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, together with some aspects of electrodynamics. The classic Boltzmann equation is deduced and the relationship between kinetic theory and fluid models is studied. The Maxwell's equations are also deduced starting from electrostatics and the special relativity is presented. A short introduction to tensor calculus is provided. 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.

The part of the course on transport theory should enable the students to start complex studies on plasma physics and on the study of ionized matter 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.

The student should have the basic knowledge of calculus and physics, as can be acquired in the courses of a bachelor’s program in industrial engineering.

NUCLEAR REACTOR PHYSICS

1 Design calculation of multiplying structures
1.1 Generation of nuclear data;
1.2 Criticality calculation; multiplication eigenvalue and physical meaning;
1.3 Integration of the neutronic calculation in the design of a nuclear reactor.

2 Neutronic models
2.1 Multigroup diffusion theory;
2.2 Homogeneous and heterogeneous reactors; reflected reactors;
2.3 Neutron transport theory.

3 Perturbation theory
3.1 Perturbation methods for eigenvalues;
3.2 Generalized perturbation techniques.

4 Nuclear reactor dynamics
4.1 Factorization methods for the solution of the neutronic equations; point kinetics and quasi-static method;
4.2 Non-linear feed-back effects;
4.3 Transmutation phenomena.

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 Ionized gases
2.1 Phenomena in ionized gases
2.2 Breakdown
2.3 Drift-diffusion model
2.4 Ambipolar diffusion

3 Completely ionized plasmas
3.1 Non-collisional systems
3.2 Vlasov equation
3.3 Landau damping
3.4 Two-stream instability

4 Non-neutral plasmas
4.1 Penning trap
4.2 Brillouin limit
4.3 Finn model
4.4 Vortex model
4.5 Diocotron instability

5 Neutronics
5.1 Slowing-down of neutrons in matter
5.2 analytical solution of the linear transport equation

6 mathematical and computational techniques
6.1 Multiple time scale method
6.2 Particle in Cell method
6.3 discrete ordinate method

In the sessions applications of the theory presented in the lectures are proposed, such as:
- Solution of problems by the multiple time scale method
- Simulation of the collisional process in a gas
- Simulation of non-collisional plasmas
- Solution of the neutron transport equation

The examination includes a written test covering transport theory and an oral test on fission reactor physics.