Pc Chapter 45
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Chapter 45 Applications of Nuclear Physics
Processes of Nuclear Energy
Fission
Fusion
A nucleus of large mass number splits into two smaller nuclei Two light nuclei fuse to form a heavier nucleus
Large amounts of energy are released in either case
Interactions Involving Neutrons
Because of their charge neutrality, neutrons are not subject to Coulomb forces As a result, they do not interact electrically with electrons or the nucleus Neutrons can easily penetrate deep into an atom and collide with the nucleus
Fast Neutrons
A fast neutron has energy greater than 1 MeV During its many collisions when traveling through matter, the neutron gives up some of its kinetic energy to a nucleus For some materials and fast neutrons, elastic collisions dominate
These materials are called moderators since they moderate the originally energetic neutrons very efficiently
Thermal Neutrons
Most neutrons bombarding a moderator will be come thermal neutrons
They are in thermal equilibrium with the moderator material Their average kinetic energy at room temperature is about 0.04 eV This corresponds to a neutron root-meansquare speed of about 2 800 m/s
Thermal neutrons have a distribution of speeds
Neutron Capture
Once the energy of a neutron is sufficiently low, there is a high probability that it will be captured by a nucleus The neutron capture equation can be written as 1 0
n+ X→ A Z
A +1 Z
X* →
A +1 Z
X+γ
The excited state lasts for a very short time The product nucleus is generally radioactive and decays by beta emission
Nuclear Fission
A heavy nucleus splits into two smaller nuclei Fission is initiated when a heavy nucleus captures a thermal neutron The total mass of the products is less than the original mass of the heavy nucleus
This difference in mass is called the mass defect
Short History of Fission
First observed in 1939 by Otto Hahn and Fritz Strassman following basic studies by Fermi Lise Meitner and Otto Frisch soon explained what had happened
Fission Equation: 235U
Fission of 235U by a thermal neutron 1 0
236 n+ 235 U → 92 92 U* → X + Y + neutrons
U* is an intermediate, excited state that exists for about 10-12 s before splitting X and Y are called fission fragments
236
Many combinations of X and Y satisfy the requirements of conservation of energy and charge
Distribution of Fission Products
The most probable products have mass numbers A ≈ 140 and A ≈ 95 There are also an average of 2.5 neutrons released per event
Fission Event Described by the Liquid-Drop Model
A slow neutron approaches the 235U nucleus The 235U nucleus captures a thermal neutron This capture results in the formation of 236U*, and the excess energy of this nucleus causes it to deform and oscillate The 236U* nucleus becomes highly elongated, and the force of repulsion between the protons tends to increase the distortion The nucleus splits into two fragments, emitting several neutrons in the process
Fission Described by the Liquid-Drop Model – Diagram
(a) Approach (c) Oscillation
(b) Absorption (d) Fission
Energy in a Fission Process
Binding energy for heavy nuclei is about 7.2 MeV per nucleon Binding energy for intermediate nuclei is about 8.2 MeV per nucleon Therefore, the fission fragments have less mass than the nucleons in the original nuclei This decrease in mass per nucleon appears as released energy in the fission event
Energy, cont.
An estimate of the energy released
Releases about 1 MeV per nucleon
8.2 MeV – 7.2 MeV
Assume a total of 235 nucleons Total energy released is about 235 MeV This is the disintegration energy, Q
This is very large compared to the amount of energy released in chemical processes
Chain Reaction
Neutrons are emitted when 235U undergoes fission
An average of 2.5 neutrons
These neutrons are then available to trigger fission in other nuclei This process is called a chain reaction
If uncontrolled, a violent explosion can occur When controlled, the energy can be put to constructive use
Chain Reaction – Diagram
Active Figure 45.3
(SLIDESHOW MODE ONLY)
Enrico Fermi
1901 – 1954 Nobel Prize in 1938 for producing transuranic elements by neutron irradiation Other contributions include theory of beta decay, free-electron theory of metal, development of world’s first fission reactor (1942)
Nuclear Reactor
A nuclear reactor is a system designed to maintain a self-sustained chain reaction The reproduction constant K is defined as the average number of neutrons from each fission event that will cause another fission event
The maximum value of K from uranium fission is 2.5
In practice, K is less than this
A self-sustained reaction has K = 1
K Values
When K = 1, the reactor is said to be critical
When K < 1, the reactor is said to be subcritical
The chain reaction is self-sustaining
The reaction dies out
When K > 1, the reactor is said to be supercritical
A run-away chain reaction occurs
Reactor Fuel
Most reactors today use uranium as fuel
Naturally occurring uranium is 99.3% 238U and 0.7% 235U U almost never fissions It tends to absorb neutrons producing neptunium and plutonium
238
Fuels are generally enriched to at least a few percent 235U
Moderator
The moderator slows the neutrons
The slower neutrons are more likely to react with 235 U than 238U
The probability of neutron capture by 238U is high when the neutrons have high kinetic energies Conversely, the probability of capture is low when the neutrons have low kinetic energies
The slowing of the neutrons by the moderator makes them available for reactions with 235U while decreasing their chances of being captured by 238U
Pressurized Water Reactor – Diagram
Pressurized Water Reactor – Notes
This type of reactor is the most common in use in electric power plants in the US Fission events in the uranium in the fuel rods raise the temperature of the water contained in the primary loop
The primary system is a closed system
This water is maintained at a high pressure to keep it from boiling This water is also used as the moderator to slow down the neutrons
Pressurized Water Reactor – Notes, cont.
The hot water is pumped through a heat exchanger The heat is transferred by conduction to the water contained in a secondary system This water is converted into steam The steam is used to drive a turbinegenerator to create electric power
Pressurized Water Reactor – Notes, final
The water in the secondary system is isolated from the water in the primary system
This prevents contamination of the secondary water and steam by the radioactive nuclei in the core
A fraction of the neutrons produced in fission leak out before inducing other fission events
An optimal surface area-to-volume ratio of the fuel elements is a critical design feature
Basic Reactor Design
Fuel elements consist of enriched uranium The moderator material helps to slow down the neutrons The control rods absorb neutrons All of these are surrounded by a radiation shield
Control Rods
To control the power level, control rods are inserted into the reactor core These rods are made of materials that are very efficient in absorbing neutrons
Cadmium is an example
By adjusting the number and position of the control rods in the reactor core, the K value can be varied and any power level can be achieved
The power level must be within the design of the reactor
Reactor Safety – Containment
Radiation exposure, and its potential health risks, are controlled by three levels of containment: Reactor vessel
Reactor building
Contains the fuel and radioactive fission products Acts as a second containment structure should the reactor vessel rupture Prevents radioactive material from contaminating the environment
Location
Reactor facilities are in remote locations
Reactor Safety – Radioactive Materials
Disposal of waste material
Waste material contains long-lived, highly radioactive isotopes Must be stored over long periods in ways that protect the environment Present solution is sealing the waste in waterproof containers and burying them in deep geological repositories
Transportation of fuel and wastes
Accidents during transportation could expose the public to harmful levels of radiation Department of Energy requires crash tests and manufacturers must demonstrate that their containers will not rupture during high speed collisions
Nuclear Fusion
Nuclear fusion occurs when two light nuclei combine to form a heavier nucleus The mass of the final nucleus is less than the masses of the original nuclei
This loss of mass is accompanied by a release of energy
Fusion in the Sun
All stars generate energy through fusion The Sun, along with about 90% of other stars, fuses hydrogen
Some stars fuse heavier elements
Two conditions must be met before fusion can occur in a star:
The temperature must be high enough The density of the nuclei must be high enough to ensure a high rate of collisions
Proton-Proton Cycle
H+11H→21 H + e + + ν
1 1
The proton-proton cycle is a series of 1 2 3 1H+ 1H→ 2 He + γ three nuclear reactions believed to Then operate in the Sun 1 3 4 + Energy liberated is 1H+ 2 He→ 2 He + e + ν primarily in the form or of gamma rays, 3 3 4 1 1 positrons and He + He → He + H + 2 2 2 1 1H neutrinos
Fusion Reactions, final
Because high temperatures are required to drive these reactions, they are called thermonuclear fusion reactions All of the reactions in the proton-proton cycle are exothermic An overview of the cycle is that four protons combine to form an alpha particle and two positrons
Advantages of a Fusion Reactor
Inexpensive fuel source
Water is the ultimate fuel source If deuterium is used as fuel, 0.12 g of it can be extracted from 1 gal of water for about 4 cents
Comparatively few radioactive byproducts are formed
Considerations for a Fusion Reactor The proton-proton cycle is not feasible for a fusion reactor The high temperature and density required are not suitable for a fusion reactor The most promising reactions involve deutrium and tritium 2 2 3 1 H H H 1 1 2 0 n Q 3.27 MeV
H 21H 31H 11H Q 403 . MeV
2 1
H 31H 42 He 01n Q 1759 . MeV
2 1
Considerations for a Fusion Reactor, cont.
Tritium is radioactive and must be produced artificially The Coulomb repulsion between two charged nuclei must be overcome before they can fuse
Potential Energy Function
The potential energy is positive in the region r > R, where the Coulomb repulsive force dominates It is negative where the nuclear force dominates The problem is to give the nuclei enough kinetic energy to overcome this repulsive force
Critical Ignition Temperature
The temperature at which the power generation rate in any fusion reaction exceeds the lost rate is called the critical ignition temperature, Tignit
The intersection of the Pgen with the Plost line is the Tignit
Requirements for Successful Thermonuclear Reactor
High temperature ~ 108 K
Plasma ion density, n
Needed to give nuclei enough energy to overcome Coulomb forces At these temperatures, the atoms are ionized, forming a plasma The number of ions present
Plasma confinement time, τ
The time interval during which energy injected into the plasma remains in the plasma
Lawson’s Criteria
Lawson’s criteria states that a net power output in a fusion reactor is possible under the following conditions
nτ ≥ 1014 s/cm3 for deuterium-tritium nτ ≥ 1016 s/cm3 for deuterium-deuterium These are the minima on the curves
Requirements, Summary
The plasma temperature must be very high To meet Lawson’s criterion, the product nτ must be large
For a given value of n, the probability of fusion between two particles increases as τ increases For a given value of τ, the collision rate increases as n increases
Confinement is still a problem
Confinement Techniques
Magnetic confinement
Uses magnetic fields to confine the plasma
Inertial confinement
Particles’ inertia keeps them confined very close to their initial positions
Magnetic Confinement
One magnetic confinement device is called a tokamak Two magnetic fields confine the plasma inside the donut
A strong magnetic field is produced in the windings A weak magnetic field is produced by the toroidal current
The field lines are helical, they spiral around the plasma, and prevent it from touching the wall of the vacuum chamber
Fusion Reactors Using Magnetic Confinement
TFTR – Tokamak Fusion Test Reactor
NSTX – National Spherical Torus Experiment
Close to values required by Lawson criterion Produces a spherical plasma with a hole in the center Is able to confine the plasma with a high pressure
ITER – International Thermonuclear Experimental Reactor
An international collaboration involving four major fusion programs is working on building this reactor It will address remaining technological and scientific issues concerning the feasibility of fusion power
Inertial Confinement
Uses a D-T target that has a very high particle density Confinement time is very short
Therefore, because of their own inertia, the particles do not have a chance to move from their initial positions
Lawson’s criterion can be satisfied by combining high particle density with a short confinement time
Laser Fusion
Laser fusion is the most common form of inertial confinement A small D-T pellet is struck simultaneously by several focused, high intensity laser beams This large input energy causes the target surface to evaporate The third law reaction causes an inward compression shock wave This increases the temperature
Fusion Reactors Using Inertial Confinement
Omega facility
University of Rochester (NY) Focuses 24 laser beams on the target
Nova facility
Lawrence Livermore National Lab (CA) Focuses 10 laser beams on the target Has achieved nτ ≈ 5 x 1014 s/cm3
Fusion Reactor Design – Energy
In the D-T reaction, the alpha particle carries 20% of the energy and the neutron carries 80%
The neutrons are about 14 MeV
Active Figure 45.14
(SLIDESHOW MODE ONLY)
Fusion Reactor Design, Particles
The alpha particles are primarily absorbed by the plasma, increasing the plasma’s temperature The neutrons are absorbed by the surrounding blanket of material where their energy is extracted and used to generate electric power One scheme is to use molten lithium to capture the neutrons The lithium goes to a heat-exchange loop and eventually produces steam to drive turbines
Fusion Reactor Design, Diagram
Some Advantages of Fusion
Low cost and abundance of fuel
Deuterium
Impossibility of runaway accidents Decreased radiation hazards
Some Anticipated Problems with Fusion
Scarcity of lithium Limited supply of helium
Helium is needed for cooling the superconducting magnets used to produce the confinement fields
Structural damage and induced radiation from the neutron bombardment
Radiation Damage
Radiation absorbed by matter can cause damage The degree and type of damage depend on many factors
Type and energy of the radiation Properties of the absorbing matter
Radiation Damage, cont.
Radiation damage in the metals used in the reactors comes from neutron bombardment
They can be weakened by high fluxes of energetic neutrons producing metal fatigue The damage is in the form of atomic displacements, often resulting in major changes in the properties of the material
Radiation damage in biological organisms is primarily due to ionization effects in cells
Ionization disrupts the normal functioning of the cell
Types of Damage in Cells
Somatic damage is radiation damage to any cells except reproductive ones
Can lead to cancer at high radiation levels Can seriously alter the characteristics of specific organisms
Genetic damage affects only reproductive cells
Can lead to defective offspring
Damage Dependence on Penetration
Damage caused by radiation also depends on the radiation’s penetrating power
Alpha particles cause extensive damage, but penetrate only to a shallow depth
Due to their charge, they will have a strong interaction with other charged particles
Neutrons do not interact with material and so penetrate deeper, causing significant damage Gamma rays can cause severe damage, but often pass through the material without interaction
Units of Radiation Exposure
The roentgen (R) is defined as
That amount of ionizing radiation that produces an electric charge of 3.33 x 10-10 C in 1 cm3 of air under standard conditions Equivalently, that amount of radiation that increases the energy of 1 kg of air by 8.76 x 10-3 J
One rad (radiation absorbed dose)
That amount of radiation that increases the energy of 1 kg of absorbing material by 1 x 10-2 J
More Units
The RBE (relative biological effectiveness)
The number of rads of x-radiation or gamma radiation that produces the same biological damage as 1 rad of the radiation being used Accounts for type of particle which the rad itself does not
The rem (radiation equivalent in man)
Defined as the product of the dose in rad and the RBE factor
Dose in rem = dose in rad x RBE
RBE Factors, A Sample
RBE Factors, Notes
The values given for RBE factors are only approximate
They vary with particle energy and with the form of damage
The RBE factor should be used as only a first-approximation guide to the actual effects of radiation
Radiation Levels
Natural sources – rocks and soil, cosmic rays
Upper limit suggested by US government
Called background radiation About 0.13 rem/yr 0.50 rem/yr Excludes background
Occupational
5 rem/yr for whole-body radiation Certain body parts can withstand higher levels Ingestion or inhalation is most dangerous
Radiation Levels, cont.
50% mortality rate
About 50% of the people exposed to a dose of 400 to 500 rem will die
New SI units of radiation dosages
The gray (Gy) replaces the rad The sievert (Sv) replaces the rem
SI Units, Table
Radiation Detectors, Introduction
Radiation detectors exploit the interactions between particles and matter to allow a measurement of the particles’ characteristics Things that can be measured include:
Energy Momentum Charge Existence
Early Detectors
Photographic emulsion
The path of the particle corresponds to points at which chemical changes in the emulsion have occurred
Cloud chamber
Contains a gas that has been supercooled Energetic particles ionize the gas along the particles’ paths
Early Detectors, Cont.
Bubble chamber
Uses a liquid maintained near its boiling point Ions produced by incoming charged particles leave bubble tracks The picture is an artificially colored bubble chamber photograph
Contemporary Detectors
Ion chamber
Electron-ion pairs are generated as radiation passes through a gas and produces an electric signal The current is proportional to the number of pairs produced A proportional counter is an ion chamber that detects the presence of the particle and measures its energy
Geiger Counter
A Geiger counter is the most common form of an ion chamber used to detect radiation When a gamma ray or particle enters the thin window, the gas is ionized The released electrons trigger a current pulse The current is detected and triggers a counter or speaker
Geiger Counter, cont.
The Geiger counter easily detects the presence of a particle The energy lost by the particle in the counter is not proportional to the current pulse produced
Therefore, the Geiger counter cannot be used to measure the energy of a particle
Other Detectors
The semiconductor-diode detector
A reverse-bias p-n junction As a particle passes through the junction, a brief pulse of current is created and measured
The scintillation counter
Uses a solid or liquid material whose atoms are easily excited by radiation The excited atoms emit photons as they return to their ground state With a photomultiplier, the photons can be converted into an electrical signal
Other Detectors, cont.
Track detectors
Various devices used to view the tracks or paths of charged particles directly The energy and momentum of these energetic particles are found from the curvature of their path in a magnetic field of known magnitude and direction
Other Detectors, Final
Spark chamber
Is a counting device that consists of an array of conducting parallel plates and is capable of recording a three-dimensional track record
Drift chamber
A newer version of the spark chamber Has thousands of high-voltage wires throughout the space of the detector
Applications of Radiation
Tracing
Radioactive particles can be used to trace chemicals participating in various reactions
Example, 131I to test thyroid action Also useful in agriculture
Materials analysis
Neutron activation analysis uses the fact that when a material is irradiated with neutrons, nuclei in the material absorb the neutrons and are changed to different isotopes
Applications of Radiation, cont.
Radiation therapy
Radiation causes the most damage to rapidly dividing cells Therefore, it is useful in cancer treatments
Food preservation
High levels of radiation can destroy or incapacitate bacteria or mold spores
Processes of Nuclear Energy
Fission
Fusion
A nucleus of large mass number splits into two smaller nuclei Two light nuclei fuse to form a heavier nucleus
Large amounts of energy are released in either case
Interactions Involving Neutrons
Because of their charge neutrality, neutrons are not subject to Coulomb forces As a result, they do not interact electrically with electrons or the nucleus Neutrons can easily penetrate deep into an atom and collide with the nucleus
Fast Neutrons
A fast neutron has energy greater than 1 MeV During its many collisions when traveling through matter, the neutron gives up some of its kinetic energy to a nucleus For some materials and fast neutrons, elastic collisions dominate
These materials are called moderators since they moderate the originally energetic neutrons very efficiently
Thermal Neutrons
Most neutrons bombarding a moderator will be come thermal neutrons
They are in thermal equilibrium with the moderator material Their average kinetic energy at room temperature is about 0.04 eV This corresponds to a neutron root-meansquare speed of about 2 800 m/s
Thermal neutrons have a distribution of speeds
Neutron Capture
Once the energy of a neutron is sufficiently low, there is a high probability that it will be captured by a nucleus The neutron capture equation can be written as 1 0
n+ X→ A Z
A +1 Z
X* →
A +1 Z
X+γ
The excited state lasts for a very short time The product nucleus is generally radioactive and decays by beta emission
Nuclear Fission
A heavy nucleus splits into two smaller nuclei Fission is initiated when a heavy nucleus captures a thermal neutron The total mass of the products is less than the original mass of the heavy nucleus
This difference in mass is called the mass defect
Short History of Fission
First observed in 1939 by Otto Hahn and Fritz Strassman following basic studies by Fermi Lise Meitner and Otto Frisch soon explained what had happened
Fission Equation: 235U
Fission of 235U by a thermal neutron 1 0
236 n+ 235 U → 92 92 U* → X + Y + neutrons
U* is an intermediate, excited state that exists for about 10-12 s before splitting X and Y are called fission fragments
236
Many combinations of X and Y satisfy the requirements of conservation of energy and charge
Distribution of Fission Products
The most probable products have mass numbers A ≈ 140 and A ≈ 95 There are also an average of 2.5 neutrons released per event
Fission Event Described by the Liquid-Drop Model
A slow neutron approaches the 235U nucleus The 235U nucleus captures a thermal neutron This capture results in the formation of 236U*, and the excess energy of this nucleus causes it to deform and oscillate The 236U* nucleus becomes highly elongated, and the force of repulsion between the protons tends to increase the distortion The nucleus splits into two fragments, emitting several neutrons in the process
Fission Described by the Liquid-Drop Model – Diagram
(a) Approach (c) Oscillation
(b) Absorption (d) Fission
Energy in a Fission Process
Binding energy for heavy nuclei is about 7.2 MeV per nucleon Binding energy for intermediate nuclei is about 8.2 MeV per nucleon Therefore, the fission fragments have less mass than the nucleons in the original nuclei This decrease in mass per nucleon appears as released energy in the fission event
Energy, cont.
An estimate of the energy released
Releases about 1 MeV per nucleon
8.2 MeV – 7.2 MeV
Assume a total of 235 nucleons Total energy released is about 235 MeV This is the disintegration energy, Q
This is very large compared to the amount of energy released in chemical processes
Chain Reaction
Neutrons are emitted when 235U undergoes fission
An average of 2.5 neutrons
These neutrons are then available to trigger fission in other nuclei This process is called a chain reaction
If uncontrolled, a violent explosion can occur When controlled, the energy can be put to constructive use
Chain Reaction – Diagram
Active Figure 45.3
(SLIDESHOW MODE ONLY)
Enrico Fermi
1901 – 1954 Nobel Prize in 1938 for producing transuranic elements by neutron irradiation Other contributions include theory of beta decay, free-electron theory of metal, development of world’s first fission reactor (1942)
Nuclear Reactor
A nuclear reactor is a system designed to maintain a self-sustained chain reaction The reproduction constant K is defined as the average number of neutrons from each fission event that will cause another fission event
The maximum value of K from uranium fission is 2.5
In practice, K is less than this
A self-sustained reaction has K = 1
K Values
When K = 1, the reactor is said to be critical
When K < 1, the reactor is said to be subcritical
The chain reaction is self-sustaining
The reaction dies out
When K > 1, the reactor is said to be supercritical
A run-away chain reaction occurs
Reactor Fuel
Most reactors today use uranium as fuel
Naturally occurring uranium is 99.3% 238U and 0.7% 235U U almost never fissions It tends to absorb neutrons producing neptunium and plutonium
238
Fuels are generally enriched to at least a few percent 235U
Moderator
The moderator slows the neutrons
The slower neutrons are more likely to react with 235 U than 238U
The probability of neutron capture by 238U is high when the neutrons have high kinetic energies Conversely, the probability of capture is low when the neutrons have low kinetic energies
The slowing of the neutrons by the moderator makes them available for reactions with 235U while decreasing their chances of being captured by 238U
Pressurized Water Reactor – Diagram
Pressurized Water Reactor – Notes
This type of reactor is the most common in use in electric power plants in the US Fission events in the uranium in the fuel rods raise the temperature of the water contained in the primary loop
The primary system is a closed system
This water is maintained at a high pressure to keep it from boiling This water is also used as the moderator to slow down the neutrons
Pressurized Water Reactor – Notes, cont.
The hot water is pumped through a heat exchanger The heat is transferred by conduction to the water contained in a secondary system This water is converted into steam The steam is used to drive a turbinegenerator to create electric power
Pressurized Water Reactor – Notes, final
The water in the secondary system is isolated from the water in the primary system
This prevents contamination of the secondary water and steam by the radioactive nuclei in the core
A fraction of the neutrons produced in fission leak out before inducing other fission events
An optimal surface area-to-volume ratio of the fuel elements is a critical design feature
Basic Reactor Design
Fuel elements consist of enriched uranium The moderator material helps to slow down the neutrons The control rods absorb neutrons All of these are surrounded by a radiation shield
Control Rods
To control the power level, control rods are inserted into the reactor core These rods are made of materials that are very efficient in absorbing neutrons
Cadmium is an example
By adjusting the number and position of the control rods in the reactor core, the K value can be varied and any power level can be achieved
The power level must be within the design of the reactor
Reactor Safety – Containment
Radiation exposure, and its potential health risks, are controlled by three levels of containment: Reactor vessel
Reactor building
Contains the fuel and radioactive fission products Acts as a second containment structure should the reactor vessel rupture Prevents radioactive material from contaminating the environment
Location
Reactor facilities are in remote locations
Reactor Safety – Radioactive Materials
Disposal of waste material
Waste material contains long-lived, highly radioactive isotopes Must be stored over long periods in ways that protect the environment Present solution is sealing the waste in waterproof containers and burying them in deep geological repositories
Transportation of fuel and wastes
Accidents during transportation could expose the public to harmful levels of radiation Department of Energy requires crash tests and manufacturers must demonstrate that their containers will not rupture during high speed collisions
Nuclear Fusion
Nuclear fusion occurs when two light nuclei combine to form a heavier nucleus The mass of the final nucleus is less than the masses of the original nuclei
This loss of mass is accompanied by a release of energy
Fusion in the Sun
All stars generate energy through fusion The Sun, along with about 90% of other stars, fuses hydrogen
Some stars fuse heavier elements
Two conditions must be met before fusion can occur in a star:
The temperature must be high enough The density of the nuclei must be high enough to ensure a high rate of collisions
Proton-Proton Cycle
H+11H→21 H + e + + ν
1 1
The proton-proton cycle is a series of 1 2 3 1H+ 1H→ 2 He + γ three nuclear reactions believed to Then operate in the Sun 1 3 4 + Energy liberated is 1H+ 2 He→ 2 He + e + ν primarily in the form or of gamma rays, 3 3 4 1 1 positrons and He + He → He + H + 2 2 2 1 1H neutrinos
Fusion Reactions, final
Because high temperatures are required to drive these reactions, they are called thermonuclear fusion reactions All of the reactions in the proton-proton cycle are exothermic An overview of the cycle is that four protons combine to form an alpha particle and two positrons
Advantages of a Fusion Reactor
Inexpensive fuel source
Water is the ultimate fuel source If deuterium is used as fuel, 0.12 g of it can be extracted from 1 gal of water for about 4 cents
Comparatively few radioactive byproducts are formed
Considerations for a Fusion Reactor The proton-proton cycle is not feasible for a fusion reactor The high temperature and density required are not suitable for a fusion reactor The most promising reactions involve deutrium and tritium 2 2 3 1 H H H 1 1 2 0 n Q 3.27 MeV
H 21H 31H 11H Q 403 . MeV
2 1
H 31H 42 He 01n Q 1759 . MeV
2 1
Considerations for a Fusion Reactor, cont.
Tritium is radioactive and must be produced artificially The Coulomb repulsion between two charged nuclei must be overcome before they can fuse
Potential Energy Function
The potential energy is positive in the region r > R, where the Coulomb repulsive force dominates It is negative where the nuclear force dominates The problem is to give the nuclei enough kinetic energy to overcome this repulsive force
Critical Ignition Temperature
The temperature at which the power generation rate in any fusion reaction exceeds the lost rate is called the critical ignition temperature, Tignit
The intersection of the Pgen with the Plost line is the Tignit
Requirements for Successful Thermonuclear Reactor
High temperature ~ 108 K
Plasma ion density, n
Needed to give nuclei enough energy to overcome Coulomb forces At these temperatures, the atoms are ionized, forming a plasma The number of ions present
Plasma confinement time, τ
The time interval during which energy injected into the plasma remains in the plasma
Lawson’s Criteria
Lawson’s criteria states that a net power output in a fusion reactor is possible under the following conditions
nτ ≥ 1014 s/cm3 for deuterium-tritium nτ ≥ 1016 s/cm3 for deuterium-deuterium These are the minima on the curves
Requirements, Summary
The plasma temperature must be very high To meet Lawson’s criterion, the product nτ must be large
For a given value of n, the probability of fusion between two particles increases as τ increases For a given value of τ, the collision rate increases as n increases
Confinement is still a problem
Confinement Techniques
Magnetic confinement
Uses magnetic fields to confine the plasma
Inertial confinement
Particles’ inertia keeps them confined very close to their initial positions
Magnetic Confinement
One magnetic confinement device is called a tokamak Two magnetic fields confine the plasma inside the donut
A strong magnetic field is produced in the windings A weak magnetic field is produced by the toroidal current
The field lines are helical, they spiral around the plasma, and prevent it from touching the wall of the vacuum chamber
Fusion Reactors Using Magnetic Confinement
TFTR – Tokamak Fusion Test Reactor
NSTX – National Spherical Torus Experiment
Close to values required by Lawson criterion Produces a spherical plasma with a hole in the center Is able to confine the plasma with a high pressure
ITER – International Thermonuclear Experimental Reactor
An international collaboration involving four major fusion programs is working on building this reactor It will address remaining technological and scientific issues concerning the feasibility of fusion power
Inertial Confinement
Uses a D-T target that has a very high particle density Confinement time is very short
Therefore, because of their own inertia, the particles do not have a chance to move from their initial positions
Lawson’s criterion can be satisfied by combining high particle density with a short confinement time
Laser Fusion
Laser fusion is the most common form of inertial confinement A small D-T pellet is struck simultaneously by several focused, high intensity laser beams This large input energy causes the target surface to evaporate The third law reaction causes an inward compression shock wave This increases the temperature
Fusion Reactors Using Inertial Confinement
Omega facility
University of Rochester (NY) Focuses 24 laser beams on the target
Nova facility
Lawrence Livermore National Lab (CA) Focuses 10 laser beams on the target Has achieved nτ ≈ 5 x 1014 s/cm3
Fusion Reactor Design – Energy
In the D-T reaction, the alpha particle carries 20% of the energy and the neutron carries 80%
The neutrons are about 14 MeV
Active Figure 45.14
(SLIDESHOW MODE ONLY)
Fusion Reactor Design, Particles
The alpha particles are primarily absorbed by the plasma, increasing the plasma’s temperature The neutrons are absorbed by the surrounding blanket of material where their energy is extracted and used to generate electric power One scheme is to use molten lithium to capture the neutrons The lithium goes to a heat-exchange loop and eventually produces steam to drive turbines
Fusion Reactor Design, Diagram
Some Advantages of Fusion
Low cost and abundance of fuel
Deuterium
Impossibility of runaway accidents Decreased radiation hazards
Some Anticipated Problems with Fusion
Scarcity of lithium Limited supply of helium
Helium is needed for cooling the superconducting magnets used to produce the confinement fields
Structural damage and induced radiation from the neutron bombardment
Radiation Damage
Radiation absorbed by matter can cause damage The degree and type of damage depend on many factors
Type and energy of the radiation Properties of the absorbing matter
Radiation Damage, cont.
Radiation damage in the metals used in the reactors comes from neutron bombardment
They can be weakened by high fluxes of energetic neutrons producing metal fatigue The damage is in the form of atomic displacements, often resulting in major changes in the properties of the material
Radiation damage in biological organisms is primarily due to ionization effects in cells
Ionization disrupts the normal functioning of the cell
Types of Damage in Cells
Somatic damage is radiation damage to any cells except reproductive ones
Can lead to cancer at high radiation levels Can seriously alter the characteristics of specific organisms
Genetic damage affects only reproductive cells
Can lead to defective offspring
Damage Dependence on Penetration
Damage caused by radiation also depends on the radiation’s penetrating power
Alpha particles cause extensive damage, but penetrate only to a shallow depth
Due to their charge, they will have a strong interaction with other charged particles
Neutrons do not interact with material and so penetrate deeper, causing significant damage Gamma rays can cause severe damage, but often pass through the material without interaction
Units of Radiation Exposure
The roentgen (R) is defined as
That amount of ionizing radiation that produces an electric charge of 3.33 x 10-10 C in 1 cm3 of air under standard conditions Equivalently, that amount of radiation that increases the energy of 1 kg of air by 8.76 x 10-3 J
One rad (radiation absorbed dose)
That amount of radiation that increases the energy of 1 kg of absorbing material by 1 x 10-2 J
More Units
The RBE (relative biological effectiveness)
The number of rads of x-radiation or gamma radiation that produces the same biological damage as 1 rad of the radiation being used Accounts for type of particle which the rad itself does not
The rem (radiation equivalent in man)
Defined as the product of the dose in rad and the RBE factor
Dose in rem = dose in rad x RBE
RBE Factors, A Sample
RBE Factors, Notes
The values given for RBE factors are only approximate
They vary with particle energy and with the form of damage
The RBE factor should be used as only a first-approximation guide to the actual effects of radiation
Radiation Levels
Natural sources – rocks and soil, cosmic rays
Upper limit suggested by US government
Called background radiation About 0.13 rem/yr 0.50 rem/yr Excludes background
Occupational
5 rem/yr for whole-body radiation Certain body parts can withstand higher levels Ingestion or inhalation is most dangerous
Radiation Levels, cont.
50% mortality rate
About 50% of the people exposed to a dose of 400 to 500 rem will die
New SI units of radiation dosages
The gray (Gy) replaces the rad The sievert (Sv) replaces the rem
SI Units, Table
Radiation Detectors, Introduction
Radiation detectors exploit the interactions between particles and matter to allow a measurement of the particles’ characteristics Things that can be measured include:
Energy Momentum Charge Existence
Early Detectors
Photographic emulsion
The path of the particle corresponds to points at which chemical changes in the emulsion have occurred
Cloud chamber
Contains a gas that has been supercooled Energetic particles ionize the gas along the particles’ paths
Early Detectors, Cont.
Bubble chamber
Uses a liquid maintained near its boiling point Ions produced by incoming charged particles leave bubble tracks The picture is an artificially colored bubble chamber photograph
Contemporary Detectors
Ion chamber
Electron-ion pairs are generated as radiation passes through a gas and produces an electric signal The current is proportional to the number of pairs produced A proportional counter is an ion chamber that detects the presence of the particle and measures its energy
Geiger Counter
A Geiger counter is the most common form of an ion chamber used to detect radiation When a gamma ray or particle enters the thin window, the gas is ionized The released electrons trigger a current pulse The current is detected and triggers a counter or speaker
Geiger Counter, cont.
The Geiger counter easily detects the presence of a particle The energy lost by the particle in the counter is not proportional to the current pulse produced
Therefore, the Geiger counter cannot be used to measure the energy of a particle
Other Detectors
The semiconductor-diode detector
A reverse-bias p-n junction As a particle passes through the junction, a brief pulse of current is created and measured
The scintillation counter
Uses a solid or liquid material whose atoms are easily excited by radiation The excited atoms emit photons as they return to their ground state With a photomultiplier, the photons can be converted into an electrical signal
Other Detectors, cont.
Track detectors
Various devices used to view the tracks or paths of charged particles directly The energy and momentum of these energetic particles are found from the curvature of their path in a magnetic field of known magnitude and direction
Other Detectors, Final
Spark chamber
Is a counting device that consists of an array of conducting parallel plates and is capable of recording a three-dimensional track record
Drift chamber
A newer version of the spark chamber Has thousands of high-voltage wires throughout the space of the detector
Applications of Radiation
Tracing
Radioactive particles can be used to trace chemicals participating in various reactions
Example, 131I to test thyroid action Also useful in agriculture
Materials analysis
Neutron activation analysis uses the fact that when a material is irradiated with neutrons, nuclei in the material absorb the neutrons and are changed to different isotopes
Applications of Radiation, cont.
Radiation therapy
Radiation causes the most damage to rapidly dividing cells Therefore, it is useful in cancer treatments
Food preservation
High levels of radiation can destroy or incapacitate bacteria or mold spores
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