Physics and Technology of Nuclear Reactors
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The following presentation was created by me (Paul Callaghan) in order to demonstrate learning on the Physics and Technology of Nuclear Reactors Course I attended from Autumn 2007 to Spring 2008 at The University of Birmingham.
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Physics and Technology of Nuclear Reactors
- 1. Physics and Technology of Nuclear Reactors Paul Callaghan Consultant Engineer
- 9. Cross-Sections (2) – Typical Reactor Material Values Source: The Elements of Nuclear Reactor Theory 2 nd Edition - Glasstone and Edlund Element Total - t (barns) Absorption - a (barns) Scatter - s (barns) H 20-80 0.32 20-80 D 2 0 15.3 0.00092 15.3 B 722 718 3.8 Zr 8.4 0.4 8.0
- 12. Absorption Cross-Section vs Neutron Energy for U 235 (1)
- 22. Prompt and Delayed Neutrons (2) Fission (Watt) Spectrum Majority 1-2 MeV Range: 0.03eV- 10MeV S(E)=0.484e -E sinh 2E
- 25. Delayed Neutrons from Fission Products (3) Properties of Delayed Neutrons in Slow Neutron Fission of U 235 Source: The Elements of Nuclear Reactor Theory 2 nd Edition - Glasstone and Edlund Half Life (Sec) Mean Life (Sec) Decay Constant (Sec -1 ) Fraction I Energy (MeV) 0.43 0.62 1.61 0.00084 0.42 1.52 2.19 0.456 0.0024 0.62 4.51 6.5 0.151 0.0021 0.43 22.0 31.7 0.0315 0.0017 0.56 55.6 80.2 0.0124 0.00026 0.25
- 26. Fission Yield Curve – U 235 Light Group Heavy Group
- 47. Requisite Knowledge (1) Where: k= number of neutrons in current generation number of neutrons in previous generation And: ρ = k - 1 k State Multiplication Factor (k) Reactivity (ρ) Sub Critical k < 1 ρ< 0 Critical k = 1 ρ = 0 Super Critical k > 1 ρ > 0
- 54. Gas Cooled Reactors – Magnox Fuel Uranium Tetrafluoride and Magnesium Control Safety Rods: Boron Steel Bulk Rods: Boron Steel Fine Control: Mild Steel Coolant CO 2 Cladding Magnox Can Moderator Graphite
- 55. Gas Cooled Reactors – AGR Fuel UO 2 fuel pellets Cladding Stainless Steel Control Coarse rods: Cr-Mo-B Alloy Fine rods: Cr-Mo Moderator Graphite Coolant CO 2
- 56. Light Water Reactors – PWR Fuel UO 2 fuel pellets (3-4% U 235 ) Cladding Zircaloy4 Burnable Poison Boric acid in primary circuit water Control Boron carbide alloy Moderator/Coolant Water (H 2 O)
- 57. Light Water Reactors – BWR Fuel Sintered UO 2 fuel pellets (2-3% U 235 ) Cladding Zircaloy Burnable Poison Gadolinium Oxide Control Boron alloy Moderator/Coolant H 2 O
- 58. Pressure Tube Reactors – CANDU Fuel UO 2 fuel pellets Cladding Zircaloy Control Short term: Gd 2 O 3 Long term: D 2 0 Moderator Deuterium (D 2 O) Coolant Deuterium (D 2 O) in separate circuit to moderator
- 59. Pressure Tube Reactors – RBMK-1000
Editor's Notes
- Nuclear reactions involve collisions of a nucleus with a particle c.f chemical reactions where the collisions are between whole atoms or molecules To do this, the particle must overcome the coulombic repulsion of nuclei owing to their positive charge approaching to within 10 -12 cm (diameter of nucleus) before interaction can occur. The coulombic energy is very large in the order of MeV and this must be overcome in order for a reaction to occur. Neutrons are ideal for use as the incident particle for these reactions as they are electrically neutral hence they are unaffected by the charge of the nucleus. Within a reactor this means that low energy slow neutrons (~0.03eV) at room temperature can interact with atomic nuclei In fact the probability of collision between a slow neutron and nucleus is greater than that between a fast neutron and nucleus as a slow neutron will spend more time within the vicinity of a nucleus than a fast neutron. In the Compound Nucleus model - a nuclear reaction occurs in 2 stages: Incident particle absorbed by target nucleus creating a compound nucleus Compound nucleus disintegrates expelling a particle (or photon) leaving a recoil nucleus. Radiative Capture is the process whereby a particle is captured and the excess energy is emitted as radiation
- Definition: A measure of the probability of occurrence of a particular nuclear reaction under prescribed conditions i.e. the probability of collision Microscopic Cross-Section - Applies to a particular process on a single nucleus Usually described by beam of light model Macroscopic Cross-Section - Is volumetric and is for a collection of nuclei Related to by = N. Where N = Number of nuclei per cm 3 Nuclear cross-sections commonly of the order 10 -22 to 10 -26 cm 2 per nucleus Unit of measurement is the barn 1 barn = 10 -24 cm 2 per nucleus Different types of macroscopic cross-section for different nuclear processes Absorbtion Cross-Section ( a ) - neutrons “lost” to the system Fission Cross-Section ( f ) – behaviour of incident particle leads to generation of new particles Scatter Cross-Section ( s) – transfer of energy from one particle to another
- Hydrogen has a high scatter cross section – a property which makes it a very effective moderator material Deuterium also has a high scatter cross section – a property which makes it effective for use as a moderator Boron has massive absorption cross section – a very useful property for a control rod / reactivity suppressant Zirconium has relatively high absorption and scatter cross-sections – making it a useful cladding material
- Resonance absorption frequently occurs with neutrons of energy between 1eV and 10 eV i.e. thermal neutrons
- For nuclides with mass number>100 examination of the absorption cross-section ( a ) with neutron energy shows 3 distinct regions: Low Energy (1/V) Region – Cross-section decreases with increasing neutron energy Resonance Region Fast Neutron Region – Cross-sections decrease steadily with increasing neutron energy Resonance Region Categorised by resonance peaks. Found in regions of low neutron energy with elements of higher mass number Reactions are (n, ) Resonance absorption cross-sections are high often 10 3 barns c.f geometric cross-section of 2 barns.
- Types of nuclear interaction As a generalized nuclear process, consider a collision in which an incident particle strikes a previously stationary particle, to produce an unspecified number of final products. If the final products are the same as the two initial particles, the process is called scattering. The scattering is said to be elastic or inelastic, depending on whether some of the kinetic energy of the incident particle is used to raise either of the particles to an excited state. If the product particles are different from the initial pair, the process is referred to as a reaction. The most common type of nuclear reaction, and the one which has been most extensively studied, involves the production of two final products. Such reactions can be observed, for example, when deuterons with a kinetic energy of a few MeV are allowed to strike a carbon nucleus of mass 12. Protons, neutrons, deuterons, and alpha particles are observed to be emitted. The nuclei are indicated by the usual chemical symbols; the subscripts indicate the atomic number (nuclear charge) of the nucleus, and the superscripts the mass number of the particular isotope. These reactions are conventionally written in the compact notation 12 C( d , d ) 12 C, 12 C( d , p ) 13 C, 12 C( d , n ) 13 N, and 12 C( d ,α) 10 B, where d represents deuteron, p proton, n neutron, and α alpha particle. In each of these cases the reaction results in the production of an emitted light particle and a heavy residual nucleus. If the residual nucleus is formed in an excited state, it will subsequently emit this excitation energy in the form of gamma rays or, in special cases, electrons. The residual nucleus may also be a radioactive species, in which case it will undergo further transformation in accordance with its characteristic radioactive decay scheme
- The hydrogen atoms in the water molecules are very close in mass to a single neutron and thus have a potential for high energy transfer, similar conceptually to the collision of two billiard balls. In addition to being a good moderator, water is also fairly effective at absorbing neutrons.
- Sb – Antimony Te – Tellurium I – Iodine Xe – Xenon Cs – Caesium Ba - Barium Xenon-135 has a huge absorption cross-section ( a ) and is “Poisonous” to a reactor due to soaking up neutrons a ( 135 Xe) = 2.7x10 6 barns
- In the periodic table of elements , the series of light elements from hydrogen up to sodium is observed to exhibit generally increasing binding energy per nucleon as the atomic mass increases. This increase is generated by increasing forces per nucleon in the nucleus, as each additional nucleon is attracted by all of the other nucleons, and thus more tightly bound to the whole. The region of increasing binding energy is followed by a region of relative stability (saturation) in the sequence from magnesium through to xenon. In this region, the nucleus has become large enough that nuclear forces no longer completely extend efficiently across its width. Attractive nuclear forces in this region, as atomic mass increases, are nearly balanced by repellent electromagnetic forces between protons, as atomic number increases. Finally, in elements heavier than xenon, there is a decrease in binding energy per nucleon as atomic number increases. In this region of nuclear size, electromagnetic repulsive forces are beginning to gain against the strong nuclear force.
- U235 fission with fast neutrons produces around 1.7 neutrons per fission - insufficient to sustain a chain reaction.
- Delayed neutrons emission increases over a period of minutes Delayed neutrons form 5 (possibly more) groups characterised by a specific half-life Total fraction of delayed neutrons is observed to be 0.0075 The spectrum is virtually the same regardless of the initial energy of the incident neutron
- These neutron-emitting fission fragments are called delayed neutron precursor atoms.
- In some cases the available energy in the beta decay is high enough to leave the residual nucleus in such a highly excited state that neutron emission instead of gamma emission occurs.
- 14 MeV Curve is fast neutron energy – Incident Particle Thermal Curve is slow neutron energy – Incident Particle Sum of Fission products is 200% as each fission results in 2 products Fission products are all radioactive (in excited state) Atomic numbers change with time due to beta decay Mass numbers are unaffected hence the yield is expressed in terms of mass number.
- Xe – Xenon Sm - Samarium Define Multiplication Factor (K) and reactivity ( )
- Xe – Xenon Sm - Samarium
- An equation used to study the nonequilibrium behavior of a collection of particles The rate of change of a function which specifies the probability of finding a particle in a unit volume of phase space is equal to the sum of terms arising from: external forces, diffusion of particles collisions of the particles. Also known as Maxwell-Boltzmann equation.
- Neutrons that are produced in the reactor but independent of the fission chain.
- Source: http://www.coolschool.ca/lor/PH11/unit9/U09L04.htm
- Source: http://www.coolschool.ca/lor/PH11/unit9/U09L04.htm
- &quot;CANada Deuterium Uranium ” At the time of its design (1950 ’ s), Canada lacked the heavy industry to cast and machine the large, heavy steel pressure vessel used in most light water reactors . Instead, the pressure is contained in much smaller tubes, 10cm diameter, that contain the fuel bundles. These smaller tubes are easier to fabricate than a large pressure vessel. In order to allow the neutrons to flow freely between the bundles, the tubes are made of a zirconium alloy (zirconium + 2.5% wt niobium), which is highly transparent to neutrons. The zircaloy tubes are surrounded by a much larger low-pressure tank known as a calandria , which contains the majority of the moderator . Canada also lacked access to uranium enrichment facilities, which were then extremely expensive to construct and operate. CANDU was therefore designed to use natural uranium as its fuel. Deuterium is used as a moderator as hydrogen in water has high neutron absorption properties which would preclude a sustainable nuclear chain reaction in fuel with a low U235 content. Source: http://www.coolschool.ca/lor/PH11/unit9/U09L04.htm
- RBMK is an acronym for the Russian reaktor bolshoy moshchnosti kanalniy: &quot;High Power Channel-type Reactor” An RBMK employs long (7 metre) vertical pressure tubes running through a graphite moderator and cooled by water Water (coolant) allowed to boil in the core at 290 C, much as in a boiling water reactor . Fuel is low- enriched uranium oxide made up into fuel assemblies 3.65 metres long. Moderation largely due to the fixed graphite, excess boiling simply reduces the cooling and neutron absorption without inhibiting the fission reaction Reactor can have a large positive void coefficient , and a positive feedback problem can arise, as with the disaster at Chernobyl . In the case of evaporation of water to steam , the place occupied by water would be occupied by water vapor, which has a density vastly lower than that of liquid water (the exact number depends on pressure and temperature; at standard conditions, steam is about 1/1350th as dense as liquid water). Because of this lower density (of mass, and consequently of atom nuclei able to absorb neutrons), light water's neutron-absorption capability practically disappears when it boils. This allows more neutrons to fission more U-235 nuclei and thereby increase the reactor power, which leads to higher temperatures that boil even more water, creating a thermal feedback loop Source: http://www.nu.no/bilder/Russland/tsjernobyl/rbmk.jpg
- Source: http://www.coolschool.ca/lor/PH11/unit9/U09L04.htm