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 1⁄100 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 ¢.[1][2]
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.[2]
ρ = keff - 1/keff
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.
In general, reactivity is not in dollars or cents, because keff measures its total value, a summation of the reactivity of both the prompt and delayed neutrons. Reactivity in dollars is dependent on the delayed neutron fraction (βeff).[2]
Reactivity in dollars = ρ/βeff
Reactivity in cents = 100 x (ρ/βeff)
When certain components or parameters change the reactivity of a nuclear reactor, the changes may be calculated as their reactivity worth. A control rod and a chemical reactor poison both have negative reactivity worth, while the addition of a neutron moderator would generally have a positive reactivity worth. Reactivity worth can be measured in dollars or cents. During the design and testing of a nuclear reactor, each component will be scrutinized to determine its reactivity worth, often at different temperatures, pressures, and control rod heights. For example, the burning of reactor poisons are important to the lifespan of the reactor core, since their reactivity worth decreases as the core ages.