Nuclear Energy

Primary energy: Energy sources found in nature (coal, oil, etc.)

Secondary energy: Energy derived from primary energy (Electricity)

Energy mix: combination of energy sources for energy demand

Energy carrier: substance or system that stores or transports energy (Electricity, Batterie, gasoline)

2 reactants -> two products

1. Total mass-energy.

2. Linear and angular momentum.

3. Charge.

4. Number of Nucleons and Leptons (e.g. electrons).

5. Matter-antimatter balance.

A compound nucleus is a short-lived, highly excited intermediate nucleus formed when an incident particle (like a neutron or proton) is completely absorbed by a target nucleus before it decays into final products.

E_x < 40 MeV

Scattering of neutrons to reduce their energy step by step until they reach thermal equilibrium

The best Moderators are Light Atoms: 𝑨 small

—> Therefore H

Stable nuclide turns into radioactive ones (compound nucleus)

—> can be useful to breed fuel

—> to remove neutrons

—> or shielding against neutron radiation

1. Low Energy Region (1/v region). —>sigma = C_2*1/V

2. Low-to-Middle Energy Region (Resonance region).

3. Middle-to-High Energy Region (Fast region)

Resonance Peaks occur when the neutron kinetic energies + the neutron binding energy have values that coincide with quantum nuclear energy levels

—> neutrons are more likely to be absorbed here

Fission increases the Binding Energy per Nucleon: Energetically Favourable

spontaneous fission: by alpha particles

Neutron-induced fission

Breeding: Nuclei can be converted into fissile nuclei by absorbing slow neutrons

• The mass number of fission fragments ranges from 70 to ~170

• probability that a fission fragment is a nuclide with mass number A

higher energy less asymetry

The kinetic energy of the two fission fragments must equal.

conservation of momentum

Prompt Neutrons:

• Released within 10-14 s

Delayed Neutrons:

• Small fraction (1% ) of neutrons are emitted as delayed neutrons: they are emitted with energies about 2MeV .

• They come from the Decay of Fission Products

Without delayed neutrons, the operation would be impossible because of the reaction time needed

The AVERAGE energy is ~ 2 MeV

heat caused by the fission products

leakage

absorption

(chain)-reaction

We want to know n´ after n neutrons have been produced

Probability that a Fast Neutron Slows down without being absorbed

Lis the thermal diffusion length: one-half of the average distance diffused by a thermal neutron before it is absorbed.

Bc^2 is the “Critical Buckling”: Related to the Geometry of the Reactor.

f is the Probability that the neutrons are absorbed by the fuel.

Number of FAST neutrons produced per absorbed neutron in fuel.

Measure with the effective multiplication factor

The infinite multiplication factor doesn’t account for leakage

—>

With 0.72 atom-% of 235U and ~99.3% of 238U the probability of resonance absorption is very high: too much 238U in the core (low p)

f also too low to compensate

—> only heavy water can be used as a moderator for natural uranium

We surround the core with a material with a HIGH scattering-to-absorption cross section: REFLECTOR

Fast: MeV range

Thermal: 0.025 eV to 10 eV range

—> Thermal reactor needs Moderator

Herny Becquerel

Marie and Pierre Curie and Ernest Rutherford

Rutherford, Walton & Cockford

J.J. Thompson

Chadwick

Otto Hahn

Chicago Pile-1 (CP1) —> 1942 from Fermi

PWR in navy reactors precursor for commercial PWR reactors

Breeder reactor 1 1951 four 200-Watt lightbulbs

Kinetic Energy of an electron accelerated in a potential of 1V

1/12 of the mass of the neutral ground-state atom 12C

1amu (or u) = 1,6605387*10^-27

A: Number of Nucleons

Z: Number of Protons

N: A-Z Number of Neutrons

X: Chemical symbol

External negatively charged atomic orbital shells

Positively charged atomic Nucleus

ratio of the atoms molecules mass to 1/12 of neutral atom of 12C

Needed if there is more than one isotope present

To calculate A

The number of atoms(nuclei) per unit volume of a substance

Number of atoms / cm^3

Probability of interaction per unit distance traveled

Depends on:

• Type of interaction

• Particle’s kinetic energy

• Material

  • Density

  • Nuclear and Atomic structure

Many mu_i not only one!!!

total amount:

The attenuation of a particle beam depends of its probability of interaction P(dx)

The Probability of Interaction in a distance dx is

Shows how a quantity decreases as it passes through a medium

The probability distribution for HOW FAR a neutral particle travels before interacting

Thickness of a medium required for HALF of the incident radiation to experience an interaction.

the cross section represents the probability of a nuclear interaction occurring between an incoming particle (like a neutron) and a target nucleus. It is measured in barns (b), where 1 barn = 10^−28 m^2

Microscopic (σ in barns):

Represents the probability of interaction per single nucleus

Macroscopic (Nσ in cm^-1):

Represents the total probability of interaction per unit length in a material.

N = Atomic number density

The Microscopic Cross Sections are a function of the energy of the particle.

The reaction rate density (often simply called the reaction rate) is a measure of the number of nuclear reactions occurring per unit volume per unit time in a material

1. COMPTON SCATTERING

• Elastic scattering of a photon by an electron.

• The energy of the photon 𝐸 is reduced to 𝐸′

2. PHOTOELECTRIC EFFECT

• A gamma-photon interacts with “ALL THE ATOM“:

• Atoms recoils (Moves backwards).

• 1 atomic electron is ejected: photoelectron.

3. PAIR PRODUCTION

Interaction with the electric field of the Nucleus

• The photon transforms its energy into MASS

• An electron and a positron appear.

They are all Linear Attenuation Coefficients

LET - Amount of energy deposited by a charged particle per unit length

Range - Total distance a particle can travel in a material before losing all its energy

HIGH LET RADIATION: alpha-particles, fission products (Neutrons), heavy ions.

LOW LET RADIATION: electrons, protons and positrons

The ranges of alpha-particles are very short

Most alpha-particles are stopped by a sheet of paper and the skin

beta particles: Less massive particles, more deflection zig-zagpaths compared to alpha

beta -particles are more strongly deflected because they are lighter.

Nuclear Fission produces two fragments of Unequal mass.

The distribution of kinetic energy has two peaks

A~95 at 100 MeV

A~140 at 68 MeV

Alpha-particle bragg curve:

energy loss of charged particles as they travel through a medium.

Peak at the end because they slow down

Utilization of the Energy released by

• Radiation

• Controlled Fission Chain Reaction in the REACTOR CORE.

Fission occurs when heavy nuclei (e.g. 235U) split into elements with lower mass.

• ABSORPTION reactions.

• LEAKAGE.

• DELAYED NEUTRONS.

Binding energy is the energy required to break apart a nucleus into its individual protons and neutrons.

It represents the strong nuclear force that holds the nucleus together

When new atoms form this energy is released

delta M is the mass defect.

heavy atoms have lower binding energy

when fission occurs the products have lover mass because of the higher binding energy required

no for higher amounts of nuclides w_Z > w_N

For A < 56 FUSION is energetically possible

For A > 56 FISSION is energetically possible.

It is a model describing the mass-energy balance:

• It allows to correlate nuclear masses and binding energies

• it is useful in explaining nuclear fission and nuclear reactions

The shell model describes the nucleus as nucleons (protons and neutrons) arranged in discrete energy levels or shells, similar to electron orbitals in atoms, with certain "magic numbers" of nucleons leading to extra stability

• Stability is increased when neutrons and protons are both paired

1. Elastic Scattering: important for MODERATION.

2. Inelastic Scattering: important for MODERATION.

3. Neutron Absorption or Capture: important for CHAIN REACTION CONTROL; and BREEDING of 239Pu and 233U.

4. Nuclear Fission: important for ENERGY PRODUCTION. 19 and Radioactive Decay: important for DECAY HEAT.

increase: Supercritical

decrease: subcritical

• Changes in temperature

• Change is fuel composition

  • decrease of fuel over time

  • more fission products

• Insertion of neutron absorbers

  • Control rods (quick turn on/off)

  • Chemical substances

  • Burnable neutron poisons (absorb neutrons —> after the formed isotopes don’t absorb anymore)

• Short time: seconds or minutes

  • changes in fuel composition ignored

  • perturbations of the reactor conditions cause reactor transients

  • object of for safety analysis calculations

• Medium time: hours to about 2 days

  • Changes in main fuel composition are still ignored.

  • Changes in the amount of some fission products by radioactive decay must be accounted for

  • Long transients; 135Xe-149Sm induced power oscillations.

• Long time: over days or months

  • Changes in fuel composition must be taken into account.

  • Fuel depletion (reduction of fissile material content) and fuel management analysis (when to change the fuel and how to place it in the core)

  
  

It measures the deviation of a reactor from criticality

Reducing the reactivity as temperature increases is crucial for preventing dangerous power excursions or overheating

Practically with an increase of temperature, the reactivity reduces through the lower moderator density which expands because of the heat and because of the Doppler broadening. This increases the probability of neutron absorption without causing fission

• Fuel burn-up

  • eta, f and therefore k_eff decreases —> reactivity rho < 1

• Fuel Breeding

  • Production of fissile nuclides by absorption of neutrons by fertile nuclides

  • eta, f and therefore k_eff increases —> reactivity rho > 1

• Fission Product accumulation

  • Fission products and their daughters absorb neutrons and decrease the Thermal Utilization Factor f

  • two examples with high thermal absorption cross section: 135Xe and 149Sm

• Burnable Poisons (absorbers)

  • neutron absorbers in the fuel assemblies 149Sm, 155Gd and 157Gd or in the moderator 10B —> all have large absorption cross section

  • Reduce over time —> increase in f

As the temperature of the core materials increases, their Maxwellian energy distribution shifts to higher energies (hotter):

—> MODERATED NEUTRONS follow the trend, since they are in thermal equilibrium.

—>

more fission for 239Pu and less for 235U

Very negative Reactivity reactor: very stable

The increase in fuel temperature causes an increase in the energy of the moderating H atoms embedded in the fuel pellets: neutrons are removed from the thermal region in large numbers

Changes in Resonance Interactions:

Mechanism

• Higher temperature increases the velocity of nuclei.

• Increases relative velocity thermal neutron-nucleus: „Doppler“.

• More thermal neutrons can interact with nuclei in the resonances.

• The effective cross section is increased Broadened (‟Doppler ”): more neutron ABSORPTION is possible.

reduces fast leakage

All elements with Z > 82(Pb) are radioactive

An unstable atom tries to reach a stable form through energy and matter release from the nucleus:

—> Sequence of radioactive decays by alpha or beta particles changing the atomic number and mass

no

behaves exponentially

Gamma decay

Alpha decay

Beta Particle Decay

Positron Decay

Electron Capture

Internal Conversion

Neutron Emission Decay

Proton Emission Decay

It is the probability of disintegration per unit time

It is the time it takes for a nuclide to decay to one-half of the initial number of atoms

The average time it takes for a nuclide to decay.

Activity A(t): In radioactive protection one is interested in the NUMBER OF DECAYS PER UNIT TIME

unit: Becquerel or Curie:

—> 1 Bq = one desintegration per second ; 1 Ci = 3,7*10^10 Bq (activity of 1g 226/88Ra)

Specific Activity Â:

Activity Normalized to the mass (g) of the radionuclide.

Bg or ci / g

Three main decay chains of Thoriumd Uranium and Actinium in the magnitude of My

Artificial radioactive sources are of concentrations that exceed natural sources

Natural radioactivity provides a reference benchmark to determine man-made harmful effects

Energetic material particles or photons that have the potential to IONIZE ATOMS OR MOLECULES through ATOMIC or NUCLEAR interactions.

The potential for causing ionization is a function of:

• THE ENERGY of the individual particles or photons, and

• NOTa function of the number of particles or photons present (intensity).

The energy required to ionize an atom or molecule varies:

• Alpha and b particles ionize because of electromagnetic interactions (ion tracks).

• Neutronsionize because of nuclear reactions.

• X-rays and gamma rays will ionize almost any molecule or atom;

• High energy ultraviolet photons can ionize molecules;

• Visible light ionizes, for instance, photographic film and some molecules involved in photosynthesis.

• Microwaves and radio waves are NON-IONIZING RADIATION.

Based on the ionization produced by x-Photons or gamma-photons in air —> Roentgen (R)

It is the ENERGY DEPOSITED by incident radiation in any material per unit mass

Absorbed Dose (D) —> Gray = 1J/kg or Rad = 100erg/g

1Gy = 100 rad

the deposition of 1 Gy of a-particles is more damaging than 1 Gy of b-particles —> caused by LET

recap LET (High: Alpha, heavy ions and neutrons; Low: X-rays, gamma rays and electrons)

—> Dose that takes into account the biological effect of radiation

units:

Sievert(Sv) if D in Gray

Rem(rem) if D in rad

radiation quality factor w_R depens on:

Type of Radiation (LET)

Type of biologial effect

Energy of radiation

• Radon(222Rn from 238U decay chain): ~ 1.26 mSv/y

• Terrestrial radiation (40K, U and Th series): ~0.48 mSv/y

• Radionuclides in the Body (40K): ~ 0.29 mSv/y

• Cosmic rays 0.38 mSv/y

• Cosmogenic Radionuclides: 0.01 mSv/y

Ionizing radiation causes atoms and molecules to become ionized or excited. These excitations and ionizations can:

• Produce free radicals that break molecules

• break chemical bonds

• produce new chemical bonds

• damage molecules that regulate vital cell processes

Yes, at low doses —> otherwise cancer

Fetus, blood-forming organs and gastrointestinal system

less bad for: Muscle, nervous system and Bone and teeth

Prompt effects (Deterministic): (immediately after large doses)

• Radiation sickness

• Radiation burns

Delayed effects (Stochastic): appear after months or years

• Caner

• Genetic effects

• Cataract formation —> blurred vision

The Linear No-Threshold (LNT) Hypothesis suggests that any amount of ionizing radiation, no matter how small, increases the risk of cancer and genetic damage linearly with dose, without a safe threshold

• As Low As Reasonably Achievable

Radiation standards and exposure limits

Safety: Freedom from Danger and Hazard

Risk: Chance of injury or loss

The prevention of the release of harmful amounts of radioactivity beyond the plant boundaries

Defense in depth:

• a series of successive barriers

• If one barrier is broken, the next one will contain the radioactive release

• The crystalline structure of the fuel.

• The metallic fuel rod clad.

• The closed circuit primary coolant system.

• The Reactor Vessel.

• The Containment.

• The selection of the place to build the power plant.

• The emergency and evacuation plans

• reliable system

• best practices and materials

• operate within regulations

“self-heal” —> fail towards safe state if possible.

• Quality Assurance

—> use of codes and standards

• Redundancy and Diversity.

Redundancy: Same system several times

Diversity: different methods to achieve the same result

• Inherent Reactor Stability.

Negative Temperature reactivity coefficients

• Reactor Protection Systems.

Purpose: To Shut the reactor down and maintain it in a safe condition in the event of a transient or malfunction that can cause damage to the core

• Reactor Trip Signals.

specific outputs from the protection system that initiates automatic protective actions

• Shut-down Cooling

Residual Heat Removal System (RHRS)

Emergency Core Cooling System

—> in case of Loss Of Coolant Accident (LOCA)

• Emergency Core Cooling System (ECCS)

• Containment

  • barrier for fission products

• Clean-up System

  • removal of radioactivity

• Hydrogen Control System

  • prevent formation of hydrogen-rich atmosphere (risk of detonation)

PWR

• High Pressure injection system

• Accumulator Injection System

• Low Pressure injection system

BWR

• High pressure core spray system

• low pressure core spray system

• low pressure injection system

• Withstand the pressure in case of LOCA

• Withstand the impact of missiles

• large margin of safety

1. Mining and Milling: produce uranium from ore (yellow cake)

2. Conversion: Uranium into U02 for HWR and UF6 for LWR

3. Enrichment: increase the concentration of 235U

4. Fuel fabrication: into fuel pellets

5. Electricity generation

6. (Optional) chemical reprocessing (after period of storage uranium and plutonium recovered for recycling)

7. Alternative storage: let radioactivity and heat diminish for up to 50 years

8. Final Disposal

1-4 Front End - before use

6-8 Back End - after use

uranium oxide (U3O8)

—> Uranium without the waste rock

For enrichment, the uranium needs to be gaseous —> Hexafluoride UF_6

• Thermal Diffusion (not used any more - energy intensive)

  • vertical film gets cooled and heated on the sides —> convection causes flow

  • light 235U gas molecules diffuse toward hot surface

• Gaseous Diffusion:

  • UF_6 gas is forced through a series of membranes (1400 stages for 3,4 %)

  • 235UF_6 lighter than 238UF_6 —> passes easier

  • very common method

• Centrifuge Separation

  • gas fed into vacuum tubes

  • fast rotation pushes heavy gas to the outside and 235UF_6 to the inside

• Electromagnetic Separation

  • Metallic uranium vaporized then ionized

  • —>Cations are deflected by a magnetic field and collected

• Laser Separation

  • Atomic vapor laser isotope separation (AVLIS)

  • —> Laser ionizes 235U atom with frequencies —> attracted to negatively-charged plate

  • Molecular laser isotope separation (MLIS)

  • —> Laser excites 235U atoms —> second laser frees a F atom leaving UF_5

Slightly enriched uranium (SEU)

• 235U concentration of 0.9% to 2%

• fuel in some heavy water reactors like the CANDU

Low-enriched uranium (LEU)

• Lower than 20% concentration of 235U

• For use in commercial light water reactors (LWR): 3-5%

• Fresh LEU used in research reactors is usually enriched 12% to 20% Maximum

Highly enriched uranium (HEU)

• has a greater than 20% concentration of 235U or 233U

• 90% or more of 235U is known as Weapon(s)-Grade

Burn-up is a measure for fuel efficiency. It refers to how much energy has been extracted from the fuel (Megawatt days per metric ton)

—> highly desirable reduces fuel, volume, and illicit diversion of plutonium

old reactors 40,000 MWd/MTU —> newer fuel technologies 60,000 MWd/MTU

Low-level waste LLW: (hospitals, laboratories and industry)

• small amounts, short lived —> low total activity

• not dangerous but careful disposal

• 90% of volume - 1% of radioactivity

Intermediate level waste ILW:

• may require special shielding

• resins, chemical sludge and irradiated reactor components

• 7% of volume - 4% of radioactivity

High-level waste HLW

• nine times the volume if fuel is not reprocessed

• requires cooling and special shielding

• 3% of volume and 95% of the radioactivity

1. A 9 meter free fall onto an unyielding surface

2. A puncture test allowing the container to free fall 1 meter onto a steel rod 15 centimeters diameter.

3. A 30-minute, all-engulfing fire at Celsius.

4. An 8-hour immersion under 800 degrees 0.9 meter of water.

5. Spent fuel in which an undamaged package must be subjected to a one-hour immersion under 200 meters of water

• Delayed for 40-50 years to let high amounts of radioactivity decay

• after that or even without decay: burial in dry, stable geological formations 500 underground

• with reprocessing: after 300 years radioactivity decayed

• Immobilize waste: borosilicate glass

• seal inside corrosion-resistant container

• surround the container with bentonite clay

• locate deep underground

convert long-lived isotopes into short-lived

fission products decay in 300 years - minor actinides and plutonium decay over thousand to million years

—> recycling of U and P

—> safer, more efficient and sustainable