# NE 150

Course Title:

Introduction to Nuclear Reactor Theory

Course Units:

3

Catalog Description:

- Neutron interactions, nuclear fission, and chain reacting systematics in thermal and fast nuclear reactors. Diffusion and slowing down of neutrons. Criticality condition and calculations of critical concentrations, mass and dimensions. Nuclear reactor dynamics and reactivity feedbacks. Production and transmutation of radionuclides in nuclear reactors.

Course Prerequisite:

- Mathematics 53 and 54
- NE 101 Nuclear Reactions and Radiation

Prerequisite Knowledge and/or Skills:

- The course uses the following knowledge and skills from prerequisite and lower-division courses:
- solution of linear, first and second order differential equations.
- vector calculus, special functions (Bessel functions, Exponential integrals).
- basic nuclear physics.
- basic interactions of radiation with matter, and concept of cross sections.

Course Objectives:

- review those aspects of neutron interactions with matter that are pertinent to understanding the establishment of a chain-reaction and of the neutron space- and energy-distribution in the nuclear reactor core.
- show how the complex neutron transport and slowing-down processes can be described by simple, though approximate, analytical models.
- develop the students' insight and understanding of neutron-related phenomena in nuclear reactors.
- show how to quantify the space-dependence, energy-dependence and time-dependence of the neutron population.
- acquaint the students with the neutronic design considerations and design constraints of nuclear reactors.
- illustrate, with examples drawn from various reactor and other neutronic systems, how nuclear reactor theory can be used to quantify the behavior of these system under various conditions.
- acquaint students with the specific features of different types of nuclear reactors, with particular emphasys on light water reactors (LWRs).

Course Outcomes:

- calculate spectrum-averaged microscopic cross-sections for thermal neutrons, macroscopic cross-sections for a single isotope and for a mixture of isotopes, reaction probabilities, mean-free-path, mean time for collision, mean energy loss per elastic collision.
- calculate spectrum-averaged microscopic cross-sections for thermal neutrons, access computerized data files of 0.0253eV cross-sections as well as of Maxwellian averaged cross-sections, of fission spectrum averaged cross-sections and of resonance integrals.
- calculate the slowing-down time, the diffusion time, mean distance of displacement while slowing-down, mean distance of displacement while diffusing as a thermal neutron.
- write mathematical formulations (equations) describing neutron balances (gains and losses) in multiplying systems: the equation of continuity, criticality conditions, the point reactor kinetics equations and the rate equations for changes in nuclide densities.
- solve the one-group and two-groups steady state diffusion equation for simplified systems, both non-multiplying and multiplying, as well as for bare and reflected systems; find the spatial neutron and associated power distributions.
- calculate the magnitude of the neutron flux from published information on the nuclear reactor (total power and fuel inventory; specific power; power density and lattice geometry and composition).
- calculate the critical concentration, critical mass and dimensions for bare and reflected cores.
- estimate the magnitude of the four-factors and of the infinite-multiplication-factor in heterogeneous systems.
- calculate the asymptotic reactor period resulting from introduction of positive and negative reactivity and calculate the reactivity that need be introduced in order to change the reactor power level by a given factor in a given time.
- estimate the reactivity effect associated with the buildup of fission products, with the change in fuel temperature and of coolant temperature, and with fuel burnup; calculate the reactivity effect of a given concentration of a thermal neutron absorber uniformly distributed across the core.
- calculate the change in concentration of fission products as a function of the reactor operating time and as a function of the reactor shutdown time.
- solve the rate-equations for the change in the concentration of different isotopes in an operating reactor.

Topics Covered:

- General description of nuclear reactors and statistics about worldwide nuclear power production.
- Review of the basic of neutron interactions: possible type of interactions; consequences of these interaction; interaction probability; microscopic and macroscopic cross sections, cross-section systematics; cross-section data.
- Slowing-down of neutrons: elastic scattering mechanics; energy loss; average logarithmic energy decrement; slowing-down time; effect of inelastic scattering; collision and slowing-down densities; resonance absorption.
- Fission chain reaction: chain reaction in thermal and fast systems; the four- and six-factor formulas; nuclear fuels; conversion and breeding.
- Neutron spectra: thermal equilibrium; typical neutron spectrum in thermal and fast reactors; effective spectrum averaged cross-sections; resonance integrals.
- Introduction to neutron diffusion theory: neutron flux and current, equation of continuity, Fick's law, transport corrections; the diffusion equation for monoenergetic neutrons, boundary conditions; elementary solutions of the steady-state diffusion equation, solutions for multiplying media, multi-group diffusion equations; solution of the two-group diffusion equation.
- Nuclear reactor theory: one-group reactor equation, criticality conditions; effect of reflectors; determination of critical concentration, dimension and mass; heterogeneity effects: fuel lumping and control-absorber lumping; calculation of thermal utilization, resonance escape probability, and fast fission factor.
- Point reactor kinetics: point reactor kinetics equations; prompt neutron lifetime; effect of delayed neutrons; definition and units of reactivity, the asymptotic reactor period versus changes in reactivity.
- Reactivity variations in operating reactors: effects of fuel and coolant temperature change; effect of coolant voiding; effect of fission products; effect of fuel depletion; BOL excess reactivity requirements for different reactor types.
- Methods for compensation of reactivity variations: control rods; coolant inlet temperature; chemical shim; burnable poison; in-core fuel management.

Textbook(s) and/or Other Required Materials:

- J.R. Lamarsh - "Introduction. to Nuclear Engineering", 2nd Edition, Addison-Wesley (1983)

Class/Laboratory Schedule:

- This is primarily a lecture course, meeting two times a week for 80-minute lectures. Illustrations are integrated within the lectures.

Contribution of Course to Meeting the Professional Component:

- This course contributes primarily to the students' knowledge of engineering topics, and does provide design experience.
- Introduction to Nuclear Reactor Theory provides the students with the understanding of the phenomena that take place in fission reactors and with the understanding of the nuclear reactor design requirements. This course provides the students with tools for, and experience in simplified design and analysis of nuclear reactor cores. It also gives the students an insight in the neutronics behavior of other systems such as source-driven subcritical systems, fusion reactor blankets and facilities for medical applications.

Relationship of Course to Degree Program Objectives:

- This course primarily serves students in the department. The information below describes how the course contributes to the undergraduate program objectives.
- This course contributes to the NE program objectives by providing education in an area (nuclear reactor theory) that is of central importance for a career in nuclear engineering.

Assessment of Student Progress Toward Course Objectives:

- Weekly (nearly) problem sets: 40%
- Two midterm Exams: 30% (15% each)
- Final Exam: 30%