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Nuclear Instrumentation

In nuclear reactors, the thermal power produced by nuclear fissions is proportional to the neutron flux level. Therefore, from a 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:

Both systems are based on the detection of neutrons. The neutron flux is usually measured by excore neutron detectors installed outside the core. These detectors belong to the so-called excore nuclear instrumentation system (NIS). The neutron flux and its distribution within the core are usually measured by an incore system installed inside the reactor. Although the nuclear instrumentation system provides a prompt response to neutron flux changes and it is an irreplaceable system, it must be calibrated. The accurate thermal power of the reactor can be measured only by methods based on the energy balance of the primary circuit or the energy balance of the 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 words, the thermal power measured by colorimetric methods is accurate. In contrast, 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:

Reaction Rate - Neutron Flux


Ф – neutron flux (neutrons.cm-2.s-1)

σ – microscopic cross section (cm2)

N – atomic number density (atoms.cm-3)

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

We must focus on the fission reaction rate to determine the thermal power. For simplicity, let’s 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 that the amount of energy released per one fission reaction is about 200 MeV/fission. It is possible to determine the rate of energy release (power) due to the fission reaction, and it is given by the following equation:

P = RR . Er . V = Ф . Σf . Er . V = Ф . NU235 . σf235 . Er . V


P – reactor power (MeV.s-1)

Ф – neutron flux (neutrons.cm-2.s-1)

σ – microscopic cross section (cm2)

N – atomic number density (atoms.cm-3)

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

V – total volume of the core (m3)



Radiation Protection:

      1. Knoll, Glenn F., Radiation Detection and Measurement 4th Edition, Wiley, 8/2010. ISBN-13: 978-0470131480.
      2. Stabin, Michael G., Radiation Protection, and Dosimetry: An Introduction to Health Physics, Springer, 10/2010. ISBN-13: 978-1441923912.
      3. Martin, James E., Physics for Radiation Protection 3rd Edition, Wiley-VCH, 4/2013. ISBN-13: 978-3527411764.
      5. U.S. Department of Energy, Instrumentation, and Control. DOE Fundamentals Handbook, Volume 2 of 2. June 1992.

Nuclear and Reactor Physics:

      1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
      2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
      3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
      4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
      5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
      6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
      7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
      8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
      9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

See above:

Nuclear Reactor