons as a function of time t and l the prompt neutron lifetime, which is the average time from a prompt neutron emission to either its absorption (fission or radiative capture) or to its escape from the system. The average number of neutrons that disappear during a unit time interval dt is n.dt/l. But each disappearance of a neutron contributes an average of k new neutrons.

Finally, the change in number of neutrons during a unit time interval dt is: where:

n(t) = transient reactor power

n(0) = initial reactor power

τe = reactor period

The reactor period, τe, or e-folding time, is defined as the time required for the neutron density to change by a factor e = 2.718. The reactor period is usually expressed in units of seconds or minutes. The smaller the value of τe, the more rapid the change in reactor power. The reactor period may be positive or negative.

References:
Nuclear and Reactor Physics:
1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
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8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.