In nuclear reactors, the thermal power produced by nuclear fissions is proportional to neutron flux level. Therefore, from reactor safety point of view, it is of the highest importance to measure and control **the neutron flux and the spatial distribution of the neutron flux **in the reactor **correctly **and by appropriate instrumentation. For this purpose, various nuclear instrumentations are installed. These measurements are usually performed outside the reactor core, but there are also measurements performed from inside the core. Therefore, nuclear instrumentations are usually categorized as:

**Excore Nuclear Instrumentation.**The neutron flux is usually measured by**excore neutron detectors**installed outside the core. These detectors belong to so called the**excore nuclear instrumentation system (NIS)**. Since the neutron flux covers a wide range (about 12 decades), three ranges of instrumentation are used to obtain accurate flux level measurements:**Incore Nuclear Instrumentation.**The incore nuclear instrumentation system measures neutron flux distribution and temperatures in the reactor core. The purposes of the incore instrumentation system are to provide detailed information on neutron flux distribution and fuel assembly outlet temperatures at selected core locations. The incore instrumentation system includes:

Both systems are based on detection of neutrons. The neutron flux is usually measured by **excore neutron detectors **installed outside the core. These detectors belong to so called the **excore nuclear instrumentation system (NIS)**. The **neutron flux** and its **distribution** within the core is usually measure by an **incore system**, which is installed inside the reactor. Although the **nuclear instrumentation system** provides prompt response on neutron flux changes and it is irreplaceable system, **it must be calibrated**. The **accurate thermal power** of the reactor can be measured only by methods based on **energy balance** of primary circuit or energy balance of secondary circuit. These methods provide accurate reactor power, but these methods are insufficient for safety systems. Signal inputs to these calculations are, for example, the hot leg temperature or the flow rate through the feedwater system and these signals change** very slowly** with neutron power changes. In other word, the thermal power measured by calorimetrical methods is accurate, while the nuclear power measured by excore neutron detectors is the only system capable of fast reactivity excursion detection.

## Reaction Rate – Proportionality between Neutron Flux and Thermal Power

See also: Reaction Rate

Knowledge of the **neutron flux** (the **total path length** of all the neutrons in a cubic centimeter in a second) and the** macroscopic cross sections** (the probability of having an interaction **per centimeter path length**) allows us to compute the rate of interactions (e.g. rate of fission reactions). **This reaction rate** (the number of interactions taking place in that cubic centimeter in one second) is then given by multiplying them together:

where:

**Ф – neutron flux (neutrons.cm**^{-2}**.s**^{-1}**)**

**σ – microscopic cross section (cm**^{2}**)**

**N – atomic number density (atoms.cm**^{-3}**)**

The reaction rate for various types of interactions is found from the appropriate cross-section type:

**Σ**_{t}**. Ф – total reaction rate****Σ**_{a}**. Ф – absorption reaction rate****Σ**_{c}**. Ф – radiative capture reaction rate****Σ**_{f}**. Ф – fission reaction rate**

To determine the** thermal power**, we have to focus on the **fission reaction rate**. For simplicity let assume that the fissionable material is uniformly distributed in the reactor. In this case, the macroscopic cross-sections are independent of position. Multiplying the **fission reaction rate** per unit volume (**RR = Ф . Σ**) by the **total volume** of the core (V) gives us the** total number of reactions** occurring in the reactor core per unit time. But we also know the amount of energy released per one fission reaction to be about **200 MeV/fission**. Now, it is possible to determine the **rate of energy release** (power) due to the fission reaction. It is given by following equation:

**P = RR . E**_{r}** . V = Ф . Σ**_{f}** . E**_{r}** . V = Ф . N**_{U235}** . σ**_{f}^{235}** . E**_{r}** . V**

where:

**P – reactor power (MeV.s**^{-1}**)**

**Ф – neutron flux (neutrons.cm**^{-2}**.s**^{-1}**)**

**σ – microscopic cross section (cm**^{2}**)**

**N – atomic number density (atoms.cm**^{-3}**)**

**Er – the average recoverable energy per fission (MeV / fission)**

**V – total volume of the core (m**^{3}**)**

We hope, this article, **Nuclear Instrumentation**, helps you. If so, **give us a like** in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about physics and reactor physics.