The design of instrumentation systems for a nuclear power plant must take into account the specific properties of the reactor for that plant. Of particular importance is the kinetic behavior of the reactor Many textbooks and monographs have been written on nuclear reactor kinetics, the reader is referred, for example, to Refs. 2 through 6 for details The following paragraphs summarize basic material particularly relevant to instrumentation systems in nuclear power reactors.

1-3.1 Point Kinetics Without Delayed Neutrons

The symbol n (neutrons/cm3) is used to designate the neutron density at a given position in a nuclear fission chain reactor. If the reactor is just critical, the effective multipli­cation factor, k, is exactly 1 and the neutron density, n, is constant. If the effective multiplication factor is increased by 6k = к — 1 (with 5k > 0), then n increases with time.

The rate of increase of n, dn/dt, is the number of extra neutrons in the next generation, n 5k, divided by the time between generations /

dn = n 5k = n(k — 1)

dt l l ( ’

Integrated, this is

п = п0е<«к//>‘ (12)

where n0 is the neutron density at t = 0 The reciprocal of the first factor, 5 k//, in the exponential has the dimensions of time and is known as the reactor period

To introduce the effect of delayed neutrons on the nuclear chain reaction, we consider the effective multiplica­tion factor to be the sum of two terms

к = (multiplication factor for prompt neutrons) + (multiplication factor for delayed neutrons)

(1 3)

T = //5k

These equations have been developed on the assumption that there is a single characteristic time between generations in a nuclear fission chain reaction This is the same as assuming that only prompt neutrons participate m the chain reaction

= k(l — j3) + k/3 (14)

where (3 is the delayed neutron fraction, or the number of delayed neutrons per fission divided by the total prompt and delayed neutrons per fission The delayed-neutron

Table 1.1—Delayed-Neutron Half-Lives and Yields in Thermal-Neutron Fission’