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The Theory Behind Nuclear Reactors

written by: Mace Moulton Spiegel • edited by: Lamar Stonecypher • updated: 1/21/2011

While nuclear reactors are very complex, powerful pieces of equipment, they operate according to just a few basic principles. With an understanding of the basic theory behind nuclear reactors, even a layman can learn to address the issues surrounding modern nuclear technology.

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    Power from Controlled Nuclear Reactions

    The core of a water-cooled research reactor operating at full power. 

    The theory behind nuclear reactors is built on the basic principles of nuclear physics. Nuclear reactors initiate fission reactions in uranium fuel, which are then controlled using moderators and neutron poisons. These reactions release energy in the form of heat, which is then converted to electricity. Nuclear reactors are useful primarily because the energy produced by nuclear reactions is greater than that produced by chemical reactions, and because the combination of factors involved in their operation allows for complex and nuanced control of power levels and other operating conditions.

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    Why Nuclear Reactions?

    Nuclear reactions include radioactive decay, nuclear fission, and nuclear fusion. In nuclear reactions, defined as reactions involving the atomic nucleus, neutrons and protons are rearranged, and in this process atoms actually change from one element to another. Chemical reactions, by contrast, involve the electrons in the outer layers of the atom. In chemical reactions, atoms are rearranged, but not inherently changed. Nuclear reactions release considerably more energy than chemical reactions, because the forces electrons exercise over one another are much weaker than the force holding together the neutrons and protons that compose the atomic nucleus. This is one reason why nuclear reactors have the potential to provide much more electricity per facility than coal or oil-fueled reactors, which depend on combustion, a chemical reaction.

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    Nuclear Fission

    A simple diagram of the fission of U-235. Nuclear fission is the process by which an atom of one element, when struck by a neutron, breaks apart into fission fragments and free neutrons, releasing a large amount of heat. The fission fragments are released at great speed; it is this kinetic energy of these fission fragments that forms the majority of the power generated by nuclear fission. Among the types of nuclei capable of undergoing fission are two of the isotopes of uranium (U-235 and U-238). Fission occurs spontaneously if a sufficient quantity of any of these elements is present; but spontaneous fission is not efficient or reliable enough to power a reactor for any length of time. Most reactors use a mixture of U-235 and U-238 as fuel.

    Because the instability that allows isotopes to fission is related to their high atomic weight, any increase in atomic weight will cause them to fission. The usual way this weight increase occurs is via the absorption of a neutron. Under the right circumstances, a fissile nucleus will absorb an extra neutron; then it will undergo fission. Nuclear reactors exploit this property by controlling the relevant conditions for fission, including the number of free neutrons available.

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    Necessary Conditions for Fission

    Fission cross-section diagram for U-235, showing the probability of fission when struck by neutrons of different energies. Probability of fission decreases with increasing neutron energy. 

    Uranium nuclei do not fission equally well under all conditions. The likelihood that uranium will absorb a neutron is dependent on the kinetic energy of the neutron relative to the atom of uranium. U-238 fissions best with "fast neutrons," which are at a much higher energy than the surrounding material. U-235 fissions best with "thermal neutrons," which have approximately the same kinetic energy as the surrounding material. Fission is also more likely if the overall number of neutrons present is high.

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    Criticality: Maintaining a Self-sustaining Fission Chain Reaction

    A diagram of the fission chain reaction shown as discrete neutron generations. For a reactor to operate efficiently, fission must occur steadily and without an outside stimulus. This state of equilibrium is referred to as "criticality." A reactor is critical when the number of neutrons in the core remains roughly constant. Neutron population is denoted by "neutron flux," which is the number of neutrons passing through a given area of space during a given interval of time. Neutron flux is manipulated in the core through the combination of fuel enrichment, moderators or coolants, and neutron poisons. Because criticality is defined only as a state of equilibrium, a nuclear reactor can be critical at any power level. This makes it possible for nuclear power reactors to operate efficiently at different power levels, which is not always the case with other types of power plant.

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    The components of the reactor core and control elements allow reactors to be constructed and operated in many different ways. Key components of the reactor core include fuel, moderators, and neutron poisons, all of which play specialized roles in the functioning of a nuclear reactor. Reactor fuel includes two isotopes of uranium, U-235 and U-238, which have different fission properties. U-235 is the more useful of the two. Fuel enrichment involves increasing the amount of U-235 in fuel. Moderators control the speed at which neutrons travel, affecting both the temperature of the core and the likelihood that neutrons will be at the right energy to cause fission. Neutron poisons such as boron and cadmium are the crucial ingredients in reactor control rods. By decreasing the number of free neutrons in the core, they reduce reactor power and can shut down the reactor entirely if fully inserted. Manipulation of these factors allows safety features like negative temperature coefficient.
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    Controlling Power Levels: Fuel Enrichment

    While both U-235 and U-238 can fission, only U-235 can maintain a self-sustaining chain reaction on its own. This is because U-235 fissions more easily than U-238, and does so in response to neutrons at a wider range of temperatures. In nature, uranium ore contains both U-238 and U-235, but U-238 is present in vastly greater quantities. Reactor fuel needs to have a somewhat higher proportion of U-235 than is found in nature in order to be efficient, so the uranium is processed to increase the amount of U-235 present. Increasing the amount of U-235 in this way is referred to as "fuel enrichment." The more highly enriched reactor fuel is, the more U-235 it contains, which means that more nuclei will fission per unit of mass, which also means that more free neutrons will be present when it is in use.

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    A moderator is a substance that affects the speed at which neutrons are traveling. Because temperature is a function of the speed at which particles travel, moderators also affect temperature, and often also serve as the reactor coolant. Common moderators include water, heavy water (deuterium), graphite, and other carbon compounds. These substances are appropriate because both carbon and hydrogen atoms are comparable to the size and mass of neutrons, allowing neutrons to "bounce off" them and transfer energy without unwanted additional effects. This is called elastic scattering. Moderators are used to slow down (thermalize) fast neutrons to the speeds at which they interact with U-235, and as reflectors, to keep neutrons inside the core.

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    Neutron Poisons

    The upper portion or 

    Neutron poisons are substances that absorb neutrons without fissioning. They make up the major ingredients in reactor control rods. The best neutron poisons for reactor control rods are those that have a high neutron cross-section, meaning that there is a high probability they will absorb neutrons at a variety of different power levels. Commonly used neutron poisons include cadmium, boron, and compounds containing those elements. When control rods are inserted into the core, they decrease the amount of free neutrons present and available for fission. This decreases the power level. If there are still enough free neutrons to maintain a self-sustaining reaction, then the reactor will resume criticality at that level. If enough neutron poison has been added to the system that the chain reaction cannot continue at any appreciable level, the reactor will shut down.

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    Reactor Core Design

    Designing a reactor core requires a thorough knowledge of the theory behind nuclear reactors. By using the complex interactions of moderator, poisons, and fuel to control neutron population, nuclear engineers can control not only how much power a reactor can generate, but how it will be affected by temperature changes. For example, all nuclear reactors in the United States (including non-power reactors) are designed in such a way that as temperature increases, the moderator can no longer slow down all of the free neutrons, so the fission reaction becomes less efficient. This important safety feature, referred to as "negative temperature coefficient," is just one of the many complex phenomena that derive from the basic principles of reactor theory.

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    Turning Nuclear Power into Electricity

    Outside of the core, the design of a nuclear power plant has a lot in common with that of other power plants. The massive amounts of heat generated by nuclear reactions is often used to boil water and run steam-powered turbines or generators. These devices must be specially designed to minimize the radiological and other risks associated with using nuclear materials, but the basic principles do not differ substantially from those behind conventional steam engines.

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    Bodansky, David. Nuclear Energy: Principles, Practices, and Prospects, 2nd Ed. Springer. New York. 2004.

    Glasstone, Samuel. Sourcebook on atomic energy. Van Nostrand. Princeton, NY. 1967.

    Nuclear Regulatory Commission: Basic References: Glossary. Last updated August 2, 2010.