Control Rods for Fission Reactors

Since the continued chain reaction of a nuclear fission reactor depends upon at least one neutron from each fission being absorbed by another fissionable nucleus, the reaction can be controlled by using control rods of material which absorbs neutrons. Cadmium and boron are strong neutron absorbers and are the most common materials used in control rods. A typical neutron absorption reaction in boron is

In the operation of a nuclear reactor, fuel assemblies are put into place and then the control rods are slowly lifted until a chain reaction can just be sustained. As the reaction proceeds, the number of uranium-235 nuclei decreases and fission by-products which absorb neutrons build up. To keep the chain reaction going, the control rods must be withdrawn further. At some point, the chain reaction cannot be maintained and the fuel must be replenished.

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Fission concepts

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Generation Time for Fission

The average time for a neutron emitted in one fission to cause another fission is called the generation time. This generation time, along with the reproduction constant k for the reactor configuration, determines the time required to double the reaction rate. For example, if the reproduction constant were k=1.001, then to double the reaction rate would require

Now if the generation time for the fission is 0.001 seconds, the time to double the rate would be

Doubling time = (693)(0.001s) = 0.693 seconds

Not much time to respond to a power surge! This is modified significantly by inclusion of the delayed neutrons.

 Logarithm combinations
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Fission concepts

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Reproduction Constant for Fission

The reproduction constant k for a nuclear fission process is defined as the average number of neutrons from each fission which subsequently cause another fission. For U-235 fission the average number of neutrons emitted is 2.4, so the maximum reproduction constant would be 2.4. While the highly enriched uranium-235 for weapons applications arranged in an optimum geometry might approach that, the reproduction constant is greatly diminished in nuclear reactors by the fact that the fuel is only about 2-3% U-235. For power reactors the reproduction constant is kept just above 1. A reactor configuration with a reproduction constant of 1 is said to be critical.

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Fission concepts

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Delayed Neutron Effect

The doubling time of a nuclear fission reaction is a reasonable measure of the response time within which reactor safety devices would have to react to some kind of emergency. This doubling time is determined by the reproduction constant of the reactor configuration and the generation time of the fission process. One margin of safety in the kinds of nuclear power reactors used in the U.S. and Canada comes from the fact that in their operating range they are only critical with the inclusion of the delayed neutrons. The effect this has on the doubling time can be seen in the following example. For k = 1.001 , it takes 693 generations to double the rate, and at generation time of 0.001 s, the doubling time is 0.693 seconds. If .65% of the neutrons are delayed by an average of 14 seconds, the doubling time is increased by almost a factor of a hundred to

693 ((.9935)(.001s) + (.0065)(14s)) = 63.8 seconds

which is sufficient time for mechanical controls to respond. For example, the Three Mile Island safety devices had shut down the reactor within 9 seconds of the event which triggered the accident.

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Fission concepts

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