Reactivity Coeffivients

Definition Of Reactivity Coefficient

The temperature coefficient of reactivity is the change in reactivity per degree change in temperature.

Important Coefficients of Reactivity

1. Moderator Temperature Coefficient.

The change in reactivity per degree change in moderator temperature. As the moderator (water) increases in temperature, it becomes less dense and slows down fewer neutrons, which results in a negative change of reactivity. This negative temperature coefficient acts to stabilize an atomic power reactor operation.

 A  reactor  is  under  moderated  when  a  decrease  in  the  moderator-to-fuel  ratio decreases  keff due  to  the  increased  resonance absorption. A reactor is over moderated when an increase in the moderator-to-fuel ratio decreases keff due to the decrease in the thermal utilization factor. Reactors are usually designed to operate in an under moderated condition so that the moderator temperature coefficient of reactivity is negative.

2. Fuel Temperature Coefficient

Fuel temperature coefficient of reactivity is the change in reactivity of the nuclear fuel per degree change in the fuel temperature. 

The coefficient quantifies the amount of neutrons that the nuclear fuel (uranium-238) absorbs from the fission process as the fuel temperature increases. It is a measure of the stability of the reactor operations. This coefficient is also known as the Doppler coefficient.

A negative temperature coefficient of reactivity is desirable because it makes the reactor more self-regulating.   An increase in power, resulting in an increase in temperature, results   in negative reactivity addition due to the temperature coefficient.  The negative reactivity addition due to the temperature increase will slow or stop the power increase.

The fuel temperature coefficient is more effective than the moderator temperature coefficient in terminating a rapid power rise because the fuel temperature immediately increases   following a power increase,   while   the   moderator temperature does not increase for several seconds.

The Doppler broadening of resonance peaks occurs because the nuclei may be moving  either  toward  or  away  from  the  neutron  at  the  time  of  interaction. Therefore, the neutron may actually have either slightly more or slightly less than the  resonant  energy,  but  still  appear  to  be  at  resonant  energy  relative  to  the nucleus.

3. Pressure Coefficient

The reactivity in a reactor core can be affected by the system pressure.  The pressure coefficient of reactivity is defined as the change in reactivity per unit change in pressure.

 The pressure coefficient of reactivity for the reactor is the result of the effect of pressure on the density of the moderator. For this reason, it is sometimes referred to as the moderator density reactivity coefficient. As pressure increases, density correspondingly increases, which increases the moderator-to-fuel ratio in the core. In the typical under moderated core the increase in the moderator-to-fuel ratio will result in a positive reactivity addition. In reactors that use water as a moderator, the absolute value of the pressure reactivity coefficient is seldom a major factor because it is very small compared to the moderator temperature coefficient of reactivity.

4. Void Coefficient

The void coefficient of reactivity is defined as the change in reactivity per percent change in void volume.

 As the reactor power is raised to the point where the steam voids start to form, voids displace moderator from the coolant channels within the core. This displacement reduces the moderator-to-fuel ration, and in an under moderator core, results in negative reactivity addition, thereby limiting reactor power rise. The void coefficient is significant in water-moderated reactors that operate at or near saturated conditions.