# Overview of Short Learning Programmes and the Dissertation

 Course name NQF level Credits Type 1 Introductory mathematics for nuclear energy UJ) 6 (2nd year BSc) 8 Bridging 2 Advanced mathematics for nuclear energy (UJ) 7 (3rd year BSc) 8 Bridging 3 Thermodynamics and electromagnetism in energy systems (UJ) 6 (2nd year BSc) 8 Bridging 4 Special relativity and quantum mechanics for nuclear applications (UJ) 7 (3rd year BSc) 16 Bridging 5 Nuclear physics for Power Reactors I (iThemba) 8 (Honours) 16 Core 6 Nuclear physics for Power Reactors II (iThemba) 8 (Honours) 16 Core 7 Radiation and radiological protection (NECSA) 8 (Honours) 8 Core 8 Numerical methods for Nuclear Science (UJ) 8 (Honours) 8 Core 9 Nuclear materials and the Nuclear Fuel Cycle (NECSA) 8 (Honours) 8 Core 10 Environmental and Nuclear waste science (NECSA) 8 (Honours) 8 Core 11 Risk analysis and safe reactor operations (BIRA) 8 (Honours) 8 Core 12 Nuclear project management (UJ) 8 (Honours) 16 Core 13 Introduction to Nuclear Engineering (UJ) 8 (Honours) 16 Core 14 Experimental projects (iThemba, NECSA, UJ) 8 (Honours) 32 Core
Course name NQF level Credits Type Disertation (In any of the fields of the Coursework) 8 (Masters) 120 100%

Breakdown of the Short Learning Programs

## 1.  Introductory mathematics for nuclear energy

• Principles of vector calculus and vector operators
• Scalar and vector products
• Gradient operator, Laplacian, curl (and forms in cylindrical and spherical coordinates)
• Principles of Gauss’s and Stoke’s theorems
• Introduction to complex analysis
• Vectors, matrices, solution of systems of linear equations, eigenvalues.
Credits: 8

## 2.  Advanced mathematics for nuclear energy

• Principles of series expansions and orthogonal functions
• Solving differential equations
• Applications of differential equations to energy related systems
• NB use examples of solutions of differential equations with specific simplified illustrative solutions in different geometries relevant to a range of applications in the nuclear industry, i.e.: Wave equation, diffusion equation, transport equation
Credits: 8

## 3.  Thermodynamics and electromagnetism in energy systems

• Temperature related behaviour of matter and phase changes
• Principles of convection, conduction, radiation and heat transport
• Principles of heat engines and the conversion of heat to work
• Behaviour of thermodynamic systems
• Principles of thermodynamic potentials
• Introduction to entropy
• Maxwell’s equations obtained by integral form as in Serway
• Electromagnetic radiation in vacuum
• The solar spectrum
• Principles of current and energy transmission
Credits: 8

## 4.  Special relativity and quantum mechanics for nuclear applications

• Relativity principles;
• Space-time;
• Four vectors;
• The Lorentz transformation,
• Energy mass equivalence
• Pair production;
• Mass deficit and origin of nuclear energy.
• Particle wave duality;
• Heisenberg uncertainty principle;
• Wave functions and probability interpretation;
• Schrödinger equation;
• Operators;
• Particle in a potential well;
• Simple harmonic oscillator (first classical, then QM);
• Introduction to Angular momentum;
• Hydrogen atom;
• Principles of Perturbation theory;
• Variational Principle,
• Parity, Exchange Symmetry,
• Introduction to Matrix formulation,
• Principles of first order scattering theory (optional)
Credits: 16

## 5.  Nuclear physics for Power Reactors I

• The Nuclear Chart,
• Radioactive decay - Statistical nature and the exponential decay equation;
• Decay mechanisms (β,α,γ), electron capture etc.;
• Decay chains;
• Half-life;
• Activity;
• Binding energy per nucleon and nuclear stability;
• Liquid drop model;
• Fission, Fusion, Capture, Decay Products,
• Applications.
Credits: 16

## 6.  Nuclear physics for Power Reactors II

• Kinematics (non-relativistic and relativistic);
• Simple Scattering, Cross-Sections, Thomson Scattering (classical);
• Compton (quantum mechanical) scattering;
• The deuteron;
• Fermi gas;
• Nuclear shell model;
• Neutron capture;
• Resonances;
• Transmutation;
• Fast neutrons;
• Breeding reactions;
• 233U and 239Pu Breeding Cycles
Credits: 16

• Detection of radiation types;
• Energy loss mechanisms;
• Detector principles,
• Photo-electric, Compton and Pair Production cross-sections,
• Signal processing,
• Statistical interpretation of data;
• Data acquisition and storage.
• Basic radiation biology;
• Radiation dose units;
• ALARA principle;
• Criticality considerations,
• Radiation limits and regulations
Credits: 8

## 8.  Numerical methods for Nuclear Science

• Introduction to Unix
• Introduction to C++
• Root finding
• Numerical Integration
• Project 1 : The Semi-Classical solution of Molecular Vibrations
• Curve fitting
• Numerical solutions to differential equations (Runga-Kutta)
• Project 2 : The QM solution for the Deuteron
• Introduction to statistical simulation methods (Monte-Carlo)
• Overview of reactor simulations
Credits: 8

## 9.  Nuclear materials and the Nuclear Fuel Cycle

• Material properties and measurement techniques;
• Wigner Energy;
• Fuel, moderator and cladding requirements and specifications;
• Basics of radiation damage in reactor materials – and effects on properties;
• Generation IV nuclear materials and intrinsic safety considerations ,
• Nuclear fuel cycle front end - Enrichment Technologies,
• Breeding Cycles(232Th => 233U and 238U => 239Pu),
• Reprocessing,
• Refueling Schemes,
• MOX,
• Remote Handling Technologies,
• Ionisation Chemistry (and radiation damage again).
Credits: 8

## 10.  Environmental and nuclear waste science

• Mining,
• Radioactive Tailings and Mine Dumps,
• Radioactive waste types and classification (fission products, actinides, LA, MA HA, etc.);
• Waste confinement criteria and technologies, waste heat considerations;
• Waste reprocessing;
• Radioactivity release mechanisms and transport into the environment;
• Nuclear reactor and plant Commissioning and decommissioning.
• Environmental Assessments
• Regulatory and Legal Frameworks.
• World Distribution of Accessible Sources of Uranium and Thorium.
Credits: 8

## 11.  Risk analysis and safe reactor operations

• Introduction to probabilistic theory: sample spaces and events,
• Laws of probability,
• Random variables and distributions,
• Relationships between distributions;
• Joint probability distributions;
• Expectation values and moments;
• Moment generating function;
• Central limit theorem;
• Convolutions;
• Stochastic processes
• Normal distribution, variance, confidence limits, hypothesis testing
• Decision theory: decision under risk, decision trees, decision under uncertainty;
• Markov chains and the Markovian decision process
• ISO standards,
• Applications to Nuclear Power facilities
Credits: 8

## 12.  Nuclear project management

• Project scheduling by PERT – CPM;
• Feasibility assessment and NPV calculations
• Industrial Economics: Bank Rate, Financing, Construction Time,
• Industrial Relations,
• Legal Framework,
• Power Distribution.
• International regulations, conventions, safeguards and non-proliferation of nuclear materials
• Management of accident scenarios and emergency .
Credits: 16

## 13.  Introduction to Nuclear Engineering

• Neutron cross sections;
• Reactor materials (fuel, moderator, reflector, control and construction);
• Criticality and reactivity;
• Neutron transport and diffusion equations;
• Reactor control;
• Delayed neutrons;
• Fission products including Reactor Poisons and Transuranic Actinides, Purity Requirements;
• Temperature effects on reactivity;
• Thermo-hydraulics;
• Enrichment Distribution
• Stability analysis;
• Accident simulation;
• Intrinsic safety criteria and generation IV reactor concepts.
• Reactors; PWR, BWR, CANDU, AGR, HTR, PBMR, EWR, Fast Reactors, High Flux Reactors.
Credits: 16

## 14.  Experimental projects

• Experiment 1 : iThemba : Compton scattering
• Experiment 2 : iThemba : alpha-particle spectra and ranges
• Experiment 3 : iThemba : Natural radioactivity
• Experiment 4 : iThemba : Gamma angular distributions to determine the spin of 19F
• Experiment 5 : iThemba : (p,n) Threshold Reactions and Neutron detection
• Experiment 6 : iThemba : Natural radioactivity
• Experiment 7 : NECSA : Neutron Activation Analysis
• Experiment 8 : NECSA : Radiation Monitoring
• Experiment 9 : NECSA : Waste processing
• Experiment 10 : iThemba : Cosmic Rays and the Muon Lifetime
• Experiment 11 : iThemba : (p,ff) Detection of fission fragments
• Experiment 12 : iThemba : Coincidence detection – Positron lifetimes
Credits 32