## Reactivity Coefficients – Reactivity Feedbacks

Up to this point, we have discussed the response of the **neutron**

** population** in a **nuclear reactor** to an **external reactivity input**. There was applied an assumption that the level of the neutron population **does not affect** the properties of the system, especially that the neutron power (power generated by chain reaction) is sufficiently **low** that the reactor core does not change its **temperature** (i.e. **reactivity feedbacks may be neglected**). For this reason such treatments are frequently referred to as the **zero-power kinetics**.

However, in an operating **power reactor** the neutron population is always large enough to generated heat. In fact, it is the main purpose of power reactors **to generate large amount of heat**. This causes the temperature of the system changes and material densities change as well (due to the **thermal expansion**).

**prompt negative temperature coefficient**at the

**TRIGA reactor**. A major factor in the prompt negative temperature coefficient for the TRIGA cores is the core spectrum hardening that occurs as the fuel temperature increases. This factor allows TRIGA reactors to operate

**safely**during either

**steady-state**or

**transient conditions**.

Source: Youtube

See also: General Atomics – TRIGA

**neutron flux spectrum**depends also on the density of moderator, these changes in turn will produce some changes in reactivity. These changes in reactivity are usually called the

**reactivity feedbacks**and are characterized by

**reactivity coefficients**. This is very important area of reactor design, because the reactivity feedbacks influence the

**stability of the reactor**. For example, reactor design must assure that under all operating conditions the temperature feedback will be

**negative**.

## How negative feedback acts against power excursion

## Example: Change in the moderator temperature.

**Negative feedback** as the moderator temperature effect influences the neutron population in the following way. If the temperature of the moderator is increased, negative reactivity is added to the core. This negative reactivity causes reactor power to decrease. As the thermal power decreases, the power coefficient acts against this decrease and the reactor returns to the critical condition. The reactor power stabilize itself. In terms of multiplication factor this effect is caused by significant changes in the resonance escape probability and in the total neutron leakage (or in the thermal utilisation factor when chemical shim is used).

## Examples: Change in the reactor power

**reactivity coefficient α**. A reactivity coefficient is defined as the change of reactivity per unit change in some operating parameter of the reactor. For example:

α = ^{dρ}⁄_{dT}

The amount of reactivity, which is inserted to a reactor core by a specific change in an operating parameter, is usually known as the **reactivity effect** and is defined as:

dρ = α . dT

**The reactivity coefficients** that are important in power reactors (PWRs) are:

**Moderator Temperature Coefficient – MTC****Fuel Temperature Coefficient or Doppler Coefficient****Pressure Coefficient****Void Coefficient**

As can be seen, there are not only **temperature coefficients** that are defined in reactor dynamics. In addition to these coefficients, there are two other coefficients:

The total power coefficient is the combination of various effects and is commonly used when reactors are at power conditions. It is due to the fact, at power conditions it is difficult to separate the moderator effect from the fuel effect and the void effect as well. All these coefficients will be described in following separate sections. The reactivity coefficients are of importance in safety of each nuclear power plant which is declared in the **Safety Analysis Report** (SAR).