This one is pretty important in the nuclear industry. Recall from prior posts (see below) that available neutrons are necessary to produce fission reaction. Each fission reaction should produce at least one more neutron that will strike another nucleus, produce fission, etc. Such as is illustrated here:
Now most fissions produce more than one extra neutron. Many fission processes produce and extra two or three. But some neutrons don't fission a nucleus. Some get absorbed by non-fissionable matter. Other simply "leak" out of the reactor. But at least one of the new neutrons (on average) have to cause one fission process in a nucleus for the fission to continue is a self-sustained chain reaction.
This simply must be self-sustaining. So there is a critical threshold that neutron availability must be kept at to keep the reaction going. In addition, recall that there are several types of neutrons. Fast neutrons are the product of fission, but if the fast neutrons strike a moderator with a large scattering cross-section, then their energy is dissipated and their speed is basically the same as the molecules of the moderator. Thus fast neutrons are slowed down and coverted into thermal neutrons. Fast neutrons are also called prompt neutrons as they are available immediately after fission. However, fission products are themselves unstable (and therefore radioactive) and themselves emit neutrons, but after-the-fact, from seconds to minutes after fission. These are called delayed neutrons. Most rectors depend on thermal neutrons to propagate the fission chain, but a few reactor types such as FBRs (see my prior post on reactor types below), depend upon fast neutrons and so are designed with a moderator with a very small scattering cross-section.
The ratio of neutron production in one generation, to the neutron absorption in a preceding generation, is called the k-factor. (also called the infinite k-factor as it is assumed that there is no neutron leakage) If the k-factor is less than unity (or less than one), the fission reaction will die off. If it is greater than one, the fission reaction will go out of control. A k-factor greater than one is essential in all nuclear weapons. In the nuclear power industry, the core is designed for the k-factor to be exactly one for the duration of the fuel burn process. This condition is called the critical condition. For nuclear weapons, critical won't do as teh reaction must be supercritical (k>1). For k<1, subcritical.
All of the above is called the neutron life cycle. Born in fission or by decay, they can only do a number of things - leak, be absorbed by fissionable material, or be absorbed by non-fissionable material. If the k-value changes in a reactor, that change is called the reactivity. There are many ways for this to happen. As an example, if the water temperature in a BWR decreases, the reactivity will be positive (and power levels will increase) simply because the colder water is denser than warmer water. Great care is taken to keep the water temperature constant. In fact, the change in reactivity per degree change in temperature is called the moderator coefficient of reactivity. (as opposed to the temperature coefficient of reactivity if the fuel changes temperature, which is termed the fuel temperature coefficient)
The fuel temperature coefficient and the moderator coefficient of reactivity are both negative, which means that any increases in temperature will quickly make the k-value lower. This is for safety. Positive reactivity could lead to a runaway reaction such as what happened in Chernobyl (read my post on that event in the light of this one). As an example, in a reactor such as the BWR in Fermi 2, if the water temperature decreased for some reason, the power output of the reactor would increase causing the water temperature to then increase, which will reduce the reaction. It simply won't run away. In addition, if for whatever reason the fuel got hotter, it would increase the water temperature and again take the reaction rate back down. A good design in my opinion.
Previously:
The Fermi Chronicles - Part 23: Davis Besse, Ohio, 2002
The Fermi Chronicles - Part 22: Nuclear Events - Chernobyl, 1986
The Fermi Chronicles - Part 21: Nuclear Events - Three Mile Island, 1979
The Fermi Chronicles - Part 20: Nuclear Events - Browns Ferry, Alabama, 1975
The Fermi Chronicles - Part 19: Nuclear Events - Fermi 1, 1966
The Fermi Chronicles - Part 18: Nuclear Events - SL-1 Event, Idaho, 1961
The Fermi Chronicles - Part 17: Nuclear Events - Windscale, UK, 1957
The Fermi Chronicles - Part 16: Nuclear Events - Chalk River, CAN, 1952
The Fermi Chronicles - Part 15: The Nuclear Business Model
The Fermi Chronicles - Part 14: Neutron Moderation
The Fermi Chronicles - Part 13: Nuclear Reactor Types
The Fermi Chronicles - Part 12: Generating Electricity
The Fermi Chronicles - Part 11: Worldwide Uranium Availability
The Fermi Chronicles - Part 10: Utilizing Nuclear Reactions To "Breed" More Fuel
The Fermi Chronicles - Part 9: Nuclear Fission
The Fermi Chronicles - Part 8: Neutron Interaction
The Fermi Chronicles - Part 7: Radioactive Decay and Half-Life
The Fermi Chronicles - Part 6: Atomic Structures
The Fermi Chronicles - Part 5: Nuclear Waste Storage
The Fermi Chronicles - Part 4: Radiation Types and Radiation "Dose"
The Fermi Chronicles - Part 3: Radiation Types
The Fermi Chronicles - Part 2: A week of training
The Fermi Chronicles - Part 1: The alpha post
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