Course: Fundamentals of reactor kinetics and theory of small space-time dependent fluctuations in nuclear reactors

Course theme

The course covers the fundamentals of nuclear reactor kinetics, with emphasis on one- and two-group diffusion theory and provides a solid and rigorous theoretical background in reactor dynamics. The course also presents a special case of reactor kinetics, i.e. small space-time stationary fluctuations in nuclear reactors, also referred to as neutron noise or power reactor noise. Emphasis is put in the course on the derivation of the governing equations and on how to solve such equations.

Learning objective

After completion of the course, the course attendees should be able to:

• Know the governing equations describing reactor kinetics in diffusion theory.
• Know the governing equations describing power reactor noise in diffusion theory.
• Know how to solve such equations either analytically for homogeneous or piece-wise homogeneous systems, and numerically for heterogeneous systems.

Target audience

• MSc students and PhD students having some background knowledge in nuclear engineering.
• Nuclear engineers.
• Reactor physicists.

Although previous knowledge in reactor physics is definitely advantageous, all equations are derived from first principles and should allow the students not familiar with advanced reactor physics to comprehend all concepts thoroughly.

Teaching approach

The course can be followed on-site in Chalmers or off-site (i.e. remotely). The course follows a “flipped classroom” set-up. Students learn asynchronously from lectures and materials made available on the web prior to attending synchronous sessions (either in the classroom for the on-site students or remotely for the off-site students). Such sessions are held in an interactive teaching room in Chalmers. The room allows mixing on-site students with remote attendees, while preserving full interaction possibilities between both audiences. Because the students learn at their own pace during the asynchronous sessions, they attend the synchronous sessions better prepared. As a result, these sessions can focus on more active forms of learning that effectively engage students, promote higher-order thinking, clarify difficult concepts and provide more personalised support.

The course thus consists of:

• Pre-recorded lectures or webcasts available to students for on-demand viewing (asynchronous sessions).
• Online quizzes embedded in the webcasts and that focus on conceptual understanding (asynchronous sessions).
• Interactive wrap-up sessions designed to summarise the key concepts presented in the webcasts and to address student needs (synchronous sessions).
• Interactive tutorials (synchronous sessions).

For the off-site attendees, the interactive wrap-up sessions and tutorials are live-broadcasted on the web.

 The course is offered in two set-ups:

• On-site attendance (limited to 20 participants).
• Off-site attendance (limited 10 participants).

Course credits

The course is worth 1.5 ECTS. A course certificate will be issued for the students attending all wrap-up/tutorial sessions and being engaged in such sessions.
For the wrap-up sessions, engagement is assessed via participation to the group discussions. For the tutorials, engagement is assessed via solving the given problems.

Literature

A handbook (about 100 pages) specifically written for the course and the corresponding lecture slides will be provided to the students.

The curriculum for the course is organised in two chapters.

Chapter 1: Space-time dependent reactor kinetics in diffusion theory:

• Static neutron transport: derivation of the static space-dependent neutron balance equations in diffusion theory, case of steady-state one-group diffusion theory, case of steady-state two-group diffusion theory.
• Dynamic neutron transport: derivation of the dynamic space-dependent neutron balance equations in diffusion theory, case of dynamic one-group diffusion theory, case of dynamic two-group diffusion theory.
• Resolution of the space- and time-dependence of the neutron flux in nuclear reactors: general discretization methods in space and time in diffusion theory, reduced Order Modelling (ROM) in diffusion theory, flux factorization methods in diffusion theory.

Chapter 2: Small space-time dependent fluctuations (power reactor noise):

• Theory of first-order neutron noise: general principles, derivation of the first-order neutron noise in one-group diffusion theory, derivation of the first-order neutron noise in two-group diffusion theory.
• Theory of first-order neutron noise in its factorized form: general principles, determination of the fluctuations of the amplitude factor, determination of the fluctuations of the shape function.
• General solution of the neutron noise in one-group diffusion theory.
• General solution of the neutron noise in two-group diffusion theory.
• Validity of the point-kinetic approximation: case of critical systems, case of subcritical systems with an external neutron source.
• Spatial discretisation methods for resolving the neutron noise in nuclear reactors.