BASIC PROFESSIONAL TRAINING COURSE Module I Nuclear physics

BASIC PROFESSIONAL TRAINING COURSE Module I Nuclear physics and reactor theory Version 1 a, September 2014 This material was prepared by the IAEA and co-funded by the European Union.

2 ATOMIC STRUCTURE OF MATTER Learning objectives After completing this chapter, the trainee will be able to: 1. Describe the terms element, atom, compound and molecule. 2. Define the atomic mass unit. 3. Define the relative atomic mass Ar. 4. Define the relative molecular mass M and calculate it from the chemical formula. 5. Calculate the mass of elements in a given mass of a compound. Basic Professional Training Course; Module I Nuclear physics and reactor theory

3 Elements and atoms • Elements are basic components of matter − 112 elements are currently known, 90 elements naturally occurring − Elements have specific names and symbols, e. g. : H – Hydrogen He – Helium Li – Lithium O – Oxygen U – Uranium … • Basic constituents of element are atoms: - Atom is the smallest particle of an element, having its chemical properties - Atoms of different elements have different chemical properties Basic Professional Training Course; Module I Nuclear physics and reactor theory

4 Compounds • Different elements bond together to make a compound • Basic constituents of a compound are molecules: − A molecule is the smallest particle of a compound, having its chemical properties • Atoms combine into molecules in chemical reactions: Hydrogen + Oxygen → Water (2 H 2 + O 2 → 2 H 2 O) Sodium + Chlorine → Sodium chloride (salt) (2 Na + Cl 2 → 2 Na. Cl) Uranium + Oxygen → Uranium dioxide Basic Professional Training Course; Module I Nuclear physics and reactor theory (U + O 2 → UO 2)

5 Atomic mass unit • Atoms are very small and very light • A mass unit used in atomic physics and chemistry: 1 atomic mass unit = 1 amu = 1 u • Definition: 1 u = 1/12 of mass of 12 C = 1. 66∙ 10 -27 kg Basic Professional Training Course; Module I Nuclear physics and reactor theory

6 Relative atomic mass Ar • Ar is the ratio of atom mass and amu: atom mass = Ar amu • The value of Ar can be found e. g. in periodic system − Examples: Hydrogen (H): Ar(H) = 1. 0079 1 Lithium (Li): Ar(Li) = 6. 941 6. 9 Boron (B): Ar(B) = 10. 81 10. 8 Carbon (C): Ar(C) = 12. 011 12 Oxygen (O): Ar(O) = 15. 9994 16 Iron (Fe): Ar(Fe) = 55. 847 55. 8 Uranium (U): Ar(U) = 238. 029 238 Basic Professional Training Course; Module I Nuclear physics and reactor theory

7 Relative molecular mass Mr • Mr is the ratio of molecular mass and amu: mass of molecule = Mr amu − Mr is calculated as the sum of relative atomic masses of atoms in the molecule: Mr (H 2 O) = 2 1 + 16 = 18 − Exercises: 1. Calculate Mr(H 3 BO 3)! 2. Calculate Mr(C 3 H 5 OH)! 3. How many molecules are there in one kg of water? Basic Professional Training Course; Module I Nuclear physics and reactor theory

8 Exercises 1. Calculate the relative molecular mass of carbon dioxide! 2. How many atoms of boron there are in 1 kg of boron? 3. How many atoms of hydrogen and how many atoms of oxygen there are in 1 kg of water? 4. What is the mass of hydrogen and the mass of oxygen in 1 kg of water? 5. What is the mass of boron in 10 kg of boric acid H 3 BO 3? 6. How many grams of oxygen need to be added to 2 g of hydrogen, in order that all hydrogen combines with oxygen into water? How much water we would get? 7. How many uranium atoms there are in 1 cm 3 of uranium? (which additional information is needed? ) Basic Professional Training Course; Module I Nuclear physics and reactor theory

9 STRUCTURE OF ATOM Learning objectives After completing this chapter, the trainee will be able to: 1. Describe the structure of an atom. 2. Name the main characteristics of an electron. 3. Define the atomic number, Z. 4. Explain the terms positive and negative ion. 5. Define the binding energy of an electron. 6. Define the unit electron-volt. 7. Describe the energy levels of electrons in an atom. 8. Explain the ground state and excited state of an atom. 9. Explain the transition of an atom from an excited state to the ground state. Basic Professional Training Course; Module I Nuclear physics and reactor theory

10 Atom • Atom: the smallest particle of an element, having it chemical and physical properties • Atom is composed of: − Nucleus, which has positive electrical charge − Negatively charged electrons, which form sort of cloud around the nucleus – the electron envelope • Size of atom ~ 10 -10 m • Diameter of atom : nucleus ~ 10000 : 1 • Mass of nucleus > 99, 95% of atom mass Basic Professional Training Course; Module I Nuclear physics and reactor theory

11 Electrons • Electrons: light particles with negative electric charge − eelectron = -1. 6∙ 10 -19 As = -1. 6∙ 10 -19 C ≡ -e 0 − melectron = 9. 1∙ 10 -31 kg 1/1820 u • Electrons move in the electron cloud. − Electron cloud determines the outer boundary of atom and the chemical, electrical and mechanical properties of an element. • Electrons are bound to positively charged nucleus with electrical force. Basic Professional Training Course; Module I Nuclear physics and reactor theory

12 Atomic number Z • Z – atomic number − equal to number of electrons in neutral atom − equal to consecutive number of element in the periodic table − all atoms of a specific element have the same number of electrons • As a rule, atom is electrically neutral negative charge of electrons = positive charge of nucleus − charge of electrons in the atom = - Z ∙ e 0 − charge of nucleus in the atom = Z ∙ e 0 Basic Professional Training Course; Module I Nuclear physics and reactor theory

13 Ions • Atom becomes: − a positive ion, if it loses electrons (positive charge of nucleus prevails) − a negative ion, if it gains electrons (negative charge of electrons prevails) Basic Professional Training Course; Module I Nuclear physics and reactor theory

14 Electron energy • Free electrons, when moving, have positive (kinetic) energy • Free electrons at rest have zero energy • Electron which is bound in atom must be supplied with energy to become free electron Energy of bound electron is negative • Binding energy is always negative; the lower (more negative) the binding energy, the stronger electron is bound Basic Professional Training Course; Module I Nuclear physics and reactor theory

15 Electronvolt • Atoms are very small and light energies of particles within atom are very small • The unit for energy on atomic scale is electronvolt (e. V): − Energy of a particle with elementary charge (e 0), accelerated with voltage of 1 V 1 e. V = 1. 6∙ 10 -19 As ∙ 1 V = 1. 6∙ 10 -19 J 1 ke. V = 103 e. V (= 1. 6∙ 10 -16 J) 1 Me. V = 106 e. V (= 1. 6∙ 10 -13 J) • Binding energies of electrons in atom: ~ e. V - ~ ke. V Basic Professional Training Course; Module I Nuclear physics and reactor theory

16 Energies of electrons in atom • Electrons moving in electron cloud can have only specific energies • Closer the electron to nucleus, lower (more negative) its energy • The specific values of energy that electrons can possess, are called energy levels of electrons in atom • Any energy level can only be occupied by one electron • Energy levels with lowest energies are occupied first • Atom is in ground state when the lowest possible energy levels are occupied • Atom is in excited state when some energy levels below those occupied are left empty Basic Professional Training Course; Module I Nuclear physics and reactor theory

17 Transitions between electron energy levels • Transition from excited state to ground state: electron falls from a higher energy level into an empty lower energy level − Energy difference is given off in the form of electromagnetic radiation – a photon is emitted • Energy difference between levels: ~ e. V visible light is emitted ~ ke. V X-ray of Roentgen radiation is emitted Basic Professional Training Course; Module I Nuclear physics and reactor theory

18 ATOMIC NUCLEUS Learning objectives After completing this chapter, the trainee will be able to: 1. Describe the basic properties of protons and neutrons. 2. Define the mass number A and write the relationship between mass number, A, atomic number, Z, and the number of neutrons in the nucleus, N. 3. Define a nuclide and an isotope and describe their notation. 4. Explain the isotopic abundance of an element. 5. Describe the systematic arrangement of nuclei in a table. 6. Describe the energy states of a nucleus. 7. Define the binding energy of a nucleon. 8. Plot the binding energy of a nucleon as a function of mass number, A. Basic Professional Training Course; Module I Nuclear physics and reactor theory

19 Composition of the nucleus • Nucleus is composed of particles called nucleons: PROTON (p) NEUTRON (n) charge +e 0 no charge mass 1, 0072766 u 1, 0086654 u • They are bound together with nuclear force (strongest force in nature) Basic Professional Training Course; Module I Nuclear physics and reactor theory

20 Protons, atomic number • Protons are nucleons with positive elementary charge (+ e 0) • Neutral atom: the number of negative charge carriers (electrons) = the number of positive charge carriers (protons) • Atomic number is also the number of protons in nucleus − Nuclei of atoms of same element have equal number of protons − Nuclei of atoms of different elements have different number of protons Basic Professional Training Course; Module I Nuclear physics and reactor theory

21 Neutrons, mass number • Neutrons are nucleons without electrical charge • Mass number A is the number of all nucleons in nucleus • The number of neutrons N is given by N = A - Z • Nuclei of the same element can have different number of neutrons Basic Professional Training Course; Module I Nuclear physics and reactor theory

22 Nuclide = Atom with a nucleus containing Ø A given number of protons and Ø A given number of neutrons • Nuclide is defined with: − − Number of protons = atomic number Z Number of neutrons = neutron number N Number of all nucleons = mass number A The element that nuclide belongs to = chemical symbol X • Nuclide fully defined already with the element and mass number AX − examples: Basic Professional Training Course; Module I Nuclear physics and reactor theory

23 Isotopes • Atoms of the same element can differ in weight: − Equal number of protons (and electrons) − Equal chemical properties − Their nuclei have different masses − The difference in masses originates from different number of neutrons • Atoms of a given element with different number of neutrons are called isotopes • (isotopes are nuclides, belonging to the same element) Basic Professional Training Course; Module I Nuclear physics and reactor theory

24 Hydrogen isotopes ordinary hydrogen (light hydrogen) heavy hydrogen deuterium superheavy hydrogen tritium 1 p, 0 n, 1 e 1 p, 1 n, 1 e 1 p, 2 n, 1 e Basic Professional Training Course; Module I Nuclear physics and reactor theory

25 Isotopic abundance • Everywhere on Earth, elements are composed from same isotopes in fixed relative proportions. • These proportions are called isotopic abundance of an element. • Examples: Element Isotopes and their relative proportions Hydrogen 1 H Boron 10 B – 19. 8% Aluminium 27 Al – 100% Iron 54 Fe – 5. 8% Uranium 234 U – 0. 0054% – 99. 985% 2 H 11 B – 0. 015% – 80. 2% 56 Fe – 91. 72% 235 U 57 Fe – 0. 72% 238 U Basic Professional Training Course; Module I Nuclear physics and reactor theory – 2. 2% 58 Fe – 0. 28% – 99. 2746%

26 Table of stable nuclides • Among ~ 3000 nuclides there are 237 stable nuclides Basic Professional Training Course; Module I Nuclear physics and reactor theory

27 Energy levels in nuclei • Nucleons can occupy different energy levels − All nucleons in lowest possible energy levels: ground state − Nucleons in higher energy levels: excited state Basic Professional Training Course; Module I Nuclear physics and reactor theory

28 Binding energy of a nucleon • Average energy needed to release one nucleon from the nucleus Basic Professional Training Course; Module I Nuclear physics and reactor theory

29 RADIOACTIVITY Learning objectives After completing this chapter, the trainee will be able to: 1. Describe the phenomenon of radioactive decay. 2. Describe the random nature of radioactive decay. 3. Define the half-life, average lifetime and the decay constant of a radioactive nuclide. 4. Define the activity of a radioactive nuclide. 5. Write the equation for the decay of activity with time. 6. Calculate using the exponential law of radioactive decay. 7. Explain the terms short-lived, long-lived and stable nuclide. 8. Describe alpha, beta and gamma radioactive decay and give the basic properties of these types of radiation. Basic Professional Training Course; Module I Nuclear physics and reactor theory

30 Stable and unstable nuclei • There are 81 elements with stable isotopes − All together 237 stable nuclides • Outside the region of stability, the nuclei are unstable − By internal changes and particle emissions unstable nuclei are converted to stable nuclei − The process of internal changes → radioactive decay − Unstable nuclei → radioactive nuclides or radionuclides − Around 3000 radionuclides are known (~ 100 natural, others man-made) Basic Professional Training Course; Module I Nuclear physics and reactor theory

31 Radioactive decay • Decay of unstable atomic nuclei − The internal energy of nucleus is decreased − The energy difference is carried away by particles and/or EM radiation (radioactive) radiation • Radioactive decay is a spontaneous process − The mode and the rate of decay cannot be influenced from the outside • Often, an isotope of one element is converted to an isotope of another element Basic Professional Training Course; Module I Nuclear physics and reactor theory

32 Statistics of radioactive decay • Unstable nuclei decay randomly and independently • One can only predict the probability of decay with time • The probability of decay per unit time is called decay constant (unit s-1) • The decay constant is independent of time and external influences Basic Professional Training Course; Module I Nuclear physics and reactor theory

33 Half-life • Half-life t 1/2 is the time in which the number of radioactive nuclei decreases by half • The number of radioactive nuclei is further halved with each passing of half-life: − t = 0: n 0 nuclei − t = t 1/2: ½ (n 0) = n 0/2 nuclei − t = 2 t 1/2: ½ (n 0/2) = n 0/4 nuclei − t = 3 t 1/2: ½ (n 0/4) = n 0/8 nuclei − … − t = m t 1/2: n 0/2 m nuclei • The number of radioactive nuclei decreases exponentially with time Basic Professional Training Course; Module I Nuclear physics and reactor theory

34 The exponential law of radioactive decay • n(t). . . number of nuclei that have not decayed after time t • n 0. . . number of radioactive nuclei at time t = 0 • t 1/2. . . half-life • Mean lifetime τ is the average time from formation of radioactive nucleus to its decay − Relation to half-life: τ = 1. 44 t 1/2 Basic Professional Training Course; Module I Nuclear physics and reactor theory

35 A comparison of nuclides with different t 1/2 • Long-lived nuclides: large t 1/2, small • Short-lived nuclides: small t 1/2, large Basic Professional Training Course; Module I Nuclear physics and reactor theory

36 Activity • Activity Ac is the number of disintegrations per unit time • Activity is the product of number of radioactive nuclei and the decay constant Ac = ∙ n • Activity changes with time in the same way as the number of radioactive nuclei – decreasing exponentially: Ac(t) = Ac 0 ∙ 2 -t/t 1/2 Ac 0 … initial activity Basic Professional Training Course; Module I Nuclear physics and reactor theory

37 Units for activity 1 Bq (becquerel) = 1 disintegration per second = 1 s-1 − 1 Bq is very small activity − A human body contains ~ 7000 Bq of natural radionuclides − Exemption limit: ~ few 10 k. Bq Old unit • 1 Ci (curie) = 3. 7∙ 1010 Bq = 37 GBq • 1 Ci activity of 1 g of radium (226 Ra) • 1 μCi = 37000 Bq = 37 k. Bq • 1 m. Ci = 37 MBq Basic Professional Training Course; Module I Nuclear physics and reactor theory

38 Specific activity • Specific activity ac is activity per unit mass or volume − units: kg-1 s-1 = Bq/kg or: m-3 s-1 = Bq/m 3 • Examples: 1. A barrel weighing 460 kg contains 69 MBq of radionuclide 137 Cs. Calculate its specific activity! 2. The measured concentration of radon in a room was 125 Bq/m 3. What is the total activity of radon in the room which is 6 m long, 4 m wide and its height is 2. 2 m? Basic Professional Training Course; Module I Nuclear physics and reactor theory

39 Types of radioactive decay • the type of radioactive decay is determined by the type of radiation emitted during disintegration • most common types of decay are: − alpha decay − beta decay − gamma decay • the result of all types of radioactive decay is ionizing radiation: − energetic particles or EM radiation that ionizes matter (removes electrons from atoms) Basic Professional Training Course; Module I Nuclear physics and reactor theory

40 Alpha decay ( decay) • Alpha decay is a consequence of repulsion between protons • heavy nuclei (A > 209) disintegrate with α decay • particle is 4 He nucleus • energies of particles are several Me. V Basic Professional Training Course; Module I Nuclear physics and reactor theory

41 Beta decay ( decay) • beta decay is a consequence of ratio between the number of protons and neutrons outside the stability range • subtypes of decay: -, +, and electron capture (ε) • nuclei with surplus of neutrons disintegrate with - decay • nuclei with surplus of protons disintegrate with + decay or ε • - particle is electron, + particle is positron • beta decay produces also neutrino ν which carries some energy − neutrino has practically no influence on matter or the environment Basic Professional Training Course; Module I Nuclear physics and reactor theory

42 - decay • during - decay, the following transition occurs inside the nucleus: n → p + e- • energies of particles: ~100 ke. V - Me. V Basic Professional Training Course; Module I Nuclear physics and reactor theory

43 + decay • during β+ decay, the following transition occurs inside the nucleus: p → n + β+ • when positron encounters a regular electron, annihilation occurs − e- and e+ disappear, 2 photons with E = 511 ke. V are created Basic Professional Training Course; Module I Nuclear physics and reactor theory

44 decay • nucleons in nucleus can occupy only specific energy levels • decay is a transition from excited state of nucleus to ground state • decay usually follows or decays • energies of rays: ~100 ke. V – Me. V Basic Professional Training Course; Module I Nuclear physics and reactor theory

45 Isomers • some excited nuclei are stable enough to exist in an excited state for a definite time • such nucleus is called isomer or Basic Professional Training Course; Module I Nuclear physics and reactor theory

46 Nuclear changes • In α and β decays, the structure of nuclei changes − radioactive decay is a spontaneous change of nuclei • In any change of structure of nuclei, the following is conserved: − number of nucleons − electric charge • Examples: − α decay: − β decay: − γ decay: Basic Professional Training Course; Module I Nuclear physics and reactor theory

47 General facts about radioactive decays • Heavy nuclei decay with alpha decay • Nuclei with surplus of neutrons decay with - decay • Nuclei with surplus of protons decay with + decay or electron capture (ε) • After or decay, the daughter nucleus is often in excited state which de-excites by decay • Excited state of the resulting nucleus is usually so short-lived that rays are attributed to the decayed nucleus Basic Professional Training Course; Module I Nuclear physics and reactor theory

48 Table of nuclides • Other (wall-sized) tables of nuclides provide a number of data for each nuclide Basic Professional Training Course; Module I Nuclear physics and reactor theory

49 Radiation characteristics name symbol characteristic alpha beta ββ+ gamma γ electrons positrons EM radiation neutron n nucleon 4 He nuclei mass charge penetration depth 4 u +2 e 0 least penetrating radiation –e 0 more penetrating +e 0 than 0 more penetrating than β 0. 00055 u – 1 u Neutrons do not result from radioactive decay but from nuclear reactions Basic Professional Training Course; Module I Nuclear physics and reactor theory

50 NUCLEAR REACTIONS Learning objectives After completing this chapter, the trainee will be able to: 1. Explain nuclear reactions. 2. Name the two key conservation laws of nuclear reactions. 3. Define the terms exoergic and endoergic nuclear reaction. 4. List the reactions of neutrons with matter. 5. Write down some important nuclear reactions. 6. Define neutron flux and the reaction cross section. Basic Professional Training Course; Module I Nuclear physics and reactor theory

51 General description of nuclear reaction • nuclear reactions occur when nuclei are bombarded with particles: a+X→I→Y+b • short notation for nuclear reaction: X (a, b) Y Basic Professional Training Course; Module I Nuclear physics and reactor theory

52 Nuclear reactions often involve nuclear changes • nuclear reactions: − nuclei react with particles or other nuclei − new nuclei are created nuclear changes • radioactive decay usually also results in a nuclear change • fundamental difference: Ønuclear reactions can be controlled Øradioactive decay is spontaneous • conservation of charge and the number of nucleons / examples: or Basic Professional Training Course; Module I Nuclear physics and reactor theory

53 Exoergic and endoergic reactions • Exoergic reaction is accompanied by a release of energy • In an endoergic reaction energy is consumed − energy must be supplied for the reaction to take place − (projectile must have energy larger than threshold energy) Basic Professional Training Course; Module I Nuclear physics and reactor theory

54 Reactions with neutrons • neutron is a neutral particle − − − neutrons do not interact with electron cloud neutrons get to nucleus without hindrance neutron interactions can be divided into scattering and absorption • Scattering − − − neutrons collide with nuclei bounce off them transfer of energy, no creation of new particles the result of the reaction is the initial nucleus and the neutron • Absorption − − − nucleus captures the neutron final nucleus and emitted particle are different than the initial nucleus and projectile nuclear change Basic Professional Training Course; Module I Nuclear physics and reactor theory

55 Neutron scattering • neutrons collide with nuclei and bounce off them • “products” of reaction (scattering) neutron and initial nucleus • nucleus gains kinetic energy with the collision • the kinetic energy of the neutron is decreased the neutron is slowed down → neutrons change from fast neutrons into slow or thermal neutrons • can be compared with billiard balls collisions n + X → X + n or (n, n) Basic Professional Training Course; Module I Nuclear physics and reactor theory

56 Neutron absorption • capture − radiative capture (n, ) – most typical − (n, ), (n, p), … • fission (neutron induced fission) Basic Professional Training Course; Module I Nuclear physics and reactor theory

57 The rate of nuclear reactions the number of nuclei reacting with neutrons in unit time • the number of reactions depends on: 1. The intensity of neutron radiation 2. The probability for neutrons to react with nuclei − (type and density of nuclei in the target) Basic Professional Training Course; Module I Nuclear physics and reactor theory

58 Neutron flux • ~ number of neutron per unit area and per unit time − units for flux: 1 m-2 s-1 = 10 -4 cm-2 s-1 − flux of neutrons in the reactor: 1012 cm-2 s-1 – 1014 cm-2 s-1 Basic Professional Training Course; Module I Nuclear physics and reactor theory

59 Reaction cross section • cross section ~ effective cross sectional area of a nucleus “seen” by a beam of particles • a measure for probability of a reaction on nucleus • cross section unit: 1 barn = 1 b = 10 -24 cm 2 • cross section values change markedly from one nucleus to another, and also relative to neutron energy number of nuclear reactions = n t Basic Professional Training Course; Module I Nuclear physics and reactor theory

60 Neutron cross sections • cross sections for individual types of reactions are marked with corresponding index − S … scattering a … absorption c … capture f … fission … radiative capture − … − − • some cross sections are related to each other, e. g. − a = c + f Basic Professional Training Course; Module I Nuclear physics and reactor theory

61 Important nuclear reactions in fuel • FISSION: discussed separately in the next chapter • Formation of Plutonium: (fuel contains > 95% of 238 U which is not fissile) 238 U (n, ) 239 U → 239 Np + - (t 1/2 = 24 min) 239 Np → 239 Pu + - (t 1/2 = 2 d) Basic Professional Training Course; Module I Nuclear physics and reactor theory

62 Important nuclear reactions in coolant • reactor coolant activation: 16 O (n, p) 16 N − this reaction possible only with very fast neutrons (E > 10 Me. V) • neutron absorption in boric acid (mixed with reactor coolant) 10 B (n, ) 7 Li − reaction 10 B (n, ) 7 Li important also for thermal neutron detection: − 7 Li ion and particle react with the detector material • tritium production in coolant: 10 B (n, 2 ) 3 H 6 Li (n, ) 3 H − Li. OH is added to reactor coolant to control its p. H Basic Professional Training Course; Module I Nuclear physics and reactor theory

63 Corrosion products, neutron sources • Corrosion product formation: 58 Fe (n, ) 59 Fe 59 Co (n, ) 60 Co 60 Ni (n, p) 60 Co 58 Ni (n, p) 58 Co 50 Cr (n, ) 51 Cr • neutrons are, as a rule, not created during radioactive decay • beryllium powder is mixed with -emitting radionuclide (226 Ra -Be, 241 Am-Be, … neutron source) 9 Be ( , n) 12 C Basic Professional Training Course; Module I Nuclear physics and reactor theory

64 NUCLEAR FISSION Learning objectives After completing this chapter, the trainee will be able to: 1. Describe the fission mechanism. 2. Define fissile and fertile nuclides. 3. Illustrate the formation of 239 Pu. 4. Name the products of fission. 5. Sketch the dependence of fission fragment yield on mass number A. 6. Explain why fission fragments are unstable. 7. Explain the terms prompt and delayed neutrons. 8. Describe the distribution of energy released by fission. 9. Estimate the consumption of fissile material in a reactor operating at a certain power level. 10. Sketch the time course of decay heat. Basic Professional Training Course; Module I Nuclear physics and reactor theory

65 Types of nuclear fission • In fission, heavy nucleus splits – usually into two lighter nuclei − spontaneous (a rare type of radioactive decay) − induced (a type of nuclear reaction) • Spontaneous fission (a rare type of radioactive decay) − nuclei split on their own accord − neutron source − A » 230 − 242 Cm (curium), t − 244 Cm, t 1/2 = 163 d 1/2 = 18 y Basic Professional Training Course; Module I Nuclear physics and reactor theory

66 Induced fission − caused by an increase of internal energy of nucleus − most frequently when nucleus absorbs a neutron • Induced fission is labelled according to energy of neutrons: − thermal fission = fission caused by absorption of thermal neutron − fast fission = fission caused by absorption of fast neutron Basic Professional Training Course; Module I Nuclear physics and reactor theory

67 The mechanism of fission • after absorbing a neutron, the intermediate nucleus in excited state increased internal energy causes oscillation and deformation • if excitation large enough, the deformation can lead to a dumb-bell shape electric repulsive forces overcome the nuclear attractive forces Basic Professional Training Course; Module I Nuclear physics and reactor theory

68 Fissile and fertile nuclides • Basic Professional Training Course; Module I Nuclear physics and reactor theory

69 Products of fission • Immediate products of nuclear fission: − fission fragments − prompt neutrons − prompt gamma rays − release of energy Basic Professional Training Course; Module I Nuclear physics and reactor theory

70 Fission fragments • medium-sized nuclei with Z: 30 ~ 64 and A: 75 ~ 160 • they carry most of energy released (~ 168 Me. V) • range ~ 10 -3 cm fragments stop within the fuel • fission yield: probability of producing a fission fragment with mass number A Basic Professional Training Course; Module I Nuclear physics and reactor theory

71 Ratio of nucleons in fission fragments Basic Professional Training Course; Module I Nuclear physics and reactor theory

72 Fission products N/Zfragments N/Zinitial heavy nucleus N/Zfragments > N/Zstable medium-sized nuclei • Fission fragments are not stable nuclei − - decays • Fission products − fission fragments and their daughter nuclides − 3 or 4 - decays to stable nucleus (5 – 20 Me. V is released) − t 1/2 of fission products: from ~0. 1 s to several million years Basic Professional Training Course; Module I Nuclear physics and reactor theory

73 Importance of fission product decay • Large quantities of heat (decay heat) is released after shutdown of the reactor and removal of this heat is necessary • Radiation from decay is dangerous to health • Emission of delayed neutrons • Some fission products are strong neutron absorbers Basic Professional Training Course; Module I Nuclear physics and reactor theory

74 Prompt neutrons and prompt gamma rays • Prompt neutrons − parameter : average number of neutrons per fission − depends on the nuclide an the neutron energy − for most nuclides, is between 2 and 3 (235 U: = 2. 43) − average kinetic energy 2 Me. V − in total they carry away 5 Me. V • Prompt gamma rays − on average, around 8 gamma rays are released per fission − in total they carry away 7 Me. V Basic Professional Training Course; Module I Nuclear physics and reactor theory

75 Delayed neutrons • emitted after - decay of some fission fragments • daughter nuclides of these fragments emit a neutron -n decay • The fission fragment that leads to neutron emission is called delayed neutron precursor • The delay time of such neutron is determined by the lifetime of its precursor Basic Professional Training Course; Module I Nuclear physics and reactor theory

76 Production of delayed neutrons Basic Professional Training Course; Module I Nuclear physics and reactor theory

77 87 Br: example of -n decay • lifetime 80 s − 87 Br disintegrates after ~ 80 s delayed neutron is born 80 s after fission Basic Professional Training Course; Module I Nuclear physics and reactor theory

78 Parameters of delayed neutrons • Delay time from fission to release of delayed neutrons: − average delay time ~ 13 s • Delayed neutron fraction : − fraction of delayed neutrons in the total number of neutrons produced per fission < 1%, but crucial for successful reactor control − depends on nuclide and neutron energy − − thermal fission of 235 U: = 0. 0065 − thermal fission of 239 Pu: = 0. 0021 − fast fission of 238 U: = 0. 0164 − due to mixture of nuclides in the fuel, the average delayed neutron fraction changes (decreases) with fuel burn-up Basic Professional Training Course; Module I Nuclear physics and reactor theory

79 Distribution of energy released by 235 U fission Prompt energy release fission fragments prompt neutrons prompt gamma rays from (n, ) reactions total prompt energy release Delayed energy release β from fission fragment decay γ from fission fragment decay β and from nuclei produced by (n, ) total delayed energy release total energy release 168 Me. V 5 Me. V 7 Me. V 6 Me. V 186 Me. V 7 Me. V 6 Me. V 1 Me. V 14 Me. V Basic Professional Training Course; Module I Nuclear physics and reactor theory range ~ 10 μm 0. 1 – 1 m ~ mm 0. 1 – 1 m 0. 001 – 1 m 200 Me. V

80 Consumption of fissile material • reactor operates 1 day at power at 1 MW power energy produced = 1 MWd • number of fissions = number of fissioned 235 U nuclei • the uranium mass that corresponds: m = 2. 7· 1021 · 235 · 1. 66· 10 -27 kg = 1. 05· 10 -3 kg ≈ 1 g • example: − 30 days of operation at power of 3000 MW: 90 kg of 235 U is consumed Basic Professional Training Course; Module I Nuclear physics and reactor theory

81 Decay heat • Energy released in the core after reactor shutdown − a consequence of - and decay of fission products • Decay heat proportional to reactor power before shutdown − with higher power, more fission products are produced • Immediately after shutdown, the decay heat diminishes rapidly − consequence of quick decay of short-lived fission products • Decay heat diminishes slower, the longer reactor has operated − more long/lived fission products have been produced Basic Professional Training Course; Module I Nuclear physics and reactor theory

82 Time dependence of decay heat decrease • depends on the reactor operating time prior to its shutdown Basic Professional Training Course; Module I Nuclear physics and reactor theory

83 Decay heat after a long operation at 3000 MWth Time after shutdown Full power fraction Decay heat 1 s 6. 2 % 185 MW 1 min 3. 6 % 107 MW 1 hour 1. 3 % 38 MW 8 hours 0. 6 % 19 MW 1 day 0. 4 % 13 MW 1 week 0. 2 % 7 MW 1 month 0. 1 % 4 MW Basic Professional Training Course; Module I Nuclear physics and reactor theory

Decay heat in the spent fuel pit of a 3000 MWth reactor Basic Professional Training Course; Module I Nuclear physics and reactor theory 84

85 NEUTRON CYCLE Learning objectives After completing this chapter, the trainee will be able to: 1. Explain the slowing down of neutrons in the core. 2. Give the properties of an effective moderator. 3. Define individual factors in the neutron cycle. 4. Define the multiplication factor, k. 5. Explain a chain reaction. 6. Define reactivity and the corresponding units. Basic Professional Training Course; Module I Nuclear physics and reactor theory

86 Division of neutrons in terms of their energy • Basic division: − fast: E > 0. 1 Me. V − epithermal: 1 e. V < E < 0. 1 Me. V − thermal E < 1 e. V • fast neutrons are produced by fission • epithermal neutrons are in the slowing-down process − slowing-down takes place in the moderator • thermal neutrons have completed the slowing-down process − their energy (Ek) depends in the temperature of matter they move in Basic Professional Training Course; Module I Nuclear physics and reactor theory

87 Slowing-down of neutrons in the reactor core • fast neutron loses its energy by scattering on nuclei in the matter − most effective is elastic scattering on light nuclei • moderator: material that slows down neutrons in the reactor core • in light-water reactors the moderator is water (hydrogen) • other possible moderators: − heavy water (deuterium) − graphite (carbon) Basic Professional Training Course; Module I Nuclear physics and reactor theory

88 Characteristics of moderator • A good moderator has: − large probability of scattering, i. e. large scattering x-section s, − large average energy loss per collision − small probability for neutron absorption, i. e. small absorption x-section a, − non-nuclear properties: stable, good thermo-hydraulic properties, low price. • Ordinary (light) water is relatively good moderator: − however, it is corrosive at high temperatures − activated in neutron flux − good thermal/hydraulic properties − cheap • Heavy water is better because of lower neutron absorption. Basic Professional Training Course; Module I Nuclear physics and reactor theory

89 Lifetime of a generation of neutrons • The majority of fissions in light water reactors is induced by thermal neutrons. • In fission, fast neutrons are produced. • What happens to a generation of fast neutrons, born in thermal fission? Basic Professional Training Course; Module I Nuclear physics and reactor theory

90 Fast fission factor ε • Some fast neutrons induce fission, mainly on 238 U in low-enriched fuel. − neutrons, born in fast fission, are fast neutrons, as well − fast fission increases the number of fast neutrons for a factor of ε: • The initial generation of n fast neutrons, born in thermal fissions, is increased to (ε ∙ n) fast neutrons, born in both, thermal and fast fissions. Basic Professional Training Course; Module I Nuclear physics and reactor theory

91 Fast fission: factor ε • Fast fission factor is always greater than one. − LWRs: ε ~ 1. 1 Basic Professional Training Course; Module I Nuclear physics and reactor theory

92 Fast non-leakage factor Pf • Probability that a fast neutron will not escape from the core: • From (ε ∙ n) fast neutrons, (Pf ∙ ε ∙ n) remain in the core. Basic Professional Training Course; Module I Nuclear physics and reactor theory

93 Fast neutron leakage: factor Pf • Fast non-leakage factor is always smaller than one − typical PWR: Pf 0. 98 Basic Professional Training Course; Module I Nuclear physics and reactor theory

94 Resonance escape probability p • As fast neutrons slow down, same of them are absorbed. • The highest probability for neutron absorption is in the epithermal energy range (resonance absorption) − most resonance absorption occurs in 238 U and 240 Pu • Probability that fast neutrons that slow down will not be absorbed in resonances: • From (Pf ∙ ε ∙ n) fast neutrons that start slowing down, (p ∙ Pf ∙ ε ∙ n) slow down to thermal energies. Basic Professional Training Course; Module I Nuclear physics and reactor theory

95 Resonance escape: factor p • resonance escape probability is always smaller than 1 − depends on the fuel enrichment Basic Professional Training Course; Module I Nuclear physics and reactor theory

96 Thermal non-leakage factor Pt • Probability that a thermal neutron will not escape from the core: • From (p ∙ Pf ∙ ε ∙ n) neutrons that slowed down to thermal energies, (Pt ∙ p ∙ Pf ∙ ε ∙ n) remain in the core. Basic Professional Training Course; Module I Nuclear physics and reactor theory

97 Thermal neutron leakage: factor Pt • Thermal non-leakage factor is always smaller than one − typical PWR: Pt 0. 99 Basic Professional Training Course; Module I Nuclear physics and reactor theory

98 Thermal utilisation factor f • Fraction of thermal neutrons absorbed in fuel relative to absorption elsewhere the core: • From (Pt ∙ p ∙ Pf ∙ ε ∙ n) thermal neutrons that remain in the core, (f ∙ Pt ∙ p ∙ Pf ∙ ε ∙ n) thermal neutrons are absorbed in the fuel Basic Professional Training Course; Module I Nuclear physics and reactor theory

99 Utilisation of thermal neutrons: factor f • The value of factor f can change significantly − it is changed intentionally, in order to control the operation of reactor Basic Professional Training Course; Module I Nuclear physics and reactor theory

100 Neutron yield per absorption • Number of fast neutrons which are released in thermal fission per thermal neutron absorbed in fuel: • From (f ∙ Pt ∙ p ∙ Pf ∙ ε ∙ n) thermal neutrons absorbed in the fuel, ( ∙ f ∙ Pt ∙ p ∙ Pf ∙ ε ∙ n) fast neutrons are produced in fission. Basic Professional Training Course; Module I Nuclear physics and reactor theory

101 Neutron reproduction: factor • Neutron yield per absorption is always greater than one. − depends significantly on fuel enrichment: − natural uranium: = 1. 34, − 3% enrichment: = 1. 84, − pure 235 U: = 2. 08. Basic Professional Training Course; Module I Nuclear physics and reactor theory

102 Neutron cycle Basic Professional Training Course; Module I Nuclear physics and reactor theory

103 Multiplication factor k • Multiplication factor, k, is the defined as the radio of the number of neutrons in one generation to the number of neutrons in the previous generation: • In the neutron cycle, as described previously, k can be expressed as a product of six factors: k = ∙ f ∙ Pt ∙ p ∙ Pf ∙ ε Basic Professional Training Course; Module I Nuclear physics and reactor theory

104 Chain reaction • each generation of neutrons leads to the birth of next generation of neutrons • chain reaction in the case k = 2: 1 st generation 2 nd generation 3 rd generation of neutrons Basic Professional Training Course; Module I Nuclear physics and reactor theory

105 Criticality • k = 1: critical chain reaction − the number of neutrons in the core does not change with time, − the number of fissions per unit time is constant, − reactor power is constant. • k > 1: supercritical chain reaction − the number of neutrons in the core increases with time, − the number of fissions per unit time increases with time, − reactor power increases. • k < 1: critical chain reaction − the number of neutrons in the core does decreases with time, − the number of fissions per unit time decreases with time, − reactor power decreases. Basic Professional Training Course; Module I Nuclear physics and reactor theory

106 Reactivity • We are usually interested in reactor conditions where k 1 − we want to avoid using a large number of decimal places • Let us introduce reactivity, which represents departure from criticality: k < 1 ρ < 0 reactor is subcritical, k = 1 ρ = 0 reactor is critical, k > 1 ρ > 0 reactor is supercritical. Basic Professional Training Course; Module I Nuclear physics and reactor theory

107 Notations for reactivity • reactivity is dimensionless quantity • several notations are used: − k/k: reactivity is calculated and the number is followed by k/k − % k/k: 1% k/k = 0. 01 k/k − pcm: 1 pcm = 0. 00001 k/k − $: 1 $ = k/k Basic Professional Training Course; Module I Nuclear physics and reactor theory

108 Positive and negative reactivity • Any change of the core properties modifies k and ρ: − burnup of fuel, production of fission products, − operator actions (boron concentration, control rods). • If changes in the core decrease the multiplication factor k: − negative reactivity has been added in the core. • If changes in the core increase the multiplication factor k: − positive reactivity has been added in the core. Basic Professional Training Course; Module I Nuclear physics and reactor theory

109 Reactivity and change of reactor power • During operation at constant power: − the reactor is critical, − multiplication factor k = 1, − core reactivity ρ = 0. • If we want to increase the power, positive reactivity has to be added in the core. • If we want to decrease the power, negative reactivity has to be added in the core. Basic Professional Training Course; Module I Nuclear physics and reactor theory

110 REACTOR KINETICS Learning objectives After completing this chapter, the trainee will be able to: 1. Explain the exponential increase in reactor power. 2. Define the period T. 3. Define the start-up rate or SUR. 4. Describe the relationship between the multiplication factor, reactivity, the period and start-up rate and sketch how power changes for different k values. 5. Explain a chain reaction by taking and without taking delayed neutrons into account. 6. Define prompt criticality. 7. Sketch the reactor power response to a step change in reactivity. Basic Professional Training Course; Module I Nuclear physics and reactor theory

111 Operation ranges of reactor Basic Professional Training Course; Module I Nuclear physics and reactor theory

112 Reactor operation at low power range • Thermal power negligible the temperature of fuel and coolant does not change perceptibly with change of power − no temperature feedback effects on reactivity • Any change of reactivity is cause exclusively with external actions, e. g. withdrawal or lowering the control rods Basic Professional Training Course; Module I Nuclear physics and reactor theory

113 Time dependence of reactor power • Basic Professional Training Course; Module I Nuclear physics and reactor theory

114 Reactor period T • Basic Professional Training Course; Module I Nuclear physics and reactor theory

115 Start-up rate • Basic Professional Training Course; Module I Nuclear physics and reactor theory

116 Supercritical reactor k > 1 ρ > 0 T > 0 SUR > 0 • Reactor power increases exponentially with time. − The higher k, the higher the core reactivity ρ and the faster reactor power increases: higher is SUR and shorter the reactor period T. • When increasing the power, the reactor is supercritical. − The operators must increase reactor power slowly and in accordance with the procedure which specifies the maximum start-up rate. Basic Professional Training Course; Module I Nuclear physics and reactor theory

117 Supercritical reactor dynamics Basic Professional Training Course; Module I Nuclear physics and reactor theory

118 Critical reactor k = 1 ρ = 0 T = ∞ SUR = 0 • At higher power levels, the number of fissions per unit of time (or number of neutrons) is higher than at lower power levels, but constant in a critical reactor (it does not change with time). Basic Professional Training Course; Module I Nuclear physics and reactor theory

119 Subcritical reactor k < 1 ρ < 0 T < 0 SUR < 0 • Reactor power decreases exponentially with time. − The smaller k, the smaller the core reactivity ρ (more negative) and the faster reactor power decreases: shorter negative period T and higher negative SUR. • When decreasing the power, the reactor is always subcritical. Basic Professional Training Course; Module I Nuclear physics and reactor theory

120 Subcritical reactor dynamics Basic Professional Training Course; Module I Nuclear physics and reactor theory

121 Neutron lifetime • Time from the birth to the disappearance of a neutron (escape, absorption). • It is divided into: − birth time: the time from fission to neutron release ~ 10 -14 s, − slowing-down time: the average time from neutron’s release to its thermalization ~ 10 -5 s, − diffusion time: the average time from a neutron’s thermalization to its disappearance ~ 10 -5 s. Basic Professional Training Course; Module I Nuclear physics and reactor theory

122 Phases of neutron lifetime • lifetime of prompt neutrons in a pressurized water reactor core is of the order of magnitude of 10‑ 4 s. Basic Professional Training Course; Module I Nuclear physics and reactor theory

123 Chain reaction with prompt neutrons • Basic Professional Training Course; Module I Nuclear physics and reactor theory

Average lifetime of prompt and delayed neutrons • Slowing-down and diffusion times of delayed neutrons are comparable to those of prompt neutrons • Birth time of delayed neutron is the life time of its precursor (for 235 U fission ~ 13 s) and is much longer that diffusion or slowing/down time. • Lifetime of delayed neutrons is essentially the lifetime of their precursors. • Average lifetime of all neutrons: l = (1 – β) ∙ lp + β ∙ l = (1 – 0. 0065) ∙ 10 -4 s + 0. 0065 ∙ 13 s 0. 1 s Basic Professional Training Course; Module I Nuclear physics and reactor theory 124

Chain reaction with prompt and delayed neutrons • Basic Professional Training Course; Module I Nuclear physics and reactor theory 125

126 Dependence of reactor period on reactivity • the graph shows absolute values of reactivity and reactor period • the shortest negative period is ‑ 80 s. − reactor can not shut down faster than the decay of most long-lived precursors Basic Professional Training Course; Module I Nuclear physics and reactor theory

127 Prompt criticality • Basic Professional Training Course; Module I Nuclear physics and reactor theory

Reactor power response to a positive step change in reactivity Basic Professional Training Course; Module I Nuclear physics and reactor theory 128

Reactor response to a negative step change in reactivity Basic Professional Training Course; Module I Nuclear physics and reactor theory 129

130 REACTIVITY CHANGES Learning objectives After completing this chapter, the trainee will be able to: 1. Give a qualitative explanation of the temperature coefficients of reactivity. 2. Describe the impact of power change on reactivity. 3. Sketch reactor power response to a step change in reactivity. 4. Describe the formation and removal of 135 Xe and 149 Sm. 5. Sketch the reactivity due to Xe and Sm as a function of time after start-up. 6. Sketch the reactivity due to Xe and Sm after shutdown. 7. Sketch how the critical concentration of boron, CB, changes relative to its burn-up rate. 8. Describe the principle of reactor control. Basic Professional Training Course; Module I Nuclear physics and reactor theory

131 Classification of reactivity changes • During reactor operation, the core properties and consequently its reactivity change. • Based on how fast the core properties or its reactivity change during reactor operation, reactivity changes are classified as: − short-term changes (~ seconds, minutes) − medium-term changes (~ hours) − long-term changes (~ months) Basic Professional Training Course; Module I Nuclear physics and reactor theory

132 Short-term reactivity changes • when reactor is in operating power range (0% - 100%), fuel and coolant temperatures change • change of temperature influences: − density of the moderator − resonance absorption in fuel − void fraction in the coolant Basic Professional Training Course; Module I Nuclear physics and reactor theory

Impact of coolant (moderator) temperature on reactivity 133 The moderator temperature coefficient, αm, is defined as the change in reactivity per degree change in the average moderator temperature. • increase in coolant (moderator) temperature decreases its density − mass of water in the core decreases, mass of fuel remains constant: 1. increase in neutron absorption in fuel relative to absorption in water increase of thermal utilization factor f 2. slowing down distance of neutrons increases resonance absorption increases: resonance escape factor p decreases • Depending on which of the two effects prevails: αm is negative or positive. • LWRs usually constructed for a negative αm Basic Professional Training Course; Module I Nuclear physics and reactor theory

134 Impact of fuel temperature on reactivity The fuel temperature coefficient, αf, is defined as the change in reactivity per degree change in the fuel temperature. • Increase in fuel temperature increases the resonance absorption of neutrons. • Commercial reactors have low enriched fuel parasitic resonance absorption in 238 U (and 240 Pu) predominates. • The fuel temperature coefficient αf is always negative. Basic Professional Training Course; Module I Nuclear physics and reactor theory

135 Impact of void fraction on reactivity The void coefficient, αv, is the reactivity change percent change in the void fraction. • Increase in fraction of voids (steam bubbles) in the core reduces the moderator density. • Impact on reactivity is similar to the impact of the moderator temperature. • Due to small total void fraction formed in the core of a PWR, the associated total reactivity change is small. • Void coefficient is important in BWRs. Basic Professional Training Course; Module I Nuclear physics and reactor theory

136 Impact of power change on reactivity The power coefficient, αp, is defined as the change in reactivity percent power change. • Change of power changes the coolant temperature, the fuel temperature, and the void fraction. • The combined effects of moderator, fuel and axial power redistribution are accounted for in the total power coefficient. • In PWRs, power coefficient is always negative. The power defect tells us how much core reactivity changes if reactor power is changed by a given value of P. Basic Professional Training Course; Module I Nuclear physics and reactor theory

Response to a step change in reactivity at operating power • At operating power range, temperature feedback effects are present (neglected in chapter “Reactor kinetics”). • Operator withdraws the control rods for a few steps • Power is stabilized at higher level Basic Professional Training Course; Module I Nuclear physics and reactor theory 137

138 Mid-term changes of reactivity • Fissions in the core result in over 200 different fission products. • Two fission products important for reactor operation: − − a = 2∙ 106 b 149 Sm – absorption cross-section for thermal neutrons = 4∙ 104 b a 135 Xe – absorption cross-section for thermal neutrons Basic Professional Training Course; Module I Nuclear physics and reactor theory

139 Production and removal of Xenon-135 • Basic Professional Training Course; Module I Nuclear physics and reactor theory

140 135 Xe during reactor start-up • After reactor start-up, 135 Xe concentration starts to grow • Equilibrium concentration of 135 Xe approx. 40 - 50 h after start-up − equilibrium conc. depends on reactor power, but dependence not linear Basic Professional Training Course; Module I Nuclear physics and reactor theory

141 135 Xe during reactor shutdown • after shut-down, 135 Xe in produced by the decay of 135 I (t 1/2 = 6. 6 h), and is removed by its own decay (t 1/2 = 9. 1 h) • maximum 135 Xe concentration reached ~ 9 h after shutdown (depending on reactor power) • after ~24 h 135 Xe concentration roughly equal to its level at shutdown • after ~ 80 – 90 h there is practically no 135 Xe in the core • during 135 Xe decay, positive reactivity is inserted into the core – possible recriticality of reactor! Basic Professional Training Course; Module I Nuclear physics and reactor theory

142 Reactivity due to 135 Xe after shutdown Basic Professional Training Course; Module I Nuclear physics and reactor theory

143 Production and removal of Samarium-149 • Basic Professional Training Course; Module I Nuclear physics and reactor theory

144 149 Sm during reactor start-up • After reactor start-up and with a fresh core, 149 Sm concentration starts to grow. • Equilibrium concentration of 135 Xe approx. 400 h after start-up and is independent of reactor power. Basic Professional Training Course; Module I Nuclear physics and reactor theory

145 149 Sm during reactor shutdown • after shut-down, 149 Sm burn-up by neutron absorption ceases, but 149 Sm is still produced by the decay of 149 Pm • maximum 149 Sm concentration reached ~ 400 h after shutdown (depending on reactor power) Basic Professional Training Course; Module I Nuclear physics and reactor theory

146 149 Sm during reactor restart • As the reactor is restarted on power, the equilibrium concentration of 149 Sm equal to its value prior to shut-down is re-established. Basic Professional Training Course; Module I Nuclear physics and reactor theory

147 Long-term changes of reactivity • With operation of a LWR through a fuel cycle: − burn-up of 235 U − burn-up of 238 U (negligible importance) − production of 239 Pu and other Plutonium isotopes − production of fission products, some of which are important neutron absorbers • With core burn-up, the reactivity of core decreases. Basic Professional Training Course; Module I Nuclear physics and reactor theory

148 Excess reactivity is defined as the amount of surplus reactivity over that needed to enable reactor operation at zero power. • Excess reactivity is compensated by adding boron to the coolant and by burnable poisons. • Since core reactivity decreases with burn-up, the concentration of boron CB in the moderator is gradually reduced over the fuel cycle. Basic Professional Training Course; Module I Nuclear physics and reactor theory

149 Critical boron concentration • The critical boron concentration (CB) is defined as the concentration of boron required for the reactor to be critical on full power with the control rods withdrawn. • Typical course of critical boron concentration over the fuel cycle: Basic Professional Training Course; Module I Nuclear physics and reactor theory

150 Reactor control • Operators primarily influence core reactivity in two ways: 1. by control rods − alloy of 80% Ag, 15% In and 5% Cd − good absorber of thermal and epithermal neutrons − compensation of short-term reactivity changes − ensure a negative reactivity reserve needed for fast reactor shut-down 2. by changing the boric acid concentration in the coolant − good absorber of thermal neutrons − compensation of mid-term and long-term reactivity changes Basic Professional Training Course; Module I Nuclear physics and reactor theory

151 SUBCRITICAL MULTIPLICATION Learning objectives After completing this chapter, the trainee will be able to: 1. Explain subcritical multiplication. 2. Define the subcritical multiplication factor, M. 3. Explain the 1/M curve for core loading. Basic Professional Training Course; Module I Nuclear physics and reactor theory

152 Neutron sources • Neutron population in core measured by excore detectors − they measure neutrons that leak out of the core − when reactor is shut down, the neutron population is low • Independent neutron sources in the core are needed: − control of the reactivity changes in the subcritical reactor, − signal on the detectors high enough for controlled approach to criticality, − verification that the excore detectors are operational. Basic Professional Training Course; Module I Nuclear physics and reactor theory

153 Types of neutron sources • Nonregenerative neutron sources: − (Pu-Be) source: α particle emitted by Pu triggers reaction 9 Be(α, n)12 C − 252 Cf: spontaneous fission • Regenerative neutron source: − (Sb-Be) source: antimony is activated in neutron flux: 123 Sb(n, )124 Sb; gammas from the decay of 124 Sb trigger reaction 9 Be( , n)2 α • Reactors that have operated for several cycles: − no need for additional neutron sources in the core − old fuel elements contain sufficient amount of 242 Cm and 244 Cm which fission spontaneously and emit neutrons Basic Professional Training Course; Module I Nuclear physics and reactor theory

154 Population of neutrons in subcritical reactor • Basic Professional Training Course; Module I Nuclear physics and reactor theory

Response to a step change of reactivity in subcritical reactor Basic Professional Training Course; Module I Nuclear physics and reactor theory 155

156 Subcritical multiplication factor • Basic Professional Training Course; Module I Nuclear physics and reactor theory

157 Example: loading of empty core • Basic Professional Training Course; Module I Nuclear physics and reactor theory

158 Loading of empty core (cont’d) • each step (adding a few more elements) gives better estimate how many more elements are needed to reach criticality step 0 1 2 3 4 5 Number of ci c 0/ci inserted elements 0 100 1 10 125 0. 8 20 166 0. 6 30 250 0. 4 40 500 0. 2 45 1000 0. 1 Basic Professional Training Course; Module I Nuclear physics and reactor theory

159 Inverse Count Rate Ratio – ICRR • base count rate can be placed anywhere • 1/M curve is renormalized to a new base count • in this case we rather speak of the ICRR curve • prediction of the criticality (ICRR = 0) remains the same Basic Professional Training Course; Module I Nuclear physics and reactor theory

160 Loading of a power reactor • ICRR is determined after loading of each fuel element − if ICRR deviates abnormally, stop all activities in the core and act in accordance with the relevant procedures • for safety reasons, the core is heavily poisoned with boric acid − even after loading all fuel elements, reactor remain subcritical Basic Professional Training Course; Module I Nuclear physics and reactor theory

161 HEAT REMOVAL FROM NUCLEAR REACTORS Learning objectives After completing this chapter, the trainee will be able to: 1. Name three modes of heat transfer. 2. Describe heat conduction. 3. Describe forced and natural convection. 4. Describe heat transfer to a fluid with phase change. 5. Explain the formation of steam bubbles. 6. Sketch and describe the boiling curve. 7. Define the boiling crisis. 8. Describe the average and maximum thermal power of a fuel rod in a PWR. 9. Describe hot channel factors and explain the reasons for their limits. Basic Professional Training Course; Module I Nuclear physics and reactor theory

162 Definition of basic quantities • Heat is energy which passes from a point of higher temperature to a point of lower temperature. If there is no difference in temperature, there can be no heat transfer. Basic Professional Training Course; Module I Nuclear physics and reactor theory

163 Modes of heat transfer 1. heat conduction through matter (diffusion) 2. heat transfer by means of fluid flows (convection) 3. radiation conduc convection radiation Basic Professional Training Course; Module I Nuclear physics and reactor theory

164 Heat conduction • process which takes place at the atomic level Basic Professional Training Course; Module I Nuclear physics and reactor theory

165 Heat conduction equation • Basic Professional Training Course; Module I Nuclear physics and reactor theory

Temperature profile in a wall made of various materials Basic Professional Training Course; Module I Nuclear physics and reactor theory 166

167 Temperature profile in fuel rod T fuel pellet gap cladding coolant TW TB 0. 01 ~0. 6 mm ~8 mm CL r 1 r 2 Basic Professional Training Course; Module I Nuclear physics and reactor theory r 3

168 Convection involves heat transferred by the flow of fluid. Convection can be natural or forced. heat sink Δh Example of natural convection in PWR: core cooling after primary pumps have been shut down Basic Professional Training Course; Module I Nuclear physics and reactor theory heat source

169 Natural convection • Convection is heat transfer by the flow of fluid. • Natural convection: the fluid moves due to a difference in fluid density (temperature difference or phase change) • Example of natural convection due to difference in liquid density is PWR core cooling after shut down of primary pumps. • Example of natural convection due to phase change is the circulation of secondary water inside a steam generator. Basic Professional Training Course; Module I Nuclear physics and reactor theory

170 Forced convection • Fluid is forced to move by means of a pump or fan. • Example in PWR: the flow of the primary coolant through the core driven by the operation of reactor coolant pumps. Basic Professional Training Course; Module I Nuclear physics and reactor theory

171 Equation of heat transfer • Basic Professional Training Course; Module I Nuclear physics and reactor theory

172 Radiative heat transfer • Basic Professional Training Course; Module I Nuclear physics and reactor theory

173 Boiling heat transfer • When heat is transferred from a solid body to a liquid and the temperature of solid body is high enough, the liquid may boil phase change • heat flux is significantly higher than in the case of natural or forced convection − similar applies for condensation, as well • saturated boiling: water is at the boiling point temperature throughout its bulk • subcooled boiling: temperature lower than boiling point, bubbles collapse when they break away from the heating surface Basic Professional Training Course; Module I Nuclear physics and reactor theory

174 Bubble formation Bubbles break away from the heating surface, “mixing” the liquid and “breaking” the laminar layer of liquid which would otherwise cause much lower heat transfer. Basic Professional Training Course; Module I Nuclear physics and reactor theory

175 Boiling curve Basic Professional Training Course; Module I Nuclear physics and reactor theory

176 4 regions of the boiling curve 1. Natural convection: small T 2. Nucleate boiling: beginning of boiling − subcooled nucleate boiling − saturated nucleate boiling 3. Partial film boiling: bubbles combine into layers next to the wall − this layer of vapour insulates the surface and reduces heat transfer − in this region, the vapour layers are not stable 4. Film boiling and radiation: stable layers of vapour form next to the heating body − poor heat transfer despite a relatively large temperature difference Basic Professional Training Course; Module I Nuclear physics and reactor theory

177 Departure from Nucleate Boiling • Point c: boiling crisis or Departure from Nucleate Boiling – DNB • nucleate boiling switches over to film boiling • heat flux at point c is called the critical or DNB heat flux. • Departure from Nucleate Boiling Ratio – DNBR: DNBR = critical heat flux actual heat flux • DNBR should always be greater than 1 − DNBR limit value is set down in the Technical Specifications Basic Professional Training Course; Module I Nuclear physics and reactor theory

178 Heat transfer in the reactor core • During normal operation and during incidents, the integrity of the reactor core must be maintained. • Design limits for the fuel pellet temperature and the boiling crisis • Power distribution in the core is uneven and depends on: − nuclear properties − thermodynamic parameters − fabrication parameters • Power distribution is described by using peaking factors − maximum value of certain parameter is a product of average value and respective peaking factor Basic Professional Training Course; Module I Nuclear physics and reactor theory

179 Average linear power density • Basic Professional Training Course; Module I Nuclear physics and reactor theory

180 Heat flux hot channel factor FQ FQ = maximum heat flux in the core average heat flux in the core • maximum allowed FQ set in the operational limits − example: Basic Professional Training Course; Module I Nuclear physics and reactor theory

181 Maximum allowed linear power density • The FQ limit ensures that: • the maximum temperature in the middle of a fuel pellet (centreline temperature) during normal operation is lower than the melting point temperature, • the maximum temperature of fuel rod cladding during a loss of coolant accident is lower than 1200° C. Basic Professional Training Course; Module I Nuclear physics and reactor theory

182 Enthalpy rise hot channel factor, FΔH F H = maximum fuel rod integral power average fuel rod integral power example: The F H limit ensures that a boiling crisis does not occur during normal operation and moderately frequent incidents. Hot channel factors calculated from periodic (~ every 1000 MWd/t) measurements of thermal neutron flux with movable neutron detectors. Basic Professional Training Course; Module I Nuclear physics and reactor theory

183 Operating conditions and DNBR = critical heat flux actual heat flux • during operation, DNBR > 2. 0 DNBR is reduced when: a) the pressure in the primary system falls, b) the flow in the primary system decreases, c) the temperature of the primary coolant rises Basic Professional Training Course; Module I Nuclear physics and reactor theory The views expressed in this document do not necessarily reflect the views of the European Commission.