**α**

**. Clearly, a reactor with**

_{T}**negative**

**α**

**is**

_{T}**inherently stable**to changes in its temperature and thermal power while a reactor with

**positive**

**α**

**is**

_{T}**inherently unstable**.

According to 10 CFR Part 50; Criterion 11:

“The reactor core and associated coolant systems shall be designed so that in the power operating range the net effect of the prompt inherent nuclear feedback characteristics tends to compensate for a rapid increase in reactivity.”

At this point, we will discuss the reactor stability at power operation. At power operation, the neutron population is always large enough to generate 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**).

These changes in reactivity are usually called the **reactivity feedbacks** and are characterized by **reactivity coefficients**. The reactivity feedbacks and their time constants are very important area of reactor design, because they determine the** stability of the reactor**.

In the previous article (Point Dynamics Equations) we have assumed a simplified feedback equation:

This equation expresses the dependence of the reactivity on various parameters. But in this case, there is a dependence on the **coolant** and the **fuel temperature** only. For PWRs, the temperature stability is of importance in overall stability, because most instabilities arise from the temperature instability. For illustration, we will use further simplified model, which assumes that there is only one temperature coefficient for fuel and moderator:

The response of a reactor to a change in temperature (i.e. the overall reactor stability) depends especially on the algebraic sign of **α**** _{T}**. Clearly, a reactor with

**negative**

**α**

**is**

_{T}**inherently stable**to changes in its temperature and thermal power while a reactor with

**positive**

**α**

**is**

_{T}**inherently unstable**. We will demonstrate the problem on following two examples.

## Positive reactivity feedback – α_{T }> 0

Assume **α**_{T }**> 0 (**temperature coefficient for fuel and moderator**). **If the temperature of the moderator is increased, positive reactivity is added to the core. This positive reactivity causes that reactor power further increases, which acts in the same direction as initial reactivity addition. Without compensation the reactivity of the system would increase and the thermal power would accelerate and increase as well (see figure).

On the other hand as the thermal power decreases, the reactor temperature decreases giving a further decrease in reactivity. This feedback would accelerate the initial decrease in thermal power and the reactor would shut down itself. In any case, the reactor power **does not stabilize itself**.

## Negative reactivity feedback – α_{T }< 0

The above situation is quite different when **α**_{T }**< 0. **In this case, if the temperature of the moderator is increased, **negative reactivity** is added to the core. This negative reactivity causes reactor power to decrease, which acts against any further increase in temperature or power. As the thermal power decreases, the power coefficient (which is also based on the sign of **α**** _{T}**) acts against this decrease and the reactor

**returns to the critical condition (steady-state)**. The

**reactor power stabilizes itself**. This effect is shown on the picture. Let assume all the changes are initiated by the changes in the

**core inlet temperature**.

At this point, it must be noted, that the temperature does not change uniformly throughout a reactor core. An increase in thermal power, for example, is reflected first by an increase in the temperature of the fuel, since this is the region, where most of the thermal power is generated. The coolant temperature and, in thermal reactors, the moderator temperature do not change until heat has been transferred from the fuel to the reactor coolant. The time for heat to be transferred to the moderator is usually measured in seconds (~5s).

Therefore it is necessary to specify the component whose temperature changes:

## Examples: Reactor Stability

## Flow Instabilities in BWRs

**Coupled Neutronic-Thermohydraulic Instability**

See also: Flow Instability

The dominant type of instabilities in commercial BWRs is the coupled neutronic-thermohydraulic instability (also known as the **reactivity instability**). The power generation in BWRs is directly related to the fuel **neutron flux**, which is strongly related to the average **void fraction** in the core channels through. This effect is known as the** reactivity feedback**. The reactivity feedback caused by changes in void fraction (void coefficient) is delayed as the voids travel upward through the fuel channel. In some cases the delay may be long enough and the **void feedback** may be strong enough that the reactor configuration becomes unstable. In this case the neutron flux may oscillate.