### Course Unit Page

• Teacher Jorge Eduardo Fernandez

• Credits 6

• SSD ING-IND/18

• Language Italian

• Campus of Bologna

• Degree Programme Second cycle degree programme (LM) in Energy Engineering (cod. 0935)

• Course Timetable from Feb 24, 2022 to May 26, 2022

### SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

## Learning outcomes

Deep understanding of the interaction and diffusion of charged particles, photons and neutrons in matter. To familiarize with the problems and solution techniques of transport theory.

## Course contents

Introduction to transport theory

• Out-of-equilibrium statistical Mechanics: transport processes. Mu and Gamma phase spaces. Density in the Gamma phase space. Liouville Theorem. Substantial derivative.
• Liouville Equation. BBJKY Hierarchy. Distribution Functions: single, double, triple, etc; Approximations: Boltzmann Equation without collisions; Vlasov Equation.
• Applications to the study of plasma dynamics : Vlasov Equation; Landau damping. Boltzmann Equation: Boltzmann collision term.
• Boltzmann H Theorem in the absence of external forces; invariance properties; Solution of the Boltzmann Equation and the Maxwellian distribution function.
• Boltzmann H Theorem with external forces; the Boltzmann factor; some paradoxes; the Fokker-Planck Equation.
• Examples of the Fokker-Planck Equation. Applications to specific problems. Onsager Theorem. Onsager Equations. Properties of the Onsager coefficients.

Neutron transport

• Fundamentals
• The simplified case of monenergetic neutrons: integral transport equation, diffusion equation, telegrapher's equation, steady state, transport correction. Problems.
• The general case: angular flux, Boltzmann equation for neutrons, integro-differential approach, integral approach; scattering mechanics and transfer function; integral transforms solution in the steady state, monoenergetic case; slowing down: lethargy, Fermi age, slowing down density; problems.
Photon transport
• Integro-differential Boltzmann equation for photons; deterministic solution.
• Photon interaction with matter; multiple scattering.
• Numerical methods in photon transport (SHAPE code).
• Integral form of the Boltzmann equation for photons.
• Extra-curricular activity: vector transport equation and polarization effects; deterministic solution; Monte Carlo solution (MCSHAPE code).

LESSON NOTES
V. BOFFI: FISICA DEL REATTORE NUCLEARE, VOL. I - LA TEORIA DEL TRASPORTO DEI NEUTRONI, ED. PATRON, BOLOGNA 1974.
J. FERNANDEZ E V. MOLINARI. PHOTON TRANSPORT SPECTROSCOPY. ADV. SCINCE AND ENGINEERING. VOL 22 PLENUM PRESS (1991).
VIRTUAL BOOKSHELF

## Teaching methods

Lectures;practical excercises; visiting lecturers; visits.

## Assessment methods

Written midterms. The student will be required to show good understanding of the basic principles and prove capable to apply them to simple practical problems.

## Teaching tools

Notes and presentations available through the web site; lectures from visiting experts; visit to radiation laboratory.