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Operational Reactor Safety 22.091/22.903
Professor Andrew C. Kadak Professor of the Practice
Spring 2008
Lecture 2: Reactor Physics Review
Prof. Andrew C. Kadak, 2008 Department of Nuclear Science & Engineering Page 1
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Topics to Be Covered – Cross Sections
– Fission Process
– Infinite Reactor Systems
– Finite Reactor Systems
– Four Factor Formula
– Criticality Control
– Diffusion Theory
– Neutron Transport (Boltzman Equation)
Prof. Andrew C. Kadak, 2008 Department of Nuclear Science & Engineering Page 2
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Nuclear Reactor Physics Review
Prof. Andrew C. Kadak, 2008 Department of Nuclear Science & Engineering Page 3
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Cross Sections
Prof. Andrew C. Kadak, 2008 Department of Nuclear Science & Engineering Page 4
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Cross Sections
Prof. Andrew C. Kadak, 2008 Department of Nuclear Science & Engineering Page 5
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Uranium Cross Sections
Prof. Andrew C. Kadak, 2008 Department of Nuclear Science & Engineering Page 6
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Fission Chain Reaction
Prof. Andrew C. Kadak, 2008 Department of Nuclear Science & Engineering Page 7
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Fission Neutron Energy
Prof. Andrew C. Kadak, 2008 Department of Nuclear Science & Engineering Page 8
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Fission Energy
Prof. Andrew C. Kadak, 2008 Department of Nuclear Science & Engineering Page 9
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Fission Product Decay Chain
Prof. Andrew C. Kadak, 2008 Department of Nuclear Science & Engineering Page 10
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Fission Yield by Mass Number
Prof. Andrew C. Kadak, 2008 Department of Nuclear Science & Engineering Page 11
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Chart of the Nuclides
Prof. Andrew C. Kadak, 2008 Department of Nuclear Science & Engineering Page 12
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Prof. Andrew C. Kadak, 2008Page 13Department of Nuclear Science & Engineering
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Conversion Chain: Fertile Fissile
Prof. Andrew C. Kadak, 2008 Department of Nuclear Science & Engineering Page 14
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Reaction Rates* • How do we make power?
• Factors to consider in design
– Changes in fuel material
– Life of reactor core
– Reactivity swing
– Refueling strategies
Prof. Andrew C. Kadak, 2008 Department of Nuclear Science & Engineering Page 15
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Prof. Andrew C. Kadak, 2008Page 16Department of Nuclear Science & Engineering
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Prof. Andrew C. Kadak, 2008Page 17Department of Nuclear Science & Engineering
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Neutron Moderation Parameters
Prof. Andrew C. Kadak, 2008 Department of Nuclear Science & Engineering Page 18
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Infinite & Finite Reactor Systems* • Infinite Systems
– Neutron Multiplication
– Four Factor Formula
• Finite Systems
– Leakage
– Six Factor Formula
• Diffusion Theory
Prof. Andrew C. Kadak, 2008 Department of Nuclear Science & Engineering Page 19
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Criticality Control
• K should = 1 for 18 to 24 months– How ?
• Fuel excess reactivity (fuel)• Balance with control rods or soluble boron• Burnable poisons in fuel to deplete with time• Leakage• On-line refueling – CANDU – Pebble Beds
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Diffusion Theory*
• One group– Neutron Balance for critical reactor– Consider production absorption and leakage
• Multi-group– Include different energy groups
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Prof. Andrew C. Kadak, 2008Page 28Department of Nuclear Science & Engineering
Diffusion Theory Fluxes and Bucklings
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Multigroup Calculations
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Prof. Andrew C. Kadak, 2008Page 30Department of Nuclear Science & Engineering
Diffusion Theory Flux Shapes
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Prof. Andrew C. Kadak, 2008Page 31Department of Nuclear Science & Engineering
Fast and Thermal Flux Shapes
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Prof. Andrew C. Kadak, 2008Page 33Department of Nuclear Science & Engineering
Boltzman Equation• Neutron Transport Theory
• Fundamental Equation of neutron interaction
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Prof. Andrew C. Kadak, 2008Page 34Department of Nuclear Science & Engineering
Homework• Knief Chapter 4
– Problems: 4.3, 5, 8, 10, 11, 14, 15
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22.091 Nuclear Reactor SafetySpring 2008
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