In the United States, 20ᵗʰ century¹, a dimensionless unit of reactivity used in nuclear engineering, specifically to focus attention on the level of reactivity at which the chain reaction in a reactor is self-sustaining on prompt neutrons (see below) alone, a condition called prompt critical. When the reactivity = 1$, the reactor is prompt critical.
The actual magnitude of the dollar differs from reactor to reactor; it depends on the design of the reactor and the fuel that it is using. Symbol, $, which should follow the numerals, although some authors ignore this rule. One dollar = 100 cents.
The energy produced by a nuclear reactor comes from fission. When a nucleus of a fissionable element like uranium-235 is hit by a neutron, the nucleus splits or fissions. Fragments that are the nuclei of new atoms fly off (their kinetic energy becomes heat), as well as radiation and one or more neutrons. These neutrons are called prompt neutrons.
In addition to the neutrons released in the fission event, the new nuclei produced as fission fragments may later spontaneously release neutrons themselves. These are called delayed fission neutrons. The average length of the delay (for U-235) is roughly 14 seconds. The average lifetime of a prompt neutron is 0.0001 second. Taking both into consideration, the mean lifetime is 0.0106 seconds. The difference between 0.0001 and 0.0106 makes all the difference. If it were not for the delayed fission neutrons, control of a nuclear power reactor would be extremely difficult. A reactor that is prompt critical can increase the number of neutrons in flight by a factor of 2000 in a second.
For a particular nuclear reactor, one dollar is the difference between the reactivity when the reactor is just capable of sustaining a chain reaction on prompt neutrons, without delayed fission neutrons, and the reactivity when the reaction is just self-sustaining on both prompt and delayed fission neutrons. In other words, it is the reactivity that is due to the delayed neutrons alone.
According to Weinberg and Wigner², the name “dollar” was first proposed by Louis Slotin, the Canadian-American physicist who died as a result of an infamous criticality accident in 1946.
If you are interested in the dollar, you might also be interested in other measures of reactivity:
1. J. P. Franz.
U.S. Atomic Energy Commission Report AECD-3260 (1951).
We have been unable to find a copy of this report. It may contain the first recorded use of the term.
2. Alvin M. Weinberg and Eugene P. Wigner.
The Physical Theory of Neutron Chain Reactors.
Chicago: University of Chicago Press, 1958.
Page 595. “The dollar is defined as that value of C which is just equal to the contribution of the delayed neutrons.” C is the criticality factor. Other authors call it the effective multiplication factor k.
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Last revised: 22 September 2007.