## Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

## Critical mass

A critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its nuclear properties (e.g. the nuclear fission cross-section), its density, its shape, its enrichment, its purity, its temperature and its surroundings. The concept is important in nuclear weapon design.

## Explanation of criticality

When a nuclear chain reaction in a mass of fissile material is self-sustaining, the mass is said to be in a critical state in which there is no increase or decrease in power, temperature or neutron population.

A numerical measure of a critical mass is dependent on the effective neutron multiplication factor k, the average number of neutrons released per fission event that go on to cause another fission event rather than being absorbed or leaving the material. When $k = 1$, the mass is critical, and the chain reaction is barely self-sustaining.

A subcritical mass is a mass of fissile material that does not have the ability to sustain a fission chain reaction. A population of neutrons introduced to a subcritical assembly will exponentially decrease. In this case, $k < 1$. A steady rate of spontaneous fissions causes a proportionally steady level of neutron activity. The constant of proportionality increases as k increases.

A supercritical mass is one where there is an increasing rate of fission. The material may settle into equilibrium (i.e. become critical again) at an elevated temperature/power level or destroy itself, by which equilibrium is reached. In the case of supercriticality, $k > 1$.

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