keff

Keff, or the effective multiplication factor, is a dimensionless quantity used in nuclear reactor physics to describe the neutron population in a reactor over successive generations. It is the ratio of neutrons produced by fission in one generation to the neutrons lost (through absorption or leakage) in the preceding generation. If keff equals 1, the reactor is at criticality and the neutron population remains steady. If keff is greater than 1, the system is supercritical and the neutron population grows; if it is less than 1, the system is subcritical and the population declines.

Keff can be interpreted as the dominant eigenvalue of the neutron transport or diffusion problem for a given reactor configuration. In an infinite, non-leaking medium, the corresponding quantity is keff,infinite, which does not account for leakage. In practice, keff reflects the combined effects of fuel composition, moderator presence, geometry, temperature, and neutron-absorbing materials.

A range of factors influence keff, including fuel enrichment, burnup, moderator density, void fraction, and temperature feedback mechanisms such as the Doppler broadening of resonances and moderator expansion. Control rods and soluble poisons alter keff by changing the absorption properties of the core.

Keff is typically estimated through numerical methods, using neutron transport or diffusion theory in deterministic codes or Monte Carlo simulations. It is also measured and validated in critical experiments and during reactor operation, where adjustments to control systems aim to maintain keff near 1 for safe, steady-state power production.