Page 82 - Dynamics and Control of Nuclear Reactors

7.3 Moderator temperature feedback in thermal reactors 75

× 10 –4
4
293 K
493 K
593 K
Fractional neutron density 2 1
3

0
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
v, Neutron velocity (m/s)
FIG. 7.2
Maxwell-Boltzmann distribution of thermal neutrons for three temperatures.

moderator. Such a change follows a change in heat removal in the secondary system.
The moderator temperature coefficient may be positive or negative and its value can
change significantly with reactor operation.
An increase in the moderator temperature of a thermal reactor causes the thermal
energy spectrum of thermalized neutrons to shift to a higher energy. Thermal neu-
trons are in equilibrium with the thermal energy of the moderator. Higher moderator
temperature means greater thermal motion of moderator atoms and a consequent
higher energy of neutrons that interact with the moderator atoms. The energy spec-
trum of moderator atoms, and consequently the energy spectrum of thermalized neu-
trons is given by the Maxwell-Boltzmann distribution. Fig. 7.2 shows distributions
for three different temperatures.
Many reactor constituents have absorption and fission cross sections that vary as
the reciprocal of neutron velocity. This is called a “1/v” dependence of the cross
section, σ. The reaction rate is given by
R ¼ N σφ (7.1)
or
R ¼ Nσ n v (7.2)
where
3
R ¼ reaction rate (number of interactions/(cm s)
3
N ¼ absorber number density (number of nuclei/cm )
2
σ ¼ microscopic cross section (cm )
3
n ¼ neutron density (number of neutrons/cm )
v ¼ neutron velocity (cm/s)