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Reactor Period
The Inhour equation used in nuclear reactor kinetics to relate reactivity and the reactor period. Inhour is short for "inverse hour" and is defined as the reactivity which will make the stable reactor period equal to 1 hour (3,600 seconds). Reactivity is more commonly expressed as per cent millie (pcm) of Δk/k or dollars. The Inhour equation is obtained by dividing the reactivity equation, Equation 1, by the corresponding value of the inhour unit, shown by Equation 2. \rho (reactivity)= \frac+\sum_^6\frac quation 1 In = \frac quation 2 ρ = reactivity l*= neutron generation time Tp= reactor period βi= fraction of delayed neutrons of ith kind λi= precursor decay constant of ith kind For small reactivity or large reactor periods, unity may be neglected in comparison with λiTp and λi3600 and the Inhour equation can be simplified to Equation 3. In = \frac quation 3 The inhour equation is initially derived from the point kinetic ...
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Nuclear Reactor
A nuclear reactor is a device used to initiate and control a Nuclear fission, fission nuclear chain reaction. They are used for Nuclear power, commercial electricity, nuclear marine propulsion, marine propulsion, Weapons-grade plutonium, weapons production and Research reactor, research. Fissile material, Fissile nuclei (primarily uranium-235 or plutonium-239) absorb single neutron, neutrons and split, releasing energy and multiple neutrons, which can induce further fission. Reactors stabilize this, regulating Neutron absorber, neutron absorbers and neutron moderator, moderators in the core. Fuel efficiency is exceptionally high; Enriched uranium#Low-enriched uranium (LEU), low-enriched uranium is 120,000 times more energy dense than coal. Heat from nuclear fission is passed to a working fluid Nuclear reactor#By coolant, coolant. In commercial reactors, this drives Turbine, turbines and electrical generator shafts. Some reactors are used for district heating, and isotopes, isoto ...
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Reactivity (chemistry)
In chemistry, reactivity is the impulse for which a chemical substance undergoes a chemical reaction, either by itself or with other materials, with an overall release of energy. ''Reactivity'' refers to: * the chemical reactions of a single substance, * the chemical reactions of two or more substances that interact with each other, * the systematic study of sets of reactions of these two kinds, * methodology that applies to the study of reactivity of chemicals of all kinds, * experimental methods that are used to observe these processes, and * theories to predict and to account for these processes. The chemical reactivity of a single substance (reactant) covers its behavior in which it: * decomposes, * forms new substances by addition of atoms from another reactant or reactants, and * interacts with two or more other reactants to form two or more products. The chemical reactivity of a substance can refer to the variety of circumstances (conditions that include temperature, pre ...
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Per Cent Mille
A per cent mille or pcm is one one-thousandth of a percent. It can be thought of as a "milli-percent". It is commonly used in epidemiology, and in nuclear reactor engineering as a unit of reactivity. Epidemiology Statistics of crime rates, mortality and disease prevalence in a population are often given in Nuclear Reactivity In nuclear reactor engineering, a per cent mille is equal to one-thousandth of a percent of the reactivity, denoted by Greek lowercase letter rho. Reactivity is a dimensionless unit representing a departure from criticality, calculated by: :\rho=(k_-1)/k_ where keff denotes the effective multiplication factor for the reaction. Therefore, one pcm is equal to: :1~\text = \rho \cdot 10^5 This unit is commonly used in the operation of light-water reactor sites because reactivity values tend to be small, so measuring in pcm allows reactivity to be expressed using whole numbers. Related units * Percentage point difference of 1 part in 100 * Percentage ( ...
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Dollar (reactivity)
A dollar is a unit of reactivity for a nuclear reactor, calibrated to the interval between the conditions of criticality and prompt criticality. Prompt criticality will result in an extremely rapid power rise, with the resultant destruction of the reactor, unless it is specifically designed to tolerate the condition. A cent is of a dollar. In nuclear reactor physics discussions, the symbols are often appended to the end of the numerical value of reactivity, such as 3.48$ or 21 ¢. Reactivity (denoted ρ or ΔK/K) is related to the effective neutron multiplication factor (''keff''), the average number of all neutrons from one fission that cause another fission. ρ = But in nuclear physics, it useful to talk about the reactivity contributed by just the prompt neutrons. This is the reactivity in dollars or cents. Reactivity in its most general sense would not be measured in dollars or cents. This is because keff measures the total value of reactivity, a summation of the react ...
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Neutron
The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nuclear fission in 1938, the first self-sustaining nuclear reactor (Chicago Pile-1, 1942) and the first nuclear weapon (Trinity (nuclear test), Trinity, 1945). Neutrons are found, together with a similar number of protons in the atomic nucleus, nuclei of atoms. Atoms of a chemical element that differ only in neutron number are called isotopes. Free neutrons are produced copiously in nuclear fission and nuclear fusion, fusion. They are a primary contributor to the nucleosynthesis of chemical elements within stars through fission, fusion, and neutron capture processes. Neutron stars, formed from massive collapsing stars, consist of neutrons at the density of atomic nuclei but a total mass more than the Sun. Neutron properties and interactions ar ...
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Delayed Neutron
In nuclear engineering, a delayed neutron is a neutron released not immediately during a nuclear fission event, but shortly afterward—ranging from milliseconds to several minutes later. These neutrons are emitted by excited daughter nuclei of certain beta-decaying fission products. In contrast, prompt neutrons are emitted almost instantaneously—within about 10−14 seconds—at the moment of fission. During fission, a heavy nucleus splits into two smaller, neutron-rich fragments (fission products), releasing several free neutrons known as prompt neutrons. Many of these fission products are radioactive and typically undergo beta decay to reach more stable configurations. In a small subset of cases, the beta decay of a fission product results in a daughter nucleus in an excited state with enough energy to emit a neutron. This neutron, emitted shortly after fission but delayed due to the beta decay process, is called a delayed neutron. The delay in neutron emission arises from ...
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Nuclear Fission Product
Nuclear fission products are the atomic fragments left after a large atomic nucleus undergoes nuclear fission. Typically, a large nucleus like that of uranium fissions by splitting into two smaller nuclei, along with a few neutrons, the release of heat energy (kinetic energy of the nuclei), and gamma rays. The two smaller nuclei are the ''fission products''. (See also Fission products (by element)). About 0.2% to 0.4% of fissions are ternary fissions, producing a third light nucleus such as helium-4 (90%) or tritium (7%). The fission products themselves are usually unstable and therefore radioactive. Due to being relatively neutron-rich for their atomic number, many of them quickly undergo beta decay. This releases additional energy in the form of beta particles, antineutrinos, and gamma rays. Thus, fission events normally result in beta and additional gamma radiation that begins immediately after, even though this radiation is not produced directly by the fission event it ...
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Prompt Neutron
In nuclear engineering, a prompt neutron is a neutron immediately emitted (neutron emission) by a nuclear fission event, as opposed to a delayed neutron decay which can occur within the same context, emitted after beta decay of one of the fission products anytime from a few milliseconds to a few minutes later. Prompt neutrons emerge from the fission of an unstable fissionable or fissile heavy nucleus almost instantaneously. There are different definitions for how long it takes for a prompt neutron to emerge. For example, the United States Department of Energy defines a prompt neutron as a neutron born from fission within 10−13 seconds after the fission event. The U.S. Nuclear Regulatory Commission defines a prompt neutron as a neutron emerging from fission within 10−14 seconds. This emission is controlled by the nuclear force and is extremely fast. By contrast, so-called delayed neutrons are delayed by the time delay associated with beta decay (mediated by the weak force) t ...
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Thermal-neutron Reactor
A thermal-neutron reactor is a nuclear reactor that uses slow or thermal neutrons. ("Thermal" does not mean hot in an absolute sense, but means in thermal equilibrium with the medium it is interacting with, the reactor's fuel, moderator and structure, which is much lower energy than the fast neutrons initially produced by fission.) A fast-neutron reactor, on the other hand, operates using high-energy neutrons that are not slowed by a moderator. These reactors can efficiently use a broader range of fuels, including plutonium and other heavy atoms, and have the capability to breed more fissile material, such as uranium-238 into plutonium-239, which is not possible in thermal reactor. In contrast to thermal-neutron reactors, integral fast reactors (IFRs) operate using fast neutrons and are designed for increased fuel efficiency. These reactors are capable of recycling nuclear waste and breeding new fuel, which enhances sustainability. Additionally, IFRs incorporate passive safety f ...
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Exponential Decay
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and (lambda Lambda (; uppercase , lowercase ; , ''lám(b)da'') is the eleventh letter of the Greek alphabet, representing the voiced alveolar lateral approximant . In the system of Greek numerals, lambda has a value of 30. Lambda is derived from the Phoen ...) is a positive rate called the exponential decay constant, disintegration constant, rate constant, or transformation constant: :\frac = -\lambda N(t). The solution to this equation (see #Solution_of_the_differential_equation, derivation below) is: :N(t) = N_0 e^, where is the quantity at time , is the initial quantity, that is, the quantity at time . Measuring rates of decay Mean lifetime If the decaying quantity, ''N''(''t''), is the number of discrete elements in a certain set (mathematics), se ...
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