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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
TIF245 - Noise techniques in nuclear systems
Syllabus adopted 2014-02-14 by Head of Programme (or corresponding)
Owner: MPNUE
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: Second-cycle
Major subject: Engineering Physics
Department: 16 - PHYSICS

Teaching language: English
Block schedule: D

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0110 Written and oral assignments 7,5 c Grading: TH   7,5 c    

In programs



Forskarassistent  Dina Chernikova
Professor  Imre Pázsit


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

It is definitely recommended to have attended the courses "Introduction to nuclear reactors, TIF215" and especially "Physics of nuclear reactors, TIF210". Having taken the elective course "Modelling of nuclear reactors, TIF205" is an advantage. Nevertheless, it is not a prerequisite to have attended any of the courses; students with a basic physics background can participate in the course. However, good command of mathematical methods, such a solving differential equations with Laplace transform methods, Fourier transforms, Green's function techniques, basic probability theory, is a prerequisite.


The course discusses the neutron fluctuations that arise in a multiplying medium: their origin, mathematical treatment and their use in reactor diagnostics and surveillance. Neutron fluctuations in low power, stationary systems, which arise due to the branching character (fission) of the neutron processes, are treated with the master equation technique. The use of the higher moments (variance and correlations) of the detector counts in determining the subcritical reactivity of a source driven system (including Accelerator Driven Systems, ADS), is discussed. The use of the higher moments of neutron counts in nuclear safeguards (identifying hidden nuclear materials) is also discussed. Neutron noise in power reactors, due to the various technological processes (boiling of the coolant, control rod and fuel vibrations etc.) are then treated with the Langevin technique of random processes. It is then shown how the information in the neutron noise, measured in nuclear reactors, can be used to detect, identify and quantify beginning anomalies, and to determine core parameters such as reactivity coefficients, two-phase flow parameters etc. in normal and abnormal state of the reactor.

Learning outcomes (after completion of the course the student should be able to)

·         Understand the origin of the fluctuations in the neutron field in zero power systems and power reactor cores

·         Get acquainted with master equations (equations for the probability distribution of random variables)

·         Formulate master equations for various stochastic processes, including (but not restricted to) the distribution of neutrons and detector counts

·         To derive and solve equations for the higher moments (beyond the mean value, i.e. variances and correlations) of the random variables involved (such as the number of detector counts in a time interval)

·         Get acquainted with the Langevin technique for describing the neutron noise in power reactors

·         Construct simple models of the perturbations in a power reactor core (two-phase flow, vibrations, temperature fluctuations)

·         Solve linearised Langevin equations with Fourier transform and Green¿s function techniques

·         Interpret the induced noise in reactor physics terms

·         Construct methods for inverting the solution in order to determine parameters of the noise source that induced the noise (reactor diagnostics).


·         Introduction to random processes

·         Introduction to master equations

·         Derivation of master equations for neutron fluctuations in zero power systems

·         Derivation and solution of equations for the higher moments

·         Reactivity measurement methods in subcritical reactors

·         Application of neutron fluctuations in nuclear safeguards

·         The Langevin equation of power reactor noise

·         The reactor kinetic approximations

·         Calculation of the neutron noise induced by various perturbations

·         Solution of the inverse task: the use of neutron noise for reactor diagnostics

o   Diagnosing perturbations

o   Determining global core parameters


·         Lectures

·         Homework


Lecture notes written at the department:

·         I. Pázsit: Noise Techniques in Nuclear Systems I: Zero Power Reactor Noise. 171 pages. Chalmers (2013)

·         I. Pázsit and C. Demazière:  Noise Techniques in Nuclear Systems II: Power Reactor Noise. 91 pages. Chalmers (2013)

·         Lecture slides will also be distributed in print for the first part (zero power reactor noise) and electronically as interactive Mathematica notebook slides for the second part (power reactor noise).

Recommended books:

·         I. Pázsit and L. Pál: Neutron Fluctuations ¿ a Treatise on the Physics of Branching Processes. 340 pages. Elsevier Science Ltd, 2008

·         M.M.R. Williams: Random Processes in Nuclear Reactors. 241 pages. Pergamon Press, 1974. Available free of charge on CD or as pdf-file, distributed by OECD.


Attendance at 75% of the lectures is compulsory for passing the course. If a student cannot reach the level of 75%, a corresponding home task will be assignedassigned or an oral exam will be requested.

The examination is made by solving home tasks and one of them has to be presented to the examiner at the whiteboard (the written solutions can be used during the presentation). These home tasks will be distributed during the course as soon as the relevant material was lectured, and they have to be completed within a given timeframe in order to pass the course. The home tasks will be used to grade the students.

Page manager Published: Thu 04 Feb 2021.