34627 - Radiation transfer and particle transport (Graduate Course)

Course Unit Page

SDGs

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

Quality education Gender equality

Academic Year 2021/2022

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).

Readings/Bibliography

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.

Links to further information

http://trasprad.ing.unibo.it

Office hours

See the website of Jorge Eduardo Fernandez