Page 61 - Dynamics and Control of Nuclear Reactors

CHAPTER

5
Subcritical operation

5.1 The neutron source
Reactors require a source of neutrons during startup in order to cause flux levels that
are readily measurable. Reactors have naturally-occurring neutron sources: sponta-
neous fissions in Uranium, neutrons from cosmic ray interactions with reactor con-
stituents and photoneutrons from high energy gamma ray interactions with certain
light isotopes present as reactor constituents. The gamma rays for photoneutron pro-
duction are from decay of precursors nuclei that were left in an excited state due to
gamma ray interaction during prior reactor operation.
But artificial sources are used to ensure that the resulting neutron flux is large
enough to cause the necessary measurable signals. Generally, these sources are a
neutron emitter (for example, Californium-252 or a mixture of an alpha particle emit-
ter and a material that undergoes (α-n) reactions, such as plutonium-beryllium or
americium-beryllium).

5.2 Relation between neutron flux and reactivity
in a subcritical reactor
The modification to the point kinetics equations needed for modeling a subcritical
reactor is simply to add a source term, S, to Eq. (3.12) or one of its other formulations.
The neutron density (or a quantity proportional to the neutron density) after reactivity
is increased, but remains subcritical, reaches a new steady state. The steady state
is described by setting the time derivatives equal to zero in the modified equations
(for example, Eqs. (3.12) and (3.13)). The steady-state value of neutron density is
given by
SΛ
n ¼ (5.1)
ρ
or
1 ρ
¼ (5.2)
n SΛ
Note that reactivity is negative because a subcritical reactor is under consideration
here. Eq. (5.2) shows that the reciprocal of the steady-state neutron density (or a

53
Dynamics and Control of Nuclear Reactors. https://doi.org/10.1016/B978-0-12-815261-4.00005-6
# 2019 Elsevier Inc. All rights reserved.