A dollar is a unit of reactivity for a
nuclear reactor
A nuclear reactor is a device used to initiate and control a fission nuclear chain reaction or nuclear fusion reactions. Nuclear reactors are used at nuclear power plants for electricity generation and in nuclear marine propulsion. Heat from nu ...
, calibrated to the interval between the conditions of
delayed criticality
Nuclear reactor physics is the field of physics that studies and deals with the applied study and engineering applications of chain reaction to induce a controlled rate of fission in a nuclear reactor for the production of energy.van Dam, H., ...
and
prompt criticality
In nuclear engineering, prompt criticality describes a nuclear fission event in which criticality (the threshold for an exponentially growing nuclear fission chain reaction) is achieved with prompt neutrons alone (neutrons that are released imm ...
. Zero dollars is defined to be the threshold of slow criticality, which means a steady reaction rate. One dollar is defined to be the threshold of prompt criticality, which means a nuclear excursion or explosion. A cent is of a dollar.
Meaning and use
Each
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 radio ...
produces several neutrons that can be absorbed, escape from the reactor, or go on to cause more fissions in a chain reaction. When an average of one neutron from each fission goes on to cause another fission, the reactor is just barely "critical" and the chain reaction proceeds at a constant power level.
Most neutrons produced in fission are "prompt", i.e., created with the
fission products in less than about 10 nanoseconds (a
"shake" of time). But certain
fission products produce additional neutrons when they decay up to several minutes after their creation by fission. These
delayed-release neutrons, a few percent of the total, are key to stable
nuclear reactor control
Nuclear reactor physics is the field of physics that studies and deals with the applied study and engineering applications of chain reaction to induce a controlled rate of fission in a nuclear reactor for the production of energy.van Dam, H., ...
. Without delayed neutrons, in a reactor that was just barely above critical, reactor power would increase exponentially on millisecond or even microsecond timescales – much too fast to be controlled with current or near-future technology. Such a rapid power increase can also happen in a real reactor when the chain reaction is sustained without the help of the delayed neutrons. This is
prompt criticality
In nuclear engineering, prompt criticality describes a nuclear fission event in which criticality (the threshold for an exponentially growing nuclear fission chain reaction) is achieved with prompt neutrons alone (neutrons that are released imm ...
, the most extreme example of which is an exploding nuclear weapon where considerable design effort goes into keeping the core deep into prompt criticality for as long as possible until the greatest attainable percentage of material has fissioned.
By definition, a reactivity of zero dollars is just barely on the edge of criticality using both prompt and delayed neutrons. A reactivity less than zero dollars is subcritical; the power level will decrease exponentially and a sustained chain reaction will not occur. One dollar is defined as the threshold between delayed and prompt criticality. At prompt criticality, on average each fission will cause exactly one additional fission via prompt neutrons, and the delayed neutrons will then increase power. Any reactivity above $0 is supercritical and power will increase exponentially, but between $0 and $1 the power rise will be slow enough to be easily and safely controlled with mechanical control rods because the chain reaction partly depends on the delayed neutrons. A power reactor operating at steady state (constant power) will therefore have an average reactivity of $0, with small fluctuations above and below this value.
Reactivity can also be expressed in relative terms, such as "5 cents above prompt critical".
While power reactors are carefully designed and operated to avoid prompt criticality under all circumstances, many small
research
Research is "creativity, creative and systematic work undertaken to increase the stock of knowledge". It involves the collection, organization and analysis of evidence to increase understanding of a topic, characterized by a particular att ...
or "zero power" reactors are designed to be intentionally placed into prompt criticality (reactivity > $1) with complete safety by rapidly withdrawing their control rods. Their fuel elements are designed so that as they heat up, reactivity is automatically and quickly reduced through effects such as
doppler broadening
In atomic physics, Doppler broadening is broadening of spectral lines due to the Doppler effect caused by a distribution of velocities of atoms or molecules. Different velocities of the emitting (or absorbing) particles result in different Dopp ...
and
thermal expansion
Thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature, usually not including phase transitions.
Temperature is a monotonic function of the average molecular kinetic ...
. Such reactors can be "pulsed" to very high power levels (e.g., several GW) for a few milliseconds, after which reactivity automatically drops to $0 and a relatively low and constant power level (e.g. several hundred kW) is maintained until shut down manually by reinserting the control rods.
Subcritical reactor
A subcritical reactor is a nuclear fission reactor concept that produces fission without achieving criticality. Instead of sustaining a chain reaction, a subcritical reactor uses additional neutrons from an outside source. There are two general c ...
s, which thus far have only been built at laboratory scale, would constantly run in "negative dollars" (most likely a few cents below
elayedcritical) with the "missing" neutrons provided by an external
neutron source
A neutron source is any device that emits neutrons, irrespective of the mechanism used to produce the neutrons. Neutron sources are used in physics, engineering, medicine, nuclear weapons, petroleum exploration, biology, chemistry, and nuclear p ...
, e.g.
spallation
Spallation is a process in which fragments of material (spall) are ejected from a body due to impact or stress. In the context of impact mechanics it describes ejection of material from a target during impact by a projectile. In planetary p ...
driven by a particle accelerator in an
accelerator-driven subcritical reactor
An accelerator-driven subcritical reactor (ADSR) is a nuclear reactor design formed by coupling a substantially subcritical nuclear reactor core with a high-energy proton or electron accelerator. It could use thorium as a fuel, which is more abund ...
.
History
According to
Alvin Weinberg and
Eugene Wigner
Eugene Paul "E. P." Wigner ( hu, Wigner Jenő Pál, ; November 17, 1902 – January 1, 1995) was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 "for his con ...
,
Louis Slotin
Louis Alexander Slotin (1 December 1910 – 30 May 1946) was a Canadian physicist and chemist who took part in the Manhattan Project. Born and raised in the North End of Winnipeg, Manitoba, Slotin earned both his Bachelor of Science and M ...
was the first to propose the name "dollar" for the interval of reactivity between barely critical and
prompt critical
In nuclear engineering, prompt criticality describes a nuclear fission event in which criticality (the threshold for an exponentially growing nuclear fission chain reaction) is achieved with prompt neutrons alone (neutrons that are released immed ...
ity, and "cents" for the decimal fraction of the dollar.
References
{{Reflist
Neutron
Units of measurement
Nuclear physics
Nuclear power
Nuclear facilities