Dollar (reactivity)

A dollar expresses the reactivity of a nuclear reactor relative to delayed and prompt criticality. A cent is 1/100 of a dollar.

Each nuclear fission 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. Without delayed neutrons, a reactor that was just barely above critical, with slightly more than one prompt neutron on average from each fission causing another fission, reactor power would increase exponentially on millisecond or even microsecond timescales -- much too fast to be controlled. 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, the most extreme example of which is an exploding nuclear weapon: considerable design effort goes into keeping it deep into prompt criticality for as long as possible until most of its fuel has been 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; if not already zero, 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; on average each prompt neutron will cause exactly one additional fission, and the delayed neutrons will then increase power. A reactivity between $0 and $1 is still supercritical and power will still increase exponentially, but because the chain reaction partly depends on the delayed neutrons the power rise will be slow enough to be easily and safely controlled with mechanical control rods. 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.

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