L8 Introduction to Reactor Physics Part 1.pdf
- 1. Introduction to Reactor Physics (Preliminary topics) ALVIE A. ASTRONOMO, Ph.D. Nuclear Reactor Operations Section Nuclear Services Division Philippine Nuclear Research Institute
- 2. Content Neutron interactions Nuclear cross section Reaction rate Neutron moderation Neutron Attenuation Research Reactors 2
- 3. Neutron Nucleus Scattering Elastic (n,n) Inelastic (n,n’) Absorption Radiative Capture (n,) Charge Production (n,p) (n, ) ... Neutron Production (n,2n) (n,3n) ... Fission (n,f) Neutron interactions 3 Nuclear Reactions EgyE 225: Nuclear Energy
- 4. Elastic Scattering • Both kinetic energy and momentum are conserved. • Target nucleus remains in the ground state. • No change in reacting particles. • Typically occurs when a neutron interacts with a light nucleus such as hydrogen. • Can be modeled as a billiard ball collision between a neutron and a nucleus. • This is the type of reaction that mostly helps fast neutrons to be slowed down to low energies in a reactor. n X n X After collision Before collision No change in reacting particles Neutron interactions 4 Nuclear Reactions EgyE 225: Nuclear Energy
- 5. Inelastic Scattering • Only the momentum is conserved. • Rebounding nuclide is left in an excited energy state. • Total kinetic energy is decreased before and after the collision. The difference accounts for the energy of excitation. • The excited nucleus subsequently de-excites by emitting -radiation. • Occurs when the neutron has KE that exceeds the excitation energy of the nucleus. γ-ray n X* n X ∗ ∗ X* is in an excited state Neutron interactions After collision Before collision 5 Nuclear Reactions EgyE 225: Nuclear Energy
- 6. γ-ray n Y n X Neutron interactions Radiative capture • The neutron is absorbed by the target nucleus to form the next higher isotope (of mass A+1), in an excited state of energy. • The new isotope de-excites by emitting -rays. • Neutron is lost in this reaction. After collision Before collision 6 Nuclear Reactions EgyE 225: Nuclear Energy
- 7. Charge and neutron production • Charge production: Interaction results in production of charged particles such as proton, deuteron or alpha particles. • Neutron production: Interaction results in production of more neutrons, 2n, 3n • These are generally threshold reactions, which means that a certain minimum neutron energy is required for the reaction to occur. n X b = , p, 2n, 3n Y n b Neutron interactions After collision Before collision 7 Nuclear Reactions EgyE 225: Nuclear Energy
- 8. Fission reaction • Most important reaction for nuclear energy. • When a neutron hits a heavy nuclide like U-235, the neutron gets absorbed in the heavy nuclide that gets energetically agitated (or excited). • If the new energy state of the heavy nuclide is sufficient for it to split, then it can split to cause fission. • Most neutrons produced in fission are fast, with an average energy of 2 MeV. Neutron interactions 8 Nuclear Reactions EgyE 225: Nuclear Energy
- 9. Definition: Measure of the probability that a neutron interaction will occur Cross-sectional area of a target atom as “seen” by an incident particle (projectile). Unit: barn, b = 10-24 cm2 = 10-28 m2 700 m/s 1,000 m/s Microscopic cross section, Nuclear cross section 9 Nuclear Reactions EgyE 225: Nuclear Energy
- 10. Total Scattering Elastic (n,n) Inelastic (n,n’) Absorption Radiative Capture (n,) Charge Production (n,p) (n, ) ... Neutron Production (n,2n) (n,3n) ... Fission (n,f) ( , ) ( , ) ( , ) , Microscopic cross section, Nuclear cross section (n,n) (n,n') (n,g) (n,p) (n,2n) (n,f) Scattering Absorption 10 Nuclear Reactions EgyE 225: Nuclear Energy
- 11. Material Cross-sections in barns Thermal neutrons (E = 0.0253 eV) Fast neutrons (E > 100 eV) Fission Capture Fission Capture Fissile 92-U-233 528.45 45.76 2.7323 0.27176 92-U-235 585.086 98.6864 1.9041 0.55549 94-Pu-239 747.401 270.329 1.7973 0.49614 Fertile 92-U-238 0.00001177 2.71692 0.042758 0.33188 90-Th-232 0.0 7.4 0.010193 0.38157 Clad 40-Zr 0.185396 0.0265766 Steel 3.08668 0.0170228 Coolant Light Water 0.664 0.00051554 Heavy Water 0.0013 0.00011459 11-Na-23 0.528 0.0027511 Control Rod 5-B-10 3840.0 2.73462 48-Cd 2524.15 0.266766 Fission Products 54-Xe-135 2636300.0 0.0059985 36-Kr-83 207.667 0.235944 62-Sm-149 40144.3 1.91883 Cross-sections of some important reactor materials Nuclear cross section 11 Nuclear Reactions EgyE 225: Nuclear Energy
- 12. Figure: Typical neutron microscopic cross section vs neutron energy. Photo reference: US DOE Handbook. Nuclear cross section 12 Nuclear Reactions EgyE 225: Nuclear Energy
- 13. Neutron classification based on spectrum regions Classification Neutron Energy, eV Speed, m/s Fast Greater than 105 Greater than 4.4106m/s Intermediate (Resonance/ Epithermal) 1 - 105 1.38104m/s - 4.4106m/s Slow (Thermal) Less than 1 Less than 1.38104m/s Nuclear cross section 13 Nuclear Reactions EgyE 225: Nuclear Energy
- 14. Nuclear cross section Depends on target material and energy of incident neutron 1E-1 1E+0 1E+1 1E+2 1E+3 1E-11 1E-8 1E-5 1E-2 1E+1 1E+4 Cross section (barns) Incident Energy (MeV) H-1 (total) C-14 (total) 1E-1 1E+1 1E+3 1E+5 1E-11 1E-8 1E-5 1E-2 1E+1 Cross section (barns) Incident Energy (MeV) B(n,a)Li B-10 (total) https://www-nds.iaea.org/exfor/endf.htm 1E-2 1E+0 1E+2 1E+4 1E+6 1E-11 1E-8 1E-5 1E-2 Cross section (barns) Incident Energy (MeV) Cd-109 (total) Cd-109 (n,g) 14 Nuclear Reactions EgyE 225: Nuclear Energy
- 15. Atom density Atom density is the number of atoms of a given type per unit volume of the material. atom density (atom/cm3) atomic mass (g/mole) mass density (g/cm3) Avogadro’s number particles/mole Nuclear cross section 15 Nuclear Reactions EgyE 225: Nuclear Energy
- 16. Macroscopic cross section, – Interaction of neutron with a certain volume of material depends not only on the microscopic cross section of a given nuclei but also on the number of nuclei within that volume. – Macroscopic cross section () is the probability of a given reaction to occur within a unit distance traveled by a neutron: where macroscopic cross section (cm-1) atom density (atoms/cm3) microscopic cross section (cm2) Nuclear cross section 16 Nuclear Reactions EgyE 225: Nuclear Energy
- 17. Macroscopic cross section, – The average distance traveled by a neutron before interaction is known as the mean free path, . – The mean free path has a unit of distance and is related to the macroscopic cross section: • Nuclear cross section 17 Nuclear Reactions EgyE 225: Nuclear Energy
- 18. Effects of temperature on cross section • Microscopic cross sections provided on most charts and tables are measured for a standard neutron speed of 2200 m/s, which corresponds to an ambient temperature of 20C. • The following formula is used to correct microscopic cross sections for temperature: where microscopic cross section corrected for temperature microscopic cross section at reference temperature temperature for which corrected value is being calculated (in K) reference temperature (in K) Nuclear cross section 18 Nuclear Reactions EgyE 225: Nuclear Energy
- 19. Atoms do not interact preferentially with neutrons from any particular direction. Photo reference: Lamarsh (2001) • Neutron flux is the total path length covered by all neutrons in one cm3 during 1 s: where neutron flux (n/cm2-s) neutron density (n/cm3) neutron speed (cm/s) • Neutron intensity ( ) is the number of neutrons per unit area and time (n/cm2-s) falling on a surface perpendicular to the direction of the beam. Neutron Flux, 19 Nuclear Reactions EgyE 225: Nuclear Energy
- 20. • Reaction rate is the number of interactions occurring in a unit volume of a material per unit time: where reaction rate (reactions/cm3-s or cm-3s-1) neutron flux (n/cm2-s) macroscopic cross section (cm-1) atom density (atoms/cm3) microscopic cross section (cm2) Reaction rate 20 Nuclear Reactions EgyE 225: Nuclear Energy
- 21. Neutron slowing down and thermalization • Fission neutrons are produced at an average energy of 2 MeV. • Neutrons slow down as a result of numerous scattering reactions with a variety of target nuclei. • After a number of collisions, the speed of a neutron is reduced to such an extent that it has approximately the same KE as the particles of the medium in which it is interacting. • This energy, ~0.025 eV at 20C, is referred to as the thermal energy. • Thermal neutrons are those with energies that have been reduced to this region (<1 eV). Neutron Migration: r1 is the distance from neutron source (S) to a point where it is thermalized (T), r2 is the distance from T to absorption point (A). Neutron moderation 21 Nuclear Reactions EgyE 225: Nuclear Energy
- 22. Neutron slowing down and thermalization • A moderator is a material used to slow down or thermalize neutrons. • An ideal moderator should have the following nuclear properties: • Large scattering cross section • Small absorption cross section • Large energy loss per collision Neutron Migration: r1 is the distance from neutron source (S) to a point where it is thermalized (T), r2 is the distance from T to absorption point (A). Neutron moderation 22 Nuclear Reactions EgyE 225: Nuclear Energy
- 23. Neutron slowing down and thermalization • A convenient measure of energy loss per collision is the average logarithmic energy decrement, where average initial neutron energy average final neutron energy • On the average, a neutron loses a fixed fraction of its energy per scattering collision. • is constant for a given material and does not depend on the initial neutron energy. Neutron moderation 23 Nuclear Reactions EgyE 225: Nuclear Energy
- 24. Neutron slowing down and thermalization • The total number of collisions ( ) necessary for a neutron to lose a given amount of energy can be obtained from : where initial neutron energy final (lower) neutron energy Neutron moderation 24 Nuclear Reactions EgyE 225: Nuclear Energy
- 25. Neutron slowing down and thermalization • In addition to the ability of a material to slow neutrons down, it is also important to consider its scattering and absorption properties. • The macroscopic slowing down power (MSDP) is the product of the logarithmic energy decrement and the macroscopic cross section ( ) for scattering in the material: • The moderating ratio (MR) is the ratio of the MSDP to the macroscopic cross section for absorption ( ): Neutron moderation 25 Nuclear Reactions EgyE 225: Nuclear Energy
- 26. Neutron slowing down and thermalization Material 𝒄 MSDP MR H2O 0.927 19 1.425 62 D2O 0.510 35 0.177 4830 Helium 0.427 42 51 Beryllium 0.207 86 0.154 126 Boron 0.171 105 0.092 0.0086 Carbon 0.158 114 0.083 216 Moderating properties of material Neutron moderation 26 Nuclear Reactions EgyE 225: Nuclear Energy
- 27. References • Lamarsh, J. R., and Anthony J. Baratta. Introduction to Nuclear Engineering. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 2001. • Lewis, E. E., Fundamentals of Nuclear Reactor Physics, Academic Press, 2008. • Turner, J.E., Atoms, Radiation and Radiation Protection (3rd ed.). Weinheim: Wiley-VCH, 2007. Research Reactors 27