nuclear physics basics

8/10/2019 Nuclear Physics Basics

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Introduction.. 1Nuclear Power Plants

Laboratory for Reactor Physics and Systems Behaviour

Introduction,Nuclear Physics Basics, Fission

R. Chawla

Power Plants and Heat Pumps:Nuclear Power Plants


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Introduction.. 2


Nuclear Power Plants

Power Plants and Heat Pumps

! Prof. Favrat 7 x 2 hrs (lectures), 14 x 1 hr (exercises)

Energy, economics and environment (general)

Thermal power plant cycles and equipment

Heat pumping technologies

!

Prof. Chawla 7 x 2 hrs (lectures, with exercises integrated therein)

Nuclear power plants

March 1, 8, 15, 29

April 12, 26

May 3


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Introduction.. 3



Nuclear Power Plants (NPPs)

! Weeks 1 & 2:Introduction, nuclear physics basics, fission, nuclear reactors

Critical size, nuclear fuel cycles, NPPs (CROCUS visit?)

! Week 3:Neutronics, reactor physics design

!

Week 4:Reactor heat transfer (thermalhydraulics), technological constraints

!

Week 5:Reactor (reactivity) control

!

Week 6:Principal types of nuclear power plants

! Week 7:Environmental aspects, nuclear safety, advanced systems (NPP visit?)

Course Material:

Elements of Nuclear Engineering, J. Ligou, Chs. 1, 3, (4), 5, (6) Effectively, English translation of Introduction au gnie nuclaire (PPUR, 1997)

Pdfs of book chapters, as also of ppt-slides (incl. solved exercises), available at:

https://documents.epfl.ch/groups/l/lr/lrs-unit/www/NPPs.2010/


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Introduction

! Nuclear (fission) energyCommercially established since 1956

Calder Hall, gas-cooled Magnox NPP at Sellafield (UK), 50 MW (later 200 MW)

Today: ~16% of worlds electricity generation (18% hydro, 66% fossil)

Switzerland: ~40% (nearly all the rest: hydro)

!

General situation

Evergrowing, worldwide energy demand (population, standard of living,..)

Acknowledged hazards of continued dependence on fossil fuels (climate change,..)

New renewables important, but not sufficiently established for medium-term

Nuclear needs to contribute to growthFusion in long-term (when?)

Fission (increase possible, but further developments needed.. safety, wastes, etc.)

Various factors importantEconomics, environmental aspects, socio-political considerations,..


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Introduction.. 5



Nuclear Physics Basics (Historical Overview)

! Structure of the atom (Rutherfords model)Mass concentrated in the nucleus (mH/me ~ 1837)

Nuclear charge: +Ze (Z: atomic number, e ~ 1.6.10-19 coulomb)

Quantum mechanical basis for atomic, nuclear structure

Classical dimensions: nucleus ~ 10-13 cm, atom ~ 10-8 cm

! Energy units (1eV ~ 1.6.10-19 J)Binding energy of outermost electrons ~ order of eV

Energy involved in chemical reactions ~ same order

Binding energy of nucleons (constituents of nucleus) ~ order of MeV !Energy in nuclear reactions ~ x 106times greater than in chemical..


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Introduction.. 6



Constituents of the Nucleus

!

Atomic mass A A gm contain NAatoms (Avogadros Number.. 6.023.1023)

1 a.m.u. (atomic mass unit) = 1/12 m (C12) = 1.66.10-24gm

The nucleus has A nucleons Z of these are protons (1H

1!p) What is the rest, (A-Z) ?

!

Discovery of the neutron (Chadwick, 1932): 2He4+ 4Be9"6C12+ 0n1, or Be9(#,n)C12 Neutral (uncharged) radiation

Interaction with hydrogenous materials results in emission of protonsElastic scattering of the neutral particles mn~ mp~ 1 a.m.u. (n: 1.0087, p: 1.0073)

! Nucleus:ZXA Z protons, (A-Z) neutrons

Isotopes: same Z, different A e.g. 1H1(99.985%), 1H

2(0.015%)

..

92U234(0.006%), 92U

235(0.72%), 92U238(99.27%)


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Introduction.. 7



Chart of the Nuclides

! Stability of nucleus depends on N/Z For light stable atoms, N~Z

For Z>20, N>Z: strongly attractive forcebetween nucleons compensates repulsive

coulombian force between protons

!

Unstable nuclei, radioactive (natural, artificial) ZX

A!Z-2YA-4+ 2He

4 (!-decay) .. heavy ZX

A!Z+1YA+ e-+ "o (#

--decay) .. n-rich ZX

A*! ZXA+$ ($-decay) .. excited

-------

Also #+, EC


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Introduction.. 8



Radioactivity Calculations-1

! Spontaneous disintegration (decay) of a nucleus radioisotope, radionuclide

! Often encountered in nuclear engineering

Nuclear fuel, activation of materials, fission products, wastes

! Fundamental law: (!: decay constant)

! Units of (radio)activity:

Historical.. 1 curie (Ci) = 3.7 x 1010dis/s (activity of 1 gm of Ra226)

Actual.. 1 becquerel (Bq) = 1 dis/s

For example: 1 mCi = 10-3Ci = 3.7 x 107Bq = 37 MBq


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Radioactivity Calculations-2

! By integration of

! Half-Life : time for N(t) or A(t) to become half initial value


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Nuclear Reactions-1

! Radioactivity, particular example of a nuclear reaction

Single reactant (cf. chemical dissociation)

! In general, X1 + X2 ! X3 + X4

Number of nucleons remains constant

Electric charge remains the same

! One sees this in the example of 2He4+ 4Be

9"6C12+ 0n

1

! Reaction used for laboratory sources of neutrons, e.g. Ra-Be, Pu-Be,


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Introduction.. 11



Nuclear Reactions-2

! Energy balance of reaction depends on binding energy of the nucleons

on mass defects ("m) of the individual nuclei

!

Mass of nucleus (bound nucleons) < Sum of masses of isolated nucleons

Mass defect: "m (X) = Z.mp + (A-Z).mn - mX

! Binding energy: Eb = "m.c2 (Einstein)


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Introduction.. 12



Atomic Mass, Mass Defect, Binding Energy

! Eb/A, measure of force between nucleons

!

Sharp increase at low A value, broad

maximum at ~ A=50

! Reactions which result in a shift towards

the broad maximum Eb , #m increase (products more stable) Energy released (reaction: exoenergetic)

! Two possibilities:

Fusionof light nuclei, e.g.

1H2+ 1H

2! 1H

3+ 1H1

Fissionof a heavy nucleus, e.g.

92U235+ 0n

1! 2 F.P. + (2 to 3) 0n

1

Binding energy / nucleon

!fission

"

fusion


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Introduction.. 13



Reaction Energy-1

! For fission (from the figure):

Eb/A $ 7.5 MeV/nucleon for 92U235

$ 8.4 MeV/nucleon for the FPs

Increase in Eb/A $ 0.9 MeV/nucleon

Release energy $ 0.9 x 235 ! 210 MeV

! In general, for a reaction X1 + X2 ! X3 + X4

Energy of reaction : Q = (Eb)3 + (Eb)4 - (Eb)1 - (Eb)2

= (#m.c2)3 + (#m.c2)4 - (#m.c

2)1 - (#m.c2)2

= (m1 + m2 - m3 - m4).c2

!fission


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Introduction.. 14



Reaction Energy-2

! Energy / mass equivalence : 1 amu $1.66.10-24g x (3.1010cm/s)2

= 1.492.10-3erg = 931 MeV

!Q = (m1 + m2 - m3 - m4).c

2

= 931. (m1 + m2 - m3- m4) MeV

! Example : 1H2+ 1H

2! 1H

3+ 1H1 ... (d,d) fusion reaction..

Q = 931. (2.0141 + 2.0141 3.0166 1.0073) MeV

$ 4.0 MeV


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Introduction.. 15



Ex. 1

What is the mass of U235fissionedper day in a nuclear reactor operating at a power of

1000 MWth?

(Take energy liberated per fission, Ef"210 MeV)


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Introduction.. 16



Ex. 1... Solution

Energy liberated per day = (1000.106 J/s) . (24 . 3600 s) = 8.64.1013J

Energy per fission of a U235nucleus = 210 MeV = 210.106 . 1.6.10-19J = 3.36. 0-11J

No. of nuclei fissioned per day = (8.64.1013) (3.36.10-11) = 2.57.1024

Mass of U235fissioned per day = (2.57.1024) . (235 g NA)

= (6.04.1026) (6.023.1023) $1 kg

NB: The quantity of oil needed would be"

2000 t !


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Introduction.. 17



Flux of Particles, Interaction Rate

! Fission, fusion are exoenergetic What is their probability of occurrence?

! Monoenergetic particle beam & a target Density of particles in beam = n (cm-3)

Intensity (flux, cm-2 s-1),I = n v

(v : velocity, cm s-1)

! Total interaction rate with nuclei in target

R %I N V = &I N V (V : volume of target, cm3)

! &: cross-section, probability of interaction Depends on type, particle energy Pro target nucleus, r = &I (&: microscopic c-s)

!

Pro cm3 of target, R = &NI = 'I

(': macroscopic cross-section)


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Cross-sections: Dimensions, Units

!&: dimensions of an area (cm2)

r (per nucleus, s-1) = &(cm2) . I (cm-2 s-1)

Effective area offered by the nucleus for the interaction-type involved

Unit : 1 barn (b) = 10-24 cm2

!

Values vary $from hundreds of barns to a few millibarns (mb)

! For ' (&N), dimensions: cm-1

R (cm-3 s-1) = '(cm-1) . I (cm-2 s-1)

!

': effectively the probability of interaction as particle traverses 1 cm of target


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Types of Interactions

! Scattering

The particle is deviated

The target nucleus:

Does not change (elastic scattering))

Is excited (inelastic scattering)

!

Absorption

The particle is absorbed by the nucleus, the products are new, e.g.

Radiative capture: ZXA+ 0n

1"ZXA+1+ (

Fission, a special case:

92U235+

0n1

!

2 F.P. + (2 to 3)

0n1

Other types (less important):

(n,2n), (n,3n), (n,#),


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Cross-section Notations

!

Scattering: &s

!Absorption: &a &a = &f+ &c (fission, capture)

! Total cross-section: &t &t = &s + &a = &s+ &f+ &c

! Macroscopic cross-sections : 't= N&t , 'a= N&a , 'f= N&f , etc.

! For a mixture of nuclei: 't= , etc.Nj "t( ) j[ ]j

#


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Introduction.. 21



Ex. 2

!A beam of 1 MeV neutrons, with an intensity of 5108ncm-2s!1strikes a

carbon target ( "100% C12, density "1.6 g/ cm3). The surface area of the target

is 0.5 cm2and its thickness is 0.05 cm. The beam has a cross-sectional area of

0.1 cm2. For 1 MeV neutrons, the total cross-section of C12is 2.6 b.

(a) Calculate #t for the target

(a) What is the macroscopic interaction rate of the neutrons with the target?

(b) What is the number of interactions per second in the target?

(b) What is the probability that a neutron will suffer a collision while traversing thetarget?


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Ex. 2 Solution

(a) %t = &t N = (2.610-24 )

[1.6(6.0231023)/ 12]

= 2.610-24[8.031022] = 0.209 cm-1

(b) Rt = %t'= 0.2095108= 1.04108 cm-3s-1

(c) No. of interactions = RtVolume

=1.04108[0.10.05] = 5.2105 s-1

(d)Probability of interaction = (5.2105 s-1) / (No. of neutrons incident per s)

= (5.2105) / [(5108)0.1] = 1.0410-2 (only $1%)


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Introduction.. 23



, Functions of Energie, e.g.

! &(U235) )as neutron energy *

No resistance from electrostatic field

of the nucleus

!

Neutrons slowed down in a reactor(use of a moderator)

! Lowest energy possible: ns in thermal

equilibrium with moderator atoms:

Eth$0.0235 eV at 20C

+ &f$600 b!


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Introduction.. 24



Fission, Fusion Differences

! For fusion reactionse.g. (d,t): 1H

2+ 1H3"2He

4+ 0n1 (d,d): 1H

2+ 1H2"1H

3+ 1H1

&= 0 for E Eth)

! Scattering, a big help in fission (slowing down), great disadvantage in fusion

! Solution: have a thermal equilibrium with Eth >Es ($10 keV "108 K !)

The ionised medium needs to be heated tremendously (plasma)

"Thermonuclear fusion still a great technological challenge!


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Introduction.. 25



Fission: History - 1

! Following the discovery of the neutron

Fermi studied the activation of the elements (neutron capture)

ZXA + 0n

1!ZXA+1!(,--decay)! Z+1Y

A+1 + ( artificial radioactivity

each time, one observed a transmutation

occurred more easily if the neutron was first slowed down

! With U (Z = 92), one expected to create transuranics (Z = 93, 94,)

Instead, one (initially) found nuclei of intermediate mass (e.g. Ba, Z = 56)


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Introduction.. 26



Fission: History - 2

! Otto Hahn and Fritz Strassmann provided the explanation (1939)

The U235 nucleus can be split into 2 fragments (discovery of fission)

92U235 + 0n

1!2 FPs + . 0n1+ 207 MeV

The emission of , i.e. $2.5, neutrons

gave the possibility of a chain reaction

Neutron excess "related to shape of

the Z-vs.-N curve of the nuclide chart !

"

"


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Introduction.. 27



Fission Products - 1

!

Asymmetric splitting, more probable

! Considering FPs from 100 fissions

Yield y(A), with Sum [y(Ai)]= 200

y(A) vs. A: double-hump curve

Most probable, FPs with Ai$94, 140

e.g. 92U235

+ 0n1!

38Sr94

+ 54Xe140

+ 2 0n1


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Introduction.. 28



Fission Products - 2

! The FPs are unstable (excess of ns)

,--radioactivity (increases Z/N), e.g.

54Xe140!(16s) 55Cs

140!(66s) 56Ba140!(12.8d) 57La

140!(40h) 58Ce140 (stable)

! Radioactivity of FPs problematic

Radiation protection (irradiated fuel)

Residual heat after reactor shutdown


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Introduction.. 29



Fission Neutrons-1

! neutrons created per fission (number varies between $0 and 5, per event)

Average value $ 2.4 to 2.9

! Energy of the fission neutrons varies Spectrum -(E)

"


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Fission Neutrons-2

! E for -max $0.75 MeV

! Eaverage:

!

Slowing down factor in a thermal reactor > 107

! ($2 MeV to 0.0253 eV)

Moderators needed (light nuclei: H2O, graphite,)


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Chain Reaction

! If each absorption were useful

+Reaction strongly divergent

! In practice, certain neutrons are lost

+Captures, Leakage! For a self-sustaining reaction (static neutron flux)

Productions = Losses = Absorptions + Leakage

(criticality condition)

! For a supercritical system, the neutron flux increases exponentially


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Control of the Chain Reaction Delayed Neutrons

!

Small fraction of the neutrons, not prompt (~ 0.6% for U235)

Produced by disintegration of FPs, e.g.

! Many different precursors

~ 6 groups (of precursors, i.e. of delayed neutrons), Ti: 0.2 56 s

! Population of delayed neutrons, rather limited (~ 0.6%), bit indispensable for control

of the chain reaction

+ Response of a reactor which becomes slightly supercritical, much slower

created (

with delay


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Introduction.. 33



Fission Energy

! Most, absorbed in the fuel

~ 180 to 190 MeV (FPs, ,-s, part of (s ), in

form of heat (recovered by coolant)

!

Following reactor shutdown

Component FP-radioactivity remains

~ 7% immediately after shutdown

Slow decrease

~ 1% after 1 day

(Very important factor for nuclear safety)

Components Energy

(MeV)

FPs 168

ns 5

(s 7

FP-radioactivity (,-, () 15

Neutrinos (non-interacting) 12

TOTAL ~ 207


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Summary, Week 1

! Nucleus: protons + neutrons (atomic number Z, atomic mass A)

! Radioactivity, specific type of nuclear reaction (spontaneous disintegration)

!

Energy in a nuclear reaction: linked to binding energies (mass defects) of reactants

- Fission, fusion: movement towards the large maximum of the BE-curve

! Different types of reactions: absorption (fission, capture,), scattering

!

Reaction rate = Flux x Cross-section (microscopic, macroscopic)

!

Fission discovered relatively soon after discovery of neutron

!

On average, (2 to 3) ns emitted per fission chain reaction rendered possible

!

Small fraction of neutrons delayed: crucial for reactor control

!

Most of fission energy deposited in fuel (as heat)

"

nuclear physics basics

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