NE 150 - INTRODUCTION TO NUCLEAR REACTOR THEORY (4 units)

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. (Spring) Vujic

Catalog Description

• 150. Introduction to Nuclear Reactor Theory. Three
  hours of lecture per week. 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 Prerequisites

• 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.

Textbook(s) and/or other required material

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

Course objectives and outcomes

Course Objectives: It is the instructor's
intention to...

• 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: Students must be
able to...

• 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.

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 undergraduate 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%