Void coefficient of reactivity
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nuclear engineering Nuclear engineering is the engineering discipline concerned with designing and applying systems that utilize the energy released by nuclear processes. The most prominent application of nuclear engineering is the generation of electricity. Worldwide ...
, the void coefficient (more properly called void coefficient of reactivity) is a number that can be used to estimate how much the reactivity of a
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 ...
changes as voids (typically
steam Steam is water vapor, often mixed with air or an aerosol of liquid water droplets. This may occur due to evaporation or due to boiling, where heat is applied until water reaches the enthalpy of vaporization. Saturated or superheated steam is inv ...
bubbles) form in the reactor moderator or
coolant A coolant is a substance, typically liquid, that is used to reduce or regulate the temperature of a system. An ideal coolant has high thermal capacity, low viscosity, is low-cost, non-toxic, chemically inert and neither causes nor promotes corr ...
. Net reactivity in a reactor depends on several factors, one of which is the void coefficient. Reactors in which either the moderator or the coolant is a liquid will typically have a void coefficient which is either negative (if the reactor is under-moderated) or positive (if the reactor is over-moderated). Reactors in which neither the moderator nor the coolant is a liquid (e.g., a graphite-moderated,
gas-cooled reactor A gas-cooled reactor (GCR) is a nuclear reactor that uses graphite as a neutron moderator and a gas (carbon dioxide or helium in extant designs) as coolant. Although there are many other types of reactor cooled by gas, the terms ''GCR'' and to a l ...
) will have a zero void coefficient. It is unclear how the definition of "void" coefficient applies to reactors in which the moderator/coolant is neither liquid nor gas ( supercritical water reactor).


Explanation

Nuclear fission Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radioactiv ...
reactors run on nuclear
chain reaction A chain reaction is a sequence of reactions where a reactive product or by-product causes additional reactions to take place. In a chain reaction, positive feedback leads to a self-amplifying chain of events. Chain reactions are one way that sys ...
s, in which each
nucleus Nucleus (: nuclei) is a Latin word for the seed inside a fruit. It most often refers to: *Atomic nucleus, the very dense central region of an atom *Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA Nucleu ...
that undergoes fission releases heat and neutrons. Each
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 nucle ...
may impact another nucleus and cause it to undergo fission. The speed of this neutron affects its probability of causing additional fission, as does the presence of neutron-absorbing material. On the one hand,
thermal neutron The neutron detection temperature, also called the neutron energy, indicates a free neutron's kinetic energy, usually given in electron volts. The term ''temperature'' is used, since hot, thermal and cold neutrons are moderated in a medium wit ...
s are more easily absorbed by fissile nuclei than
fast neutron The neutron detection temperature, also called the neutron energy, indicates a free neutron's kinetic energy, usually given in electron volts. The term ''temperature'' is used, since hot, thermal and cold neutrons are moderated in a medium with ...
s, so a
neutron moderator In nuclear engineering, a neutron moderator is a medium that reduces the speed of fast neutrons, ideally without capturing any, leaving them as thermal neutrons with only minimal (thermal) kinetic energy. These thermal neutrons are immensely ...
that slows neutrons will increase the reactivity of a nuclear reactor. On the other hand, a neutron absorber will decrease the reactivity of a nuclear reactor. These two mechanisms are used to control the thermal power output of a nuclear reactor. In order to extract useful power from a nuclear reactor, and (for most reactor designs) to keep it intact and functioning, a cooling system must be used. Some reactors circulate pressurized water; some use liquid
metal A metal () is a material that, when polished or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, electricity and thermal conductivity, heat relatively well. These properties are all associated wit ...
, such as
sodium Sodium is a chemical element; it has Symbol (chemistry), symbol Na (from Neo-Latin ) and atomic number 11. It is a soft, silvery-white, highly reactive metal. Sodium is an alkali metal, being in group 1 element, group 1 of the peri ...
, NaK,
lead Lead () is a chemical element; it has Chemical symbol, symbol Pb (from Latin ) and atomic number 82. It is a Heavy metal (elements), heavy metal that is density, denser than most common materials. Lead is Mohs scale, soft and Ductility, malleabl ...
, or mercury; others use gases (see
advanced gas-cooled reactor The advanced gas-cooled reactor (AGR) is a type of nuclear reactor designed and operated in the United Kingdom. These are the generation II reactor, second generation of British gas-cooled reactors, using Nuclear graphite, graphite as the neutron ...
). If the coolant is a liquid, it may boil if the temperature inside the reactor rises. This boiling leads to ''voids'' inside the reactor. Voids may also form if coolant is lost from the reactor in some sort of accident (called a loss of coolant accident, which has other dangers). Some reactors operate with the coolant in a constant state of boiling, using the generated vapor to turn turbines. The coolant liquid may act as a neutron absorber, as a neutron moderator, usually as both but with one or other role as the most influential. In either case, the amount of void inside the reactor can affect the reactivity of the reactor. The change in reactivity caused by a change of voids inside the reactor is directly proportional to the ''void coefficient''. A positive void coefficient means that the reactivity increases as the void content inside the reactor increases due to increased boiling or loss of coolant; for example, if the coolant acts predominantly as neutron absorber. This positive void coefficient causes a
positive feedback Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop where the outcome of a process reinforces the inciting process to build momentum. As such, these forces can exacerbate the effects ...
loop, starting with the first occurrence of steam bubbles. This can quickly boil all the coolant in the reactor, if not countered by an (automatic) control mechanism, or if said mechanism's response time is too slow. This happened in the
RBMK The RBMK (, РБМК; ''reaktor bolshoy moshchnosti kanalnyy'', "high-power channel-type reactor") is a class of graphite moderated reactor, graphite-moderated nuclear reactor, nuclear power reactor designed and built by the Soviet Union. It is so ...
reactor that was destroyed in the
Chernobyl disaster On 26 April 1986, the no. 4 reactor of the Chernobyl Nuclear Power Plant, located near Pripyat, Ukrainian Soviet Socialist Republic, Ukrainian SSR, Soviet Union (now Ukraine), exploded. With dozens of direct casualties, it is one of only ...
due to positive void coefficient and fast power coefficients present at lower reactor power levels, the EPS scram accelerating rather than dampening reactivity resulting in the explosion. A negative void coefficient means that the reactivity decreases as the void content inside the reactor increases—but it also means that the reactivity increases if the void content inside the reactor is reduced. In boiling-water reactors with large negative void coefficients, a sudden pressure rise (caused, for example, by unplanned closure of a streamline valve) will result in a sudden decrease in void content: the increased pressure will cause some of the steam bubbles to condense ("collapse"); and the thermal output will possibly increase until it is terminated by safety systems, by increased void formation due to the higher power, or, possibly, by system or component failures that relieve pressure, causing void content to increase and power to decrease. Boiling water reactors are all designed (and required) to handle this type of transient. On the other hand, if a reactor is designed to operate with no voids at all, a large negative void coefficient may serve as a safety system. A loss of coolant in such a reactor decreases the thermal output, but of course heat that is generated is no longer removed, so the temperature could rise (if all other safety systems simultaneously failed). Thus, a large void coefficient, whether positive or negative, can be either a design issue (requiring more careful, faster-acting control systems) or a desired quality depending on reactor design. Gas-cooled reactors do not have issues with voids forming.


Reactor designs

*
Boiling water reactor A boiling water reactor (BWR) is a type of nuclear reactor used for the generation of electrical power. It is the second most common type of electricity-generating nuclear reactor after the pressurized water reactor (PWR). BWR are thermal neutro ...
s generally have negative void coefficients, and in normal operation the negative void coefficient allows reactor power to be adjusted by changing the rate of water flow through the core. The negative void coefficient can cause an unplanned reactor power increase in events (such as sudden closure of a streamline valve) where the reactor pressure is suddenly increased. In addition, the negative void coefficient can result in power oscillations in the event of a sudden reduction in core flow, such as might be caused by a recirculation pump failure. Boiling water reactors are designed to ensure that the rate of pressure rise from a sudden streamline valve closure is limited to acceptable values, and they include multiple safety systems designed to ensure that any sudden reactor power increases or unstable power oscillations are terminated before fuel or piping damage can occur. *
Pressurized water reactor A pressurized water reactor (PWR) is a type of light-water nuclear reactor. PWRs constitute the large majority of the world's nuclear power plants (with notable exceptions being the UK, Japan, India and Canada). In a PWR, water is used both as ...
s operate with a relatively small amount of voids, and the water serves as both moderator and coolant. Thus a large negative void coefficient ensures that if the water boils or is lost the power output will drop. *
CANDU The CANDU (CANada Deuterium Uranium) is a Canadian pressurized heavy-water reactor design used to generate electric power. The acronym refers to its deuterium oxide (heavy water) neutron moderator, moderator and its use of (originally, natural ...
reactors have positive void coefficients that are small enough that the control systems can easily respond to boiling coolant before the reactor reaches dangerous temperatures (see References). Furthermore, a
loss of coolant accident A loss-of-coolant accident (LOCA) is a mode of failure for a nuclear reactor; if not managed effectively, the results of a LOCA could result in reactor core damage. Each nuclear plant's emergency core cooling system (ECCS) exists specifically to ...
automatically
scram A scram or SCRAM is an emergency shutdown of a nuclear reactor effected by immediately terminating the fission reaction. It is also the name that is given to the manually operated kill switch that initiates the shutdown. In commercial reactor ...
s the reactor and unlike in
light water reactor The light-water reactor (LWR) is a type of thermal-neutron reactor that uses normal water, as opposed to heavy water, as both its coolant and neutron moderator; furthermore a solid form of fissile elements is used as fuel. Thermal-neutron react ...
s, the introduction of "regular" water to the reactor core—for example as an emergency coolant—does not pose the risk of criticality as a CANDU can only reach criticality in the absence of the neutron absorption that is present in significant quantities of light water. *
RBMK The RBMK (, РБМК; ''reaktor bolshoy moshchnosti kanalnyy'', "high-power channel-type reactor") is a class of graphite moderated reactor, graphite-moderated nuclear reactor, nuclear power reactor designed and built by the Soviet Union. It is so ...
reactors, such as the reactors at Chernobyl, had a dangerously high positive void coefficient. This allowed the reactor to run on unenriched
uranium Uranium is a chemical element; it has chemical symbol, symbol U and atomic number 92. It is a silvery-grey metal in the actinide series of the periodic table. A uranium atom has 92 protons and 92 electrons, of which 6 are valence electrons. Ura ...
and to require no
heavy water Heavy water (deuterium oxide, , ) is a form of water (molecule), water in which hydrogen atoms are all deuterium ( or D, also known as ''heavy hydrogen'') rather than the common hydrogen-1 isotope (, also called ''protium'') that makes up most o ...
, saving costs; RBMKs were also capable of producing weapons-grade plutonium, unlike the other main Soviet design, the
VVER The water-water energetic reactor (WWER), or VVER (from ) is a series of pressurized water reactor designs originally developed in the Soviet Union, and now Russia, by OKB Gidropress. The idea of such a reactor was proposed at the Kurchatov Instit ...
. Before the Chernobyl accident these reactors had a positive void coefficient of 4.7
beta Beta (, ; uppercase , lowercase , or cursive ; or ) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Ancient Greek, beta represented the voiced bilabial plosive . In Modern Greek, it represe ...
, which after the accident was lowered to 0.7 beta so they could safely remain in service. *
Fast breeder reactor A breeder reactor is a nuclear reactor that generates more fissile material than it consumes. These reactors can be Nuclear fuel, fueled with more-commonly available isotopes of uranium and Isotopes of thorium, thorium, such as uranium-238 and t ...
s do not use moderators, since they run on
fast neutron The neutron detection temperature, also called the neutron energy, indicates a free neutron's kinetic energy, usually given in electron volts. The term ''temperature'' is used, since hot, thermal and cold neutrons are moderated in a medium with ...
s, but the coolant (often
lead Lead () is a chemical element; it has Chemical symbol, symbol Pb (from Latin ) and atomic number 82. It is a Heavy metal (elements), heavy metal that is density, denser than most common materials. Lead is Mohs scale, soft and Ductility, malleabl ...
or
sodium Sodium is a chemical element; it has Symbol (chemistry), symbol Na (from Neo-Latin ) and atomic number 11. It is a soft, silvery-white, highly reactive metal. Sodium is an alkali metal, being in group 1 element, group 1 of the peri ...
) may serve as a neutron absorber and reflector. For this reason they have a positive void coefficient. *
Magnox Magnox is a type of nuclear power / production reactor that was designed to run on natural uranium with graphite as the moderator and carbon dioxide gas as the heat exchange coolant. It belongs to the wider class of gas-cooled reactors. The ...
reactors,
advanced gas-cooled reactor The advanced gas-cooled reactor (AGR) is a type of nuclear reactor designed and operated in the United Kingdom. These are the generation II reactor, second generation of British gas-cooled reactors, using Nuclear graphite, graphite as the neutron ...
s and
pebble bed reactor The pebble-bed reactor (PBR) is a design for a graphite- moderated, gas-cooled nuclear reactor. It is a type of very-high-temperature reactor (VHTR), one of the six classes of nuclear reactors in the Generation IV initiative. The basic desig ...
s are gas-cooled and so void coefficients are not an issue. In fact, some can be designed so that total loss of coolant does not cause core meltdown even in the absence of active control systems. As with any reactor design, loss of coolant is only one of many possible failures that could potentially lead to an accident. In case of accidental ingress of liquid water into the core of pebble bed reactors, a positive void coefficient may occur.
Magnox Magnox is a type of nuclear power / production reactor that was designed to run on natural uranium with graphite as the moderator and carbon dioxide gas as the heat exchange coolant. It belongs to the wider class of gas-cooled reactors. The ...
and UNGG reactors were designed with the dual purpose of producing
electrical power Electric power is the rate of transfer of electrical energy within a electric circuit, circuit. Its SI unit is the watt, the general unit of power (physics), power, defined as one joule per second. Standard prefixes apply to watts as with oth ...
and weapon grade plutonium. * The Advanced CANDU reactor, a never built proposed reactor type based on the CANDU, promises a negative void coefficient but it must use slightly enriched uranium as a fuel and cannot operate with
natural uranium Natural uranium (NU or Unat) is uranium with the same isotopic ratio as found in nature. It contains 0.711% uranium-235, 99.284% uranium-238, and a trace of uranium-234 by weight (0.0055%). Approximately 2.2% of its radioactivity comes from ura ...
as the "regular" CANDU does. * In a
molten salt reactor A molten-salt reactor (MSR) is a class of nuclear fission reactor in which the primary nuclear reactor coolant and/or the fuel is a mixture of molten salt with a fissile material. Two research MSRs operated in the United States in the mid-20th ...
the salt is usually neither a strong moderator nor a neutron poison. If a
thermal neutron The neutron detection temperature, also called the neutron energy, indicates a free neutron's kinetic energy, usually given in electron volts. The term ''temperature'' is used, since hot, thermal and cold neutrons are moderated in a medium wit ...
spectrum is used, external moderators such as nuclear graphite are usually employed. Volatile fission products can "bubble out" of solution and as the fuel is dissolved in the salt, this decreases reactivity at and around the site of the bubble. Furthermore, most of the fission product noble gases—chief among them
Xenon-135 Xenon-135 (135Xe) is an Isotope#Radioactive, primordial, and stable isotopes, unstable isotope of xenon with a half-life of about 9.2 hours. 135Xe is a fission product of uranium and it is the most powerful known neutron-absorbing nuclear poison ...
are strong neutron poisons. As the boiling point of the involved salts is relatively high (at a point at which the structural integrity of the housing for the molten salt would be in question), there is usually little to no emphasis put on the consequences of it boiling off. Frequently molten salt reactors employ a melt plug that melts at much lower temperatures than the boiling point of the salts and allows them to solidify in a core catcher.


See also

*
Nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies th ...


Notes

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References


Chernobyl - A Canadian Perspective
- A brochure describing nuclear reactors in general and the RBMK design in particular, focusing on the safety differences between them and
CANDU The CANDU (CANada Deuterium Uranium) is a Canadian pressurized heavy-water reactor design used to generate electric power. The acronym refers to its deuterium oxide (heavy water) neutron moderator, moderator and its use of (originally, natural ...
reactors. Published by Atomic Energy of Canada Ltd. (AECL), designer of the CANDU reactor. * J.J. Whitlock
Why do CANDU reactors have a "positive void coefficient"?
- An explanation published on The Canadian Nuclear FAQ, a website of "frequently-asked questions" and answers about Canadian nuclear technology. * J.J. Whitlock

- An explanation published on The Canadian Nuclear FAQ, a website of "frequently-asked questions" and answers about Canadian nuclear technology. Nuclear reactor safety