## Prompt Neutron Lifetime

**Prompt neutron lifetime, l**, is the **average time from a prompt neutron emission** to **its absorption** (fission or radiative capture) or **its escape** from the system. This parameter is defined in multiplying or also in non-multiplying systems. In both systems the prompt neutron lifetimes depend strongly on:

- the material composition of the system
- multiplying – non-multiplying system
- the system with or without thermalization
- isotopic composition of the system

- the geometric configuration of the system
- homogeneous or heterogeneous system
- the shape of the entire system

- size of the system

In an infinite reactor (without escape), prompt neutron lifetime is the sum of **the slowing downtime and the diffusion time**.

**l=t _{s} + t_{d}**

In an infinite thermal reactor **t _{s} << t_{d}** and therefore

**l ≈ t**. The typical prompt neutron lifetime

_{d}**in thermal reactors**is on the order of

**10**. Generally, the longer neutron lifetimes occur in systems in which the neutrons must be thermalized to be absorbed.

^{−4}secondsMost neutrons are absorbed in higher energies, and the neutron thermalization is suppressed (e.g.,, in fast reactors) has much shorter prompt neutron lifetimes. The typical prompt neutron lifetime **in fast reactors** is on the order of **10 ^{−7} seconds**.

Slowing Down and Diffision Times for Thermal Neutrons in an Infinite Medium

Source: Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.

## Prompt Generation Time – Mean Generation Time

In multiplying systems, the absorption of a prompt fission neutron can initiate a fission reaction, l is equal to the average time between two generations of prompt neutrons (at k_{eff}=1). This time is known as the **prompt neutron generation time**.

**Prompt Neutron Generation Time** (or **Mean Generation Time**), **Λ**, is the average time **from a prompt neutron emission** **to a capture that results only in fission**. The prompt neutron generation time is designated as:

**Λ = l/k _{eff}**

In power reactors, **the prompt generation time** changes with the fuel burnup. In LWRs increases with the fuel burnup. It is simple, and fresh uranium fuel contains much fissile material (in the case of uranium fuel, about 4% of ^{235}U). This causes significant excess of reactivity, and this **excess must be compensated** via chemical shim (in case of PWRs) or burnable absorbers.

Owing to these factors (high probability of absorption in fuel and high probability of absorption in moderator) the prompt neutron lives much shorter and prompt neutron lifetime is low. With fuel burnup the amount of fissile material as well as the absorption in moderator decreases and therefore the prompt neutron is able to “live”much longer.

Dependencies of asymptotic time period on the reactivity required for different reactor types with different prompt neutron lifetimes. Source: http://www.hindawi.com/journals/ijne/2014/373726/

## Example – Infinite Multiplying System Without Source and Delayed Neutrons

An equation governing the neutron kinetics of the system without source and with the absence of delayed neutrons is **the point kinetics equation** (in a certain form). This equation states that the time change of the neutron population is equal to the **excess of neutron production** (by fission) **minus neutron loss** by absorption** in one prompt neutron lifetime**. The role of prompt neutron lifetime is evident. Shorter lifetimes give simply faster responses to multiplying systems.

If there are neutrons in the system at t=0, that is, if n(0) > 0, the solution of this equation gives the simplest form of point kinetics equation (without source and delayed neutrons):Let us consider that **the prompt neutron lifetime is ~2 x 10 ^{-5}** and k (k

_{∞}– neutron multiplication factor) will be step increased

**by only 0.01%**(

**i.e., 10pcm or ~1.5 cents**), that is k

_{∞}=1.0000 will increase to k

_{∞}=1.0001.

It must be noted such reactivity insertion (10pcm)** is very small** in case of LWRs. The reactivity insertions **of the order of one pcm** are for LWRs **practically unrealizable**. In this case the reactor period will be:

**T = l / (k _{∞ }– 1) = 2 x 10^{-5 }/ (1.0001 – 1) = 0.2s**

**This is a very short period.** In one second, the reactor’s neutron flux (and power) would increase by a factor of e^{5} = 2.718^{5}. In 10 seconds, the reactor would pass through 50 periods, and the power would increase by e^{50} = ……

Furthermore, in the case of fast reactors in which prompt neutron lifetimes are **of the order of 10 ^{-7} seconds**, the response of such a small reactivity insertion will be even more unimaginable. In the case of 10

^{-7}, the period will be:

**T = l / (k _{∞ }– 1) = 10-7 / (1.0001 – 1) = 0.001s**

**Reactors with such kinetics would be very difficult to control.** **Fortunately, this behavior is not observed** in any multiplying system. Actual reactor periods are observed to be considerably longer than computed above, and therefore the nuclear chain reaction can be **controlled more easily**. The longer periods are observed due to the presence of **the delayed neutrons.**

## Interactive chart – Infinite Multiplying System Without Source and Delayed Neutrons

Press the “**clear and run**” button and try to stabilize the power at 90%.

Look at the reactivity insertion you need to insert to stabilize the system (of the order to the tenth of pcm).

Do you think that such a system is controlable?