PORTALE DELLA DIDATTICA

### Nuclear fission reactor physics and transport theory

01TWMND

A.A. 2020/21

2020/21

Nuclear fission reactor physics and transport theory

The course provides the specific physical and mathematical bases to be used in the study of the physics of fission and fusion reactors. The course is made of two parts. In the first, the kinetic theory is treated. The classic Boltzmann equation is deduced and the relationship between kinetic theory and fluid models is studied. In the second part the neutron transport equation and the physical principles of nuclear fission reactors are illustrated. Some simplified models and approximations for the description of the neutronics of multiplying systems are then presented, together with the fundamentals of criticality theory, reactor dynamics and perturbation theory.

Nuclear fission reactor physics and transport theory

The course provides the specific physical and mathematical bases to be used in the study of the physics of fission and fusion reactors. The course is made of two parts. In the first part the kinetic theory is treated. The classic Boltzmann equation is deduced and the relationship between kinetic theory and fluid models is studied. In the second part the neutron transport equation and the physical principles of nuclear fission reactors are illustrated. Some simplified models and approximations for the description of the neutronics of multiplying systems are then presented, together with the fundamentals of criticality theory, reactor dynamics and perturbation theory.

Nuclear fission reactor physics and transport theory

The part of the course on transport theory should enable the students to understand the fundamentals of kinetic theory and the link to neutronics and fluid-dynamics. The student should also acquire the basic knowledge on some of the mathematical physical models for the design of the cores of nuclear reactors. He should be able to carry out calculations and simulations of the neutronics of multiplying systems, criticality calculations and evaluations on the dynamics of nuclear reactors, and he should acquire the capability to physically interpret the results.

Nuclear fission reactor physics and transport theory

The part of the course on transport theory should enable the students to understand the fundamentals of kinetic theory and the link to neutronics and fluid-dynamics. The reactor physics part allows the student to acquire the basic knowledge on some of the mathematical physical models for the design of the cores of nuclear reactors. Students are expected to learn how to carry out calculations and simulations of the neutronics of multiplying systems, criticality calculations and evaluations on the dynamics of nuclear reactors, and to physically interpret the results.

Nuclear fission reactor physics and transport theory

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.

Nuclear fission reactor physics and transport theory

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.

Nuclear fission reactor physics and transport theory

1 Kinetic theory of gases 1.1 Rarefied gases 1.2 Binary collisions 1.3 Boltzmann equation 1.4 H theorem 1.5 Equations of fluid-dynamics 2 Design calculation of multiplying structures 2.1 Generation of nuclear data; 2.2 Criticality calculation; multiplication eigenvalue and physical meaning; 2.3 Integration of the neutronic calculation in the design of a nuclear reactor. 3 Neutronic models 3.1 Multigroup diffusion theory; 3.2 Homogeneous and heterogeneous reactors; reflected reactors; 3.3 Neutron transport theory. 3.4 Slowing-down of neutrons in matter 4 Perturbation theory 4.1 Perturbation methods for eigenvalues; 4.2 Generalized perturbation techniques. 5 Nuclear reactor dynamics 5.1 Factorization methods for the solution of the neutronic equations; point kinetics and quasi-static method; 5.2 Non-linear feed-back effects; 5.3 Transmutation phenomena. 6 Mathematical and computational techniques 6.1 Spherical harmonics method 6.2 Discrete ordinate method 6.3 Analytical solution of the linear transport equation

Nuclear fission reactor physics and transport theory

1. Kinetic theory 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 Design calculation of multiplying structures 2.1 Generation of nuclear data; 2.2 Criticality calculation; multiplication eigenvalue and physical meaning; 2.3 Integration of the neutronic calculation in the design of a nuclear reactor. 3 Neutronic models 3.1 Multigroup diffusion theory; 3.2 Homogeneous and heterogeneous reactors; reflected reactors; 3.3 Neutron transport theory. 3.4 Slowing-down of neutrons in matter 4 Perturbation theory 4.1 Perturbation methods for eigenvalues; 4.2 Generalized perturbation techniques. 5 Nuclear reactor dynamics 5.1 Factorization methods for the solution of the neutronic equations; point kinetics and quasi-static method; 5.2 Non-linear feed-back effects; 5.3 Transmutation phenomena. 6 Mathematical and computational techniques 6.1 Spherical harmonics method 6.2 Discrete ordinate method 6.3 Analytical solution of the linear transport equation

Nuclear fission reactor physics and transport theory

Nuclear fission reactor physics and transport theory

Nuclear fission reactor physics and transport theory

In the sessions applications of the theory presented in the lectures are proposed, such as: - Simulation of the collisional process in a gas - analytical solution of a 0D kinetic model - Analitycal solution of the neutron transport equation in the infinite medium

Nuclear fission reactor physics and transport theory

In the sessions applications of the theory presented in the lectures are proposed, such as: - Simulation of the collisional process in a gas - Analytical solution of a 0D kinetic model - Analitycal solution of the neutron transport equation in the infinite medium - Criticality problems in different configurations (reflected systems, multigroup model, ...) - Solution of neutron dynamic models: point kinetics and quasi-statics

Nuclear fission reactor physics and transport theory

- 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

Nuclear fission reactor physics and transport theory

- 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

Nuclear fission reactor physics and transport theory

Modalita di esame: Prova orale obbligatoria;

Nuclear fission reactor physics and transport theory

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 can present an argument of his choice. In the second part the student is asked to answer questions on both general transport theory and nuclear reactor physics.

Nuclear fission reactor physics and transport theory

Exam: Compulsory oral exam;

Nuclear fission reactor physics and transport theory

The evaluation consist in an oral interview, 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 can present an argument of his choice. In the second part the student is asked to answer questions on both general transport theory and nuclear reactor physics. The evaluation concerning the two parts of the course can be carried out simultaneously or in different sessions, and the final grade is obtained as an average of the single evaluations.

Nuclear fission reactor physics and transport theory

Modalita di esame: Prova orale obbligatoria;

Nuclear fission reactor physics and transport theory

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 can present an argument of his choice. In the second part the student is asked to answer questions on both general transport theory and nuclear reactor physics.

Nuclear fission reactor physics and transport theory

Exam: Compulsory oral exam;

Nuclear fission reactor physics and transport theory

The evaluation consist in an oral interview, 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 can present an argument of his choice. In the second part the student is asked to answer questions on both general transport theory and nuclear reactor physics. The evaluation concerning the two parts of the course can be carried out simultaneously or in different sessions, and the final grade is obtained as an average of the single evaluations.