Subcritical
When \(k_{\mathrm{eff}} < 1\), each generation produces fewer effective neutrons than the last. Without an external source, the neutron population decays.
Nuclear reactor physics
Supercriticality modes: how neutron populations change.
Supercriticality describes a chain reaction state where each generation produces more neutrons than the previous one. This page explains the physics using safe conceptual models, not operational reactor instructions.
Interactive model
Adjust the effective multiplication factor.
The animation shows qualitative neutron population behavior. It is scaled for learning clarity and is not a reactor design, safety, or operation calculator.
Critical
When \(k_{\mathrm{eff}} = 1\), the chain reaction is steady in the simplified generation picture. Power can remain stable if heat removal and control systems are balanced.
Delayed supercritical
When \(k_{\mathrm{eff}}\) is slightly above one but delayed neutrons still dominate the response, neutron population rises on a controllable time scale in reactor-physics models.
Prompt supercritical
When reactivity exceeds the delayed-neutron contribution, prompt neutrons can dominate the response. The rise becomes very rapid and is treated as a severe safety boundary.
Shutdown margin
Control absorbers, negative temperature feedback, geometry, moderation, and poison effects are used conceptually to move a system away from supercritical behavior.
Criticality safety
Criticality safety is the discipline of preventing unintended chain reactions through conservative limits, independent checks, monitoring, and engineered barriers.
Equations
The conceptual quantities.
These equations define learning-level reactor-physics language without operational constants or facility-specific instructions.
Multiplication factor
\[k_{\mathrm{eff}}=\frac{\text{neutrons in one generation}}{\text{neutrons in the previous generation}}\]
If \(k_{\mathrm{eff}}\) is below, equal to, or above one, the simplified chain reaction tends to fall, hold steady, or rise.
Reactivity
\[\rho=\frac{k_{\mathrm{eff}}-1}{k_{\mathrm{eff}}}\]
Reactivity is a compact way to describe departure from criticality. Positive reactivity raises neutron population in the simplified model.
Delayed neutrons
\[\beta_{\mathrm{eff}}=\frac{\text{delayed neutron contribution}}{\text{total effective neutron contribution}}\]
Delayed neutrons are a small but essential fraction that make controlled reactor behavior possible in power systems.
Related learning
Continue into nuclear physics.
Supercriticality is one topic inside the larger field of nuclear structure, decay, reactions, fission, fusion, radiation, and detectors.