I ntroduction A major objective of this course is to determine the neutron flux as a function of both position within a reactor core and the neutron energy. Neutron life cycle analysis is the first method that we will examine for this purpose. It was the principal means of design for nuclear reactors in the 1950s, before the advent of significant computational power. It remains an important tool for qualitative understanding and, in some cases, for quantitative analysis of criticality. Neutron life cycle analysis involves the assumption that the neutron flux exhibits no spatial dependence. Also, while it could be used for either fast or thermal reactors, it is most often associated with thermal ones. Our purpose in studying it here is to: 1) develop an understanding of neutron behavior as a function of neutron energy, and 2) utilize the method for criticality analysis.
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Need for Neutron Moderation: As a first step in studying the neutron life cycle, we examine the fission energy spectrum and note that the neutrons are born at energies that are well above both the thermal (0.025 eV) and epithermal (keV range) regions. Such neutrons, both prompt and delayed, are termed “fast.” Next, re-examine the absorption crosssection for U-235. Note that the probability of a fast neutron’s being absorbed is very small. However, it is substantial (~582 barns) for thermal energies. So, in order for a fission chain reaction to be sustained, it is essential that the fission neutrons be slowed down or thermalized. This process is called neutron moderation and there are several constraints imposed on it: —
Maintenance of the fission chain reaction requires that the fission neutrons be thermalized.
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The amount of moderator present needs to be sufficient for the thermalization process and yet not excessive. It is imperative for safety reasons that reactors be designed so that an increase in moderator temperature or a decrease in moderator density result automatically in a decrease in neutron thermalization. This is a passive safety feature known as a “negative temperature coefficient of reactivity.” It precludes power excursions. For this reason, we need to minimize moderator mass. (Note: This topic is discussed at length later in the course.)
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Moderators often double as coolants. If so, the amount of moderator present must be sufficient to remove the heat generated by the fission process. This requirement usually results in a desire to maximize moderator mass.
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The moderator material contributes to the shielding that protects plant operators. This is especially true during maintenance when most external shielding has been removed. So, again there is a motivation to maximize moderator mass.
The ratio of fuel to moderator is often termed the “metal-to-water” ratio and safety factors are sometimes parameterized in terms of it. The competing functions of the moderator illustrate a frequent paradox in nuclear engineering. Safety issues often involve conflicting goals. Here there are strong safety arguments for both minimizing and maximizing the moderator mass. 3.
Neutron Slowing Down: The slowing down of neutrons will be covered in more detail later in this course. For now, we note that neutrons are slowed down by collisions. From energy and momentum conservation, it can be shown that the maximum energy transfer between two particles in a head on collision is:
Qmax =
Where: Qmax m M E
4mM
(m + M )2
E
is the energy transferred
is the mass of the incident particle
is the mass of the moderator material, and
is the energy of the incident particle.
This relation indicates that:
A head-on collision between a neutron and another particle of equal mass (e.g., a proton) will result in a complete transfer of energy from the neutron to the proton. In contrast, a collision between a neutron and a particle of large mass (i.e., m
