NUCE 304: Evaluative Methods for Nuclear Non-proliferation and Security Lecture Notes PDF

NUCE 304: Evaluative Methods for Nuclear Non-proliferation and Security Neutron Interactions Dr. Ahmed Alkaabi 1  Learning Objectives Nuclear and Reactor Physics Objectives: Be able to explain how nuclear power produc...

NUCE 304: Evaluative Methods for Nuclear Non-proliferation and Security Neutron Interactions Dr. Ahmed Alkaabi 1  Learning Objectives Nuclear and Reactor Physics Objectives: Be able to explain how nuclear power produces electrical power Be able to explain how and why nuclear power works Be able to explain why fission products and radiation are major issues for nuclear power Be able to explain the role of neutron interactions in nuclear power 2  Primary Learning Objective Know the different ways neutrons interact with matter Understand how neutron interactions enable nuclear reactors to function in a controllable fashion Take away from this lecture: Main ways neutrons interact with matter 3  Lecture Outline 1. Neutron Interactions Scattering Absorption Fission 2. Cross Sections and neutron interaction rates 4  Neutron Interactions Neutrons have zero net electrical charge. They pass through electron clouds and interact with atomic nuclei. Types of neutron interactions: – Scattering Elastic Scattering – the most important process of slowing down neutrons in nuclear reactors Inelastic Scattering – Absorption Radiative Capture Charged-Particle Reactions Neutron-Producing Reactions Fission Image from US NRC (http://www.flickr.com/photos/nrcgov/) 5  Elastic Scattering (n, n’) A neutron strikes a nucleus; the target nucleus is almost BEFORE nʹ always in its ground state. n A Z X A Z X AFTER Some kinetic energy is transferred from the neutron to the target nucleus. The neutron reappears (the initial and final neutrons are not necessarily the same). The target nucleus is left in its ground state – there is no energy transferred into nuclear excitation. Total kinetic energy is conserved! 6  Inelastic Scattering (n, n’) The target nucleus absorbs the incident neutron: nʹ a compound nucleus is formed. n A Z X A X Z The compound nucleus emits a neutron of lower kinetic g energy; the target nucleus is left in an excited state. A Z X The target nucleus will reach its ground state by emitting one or more gamma rays. Total energy is conserved (but not the kinetic energy!): Initial kinetic energy = Kinetic energy of the emitted neutron + of incident neutron kinetic energy of the target nucleus + energy of all emitted gamma rays 7  Radiative Capture (n, γ) The target nucleus absorbs the incident neutron a compound nucleus is formed. The compound nucleus immediately emits a gamma ray. g n A A1 Z X Z X In this case, nuclide X can be called a “neutron poison” 8  Charged-Particle Reactions (n,α), (n, p), (n, d), (n, t) The target nucleus absorbs the incident neutron A compound nucleus is formed. The compound nucleus possess relatively high excitation energy: it ejects a charged particle (e.g. proton, alpha particle, etc.) n A A3 Z X Y Z 2 a 9  Neutron-Producing Reactions (n,2n), (n,3n), (n,xn) These reactions occur with energetic neutrons. The (n, 2n) reaction is important in reactors containing heavy water or beryllium. Be-9 undergoes an (n,2n) neutron reaction to become Be-8. nʹ n A A1 Z X Z X nʺ 10  Nuclear Fission Nuclear Fission is a process in which an atomic nucleus splits and a large amount of energy is released in the form of radiation and energetic fission products. A1 n n A A1 * W Z1 n Z X Z X A2 Z2 Y n Typical nuclear fission reaction: 1 0 n  235 92 U  236 92  * U Cs  140 55 Rb  3 n 93 37   1 0 11  Nomenclature Spontaneous Fission: – when a nucleus spontaneously decays by fission. Neutron-Induced Fission: – when a fission reaction is induced by the absorption of a neutron into a nucleus. Thermal Fission: – when a fission reaction is induced by the absorption of a room-temperature thermal neutron into a nucleus. Fast Fission: – when a fission reaction is induced by the absorption of a fast (around 1-MeV) neutron into a nucleus. 12  Neutron Interactions To safely and efficiently operate a nuclear reactor we need to be able to predict and control the neutron population over time and space Neutron populations can change for lots of reasons… (scattering, absorption, fission, capture, other.). Our ability to calculate (predict) and control the reactor’s neutron population depends on our ability to calculate what fraction of all the neutron interactions are of which type. We also need to know the rate at which each type of neutron interaction occurs. 13  Types of Neutron Interactions Scattering: neutron collides with an atomic nucleus – Elastic Scattering (n, n) – Inelastic Scattering (n, n’) Absorption – Radiative Capture (n, γ) – Charged-Particle Reactions (n,α), (n, p), (n, d), (n, t) – Neutron-Producing Reactions (n,2n), (n,3n), (n,xn) – Fission How can we compute the rate at which each of these interactions occur? 14  Number of Interactions per unit time In entire target, N [atoms/cm3] Number A [cm2] of interactions =  N A dx I per second dx [cm]  is called the microscopic cross-section n [neutrons/cm3] v [cm/s] I = n ∙ v [neuts/cm2-sec]  is the proportionality constant that depends on (1) the speed (energy) of the incident particles and on (2) characteristics of the target nuclei. Author: Dr. Charlton, NUEN, TAMU 15  Microscopic Cross Section Symbols Microscopic cross section () is the probability of a particular interaction occurring between a neutron and a target nucleus. Microscopic cross sections are expressed in units of barns, where 1 barn = 10-24 cm2. Each of the types of interactions discussed previously has a characteristic microscopic cross section – e : Elastic scattering cross section – I : Inelastic scattering cross section – γ : Radiative capture cross section – f : Fission cross section – α : (n, α) cross section – 2n : (n,2n) cross section 16  Microscopic Cross Section Symbols (continued) The sum of all cross sections is known as the total cross section (σt)  t   e  i  g  f  a  The sum of all absorption reaction cross sections is known as the absorption cross section (σa)  a   g   f   p   d  a   The sum of all scattering reaction cross sections is known as the total scattering cross section (σs)  s   e  i 17  Microscopic Cross Sections Dependencies The microscopic cross section is a function of – The target nuclide – The incident particle – The relative speed between the incident particle and the target nuclide We will often assume the target nuclide is at rest Then the microscopic cross section is a function of – The target nuclide – The incident particle – The energy of incident particle. 18  Where to get cross section data? The cross sections for most isotopes have already been measured/calculated: – Chart of the Nuclides – Online: ∙ http://www.nndc.bnl.gov/nudat2/index.jsp http://sutekh.nd.rl.ac.uk/CoN/ http://wwwndc.tokai.jaeri.go.jp/CN03/index.html http://atom.kaeri.re.kr/ton/ The microscopic cross sections provided on most charts and tables are measured for a standard neutron velocity of 2200 meters/second (ambient temperature of 68F). Cross sections must be corrected for the temperature of the target material. 19  Elastic Scattering Cross Section Versus Energy of Incident Neutron 12 C Elastic Scattering Cross Section Versus Energy Cross Section (b) 10 1 Resonance Potential scattering region region 0.1 1.E-05 1.E-02 1.E+01 1.E+04 1.E+07 Energy (eV) Author: Dr. Charlton, NUEN, TAMU 20  235U Fission and Radiative Capture Cross Sections f : U-235 585 barns fission radiative capture 0.025eV 1 MeV From NUEN-611 lecture notes. 10 MeV 21  238U Fission and Radiative Capture Cross Sections U-238 fission c : 2.66 barns radiative 0.025eV capture From NUEN-611 lecture notes. 10 MeV 22  Cross Sections Versus Temperature Cross sections can vary with material temperature Temperature is related to the relative motion of the nuclei within a material These temperature changes mainly affect the resonances – Resonances broaden at higher temperatures The temperature effect on resonances is called Doppler Author: Dr. Charlton, NUEN, TAMU broadening 23  Collision Density Recall: the number of interactions N [atoms/cm3] per unit time (in the target): A [cm2] interactio ns   t N A dx I second dx [cm] n [neutrons/cm3] Collision density (F ) is the number of v [cm/s] interactions per unit volume per unit time: N [atoms/cm3] interactio ns F  t N I s  cm 3 A [1 cm2] The product of the atom density N and X [1 cm] a microscopic cross-section is called the macroscopic cross-section, Sigma. Σ = N 24  Macroscopic Cross-section Macroscopic cross-section (Σ) is the probability of an interaction per unit length of travel of an incident particle. Macroscopic cross-section Σ has units of cm-1. The macroscopic cross-section depends on – The target atom density N (a macroscopic quantity) – Interaction type (i.e., the microscopic cross-section) – Projectile energy Macroscopic total cross section Σt = N t Macroscopic scattering cross section Σs = N s Macroscopic absorption cross section Σa = N a , etc. 25  Example Solution The fractional abundance of 235U is 0.0072. f(235U) Atomic weight of U is 238.0289; density of U is 19.1 g/cm3. The microscopic absorption cross-section for 235U is 680.8 b. Avogadro number NA = 0.6022 × 1024 mol-1 Recall: number of atoms per unit volume, N = ρNA/M Then the macroscopic absorption cross-section for 235U is a   U  N f 235   U  a 235  235 U  3 19.1 gm/cm * (0.6022  10 atoms/gm-mole) 24  (0.0072) * 680.8  10 24 2 cm /atom 238.0289 gms/gm-mole 1  0.237 cm 26  Mean Free Path The average distance a neutron travels without an interaction is called a mean free path (λ) 1  t Example 1. Suppose Σt for Example 2. Suppose Σ a for thermal neutrons in a research thermal neutrons in a research reactor is 10 cm-1. On average, reactor is 4 cm-1. On average, how far do thermal neutrons how far do thermal neutrons travel between collisions? travel before they are absorbed? 1 1    0.1  cm   0.25  cm t a 27  Several Neutron Beams Bombard a Small Target I2 Consider an experiment in which several n2, v neutron beams bombard a small target – The intensities of the beams are different – The neutrons in all the beams have the same I3 speed (same energy) n 3, v Then the total collision density is given by I1 n1, v Ftotal  t I1  I 2  I 3    t n1v  n2v  n3v    t n1  n2  n3  v  t nv where n is the total density of neutrons striking the target, n = n1 + n2 + n3 + … 28  Neutron Flux The situation at any point in a reactor is a generalization of this experiment with a very small sample and beams from all directions; thus, our equation F = Σt nv is valid for any point in a reactor. The quantity nv is called the neutron flux and denoted by the symbol f f  nv The units of neutron flux are the same as the units of beam intensity: neutrons/cm2-s Then the collision density is F   t n v   tf 29  Neutron Flux (continued) Neutron fluxes can be conceptually viewed as – Related to the overall population of neutrons in a volume – The number of neutron track lengths per unit volume per unit time – The number of neutrons passing through a unit area per unit time 30  Neutron Flux (continued) Another way to define neutron flux is The total track length traveled by all neutrons in a unit volume per unit time  track length   particles   track length  f   n  v   volume  time   volume   time  In this case the units on Φ would be neutron - cm cm3 - sec We will usually write the units as neutrons/cm2-sec 31  Neutron Flux f  nv Z UO2 H2O R Reactor Core 32  Neutron Flux f  nv Neutrons cm2-sec = Neutron-cm cm3-sec Z φ φ R r 33  Neutron Flux and Reactor Power Example: A research reactor core has a volume of 60 x 103 cm3. Calculate the power of the reactor if the neutron flux is 1.2 x 1013 neutrons/cm2-s and the fission macroscopic cross-section (Σf ) is 0.1 cm-1. Solution: F   ff – Find fission rate in the reactor F = No. of fission interactions per – Energy released per fission = 200 MeV second per cm3 – Power = Energy release per fission x fission rate (Units for power: 1 Watt = 6.242 x 1012 MeV/s) Total Fission Rate  V Σ f f  60 103 (0.1) 1.2 1013  7.2 1016 fission/s 7.2 1016 (200) Power   2.3  10 6 W  2.3 MW 6.242 10 12 34  Neutron Flux (Φ) is very Useful for Calculating Important Reactor Quantities Recall: The macroscopic cross-section depends on -- The target atom density N (a macroscopic quantity) -- Interaction type (i.e., the microscopic cross-section) -- Projectile and target energy Macroscopic total cross section Σt = N t Macroscopic scattering cross section Σs = N s Macroscopic absorption cross section Σa = N a , etc. Therefore: Fission rate = Σf*Φ fissions/cm3-sec Scattering rate = Σs*Φ scattering events/cm3-sec Absorption rate = Σa*Φ absorptions/cm3-sec The rate of “any” interaction = Σany*Φ “any-event”/cm3-sec 35  Neutron Moderation In typical power reactors, neutron-induced fission is more likely when the neutrons have low energy, less than 1 eV (0.025 eV at 20°C, i.e., “thermal neutrons”). Since neutrons from fission events are fast neutrons (born at high energies, up to several MeVs), they must be slowed down to thermal energies (v = 2200 meters/sec) to induce enough fission reactions. The energy of a neutron is reduced (i.e, the its velocity R is “slowed down”) through scattering. This process is known as thermalization or moderation. The material used for the purpose of reducing neutron energies is called a moderator. 36  Why We Need to Moderate the Neutrons 235U Fission and Radiative Capture Cross Sections f : 585 barns U-235 fission f : ~1 barn radiative capture 0.025eV 2.0 MeV From NUEN-611 lecture notes. Author: Unknown. 37  Moderator We want a moderator that will slow the neutrons quickly but not absorb them Thus for an ideal moderator, we want material that has a – Large energy loss per collision Need to slow down neutrons in a small number of collisions – Small absorption cross section So most neutrons are not absorbed by moderator 38  Neutron Moderation (continued) Moderator A Average number of collisions to thermalize H2O 17 19 D 2O 18 35 He 4 42 Be 9 86 C 12 114 39  Fission Chain Reaction Fission reactions not only generate an enormous amount of energy but also emit additional neutrons. Some number of the fast neutrons produced by fission in one generation will undergo moderation and eventually cause fission in the next generation. This leads to the possibility of a self-sustaining neutron- induced fission chain reaction Nuclear power plants operate by precisely controlling the rate at which nuclear reactions occur. 40  Steady-State Reactor Operation For a nuclear chain reaction to continue at steady-state, the neutron production rate must be perfectly balanced with the neutron loss rate Any deviation from this balance will result in – A time-dependence of the neutron population – A time-dependence of the power level of the reactor 41  Neutron Balance Equation To safely and efficiently operate a nuclear reactor, we must be able to predict and control the neutron population and changes to that population over time and space. We will use a balance equation of the form  change rate of   rate of   rate of       neutron population   gain   loss  42  Neutron Production and Loss Rates  change rate of   rate of   rate of       neutron population   gain   loss  The production rate is given by – Production rate due to fixed neutron sources – Production rate due to neutron producing reactions [e.g., fission, (n,2n), etc.] R The loss rate is given by – Loss rate due to absorption reactions – Loss rate due to “leakage” 43  Life Cycle of a Neutron Fast Neutrons PFNL 1-PFNL Don’t Leaks Leak p 1-p Slow to Absorbed Thermal while Fast PTNL 1-PTNL 1-uF uF ntherm nfast Don’t Absorbed in Absorbed in Leaks Leak Other Fuel f 1-f 1-PFAF PFAF Absorbed in Absorbed in Capture Fission Fuel Other PTAF 1-PTAF Fission Capture Source: NUEN 611 notes. Author: Dr. W. Charlton, NUEN, TAMU 44  Criticality The effective neutron multiplication factor (k) defines the criticality condition for the system: # neutrons in given generation k # neutrons in previous generation – Without a source present The value of k immediately tells us what the time evolution of the system will be 45  Criticality (continued) # neutrons in given generation k # neutrons in previous generation With a source of fission neutrons present and without any externally injected neutrons (i.e., fission neutrons only) – k < 1, neutron population will decrease called a subcritical reactor R – k = 1, neutron population will stay constant called a critical reactor – k > 1, neutron population will increase called a supercritical reactor 46  Criticality (continued) We will traditionally use a more convenient definition for criticality – Every neutron in a single generation is lost by some mechanism and – The only neutrons in a given generation (when the external source is not present) are those produced from fission – Thus: rate of neutron production k rate of neutron loss Same ratio # neutrons in given generation k as before # neutrons in previous generation 47  Criticality (continued) For an infinitely large reactor, which has no neutron leakage, this is production rate k  absorption rate R For a more realistic system, this will be production rate k absorption rate  leakage rate Question: Neutron Production Comes from ____?____ and _____?____ 48  Role of Delayed Neutrons From fission, neutrons are emitted and fission products are created – From the decay of these fission products, additional neutrons are generated a relatively long time after the fission event – These neutrons from fission products represent only a small fraction (1 We will change the value of 2.5 k