99552 - RADIATION TRANSFER AND PARTICLE TRANSPORT M

Learning outcomes

At the end of the course the student: -reaches a deep understanding of the interaction and diffusion of charged particles, photons and neutrons in matter; - becomes familiar with the techniques of transport theory and their scientific and technological applications, in particular, biomedical applications and material analysis.

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 simpler 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

Teacher's notes; V. Boffi: Fisica del reattore nucleare, Patron, Bologna; B.D. Ganapol: Analytical benchmarks for nuclear engineering applications. 2008. NEA No. 6292, available on line at https://www.oecd-nea.org/upload/docs/application/pdf/2019-12/db-doc2008-1.pdf 

Teaching methods

Lectures; practical excercises.

Assessment methods

Written assignements. Oral final. 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

Transparencies, projector, lecturers. Instructro's notes will be available on line (at present on https://virtuale.unibo.it/), and students are asdvised to print them out and bring them to class. The same material will be made available also at the copy center on the 1st floor of the Old Engineering bdg., just next to the school library.

Office hours

See the website of Domiziano Mostacci

See the website of Jorge Eduardo Fernandez