NUEN 301 Course Notes With Equations, Marvin Adams, Fall 2009 Ch. IV. Physics, Reactos, & Breeding

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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.

NUEN 301 Course Notes With Equations, Marvin Adams, Fall 2009 Ch. IV. Physics, Reactos, & Breeding

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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.

NUEN 301 Course Notes With Equations, Marvin Adams, Fall 2009 Ch. IV. Physics, Reactos, & Breeding

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Fertile nuclides are those that are non-fissile but can produce a fissile nuclide after absorbing a neutron. Two important examples:

U-238: U92238 (n, γ) U92

239

Th-232: Th90232 (n, γ) U90

233

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.]

NUEN 301 Course Notes With Equations, Marvin Adams, Fall 2009 Ch. IV. Physics, Reactos, & Breeding

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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.

NUEN 301 Course Notes With Equations, Marvin Adams, Fall 2009 Ch. IV. Physics, Reactos, & Breeding

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Figure 1. Variation of η with energy of the incident neutron, for 233U, 235U, and 239Pu. The 235U curve has been smoothed in the eV region. (Figure taken from Lamarsh.)