1 Criticality of Nuclear reactors and Geometric Buckling

1 Criticality of Nuclear reactors and Geometric Buckling Derek Smith Eastern Illinois University

2 How do you make Nuclear energy safe? 1. Understand a basic reactor.

3 http: //www. cameco. com/uranium_101/uran ium_science/nuclear_reactors/

4 How to understand Nuclear Energy 1. Understand a basic reactor. 2. Understand how the control rods maintain reactor criticality.

https: //commons. wikimedia. org/wiki/File: Control_rods_s chematic. svg 5 Farther down= more neutrons absorbed & less heat Farther up= less neutrons absorbed & higher heat

6 http: //www. lanl. gov/quarterly/q_f all 03/reactor. shtml

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8 How to understand Nuclear Energy 1. Understand a basic reactor. 2. Understand how the control rods maintain reactor criticality. 3. what is criticality?

9 Criticality may be defined as the “attainment of physical conditions such that a fissile material will sustain a chain reaction” Accidental criticality is the highest hazard a health physicist deals with. This can be maintained with efforts to prevent accidental criticality with Criticality control or Nuclear safety

10 Accidental criticality U 235 nucleus Alpha particle

11 Uncontrolled chain reaction: from accidental criticality

12 Criticality Subcritical- if more neutrons are lost by escape or nonfission absorption than are produced, and the chain reaction isn’t self sustaining and dies out Supercritical- a sustained chain reaction with the rate of fission neutron production exceed the rate of loss Critical- when exactly one neutron per fission is available for initiating another fission.

13 Sub-critical

14 Criticality Subcritical- if more neutrons are lost by escape or nonfission absorption than are produced, and the chain reaction isn’t self sustaining and dies out Supercritical- a sustained chain reaction with the rate of fission neutron production exceed the rate of loss Critical- when exactly one neutron per fission is available for initiating another fission.

15 Super-Critical

16 Criticality Subcritical- if more neutrons are lost by escape or nonfission absorption than are produced, and the chain reaction isn’t self sustaining and dies out Supercritical- a sustained chain reaction with the rate of fission neutron production exceed the rate of loss Critical- when exactly one neutron per fission is available for initiating another fission.

17 Critical

18 Criticality Control Accidental 1. 2. 3. 4. 5. 6. 7. criticality depends on the following: Quantity of the fissile material Geometry of the fissile assembly Presence or absence of a moderator Presence or absence of a neutron reflector Presence or absence of a strong neutron absorber (poison) Concentration of fissile material, if the fissile material is in solution Interaction between two or more assemblies or arrays of fissile material, each one of which is subcritical by itself. Consideration of this possibility is important in the transport and storage of fissile materials.

19 Criticality control Nuclear safety can be assured by limiting at least one of the factors that determines criticality 1. Mass control- limiting the mass of fissile material to less than the critical mass under any conceivable condition 2. Geometry control- having a geometric configuration that can never become critical because the surface-to-volume ratio is such that excessive neutron leakage makes it impossible to attain a multiplication factor as great as 1. 3. Concentration control- if the solution of fissile material is sufficiently dilute, absorption of neutrons by the hydrogen atoms makes a sustained chain reaction impossible. The degree of enrichment of 235 U is important to this control.

20 How to understand Nuclear Energy 1. Understand a basic reactor. 2. Understand how the control rods maintain reactor criticality. 3. what is criticality? 4. Understanding Fission

21 Nuclear Fission: Uranium relation Nuclei with odd numbers of nucleons are more easily fissioned than those with an even number of nucleons. For example which fissions after capturing a thermal neutron, Whereas which can also capture a thermal neutron, is transformed into an even-odd nucleus and rids itself of its excitation energy by emitting a gamma ray http: //scienceblogs. co m/startswithabang/20 09/04/is_uranium_the _heaviest_natura. php

22 Nuclear Fission: fission fragments When an atom fissions, it splits into two fission fragments plus several neutrons (the mean number of neutrons per fission of is 2. 5) plus gamma rays according to the conservation equation: An approximate distribution of this energy is as follows: Fission fragments, kinetic energy 167 Me. V Neutron kinetic energy 6 Fission gamma rays 6 Radioactive decay Beta particle 5 Gamma rays 5 neutrinos 11 200 Me. V

23 Nuclear Fission: Spontaneous fission For the possibility of fission the following mass- energy relationship must hold: This condition can only be met by isotopes whose atomic number and atomic mass are such that: Although its likelihood is very small spontaneous fission (can cause accidental criticality) is very important in criticality control. If an isotope : the nucleus is unstable toward fission and would undergo spontaneous fission. http: //acadine. physics. jmu. edu/mai n/phys 215_transparencies/12. nucl ear_fission/61_liquid_drop_model. J PG

24 Uncontrolled chain reaction: from accidental criticality

25 Nuclear Fission: Rate of Fission Most of the energy dissipated in the critical assembly is heat energy. Using a mean value of 190 Me. V (millionelectron volts) heat energy per fission, the rate of fission to generate one watt of power is calculated as follows:

26 How to understand Nuclear Energy 1. Understand a basic reactor. 2. Understand how the control rods maintain reactor criticality. 3. what is criticality? 4. Understanding Fission 5. Putting a value on criticality

27 Multiplication factor: The Four. Factor Formula Criticality, also known as the value of Keff depends on the supply of neutrons of proper energy to initiate fission and also on the availability of fissile atoms.

28 FOUR FACTOR FORMULA: INFINITE MULTIPLICATION FACTOR • ηis the mean number of neutrons emitted per absorption of Uranium, so n thermal neutrons will result in ηn fission neutrons. • Є=fast fission factor with max value= 1. 29 • p=Resonance capture is called Resonance escape probability or p and is defined as the fraction of the fast, fission produced neutrons that finally become thermalized. The value of p depends on the ratio of moderator to fuel. • f=The fraction of the total number of thermalized neutrons absorbed by the fuel (including all the uranium) is called thermal utilization factor, f

29 Reactivity and Reactor Control Increase in the neutron multiplication factor >1 is called excess reactivity, defined by: For neutrons in one generation, we have additional neutrons in succeeding generation. The time rate of change of neutrons is: generation , is the lifetime of the neutron

30 Reactivity and Reactor Control 0. 001 s is the mean lifetime of a neutron from its birth to its absorption in pure 235 U When the excess reactivity is 0. 1%, that is ∆k = 0. 001, the reactor period is: T=0. 001/0. 001= 1 s and the power level increases by a factor of e, or 2. 718 each second. If ∆k were increased to 5% then: T= 0. 001/0. 005= 0. 2 s , and the power lever increases in 1 s would be by a factor of 150.

31 How to understand Nuclear Energy 1. Understand a basic reactor. 2. Understand how the control rods maintain reactor criticality. 3. what is criticality? 4. Understanding Fission 5. Putting a value on criticality 6. Multiplying medium

Reactor Physics Multiplying Medium A multiplying medium is one in which fission, eithermal or fast or both, does occur. = absorption = fission both terms have the same mathematical form cross section times a flux

33 How to understand Nuclear Energy 1. Understand a basic reactor. 2. Understand how the control rods maintain reactor criticality. 3. what is criticality? 4. Understanding Fission 5. Putting a value on criticality 6. Multiplying medium 7. Buckling

Bare Slab Reactor = flux boundaries Center line x y X Z Extrapolation distance (d) (-a/2 -d) -a/2 0 a/2 (a/2+d)

Buckling The neutron diffusion equation for the bare slab reactor can be written as would be: in which B 1 is called Buckling is the measurement of extent to which the flux curves or "buckles". buckling can be used to infer leakage. The greater the curvature the more leakage expected. For critical reactivity the material buckling should be equal to geometrical buckling. Hence reactivity can be controlled with proper buckling incorporated in reactor’ s design.

36 How to understand Nuclear Energy 1. Understand a basic reactor. 2. Understand how the control rods maintain reactor criticality. 3. what is criticality? 4. Understanding Fission 5. Putting a value on criticality 6. Multiplying medium 7. Buckling 8. Determination of reactor’s critical dimension

37 Reactor’s critical dimension • Rearranging the Buckling equation we get: • We can then solve for Rex

38 Sources Ferguson, C. D. (2011). Nuclear Energy- what everyone needs to know. New York, New York: Oxford University Press, Inc. Cotton, S. (n. d. ). Uranium Hexafluoride - UF 6. Retrieved February 26, 2012, from chm. bris. ac. uk: www. chm. bris. ac. uk/motm/uf 6 v. htm Hewitt, P. G. (2006). Conceptual Physics 10 th edition. St. Petersburg: Pearson-Addison Wesley. Moniz, E. (2011). Why We Still Need Nuclear Power. Foreign Affairs , 83 -94. Nuclearfiles. org. (n. d. ). from nuclear proliferation to nuclear testing. Retrieved February 25, 2012, from Nuclearfiles: project of the nuclear age peace foundation: http: //www. nuclearfiles. org/? gclid=CN 2 Av. L 3 vy. K 4 CFQz. GKgod 62 Oz. Bg