At the end of the course the student should: ELO 1 - know the linear transport equation for neutrons in its different mathematical forms (integro-differential and integral); ELO 2 - know the physico-mathematical models and approximation adopted for the design of the cores of nuclear reactors; ELO 3 - know the concept of criticality in a multiplying assembly and its mathematical representation; ELO 4 - understand the physical phenomena at the basis of the steady-state and dynamic behaviour of a nuclear reactor and how they can be described through physico-mathematical models; ELO 5 - be able to write down the balance equation for neutrons in steady-state and time-dependent conditions under different approximation (diffusion, spherical harmonics expansion, discrete ordinates, ...); ELO 6 - know the hypotheses, limitations and field of application of perturbation theory; ELO 7 - know the hypotheses and limitations of point kinetic models and, more in general, of approximate models for the transient analysis of nuclear reactors; ELO 8 - perform the solution to simplified models for the description of neutron behavior in a multiplying system and physically interpret the results; ELO 9 - know the fundamentals of kinetic theory; ELO10 - understand the physical significance of kinetic entropy and its link to thermodynamics; ELO 11 - understand the connection of kinetic theory to neutronics and fluid-dynamics.

The student should have the basic knowledge of mathematics and physics, as can be acquired in the courses of a bachelor?s program in industrial engineering. A previous knowledge on basic aspects of nuclear reactor physics as the ones given in the frame of the bachelor program in energy engineering is surely helpful but not compulsory for the understanding of the contents of the course.

1. Kinetic theory (20h) 1.1 Ergodic hypothesis 1.2 Canonical distribution. Examples 1.3 Boltzmann theory for the gases 1.4 Theorem of entropy 1.5 Deduction of the equations of the fluid dynamics 2 Neutronic models (15h) 2.1 Recap of basics of neutron/radiation interactions 2.2 Neutron transport theory 2.3 Multigroup models 2.4 Diffusion theory; 2.5 Homogeneous and heterogeneous reactors; reflected reactors; 3 Design calculation of multiplying structures (13h) 3.1 Generation of nuclear data; 3.2 Criticality calculation; multiplication eigenvalue and physical meaning; 3.3 Integration of the neutronic calculation in the design of a nuclear reactor. 4 Mathematical and computational techniques (15h) 4.1 Spherical harmonics method 4.2 Discrete ordinate method 4.3 Importance equation 5 Perturbation theory (8h) 5.1 Perturbation methods for eigenvalues; 5.2 Generalized perturbation techniques. 6 Nuclear reactor dynamics (9h) 6.1 Factorization methods for the solution of the neutronic equations; point kinetics and quasi-static method; 6.2 Non-linear feed-back effects;

The course is composed by lectures and exercise sessions, where the concepts illustrated are complemented by numerical applications on simplified cases to improve understanding. The examples of solution presented can be treated both on paper and using computational tools such as MATLAB. Examples of simplified problems illustrated during the exercise sessions: - Simulation of the collisional process in a gas - Analytical solution of a 0D kinetic model - Criticality problems in different configurations (reflected systems, multigroup model, ...): numerical solution of the eigenvalue problem - Application of perturbation theory in two-group diffusion: simulation of control rod worth - Solution of neutron dynamic models: point kinetics and quasi-statics

- Bell, G. I., and Glasstone, S. Nuclear Reactor Theory, Van Nostrand Reinhold Inc.,U.S., 1970 - A. F. Henry, Nuclear-reactor Analysis, MIT Press, 1975 - K. M. Case, P. F. Zweifel, Linear transport theory, Addison-Wesley, 1967 - R. V. Meghreblian, D. K. Holmes, Reactor Analysis, McGraw-Hill, 1960 - K. Huang, Statistical Mechanics, Wiley, 2008 - D. Tong, Lectures on Statistical Physics, University of Cambridge,2012

Lecture slides; Exercise with solutions ; Video lectures (previous years);

Exam: Compulsory oral exam;

The evaluation is carried out by an oral examination, to verify that the student knows the basic principles of particle transport, the fundamentals of nuclear reactor physics and the methods to solve neutron transport problems in steady state and in transient regimes. In the first part of the exam the student may be asked to present a subject of their choice, and the resulting discussion will in principle cover the whole program of the course. The student is requested to demostrate to have acquired both the understanding of the physical phenomena at the basis of the functioning of a nuclear reactor and the capability to use the mathematical models developed for the study of reactor physics and transport theory.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.