## Subcritical – Critical – Supercritical Reactor

**The basic classification** of states of a reactor is according to the **multiplication factor** **as eigenvalue** which is a measure of the change in the fission neutron population from one neutron generation to the subsequent generation.

**k**. If the multiplication factor for a multiplying system is_{eff}< 1**less than 1.0**, then the**number of neutrons is decreasing**in time (with the mean generation time) and the chain reaction will never be self-sustaining. This condition is known as**the subcritical state**.

**k**. If the multiplication factor for a multiplying system is_{eff}= 1**equal to 1.0**, then there is**no change in neutron population**in time and the chain reaction will be**self-sustaining**. This condition is known as**the critical state**.

**k**. If the multiplication factor for a multiplying system is_{eff}> 1**greater than 1.0**, then the multiplying system produces**more neutrons**than are needed to be self-sustaining. The number of neutrons is exponentially increasing in time (with the mean generation time). This condition is known as**the supercritical state**.

The definitions described above are fully applicable to a reactor at **zero power level**, that is at such power level in which **all thermal considerations** are not important to the chain reaction (let say **from zero power to 1% of rated power**).

See also: Criticality of Power Reactor

## Prompt Criticality

**The basic classification** of states of a reactor may be in some case **insufficient** and a finer classification is needed. The finer classification takes into account the two groups of neutrons that are produced in fission.

**The prompt critical state is defined as:**

**k**, where the reactivity of a reactor is higher than the effective delayed neutron fraction. In this case, the production of prompt neutrons alone is enough to balance neutron losses and increase the neutron population. The number of neutrons is_{eff}> 1; ρ ≥ β_{eff}**exponentially increasing**in time (as rapidly as the prompt neutron generation lifetime ~**10**).^{-5}s

**The prompt subcritical and delayed supercritical state is defined as:**

**k**, where the reactivity of a reactor is_{eff}> 1; 0 < ρ < β_{eff}**higher than zero**and**lower than**the effective delayed neutron fraction. In this case, the production of prompt neutrons alone is**insufficient**to balance neutron losses and the delayed neutrons are needed in order to sustain the chain reaction. The neutron population increases, but**much more slowly**(as the mean generation lifetime with delayed neutrons ~0.1 s).

**The prompt subcritical and delayed critical state is defined as: **

**k**, where the reactivity of a reactor is_{eff}= 1; ρ = 0**equal to zero**. In this case, the production of prompt neutrons alone is insufficient to balance neutron losses and the delayed neutrons are needed in order to sustain the chain reaction. There is no change in neutron population in time and the chain reaction will be self-sustaining. This state is the same state as the critical state from basic classification.

**The prompt subcritical and delayed subcritical state is defined as:**

**k**, where the reactivity of a reactor is lower than zero. In this case, the production of all neutrons is insufficient to balance neutron losses and the chain reaction is not self-sustaining. If the reactor core contains external or internal neutron sources, the reactor is in the state that is usually referred to as the_{eff}< 1; ρ < 0**subcritical multiplication**.