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NUEN 301 Course Notes With Equations, Marvin Adams, Fall 2009
Ch. IV. Physics, Reactos, & Breeding
IV. Physics, Reactors, and Breeding
Introduction
Nuclear fission reactors actually produce new fuel as they operate. If they produce more useful
fuel than they destroy, they are called breeder reactors. Otherwise, they are simply converters.
Commercial reactors in operation today are converters.
The physics
If we split (fission) a heavy nucleus, we know that energy is released. This is because heavy
nuclei are not “bound” as tightly as nuclei that are somewhat lighter. In fact, if we plot binding
energy per nucleon as a function of mass number, we get a curve like this:
10
8
6
4
2
50
100
150
200
Since fission of heavy nuclei is favored energetically, we might ask why it does not occur
spontaneously. First, because of short-range nuclear forces there is a potential barrier (of
several MeV) that must be overcome before a nucleus is free to fly apart. That is, the nucleus
must climb a several-MeV hill before it can fall off of a many-MeV cliff. Second, spontaneous
fission does occur, because of quantum-mechanical “tunneling” through the potential barrier.
This is a rare event in most heavy nuclides; for example, the half-life for spontaneous fission in
U-238 is 6.5•1015 years. However, there are exceptions: Californium-252, with a half-life for
spontaneous fission of only 66 years, is often used as a neutron source in reactors.
We must design our reactors so that heavy nuclei can routinely overcome the several-MeV
fission barrier. There are at least two ways to overcome the barrier:
1)
2)
let the nuclei
We use the second approach in our reactors, partly because multi-MeV particles are not available
in sufficient quantity to use the first, and partly because neutrons are emitted from fission, which
suggests the potential of a self-sustaining chain reaction.
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NUEN 301 Course Notes With Equations, Marvin Adams, Fall 2009
Ch. IV. Physics, Reactos, & Breeding
30
Fissile, Fissionable, and Fertile Nuclides
If a nuclide is reasonably likely to fission after absorbing a very slow neutron, it is called
Fissile nuclei surpass the fission barrier with only the
some
fissile nuclei:
If a nuclide is reasonably likely to fission after absorbing a neutron with kinetic energy of an
MeV or two, but not less, it is called
Fissionable nuclei need the binding energy of another neutron,
to make it over the fission barrier.
some
fissionable
nuclei:
Fission in fissionable nuclei is not a true threshold reaction, in the following sense: the cross
section is not zero below any threshold neutron energy, because fission (which you will
remember is energetically favored!) can occur by quantum-mechanical tunneling even when
there’s not enough energy to get over the barrier. It’s just a lot less likely. The figure below
shows the fission cross sections for some fissile and fissionable nuclides.
Fission cross sections of some key nuclides.
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NUEN 301 Course Notes With Equations, Marvin Adams, Fall 2009
Ch. IV. Physics, Reactos, & Breeding
31
Fertile nuclides are those that are non-fissile but can produce a fissile nuclide after absorbing a
neutron. Two important examples:
U-238:
238
239
9 2U (n, γ) 9 2U
Th-232:
232
233
9 0Th(n, γ) 9 0U
Conversion & Breeding
Reactors that contain fertile material convert some of it to fissile material. They are called
All reactors convert to some extent, and most commercial reactors convert a significant amount
of U-238 to Pu-239. Other “actinides” (elements with Z > 88, some of which are fissile) are also
produced. These new nuclides produce a significant portion of a reactor’s power, especially at
the end of a fuel cycle. It is possible to extract this material from spent reactor fuel and use it in
later fuel cycles.
[Aside: Policy issues surrounding recycling.
At present we do not recycling the useful material out of spent fuel in the U.S., but recent policy
changes (including the Energy Policy Act of 2005) have opened the door for this.
Other countries (with France a notable example) do limited recycling, taking the Pu out of
spent fuel that originally had no Pu, and making new fuel by mixing this Pu with U. (Both the
Pu and U are in oxide form; thus, the new fuel is called mixed-oxide fuel, or “MOX.”)
To fission significant portions of the actinides that are created in reactors, we need to put them
in a reactor with a fast neutron spectrum – a reactor that does not slow many neutrons to low
energies. The most US strategy is to explore the possibility of having some fast-spectrum
reactors to burn up the actinides. When coupled with the technology to extract essentially all the
actinides from spent fuel, this would accomplish two highly desirable goals:
-
It would dramatically reduce the amount of waste needing disposal and the time that
the waste would need to be isolated. It is the actinides that cause the waste to be
significantly radioactive for thousands of years. Without actinides, the waste would
decay in a few hundred years to radiation levels lower than the original U ore!
-
It would allow full utilization of our uranium resources. In the once-through cycle
in place today, we extract less than 1% of the potential nuclear energy in the
uranium that we mine.
end of aside on policy issues.]
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NUEN 301 Course Notes With Equations, Marvin Adams, Fall 2009
Ch. IV. Physics, Reactos, & Breeding
32
For any given reactor, we define:
conversion ratio
=
(1)
If this ratio is greater than unity (which is quite possible!), the reactor is called a
reactor. In this case the conversion ratio is called the
If we define “fuel” to mean “fissile atoms,” then breeder reactors produce more fuel than they
consume. This cannot go on indefinitely; at some point the world’s supply of fertile material
would run out. However, the world’s supply of fertile material is far, far greater than its supply
of fissile material. Because of this, breeder reactors could extend the lifetime of fission power
into the distant future (many, many centuries).
Breeding in a reactor is possible only if the following inequality is true.
η
= reproduction factor
=
(2)
Note in particular that η will depend on
In fact, η tends to increase substantially at neutron energies above 100 keV (0.1 MeV) for most
fissile materials. For this reason, breeders are usually “fast” rather than “thermal” reactors.
However, it is possible to design a thermal breeder reactor using Thorium-232 as the fertile fuel
and U-233 as the fissile fuel.
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NUEN 301 Course Notes With Equations, Marvin Adams, Fall 2009
Ch. IV. Physics, Reactos, & Breeding
33
Figure 1. Variation of η with energy of the incident neutron, for 233U, 235U, and 239Pu. The
235
U curve has been smoothed in the eV region. (Figure taken from Lamarsh.)
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