## Reactor Dynamics

In preceding chapters (Nuclear Chain Reaction), the classification of states of a reactor according to **the effective multiplication factor – k**** _{eff}** was introduced. The effective multiplication factor –

**k**

**is a measure of the change in the fission**

_{eff}**neutron population**from one neutron generation to the subsequent generation. Also the reactivity as a measure of a reactor’s relative departure from criticality was defined.

In this section, amongst other things it will be briefly described how **the neutron flux** (i.e. the reactor power) changes if **reactivity** of a multiplying system is not equal to zero. We will study the **time-dependent behaviour** of nuclear reactors. An understanding of the **time-dependent behavior** of the neutron population in a nuclear reactor in response to either a **planned** change in the reactivity of the reactor or to **unplanned** and abnormal conditions is of the most importance in the nuclear reactor safety. This chapter is named the **Reactor Dynamics**, but also comprises the **reactor kinetics**. **Nuclear reactor kinetics** is dealing with transient **neutron flux changes** resulting from a departure from the critical state, from some reactivity insertion. Such situations arise during operational changes such as control rods motion, environmental changes such as a change in boron concentration, or due to accidental disturbances in the reactor steady-state operation.

In general:

**Reactor Kinetics.**Reactor kinetics is the study of the time-dependence of the neutron flux for postulated changes in the macroscopic cross sections. It is also referred to as reactor kinetics**without feedbacks**.**Reactor Dynamics.**Reactor dynamics is the study of the time-dependence of the neutron flux, when the macroscopic cross sections are allowed to depend in turn on the neutron flux level. It is also referred to as reactor kinetics**with****feedbacks**and with spatial effects.

Time-dependent behaviour of nuclear reactors can be also classified by the time scale as:

**Short-term kinetics**describes phenomena that occur over times shorter than a few seconds. This comprises the response of a reactor to either a**planned**change in the reactivity or to**unplanned**and abnormal conditions. In this section, we will introduce especially**point kinetics equations**.**Medium-term kinetics**describes phenomena that occur over the course of several hours to a few days. This comprises especially effects of neutron poisons on the reactivity (i.e.**Xenon poisoning**or**spatial oscillations**).**Long-term kinetics**describes phenomena that occur over months or even years. This comprises all long-term changes in fuel composition as a result of**fuel burnup**.

This chapter is concerned with short-, medium- and long-term kinetics, despite the fact the fuel burnup and other changes in fuel composition are usually not a dynamic problem. At first, we have to start with an introduction to **prompt and delayed neutrons** because they play an important role in short-term reactor kinetics. Despite the fact the **number of delayed neutrons** per fission neutron **is quite small (typically below 1%)** and thus does not contribute significantly to the power generation, **they play a crucial role in the reactor control** and are essential from the point of view of reactor kinetics and **reactor safety**. Their presence completely **changes the dynamic time response** of a reactor to some reactivity change, making it controllable by control systems such as the control rods.