Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2018/2019
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Insegnamento 096044 - FISSION REACTOR PHYSICS
Docente Padovani Enrico
Cfu 10.00 Tipo insegnamento Monodisciplinare

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento

Obiettivi dell'insegnamento

The aim of the course is to provide the fundamental knowledge on how neutrons are distributed in the matter - with particular emphasis on materials of interest for nuclear fission reactors - and the effect they produce. More specifically:

- The distribution of the neutron flux is described, for simple cases, as a function of spatial variables alone, of energy alone, of time alone, or jointly as a function of space and energy.

- The reactions resulting from the presence of neutron flux lead to changes in the materials, which are described in detail.

- The temporal variation of the neutron flux, and therefore of the power generated, is described both in the absence and in the presence of feedbacks.

- The solution of simple problems is mainly done through the use of mathematical tools, and sometimes also through the Monte-Carlo method.


Risultati di apprendimento attesi

The student:

- understands the meaning of the variables introduced, and knows the unit of measure, the transformation law when changing the independent variable and the field of use.

- knows the meaning and value of the main physical and engineering parameters related to the topics and examples discussed.

- is able to build starting equations, and is able to follow logical and mathematical steps to derive the application formulas and the main results from the theory.

- is able to expose the topics covered using correct and appropriate scientific terminology and language.

Argomenti trattati

Fission. The physics of nuclear fission, energy yield, prompt and delayed emissions, decay chains.

Neutron cross sections. Definition, reaction channels, Breit-Wigner formula, Maxwell's distribution vs. energy and speed, average values​​, thermal motion, Doppler broadening of neutron resonances.

Balance equations for thermal neutrons. Isotropic distribution. Change of variables. Mean squared crow-flight distance. Neutron flux and current density. Linearity and superposition. The diffusion approximation, Fick's law, analytical solution of simple problems.

Multiplying materials. One group criticality. Buckling and flux expressions for some simple geometries, peak factors. Evaluation of the diffusion length (sigma pile).

Slowing down of neutrons. Elastic collision, energy distribution, collision density and slowing-down density, lethargy, Placzek oscillations.

Fermi’s age equation. Assumptions, examples of analytical solution, the case of hydrogen. Age and mean squared slowing down distance.

Resonances. “Narrow Resonance” and “Narrow Resonance Infinite Mass” approximations, effective resonance integral, temperature effect.

K-effective. The four factors and the six factors formulae.

Criticality. Modified (hybrid) one-group scheme and notes on two-group scheme without and with reflector, reflector saving.

Heterogeneous reactors. Homogenized cell, the four factors in the heterogeneous case.

Temperature coefficients of reactivity: definition, examples.

Saturable poisons. Balance equations, exponential matrix, transient behavior, flux oscillations (notes).

Fuel evolution. Balance equations, burning, residual radio-toxicity.

Point Kinetics. The kinetic equations, in-hour equation, prompt jump, shut-down.

Introduction to dynamics. Feedbacks, PWR and BWR simplified schemes.

An introduction to the Monte Carlo method. Analog simulation of neutron transport and slowing down, sampling, simple exercises.


For a profitable learning, a good familiarity with mathematical analysis is indispensable, and knowledge of classical mechanics and nuclear physics is very useful. The required level is the one of first-level scientific and/or engineering courses.

Finally, it is necessary to know the Greek alphabet.

Modalità di valutazione

The exam consists of an oral trial. The purpose is to evaluate the knowledge and understanding of the topics of the course. The student is required to answer questions or perform exercises in writing, with introductory parts or supporting comments in oral form.

By rule, 3-4 main questions are asked and the solution of 1-2 simple exercises is required. In addition, many requests for clarification and questions on specific points are solicited.

The exam evaluates in particular the ability of:

- knowing the meaning, the unit of measure and the use of the variables introduced in the course. The request to specify the unit of measurement is done by filling in appropriate tables and/or through numerous requests for dimensional checks on variables and equations.

- knowing the value of the main physical and engineering parameters met in the course, and recognizing the particular importance of some of them.

- answering the questions by connecting the introduced variables and physical phenomenology in a logical way. As a rule, the development of the topics is based on a starting equation, which is then appropriately manipulated to arrive at final equation and/or result. The student is asked to build the starting equation of the neutron diffusion theory for a diffusing or multiplying material, the neutron energy distribution after one and two collisions, the Fermi’s age equation, the time evolution equations for poisons, the point kinetics equations. The explanations provided in support of the construction of the starting equation alone represent half of the score assigned to the answer.

- employing the scientific terminology and language in an exact way. Every scientific term, as well as every word of natural language, has its meaning. The correct use of both, which determine the precision and clarity of the exposition, are elements that are well correlated to the level of understanding and knowledge of the topics of the course, and therefore also constitute a valid tool of judgment.

Risorsa bibliografica obbligatoriaJohn R. Lamarsh, Introduction to NUCLEAR REACTOR THEORY, Editore: Addison Wesley. Reprint c/o American Nuclear Society (2002), Anno edizione: 1966 http://www.new.ans.org/store/i_300030

Chapters 1, 2, 3, 4, 5, 8 (§ 8.1-8.5, § 8.9), 6, 7, 9, 10 (w/o formulae in pages 327-339, w/o § 10.4), 11 (w/o pages 373- 385, w/o pages 388-389, w/o pages 403-406), 12 (w/o § 12.11), 13 (w/o § 13.4).

Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Informatico
Laboratorio Sperimentale
Laboratorio Di Progetto
Totale 100:00 150:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese
schedaincarico v. 1.6.1 / 1.6.1
Area Servizi ICT