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## Basic Physics of Nuclear Reactors

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**Basic Physics of Nuclear Reactors**Prof. Paddy Regan, Dept. of Physics University of Surrey Guildford, UK Feb, 2014**Several components are important for a controlled nuclear**reactor: • Fissionable fuel • Moderator to slow down neutrons • Control rods for safety and reactor criticality control • Reflector to surround moderator and fuel in order to contain neutrons and thereby improve efficiency • Reactor vessel and radiation shield • Energy transfer systems if commercial power is desired • Two main effects can “poison” reactors: (1) neutrons may be absorbed without producing fission [for example, by neutron radiative capture]; (2) neutrons may escape from the fuel zone.**Outline**• 1: Basic Nuclear Energetics • Nuclear masses; binding energy; binding energy per nucleon; nucleon separation energies. • 2: Neutron Interactions • Definition of cross-section; elastic collisions and neutron moderation; neutron attenuation; neutron mean free path; definition of neutron flux; definitions of neutron mean time/collision probability per unit time; reactor power; elastic and inelastic scattering. • 3: Basics of Nuclear Fission • Fissile materials 235,238U; energetics of fission; beta-delayed neutrons; odd-even effects; cross-sections for neutron interactions on 235,238U; Fission fragment mass distributions; neutrons per fission; fission neutron energy spectra; moderator materials and kinetics. • 4: Criticality • Concept of the chain reaction; 4 and 6 factor formulae; Definition of criticality and reactivity; reasons for Uranium enrichment; moderator materials; control rod materials; neutron cycle; delayed neutrons; Simple criticality calculations; reactor poisons; fast fission • 5: Breeder Reactors • Fissile and Fertile Materials; Formation of 239Pu; Use of 232Th; Breeding ratio.**Useful web-sites for more notes, examples etc. etc:**http://canteach.candu.org/aecl.html http://www.neutron.kth.se/courses/reactor_physics/lecturenotes.shtml http://www.if.uidaho.edu/~gunner/Nuclear/LectureNotes/Lecture18_Reactor_Physics.pdf http://physics.ukzn.ac.za/~moodleym/ReactorTheory/ http://www.atomeromu.hu/mukodes/lancreakcio-e.htm**136**136 137 54 54 54 82 82 83 Nomenclature Ionic Charge A Xe = Chemical symbol Z N = A-Z Where A = Mass Number, Z = Proton Number N = Neutron Number = A – Z Ionic Charge = charge on the ion. If neutral it is left blank ( d,p ) Xe Reactions :- Xe 2 Where d = H represents the deuteron and p the proton 1 1**Mass and Energy** From Special Relativity:- m = m0 1-(v/c)2 when v = 0 then E = m0c2 • For an electron E0 = m0c2 = (9.11 x 10-31)(3 x 108)2 = 8.2 x 10-14 J = 0.511 MeV For 1 unit of atomic mass = 1/12 of the mass of a carbon atom = 1.66 x 10-27 kg = 931.5 MeV • Matter can be converted into energy and energy can be converted into matter.** We can find some 283 stable or long-lived nuclei on the**Earth’s surface. We define the proton (Sp = 0) and neutron (Sn = 0) drip-lines?. About 6-7000 species live long enough to be studied in principle.**Binding Energy**• Z protons and N = A-Z neutrons can be brought together to form a nucleus which has a total mass M(A,Z) which is LESS THAN THE SUM OF ZmP + (A-Z)mN Some of the mass has been “used up” in binding the particles together. This difference in mass is equal to B or energy B/c2 is the Binding Energy. Variations in atomic masses due to variations in binding energy are very small compared with u 931 MeV The atomic mass is often given in the form (M(A,Z) – A) called the Mass Excess The Binding Energy increases with mass and proton number. This is reflected in the Chart of the Nuclides, the plot of the stable nuclides as a function of N and Z.**Separation Energies.** If we want to remove one neutron or proton from the nucleus it “costs” energy. This leads to the definition of the neutron separation energy SN = B(A,Z) –B(A-1,Z) = [ M(A-1,Z) –M(A,Z) + MN]c2 • Similarly the proton separation energy is defined as SP =B(A,Z) –B(A-1,Z-1) = [ M(A-1,Z-1) –M(A,Z) + MH]c2 where we are working with atomic masses. • These quantities are analogous to the Ionisation energies in atoms. Effectively they give us the amount of energy required to remove the last neutron or proton, i.e. how well bound the last particle is. Plotted as a function of A they reveal evidence of Shell structure.**The variation of Binding Energy per nucleon with A**8 MeV/A Binding Energy Slope= 8 MeV/A A B (Z, A) » 8 ´ A MeV Þ binding is via a short range force Deviations from the “constant” 8 MeV/A Þfission and fusion can release energy**A = 56**Nuclear binding Mnucleus < Sum of the constituent nucleon masses. B(Z,A)/c2 = ZMp + NMn – M(Z,A) ( > 0)**Coefficients (values obtained from fits to experimental**data) av = 15.56 MeV ; as = 17.23 MeV ; ac = 0.697 MeV ; aA = 23.285 MeV ; aP = 12.0 MeV**In fission a nucleus separates into two fission fragments.**One fragment is typically somewhat larger than the other. • Fission occurs for heavy nuclei because of the increased Coulomb forces between the protons. • We can understand fission by using the semi-empirical mass formula based on the liquid drop model. • For a spherical nucleus of with mass number A ~ 240, the attractive short-range nuclear forces offset the Coulomb repulsive term. • As a nucleus becomes nonspherical, the surface energy is increased, and the effect of the short-range nuclear interactions is reduced. • Nucleons on the surface are not surrounded by other nucleons, and the unsaturated nuclear force reduces the overall nuclear attraction. For a certain deformation, a critical energy is reached, and the fission barrier is overcome.**EXAMPLE:**SOLUTION:**Standard unit for cross-section is the ‘barn’ where 1**barn = 10-28m2 = 10-24cm2**(see later re criticality and**discussion on effects of delayed neutrons on reactor control).**Reactor Power**The Reactor Power (= energy released per unit time in the reactor volume) can be given by the product of the Energy per fission reaction x the fission reaction rate per unit volume x reactor volume Note that since the (fission) reaction rate per unit volume ( = Rf ) is the equal to the product of the collision probability per unit path length times the neutron flux (in neutrons/ per unit area per unit time), then we can write (recall s.N=S) Power (in units of J/s = Watts) = [Joules ] x [ 1/length] x [1/length2 . time] x [length3]**Example:**A research reactor has a cubic shape, with a typical neutron flux of 1013 n/cm2s through its volume and sides of length 0.8m. If the probability of fission per unit length, Sf=0.1cm-1, what is the power of the reactor? Solution Assuming typical energy release per fission = 200 MeV