Teachin g N o tes
Operation a l Reacto r Saf et y Course
Lecture : 2 – Reacto r Ph ysic s Review
Objectiv e:
To provide a funda m e ntal review of m a terial that should have been learned in the earlier classes, which will cov e r cross sections, fi ssion process, infinite an d f i nite rea cto r system s f o ur f actor f o rmula, asses s m ent of critica lity co ntrol, dif f u sion theory and neutron transport. W hat we want to do here is a quick review of the f u n d am entals s o the students will be prepar e d to deal with f u ture to pics tha t will be cover e d in subsequent lectu r es.
Ke y Point s t o Brin g Out:
Slid e num ber Point s
3 The purpose here is to appreciat e the different types of reactions that m i ght occur when a neutron is absorbed by a uranium atom, such as uranium 235. The key feat ures are scattering, of various types, and c a pture whic h m a y result in m u ltiple neutron pro duction as well as fission.
4 Mechanism s of scattering and ab sorp tion in term s of the vario u s possibilities and the cross sections as sociated with those. Exp l ore what cross section is (probabilist ic likelihood of interaction) and units – Barns.
5 Table of typical therm a l neutr on cross section param e ters. One m i ght want to em phasize the relative ly high fission cross section of uranium 235 and plutonium 235. The ot her key feature is to note the num ber of neutrons produced per fission.
6 Cross section for uranium 235 and 238 for fission are shown indicating a clear absorp tion res onance zone region and to point
out that uranium 238 also fissions but at very hi gh neutron energies.
7 The key point is to iden tif y the m u ltiplica tion of neutrons ne e d ed for criticality. A neutron balance for criticality requires a neutron population wherein production equals losses.
8 Typical fiss ion energy sp ectrum associated with the energy of the neutron upon fissioning. The key point here is to show that most of the neutrons are em itted at a 1-2 m ev range with much higher neutron but much lower energies possible.
9 The key point is the total am ount of energy released per fission, noting that the fission fragm ents produce by far the largest amount of energy, and delay radiations in term s of beta and gamma produce th e rest for to tal ener gy released per fission of approxim ately 200 Mev in term s of a c tual heat produced.
10 A typical g r aphic of the fission prod uct decay ch ain. The key point here is to show that upon fissi oning with a certain group chain of fission fragm e nts, there is a deca y leading to stable isotopes.
11 Shows the approxim a te fission yiel d in term s of fission products produced as a result of the spli tting of the uranium atom which yields a roughly equal distributi on of isotopes indicated by the two peaks of atom ic m a ss number.
12 Sa m ple chart of the nuclides. Tim e should be spent on this particular chart by explaining what each of those sym bols m e an on the tab l e so that the students learn how to use this chart of nuclides to iden tify the decay ch ains, th e half lives, as w e ll as the relationship between each of the radi oactiv e iso t o p es and the stable isotopes in the chart.
13 A typical decay chain that you c ould use to further am plify the processes by which isotopes, either by neutron absorption, or decay, transf orm them selves into o t her isotopes. T h is is im portant for the students to understand so th at they can learn how to m o ve about the chart of the nuclides.
14 There is a process by which fertile, w hich m e ans non-fissioning isotopes, can becom e fis ile on neutron capture and subsequent decay. The case shown here is thorium and uranium 238.
15 This is a k ey slide b ecaus e is takes so m e of the fundam entals of reactor physics and begins to convert them in term s of what is im portant relative to power produc tion and that is reaction rates which is related to how we m a ke power. The m e ssage here would be focused on using the f i ssion process and the energy release per
fission to create heat which then m ust be rem oved by the coolant. In determ ining how to accom p lish this m i ssion one m u st consider certain factors when designing a core, such as, how long do we want to design the reactor in te rm s of tim es between refueling.
This affects the in itial en richm ent . Establish the refueling strategy such as online, Full batch, 1/3 core , etc which define how the core is designed in term s of reactivity swing.
16 In therm a l reacto r s, we need to s l ow down the neutrons. W e need to take neutrons born in fast (a t high energies) an d scatter them down to an energy level where the neutrons are in the therm a l energy range at which they are m ore effective at fission.
17 Shows a typical curve fo r cross sec tion as a function of energy that should give the students an apprec iation of the need to slow down for fissioning.
18 Addresses the types of moderators that can be used to provide the slowing down function that with a note that hydrogen and carbon are very efficient m oderators fo r slowing down because this causes the neutrons to lose m ore energy per collision.
19 Introduces sim ple diffus i on theory for infinite and finite system s. Calcula tions f o r inf i nite system s use the factor fo rm ula and the finite sys t em s need to consider leak age from the reactor.
20 Shows the chart of how neutrons are born and lost. I suggest start track ing at initial f i ss ion neutr on and follow the cycle clockwise being sure that the students appr eciate the production and lost processes.
21 A m o re deta iled g r aphic al illus t ra tion showing som e of the more essential term s that are involved but it is essentially a repeat of the past slides w ith m ore detail. One of the key points here is to take the 6 factor for m ula and show how the population of fast neutrons are los t , and therm alized between each generation.
22-24 Sim p le definitions of the te rms used in p r e v ious slides for referenc e.
25 Explains neutron lost mechanism s . Key point here is associated with the scale of the likelihood of loss in reactor in a sense of the therm a l neutron could escape from the reactor. Th e other losses are obviously absorbers, by capture in st ructural m a terials, and coolant.
26 Key point is to identify how criticality is m a intained once the reactor is started up with excess reactivity in term s of higher
enrichm e nt, burnable poisons (neutron absorbers) use of control rods and soluble boron. Make th e destinction between PW Rs (soluble boron) and BWRs (no so luble boron but use of burnable poisons in f u el and con t rol rods for reactivity su mp control).
Mention online refueling system s such as pebble bed or CANDU reactors require little excess reactivity to com pensate for burnup.
27-28 An introdu ction to diffusion theory for o n e group an d m u lti-g r ou p considerations. The key points here to m ake are that the m ateria l buckling which will be defined in class notes for the blackboard as will be the g eom etric buckling, whic h is sim p ly a function of the geom etry of the reactor, need to be equal for a critical system .
Shown on slide num ber 28 are the material bucklings for typical geom etries.
29 Introduces the notion of multi group calcu lations, the key point here is to show the im portance of selecting the ap propriate number of groups to be sure that im por t phenom enon are captured in term s of neutron cross section for that group distribution. This selection will af f ect th e results of the critic ality calcu lations .
30 Shows nor malized flux versus distance or certain geom etric conditions which are approxim a te ly are about the sam e basic cosine shapes.
31 Com pares one versus two group diffusion theory results and shows the quite dif f erent flux distributions for fast and therm a l energy groups a tw o group core with a reflector.
32 Identifies a typical sequence for a Monte Carlo calculation. T h is is described generally in the Knie f book, but the key point to m a ke here is that in Monte Carlo, each neu t ron is track ed as a function of energy, direction and po sition. Th e n e utron is tracked in terms of interactions and absorption such as fission or scattering. Neutrons are tracked by num b er, energy and location. A tally is kept to determ ine whether the reactor is critical, in term s of neutron population for each gen e ration.
33 The Boltzmann equation is intr oduced, neutron transport. This equation is useful since it provide s an instructive tool on som e of the m o re interesting asp ects of neutron interact ion and neutron balance as a function of tim e.
MIT OpenCourseWare http://ocw.mit.edu
22.091 / 22.903 Nuclear Reactor Safety
Spring 200 8
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