In nuclear engineering, an assembly is prompt critical if for each nuclear fission event, one or more of the immediate or prompt neutrons released causes an additional fission event. This causes either a self-sustaining fission reaction (in the case of critical), or a rapidly exponential increase in the number of fission events and, if left unmanaged, a resulting explosion (in the case of supercritical). However, an assembly can be either without being prompt critical. Nuclear engineering is the practical application of the atomic nucleus gleaned from principles of nuclear physics and the interaction between radiation and matter. ... An induced nuclear fission event. ... In nuclear engineering, a prompt neutron is a neutron immediately emitted by a nuclear fission event, as opposed to a delayed neutron which is emitted by one of the fission products anytime from a few milliseconds to a few minutes later. ... In mathematics, a quantity that grows exponentially (or geometrically) is one that grows at a rate proportional to its size. ... A sphere of plutonium surrounded by neutron-reflecting blocks of tungsten carbide. ...

An assembly is merely critical if each fission event causes, on average, exactly one other. This causes a self-sustaining fission chain reaction. When a uranium-235 (U-235) atom undergoes nuclear fission, it typically releases 2 or 3 thermal neutrons (with the average being about 2.4). Thermal neutrons are neutrons with a speed such that they are capable of initiating further fission events. In this situation, an assembly is critical if every released neutron has a 1/2.4 = 0.42 = 42% probability of causing another fission event before it is absorbed by a non-fissile atom. In this state, every fission event (triggered by one neutron) causes another, which releases several neutrons, one of which triggers a further fission event, and so on. The criticality or effective neutron multiplication factor k = 1. A controlled critical state is the goal of a nuclear fission power reactor, which may achieve a controlled critical state by absorbing excess neutrons, on the one hand, to reduce the rate of reaction, or by using a neutron moderator, on the other hand, to slow down fast neutrons so that they become thermal neutrons and are more likely to initiate fission events. Albert Einsteins letter to President Roosevelt in 1939 about his concern, about (Nuclear chain reactions) Click for closeup of letter A nuclear chain reaction occurs when on average more than one nuclear reaction is caused by another nuclear reaction, thus leading to an exponential increase in the number of... General Name, Symbol, Number uranium, U, 92 Chemical series actinides Group, Period, Block n/a, 7, f Appearance silvery gray metallic; corrodes to a spalling black oxide coat in air Atomic mass 238. ... An induced nuclear fission event. ... This article does not cite its references or sources. ... Albert Einsteins letter to President Roosevelt in 1939 about his concern, about (Nuclear chain reactions) Click for closeup of letter A nuclear chain reaction occurs when on average more than one nuclear reaction is caused by another nuclear reaction, thus leading to an exponential increase in the number of... In nuclear engineering, a neutron moderator is a medium which reduces the velocity of fast neutrons, thereby turning them into thermal neutrons capable of sustaining a nuclear chain reaction. ... A fast neutron is a free neutron with a kinetic energy level close to 1 MeV (10 TJ/kg, hence a speed of 14,000 km/s. ... This article does not cite its references or sources. ...

In a subcritical assembly, each fission event triggers, on average, less than one other (k < 1). For example, if 2.4 neutrons are released per fission event, then if the probability of a neutron causing a further event is less than 1/2.4 = 0.42, the assembly is sub-critical and a self-sustaining fission reaction cannot occur.

If each fission event causes, on average, more than one further fission event, the assembly is said to be supercritical (k > 1). Each fission event triggers many more, leading to an exponential increase in the number of fission events, and potentially an explosion. This occurs in a fission bomb. For example, if on average 2.4 neutrons are released from each fission event, and each neutron has an 83% chance of initiating a further fission event, then a single fission event will (on average) release 2.4 neutrons and trigger 2 further events; those events will in turn release 5 neutrons and trigger 4 further events; in the next "generation" 8 events will occur, then 16, and so on. In mathematics, a quantity that grows exponentially (or geometrically) is one that grows at a rate proportional to its size. ... The mushroom cloud of the atomic bombing of Nagasaki, Japan, in 1945 lifted nuclear fallout some 18 km (60,000 feet) above the epicenter. ...

However, not all neutrons released during nuclear fission are released immediately. Some are released more or less immediately (and are termed prompt neutrons); other neutrons are released by fission breakdown products as these breakdown products themselves undergo nuclear decay (and these are termed delayed neutrons). For every 100 fissions in U-235, 242 neutrons are emitted essentially immediately and 1.58 are emitted later. Thus, the ratio of delayed to prompt neutrons is β = 0.0065. Prompt neutrons have a lifetime of about 0.0001 s from the fission event that generated them, and delayed neutrons have a "lifetime" (time to be generated plus time before they are absorbed) of about 10 s, so the average neutron "lifetime" is about 0.1 s. In nuclear engineering, a prompt neutron is a neutron immediately emitted by a nuclear fission event, as opposed to a delayed neutron which is emitted by one of the fission products anytime from a few milliseconds to a few minutes later. ... In nuclear engineering, a prompt neutron is a neutron immediately emitted by a nuclear fission event, as opposed to a delayed neutron which is emitted by one of the fission products anything from a few milliseconds to a few minutes later. ...

The fraction of excess neutrons produced in each generation is ρ = (k - 1)/k. For a reactor operating close to criticality (k approximately equal to 1) this may be approximated by ρ = k - 1. If 0 < ρ < β, the reactor is delayed critical — that is, the reactor is subcritical with respect to the prompt neutrons and goes supercritical only with the contribution of the delayed neutrons. This is a normal and controllable state for a nuclear reactor; power changes are slow. If ρ > β, however, the reactor is prompt critical (supercritical considering only the prompt neutrons), which is dangerous.

Thus, a prompt critical mass is a supercritical mass that is supercritical without needing the contribution of neutrons whose release is delayed after the triggering of each fission event. Supercriticality is achieved using only prompt neutrons. The reaction therefore accelerates faster than that of a (merely) supercritical mass. A sphere of plutonium surrounded by neutron-reflecting blocks of tungsten carbide. ... In nuclear engineering, a prompt neutron is a neutron immediately emitted by a nuclear fission event, as opposed to a delayed neutron which is emitted by one of the fission products anytime from a few milliseconds to a few minutes later. ...

Prompt criticality must be avoided in the operation of a nuclear reactor, and reactors are designed to make it as unlikely as possible that it will occur. Only two reactor accidents are suspected of having achieved prompt criticality, those of Chernobyl #4 and SL-1. In both cases there is doubt that prompt criticality occurred, although in both the uncontrolled surge in power was sufficient to cause an explosion that destroyed the reactor. At Chernobyl, in 1986, the heat of an overheated reactor core led to the meltdown of the core, vaporization of steam and a steam explosion. The containment vessel around the nuclear reactor core was inadequate to contain the explosion, and radioactive material escaped the core. A further explosion (possibly a hydrogen explosion) followed. This was compounded by a graphite fire. Thus, the accident was due to a non-nuclear explosion, but with the escape of large quantities of highly radioactive material. Core of a nuclear reactor A nuclear reactor is a device in which nuclear chain reactions are initiated, controlled, and sustained at a steady rate (as opposed to a nuclear explosion, where the chain reaction occurs in a split second). ... The nuclear power plant at Chernobyl prior to the completion of the sarcophagus. ... The SL-1, the Stationary Low-Power Reactor Number One, was a U.S. experimental military nuclear power reactor. ... A nuclear meltdown occurs when the core of a nuclear reactor melts. ... A steam explosion (also called a littoral explosion, or fuel-coolant interaction, fci) is a violent boiling or flashing of water into steam, occurring when water is either superheated, or rapidly heated by fine hot debris produced within it. ... General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ... Graphite (named by Abraham Gottlob Werner in 1789, from the Greek γραφειν: to draw/write, for its use in pencils) is one of the allotropes of carbon. ...

Many reactor designs do succeed in making prompt criticality practically impossible. A pressurized water reactor (PWR), for example, does not contain enough fuel of high enough enrichment to make a prompt critical assembly with the materials in the core, however they are reconfigured. A pressurized water reactor (PWR) is a type of nuclear power reactor that uses ordinary light water for both coolant and for neutron moderation. ...

In the design of nuclear weapons, on the other hand, achieving prompt criticality is essential. Indeed, one of the problems to be overcome in constructing a plutonium-fueled bomb is to achieve prompt criticality and an explosion before the energy released by the reaction in an assembly that is merely supercritical destroys the bomb. This is also the reason that high-grade plutonium is used: lower grades make the timely assembly of a prompt critical configuration even more difficult. The mushroom cloud of the atomic bombing of Nagasaki, Japan, 1945, rose some 18 km (11 mi) above the hypocenter. ... General Name, Symbol, Number plutonium, Pu, 94 Chemical series actinides Group, Period, Block ?, 7, f Appearance silvery white Atomic mass (244) g/mol Electron configuration [Rn] 5f6 7s2 Electrons per shell 2, 8, 18, 32, 24, 8, 2 Physical properties Phase solid Density (near r. ...

See also

• nuclear chain reaction
• prompt neutron
• fast neutron
• thermal neutron
• neutron moderator
• void coefficient
• critical mass
• criticality accident
• nuclear reaction
• nuclear weapon design
• subcritical reactor

Albert Einsteins letter to President Roosevelt in 1939 about his concern, about (Nuclear chain reactions) Click for closeup of letter A nuclear chain reaction occurs when on average more than one nuclear reaction is caused by another nuclear reaction, thus leading to an exponential increase in the number of... In nuclear engineering, a prompt neutron is a neutron immediately emitted by a nuclear fission event, as opposed to a delayed neutron which is emitted by one of the fission products anytime from a few milliseconds to a few minutes later. ... A fast neutron is a free neutron with a kinetic energy level close to 1 MeV (10 TJ/kg, hence a speed of 14,000 km/s. ... This article does not cite its references or sources. ... In nuclear engineering, a neutron moderator is a medium which reduces the velocity of fast neutrons, thereby turning them into thermal neutrons capable of sustaining a nuclear chain reaction. ... In nuclear engineering, the void coefficient (more properly called void coefficient of reactivity) is a number that can be used to estimate how much the thermal output of a nuclear reactor increases (or decreases, if negative) as voids (steam bubbles) form in the reactor moderator or coolant. ... A sphere of plutonium surrounded by neutron-reflecting blocks of tungsten carbide. ... A criticality accident (also sometimes referred to as an excursion or power excursion) occurs when a nuclear chain reaction is accidentally allowed to occur in fissile material, such as enriched uranium or plutonium, or compounds thereof This releases neutron radiation which may be highly dangerous to surrounding personnel and which... In nuclear physics, a nuclear reaction is a process in which two nuclei or nuclear particles collide, to produce products different to the initial products. ... The first nuclear weapons, though large, cumbersome and inefficient, provided the basic design building blocks of all future weapons. ... A subcritical reactor is a nuclear fission reactor that produces fission without achieving criticality. ...

References and links

• "Nuclear Energy: Principles", Physics Department, Faculty of Science, Mansoura University, Mansoura, Egypt; apparently excerpted from notes from the University of Washington Department of Mechanical Engineering; themselves apparently summarized from Bodansky, D. (1996), Nuclear Energy: Principles, Practices, and Prospects, AIP
• DOE Fundamentals Handbook