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Westinghouse Technology Systems ManualSection 2.1Reactor Physics Review

TABLE OF CONTENTS2.1 REACTOR PHYSICS REVIEW . 2.1-12.1.1 Introduction . 2.1-12.1.2 Fission Process . 2.1-22.1.3 Moderation . 2.1-32.1.4 Nuclear Cross Section . 2.1-42.1.5 Neutron Multiplication . t Fission Factor . 2.1-6Fast Nonleakage Factor . 2.1-6Resonance Escape Probability . 2.1-7Thermal Nonleakage Factor . 2.1-7Thermal Utilization Factor . 2.1-8Neutron Production Factor . 2.1-82.1.6 Reactivity and Reactivity Coefficients . 2.1-82.1.6.12.1.6.22.1.6.32.1.6.42.1.6.5Fuel Temperature Coefficient . 2.1-10Moderator Temperature Coefficient . 2.1-12Void Coefficient . 2.1-14Pressure Coefficient . 2.1-14Power Coefficient and Power Defect . 2.1-152.1.7 Poisons . 2.1-152.1.7.1 Uncontrollable Poisons . 2.1-152.1.7.2 Controllable Poisons . 2.1-182.1.8 Reactor Response to Reactivity Changes . 2.1-182.1.9 Reactor Kinetics . 2.1-212.1.10 Subcritical Multiplication . 2.1-23LIST OF TABLES2.1-1 Particles and Energy Produced per Fission Event . 2.1-252.1-2 Neutrons per Fission . 2.1-25NRC HRTD2.1-iiRev 1208

2.1-3 Typical Neutron Balance for U-235 . 2.1-26LIST OF 2.1-182.1-192.1-202.1-21.Fission Neutron Energy. Flux Distribution. Total Cross Section for U-235. Cross Section Curve. Doppler Temperature Coefficient, BOL and EOL. Doppler Only Power Coefficient, BOL and EOL. Doppler Only Power Defect, BOL and EOL. Moderator Temperature Coefficient. Total Power Coefficient, BOL and EOL. Total Power Defect, BOL and EOL. Fission Yield versus Mass Number. Equilibrium Xenon Worth vs. Percent of Full Power. Xenon Transients. Xenon Transients Following a Reactor Trip. Xenon Transients Following a Reactor Trip and Return to Power. Samarium Transients. Samarium Transients Starting with a Clean Core. Samarium Transients Starting with a Clean Core. Samarium Shutdown Transients.Integral and Differential Rod Worth. Reactivity versus Startup RateNRC HRTD2.1-iiiRev 1208

2.1 REACTOR PHYSICS REVIEWLearning Objectives:1. Define the following terms:a.b.c.d.e.f.g.h.i.KeffReactivityReactivity coefficientPower p rate2. Describe the following reactivity coefficients and explain how their values changewith core life and reactor power level:a.b.c.d.Moderator temperatureDoppler-only powerVoidPower3. Explain the relative effects of the following poisons in plant operations:a. Xenonb. Samarium4. Explain how the following controllable poisons affect core reactivity:a. Control rodsb. Chemical shim5. Explain the inherent response of the reactor to the following transients:a. Secondary load changesb. Reactivity additions from control rod motion or boron concentration changes6. Explain how the neutron population of a subcritical reactor changes in responseto reactivity changes.2.1.1 IntroductionThis section represents a summary of basic nuclear physics and nuclear reactordesign principles and terminology. The material presented is broader in scope thancan be conveniently covered in the classroom time allotted; therefore, all the writtenmaterial is not covered in detail. Basic explanations and definitions of concepts areUSNRC HRTD2.1-1Rev 1208

given in the classroom. It is emphasized that the written material is only a summaryof the subject.2.1.2 Fission ProcessNuclear fission is the splitting of the nucleus of an atom into two or more separatenuclei accompanied by the release of a large amount of energy. The reaction canbe induced by a nucleus absorbing a neutron, or it can occur spontaneously,because of the unstable nature of some of the heavy isotopes. Very few isotopeshave been excited to the state where the fission reaction occurs. These have beenin the heavy elements, generally uranium and above on the chemical scale.Nearly all of the fissions in a reactor are generated in the fuel by neutron absorption,which can result in the splitting of the fissionable atoms that make up the fuel. Onlya few of the heavy isotopes are available in quantities large enough or present asufficient probability of fission to be used as reactor fuel. These are uranium-233(U-233), uranium-235, (U-235), uranium-238 (U-238) for fast or high-energy fissiononly, plutonium-239 (Pu-239), and plutonium-241 (Pu-241). Several other isotopesundergo some fission but their contribution is always extremely small. U-235 and U238 are naturally occurring isotopes with very long half-lives; they are generally thefuels used for reactors. Artificially produced fuels include U-233, which is producedby the irradiation of thorium-232 (Th-232) in a reactor, and Pu-239 (produced byirradiation of U-238 in a reactor). Th-232 and U-238 are called fertile materials andare generally placed in the core or in a blanket surrounding the reactor for theexpress purpose of producing fuel (fissionable material) as the original fuel is usedup in fission. The ratio of the amount of fuel that is produced in a reactor to theamount that is used during any period of time is called the conversion ratio of thereactor. If the amount of fuel produced is greater than the amount consumed, thenthe excess fuel produced is called a breeding gain. The fissile nucleus absorbs aneutron, and almost immediately, fission occurs. In the case of U-235, the reactionis represented by the following:U-235 n -- (U-236)*(U-236)*-- FP1 FP2 2.43 n Energywhere FP fission product,n neutron, andA*@ indicates the isotope is unstable.In atomic studies it has become the practice to express energies in "electron volt"units, abbreviated It has been determined that gamma energies are frequentlyon the order of a million electron volts (MeV); the MeV has thus become aconvenient unit for stating these (and related) energies.The fission of any of the fissionable isotopes produces gammas, neutrons, betas,and other particles. The total energy released per fission is about 207 MeV for U235; this energy is distributed as shown in Table 2.1-1.USNRC HRTD2.1-2Rev 1208

The energy of the neutrinos, which accompany the radioactivity, is not available forproducing power because these particles do not interact appreciably with matter;thus, the net energy available is 197 MeV, or roughly 200 MeV per fission. Table2.1-1 lists the particles and the energy each particle produces per fission event.Neutron production (neutrons per fission) varies with the different fissionableisotopes and with the energy at which the fission reaction is caused to take place.Table 2.1-2 shows some relative values for neutrons per fission for some of thecommon fuels that are now being used in reactors.More than 99.3% of the neutrons produced are produced within 10-14 seconds;these are called prompt neutrons. It should be noted that each fission event doesnot produce the same number of neutrons. The number of neutrons per fissiongiven in the referenced table represents an average number produced per fission.The neutrons released from fission are not monoenergetic neutrons (neutronshaving a single energy); they vary in energy from essentially thermal energy up toabout 15 MeV. The energy distribution of these prompt neutrons is shown in Figure2.1-1. The horizontal axis shows the range of prompt neutron energy distribution inMeV and the vertical axis shows the fractional neutron distribution in an incrementalband (delta) around a selected energy level. The units for the vertical axis arefractional distribution per MeV. It can be seen that the area under the curve in anincremental band around 0.65 MeV yields the highest fraction of neutrons. Usingthe area under the curve it can also be seen that approximately 98% of all promptneutrons are born at an energy level less than 8 MeV, and the average promptneutron energy is approximately 2 MeV.2.1.3 ModerationIn an actual operating reactor the probability of fission for typical reactor fuels isdependent on the energy of the incident neutrons. Fission neutrons are born fast (athigh energies), and the probability that they will cause a fission in U-235 at thatenergy is very small. It is necessary to reduce this kinetic energy in order toincrease the chance that they will cause fission. This is accomplished byinterposing relatively non-absorbing nuclei as collision media to absorb the kineticenergy of fission neutrons through the process of elastic scattering. This medium iscalled the It acts to slow down or the fission neutrons.Typical moderators are hydrogen, beryllium, and carbon. It should be clear thatfewer collisions are necessary in a hydrogen medium to cause complete moderationthan in carbon, since the nuclear mass of hydrogen is smaller and therefore morelikely to absorb the kinetic energy of the neutron by the elastic scattering process.The amount of moderator in a multiplying system (a reactor, for instance) greatlyinfluences the degree of slowing down that occurs. If there is too little moderator,the neutrons are not adequately slowed down. Therefore, the probability of fissionis small when compared with optimum. If there is too much moderator, then theprobability that a thermal neutron will be captured by the moderator (or some othernonfissionable material) is greatly increased. Figure 2.1-2 shows a snapshot of theneutron energy spectrum for a light water moderated reactor. The horizontal axis isUSNRC HRTD2.1-3Rev 1208

neutron energies in electron volts (eV) on a logarithmic scale, while the vertical axisis the neutron flux per unit energy. Neutron flux, φ, is the product of the neutron3density (typical unit of measurement: neutrons/cm ) and the neutron velocity (typicalunit: cm/sec), and is usually expressed in terms of neutrons/cm2 sec. As shown inthis figure two peaks occur. The first peak is at fast neutron energies due to the-14prompt neutron production (within 10 sec) of the fission events. The second peakoccurs at thermal neutron energy levels. This is caused by the diffusion of thethermal neutrons until they are absorbed by either a poison or the U-235 fuel. Thetime it takes a neutron to slow down from fast to thermal energy is relatively short, 5microseconds, as compared to the thermal diffusion time of 210 microseconds.This results in a relatively low number of intermediate energy neutrons and the peakat the thermal energy level.2.1.4 Nuclear Cross SectionThe previous discussions of neutron reactions alluded to the fact that they havedifferent probabilities of occurrence. A measure of the relative probability that agiven reaction will occur is defined as the cross section of the nucleus for thatspecified reaction. More precisely, this measure is referred to as the microscopiccross section. In an approximate sense, the microscopic cross section may beconsidered as the effective area for interaction that the nucleus presents to theneutron.The microscopic cross section has units of area (cm2), and it is often expressed inunits of barn