Principi fisici dell’energia nucleare

F.V. Frazzoli

Giornata di studioEnergia nucleare - Nuove prospettive ed opportunità

Terni 7Marzo 2008

• energy - electron-volt1 electron-volt = kinetic energy of an electron when

moving through potential difference of 1 Volt;• 1 eV = 1.6 × 10-19 Joules• 1 kW•hr = 3.6 × 106 Joules = 2.25 × 1025 eV• 1 MeV = 106 eV

• mass - eV/c2

• 1 eV/c2 = 1.78 × 10-36 kg• electron mass = 0.511 MeV/c2

• proton mass = 938 MeV/c2

• neutron mass = 939.6 MeV/c2

• amu = (mass of 121266CC atom)/12

• amu = 1.66 x 10-27kg • amu = 931.494 MeV/c2

About Units

• Proton – Charge = 1 elementary charge e = 1.602 x 10-19 C– Mass = 1.673 x 10-27 kg = 938.27 MeV/c2 =1.007825 u

= 1836 me– spin ½, magnetic moment 2.79 eħ/2mp

• Neutron– Charge = 0– Mass = 1.675 x 10-27 kg = 939.6 MeV/c2 = 1.008665 u =

1839 me– spin ½, magnetic moment -1.9 eħ/2mn

Properties of Nucleons

Symbolism

XAZ

• X: Chemical symbol of the element• Z : Atomic number = number of protons in nucleus• A: Mass Number = Z+N

• N: Number of neutrons in nucleusExample:

» Mass number is 27» Atomic number is 13» Contains 13 protons» Contains 14 (27 – 13) neutrons

Al2713

n-p and p-p interactions

Beta- DecayAZ A(Z+1) + e- + an anti-neutrino

• A neutron has converted into a proton, electron and an anti-neutrino.

Beta+ DecayAZ A(Z-1) + e+ + a neutrino

• A proton has converted into a neutron, positron and a neutrino.

Electron CaptureAZ + e- A(Z-1) + a neutrino

• A proton and an electron have converted into a neutron and a neutrino.

~9944

9943 ν++→ −eRbTc

ν++→ +eCN 126

127

ν+→+ − CeN 126

127

Radioactivity

• Alpha DecayAZ A-4(Z-2) + 4He

• Number of protons is conserved.• Number of neutrons is conserved.

• Gamma EmissionAZ* AZ + γ

• An excited nucleus loses energy by emitting a photon.

HePbPo 42

20682

21084 +→

)140(9943

*9943 keVTcTc γ+→

• Activity A: number of decays per unit time

• decay constant λ: probability of decay per unit time

• Rate of decay ∝ number N of nuclei

• Solution of diff. equation (N0 = nb. of nuclei at t=0)

• Mean life τ = 1/ λ

Law of radioactive decay.

dtdNA =

.NdtdN λ−=

.)( 0teNtN λ−=

λτ

λ

λ

1

0

0 ===

∫

∫

∫∫

∞−

∞−

dte

dtet

dN

dNt

t

t

• The decay curve follows the equation– N = No e- λt

• The half-life is also a useful parameter– The half-life is defined as the

time it takes for half of any given number of radioactive nuclei to decay

Decay Curveλλ

0.6932ln21 ==T

Radioactive Decay Paths

• It has a single bound state with a binding energy of 2.22463 ± 0.00004 MeV, which is measured with

- the formation reactions

- or inverse reaction

γ dn p +→+

n p d +→+γ

Properties of the Deuterium

ΔE = Nuclear binding energy = ∆mc2

1 proton 1.00728 u1 neutron 1.00866 u mass of deuterium:2.01355 u

________mass of parts: 2.01594 u missing mass 0.00239 u

The photon released in forming deuterium has anenergy of 2.225 MeV, equivalent to the 0.00239 u

PH320 APPLIED NUCLEAR PHYSICS PH320 APPLIED NUCLEAR PHYSICS –– PartPart 1 1 –– INTERACTIONS INTERACTIONS 17

~0.025eV THERMAL ~1eV EPITHERMAL ~1keV SLOW 100 keV – 100 MeV FAST >100 MeV HIGH ENERGY

They are calledthermal because they

are in thermalequilibrium with their

surroundings

Neutrons are classified in vague groups depending on their kinetic energy

1 keV 10 keV 100 keV 1 MeV 10 MeV

Fission

NuclearReactions

Radiative Capture

Elastic Scatter

Inelastic Scatter

Neutron energies

σ: Microscopic Cross Section

• Units: cm2

• Describes the theoretical “size” that an atom presents, like a target, to be hit by an approaching neutron

• Frequently reported in “barns”• 1 barn = 10-24 cm2

H1 σ (n,el)σ (n,γ)

Reaction Rate (R)

• Basic Equation:

R=NΦσ

interactions/cm3•s

atoms/cm3

neutrons/cm2•s

cm2

( ) neutronsYXUnU ++→→+*236

9223592

σ (n,f)fissile isotopesU233, U235, Pu239

σ (n,f)fertile isotopesTh232, U238

Prompt Fission Neutron Energy Spectrumfor Thermal Fission of Uranium-235

Delayed neutron emission

σ (n,f) U235, σ (n,γ) U235

ν: number of neutrons per fissionη: number of neutrons in fission per neutron absorbed

3.042.582.51

Fast (>0.5 MeV)

2.932.492.42

Thermal (0.025eV)

ν

239Pu

233U

235U

Isotope(100%)

2.902.152.402.292.352.07

Fast (>0.5 MeV)

Thermal (0.025eV)

η

fa

f

σσ

αα

νσσ

νη γ=+

=×= ,1

• Thermal fission U235 • LWR reactor (PWR)

JMeVQ

bbf

af

11102.3200:07.2:42.2:

%5.17:,681:,584:

−=

=

ην

σσ

ασσ γ

yearperrefuelling

tonUGWdupburnfuelwatercoolant

tonfueltotalCdInAGorCBrodcontrol

UUOfueldiametermlengthmcore

MWpowerelectricalefficiency

MWpowerthermal

e

th

31:

/33::

115::

)%3.3(:)(4.3),(2.4:

1300:%34:

3800:

4

2352

−

−−

⇒≈

⇒≈

dUKgdfissions

/7.4/10

235

25

Properties of some important moderators

0.00450.0010.66σa (barns)

4.710.643.8σs (barns)

1153620no. of collision tothermalize

fissionneutrons

GraphiteHeavywaterD2O

WaterH2O

Kinetic Energy of Fission Products 167 MeV Energy of Fission Neutrons 5 “Instantaneous Gamma-rays Energy 5 “Capture Gamma-rays Energy 10 “Beta Particles From Fission Products 7 “Gamma-rays from Fission Products 6 “

_________200 MeV

Recoverable Energy from Fission

Neutron cycle in reactor

Follow the fate of a neutron from one generation to the nextwith conditional probabilities of various loss mechanisms.

Fissionneutron

Leak out of system

Absorbed in system

Absorbed in fuel

Radiativecapture

Fission

Absorbed innon-fuel

ν new fission neutrons

Neutron Economy Equation

LCRRdtdn −−×+−×= )1( αν

neutrons/fission

fission rate

capture-to-fission ratio

fertile conversion rate

neutron loss rate

σ (n,f)U235, U238

σ (n,γ)U235, U238

Conversion or Breeding

238 23992 92U Un γ+ → +

23993 Np β ν−+ +

23.5min

23994 Pu β ν−+ +

2.35 d

24110 yr

Fertile:

Fissile:

232 23390 90Th Thn γ+ → +

23391Pa β ν−+ +

22.3min

23392 U β ν−+ +

27.0 d

159200 yr

average number of neutrons/absorption for breeding

21

1)(

)(>

+×=×=

αν

σσνηabsorption

fission

Characteristics of spent fuel

• Highly radioactive– Emits very strong radiation – needs shielding– Emits heat – needs cooling– Contains many different nuclides – with very

different half life (seconds to millions of years)

• Contains valuable material (U, Pu)

Composition of a PWR assembly

Fresh Fuel

Spent Fuel

Uranium (4% 235U) : 500 kg

Uranium (0,9% 235U) : 475 kg Pu : 5kg FP : 20 kgrecyclables

480 Kg U238+20 Kg U235

470.7 Kg U238+4.3 Kg U235

1E+00

1E+01

1E+02

1E+03

1E+04

1E+05

1E+06

1E+07

1E+08

1E+09

10 100 1 000 10 000 100 000 1 000 000

Time (years)

Pote

ntia

l rad

ioto

xici

ty*

(Sv/

thm

) Classic glass (MA + FP)

Spent fuel without reprocessing(Pu + MA + FP)

Light glass (FP)

Initial Uranium in mined ore

* as if incorporated, per tonnes of heavy metal

Partitioning & Transmutation• P&T is a potential HLW

management strategy toprocess the waste bypartitioning specific hazardouselements or nuclides and thentransmuting them into lesshazardous forms

• P&T aims to reduce the radiotoxicity of disposed wasteor reduce the duration forwhich the waste represents a threat to the environment

Transmutation technologies under investigation:

• neutron flux in a fast reactor• neutron flux in a thermal reactor• fast sub-critical reactor coupled

to a particle accelerator

Np237 burning with fast and thermal neutron fluxes