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Syllabus for

Academic year
TIF070 - Transport theory and random processes
Owner: TTFYA
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: D
Department: 16 - PHYSICS

Teaching language: English

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0105 Written and oral assignments 5,0 c Grading: TH   5,0 c    

In programs



Professor  Imre Pázsit


For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

Basic course in Reactor Physics
Complex maths and probability theory


The aim of the course is to give an introduction to the transport theory of neutrons, as well as fluctuations in classical particle transport. Another goal of the course is to serve as an advanced course in reactor theory. The basic reactor physics course only treats the diffusion equation, which is a simplified approximation of the transport equation.
The course has a theoretical and mathematical character, suitable also for students of wider interest in e.g. mathematical physics, atomic collisions and electron transport. The course is suitable as an elective graduate (PhD) course.


1. Transport theory

Derivation of the transport equation.
Boundary conditions. Integro-differential and integral form.
Time dependence and criticality. Different forms of criticality (eigenvalue) equations.
One-speed transport theory in slab geometry.
Solution in infinite medium with Fourier transform and with singular eigenfunctions. Methods of complex function analysis. Expansion in Legendre polynomials. The PN method and diffusion theory. Multi-group methods.
The adjoint transport equation, the importance function. Relationship to the Green's function. Applications in perturbation theory.

2. Theory of neutron fluctuations in a
steady medium ("zero power noise")

Introduction to stochastic processes. Discrete Markovian processes. Master equations. Forward and backward form.
Master equations of neutron transport without space- and energy dependence.
Determining of the reactivity from the variance of the neutron counts (Feynman- and Rossi alpha methods), with applications in accelerator driven systems. Derivation and solution both with the forward and the backward approach.

3. Theory of neutron noise in power reactors, with applications to reactor diagnostics

One-group diffusion theory with space- and time-dependence and one group of delayed neutrons.
Reactor kinetic approximations.
Neutron fluctuations induced by fluctuations in the reactor material.
Langevin equation. Korrelations and power spectra. Wiener-Khinchin theorem.
List of applications of power reactor diagnostics.
Some selected cases:
Neutron noise induced by bubbles in a boiling water reactor and by vibrations of a control rod in a pressurized water reactor: how one can determine void fraction and localise vibrating control rods from neutron noise. Core diagnostics with neutron noise in Swedish and foreign reactors.


Lectures 6 hrs/week.
The tasks/exercises to be solved for the exam will be distributed during the course.


Transport theory and stochastic processes. Lecture notes av Imre Pazsit, printed at the Department.
As a complement, the following books are recommended:
G.I. Bell and S. Glasstone: Nuclear Reactor Theory, Van Nostrand, NY, 1970
M.M.R. Williams: Random Processes in Nuclear Reactors, Pergamon Press, Oxford, 1974


Calculational exercises/tasks to be submitted as written reports

Page manager Published: Thu 03 Nov 2022.