1. Sources of Radiation
Fission and Fusion
Day 4 – Lecture 2

2. Objective
To discuss fission and fusion reactions and the concept of criticality

3. Content Fission Reaction Fission Products and Trnsuranium elements
Criticality and Control of Fission
Fusion Reaction
Fission Fuels
Advantages and Disadvantages of Fusion

4. Fission
gamma
free
neutron
fission
fragment
beta
alpha
energy
nucleus

5. Fission Sample fission reactions:
235U + n  141Ba + 92Kr + 3n MeV
235U + n  94Zr + 139La + 3n MeV
The fission reaction in U‑235 produces fission products such as Ba, Kr, Sr, Cs, I and Xe with atomic masses distributed around 95 and 135. Examples of typical reaction products are listed in this slide.
In these equations, the number of nucleons (protons + neutrons) is conserved, e.g = A small loss in atomic mass is the source of the energy released. Both the barium and krypton isotopes subsequently decay and form more stable isotopes of neodymium and yttrium, with the emission of several electrons from the nucleus (beta decays). It is the beta decays, with some associated gamma rays, which make the fission products highly radioactive although the radioactivity decreases with time.
The total energy released in fission varies with the precise break up. For 235U it averages about 200 MeV or 3.2 x 10‑11 joule.
For Pu‑239 it averages about 210 MeV per fission. This is the total available energy released consisting of kinetic energy values (Ek) of the fission fragments plus neutron, gamma and delayed energy releases which add about 30 MeV.
This contrasts with 4 eV or 6.5 x 10‑19 J per molecule of carbon dioxide released in the combustion of carbon in fossil fuels.

6. Fission Follows neutron capture
Thermal neutrons fission 233U, 235U, 239Pu which have odd number of neutrons
For isotopes with even number of neutrons, the incident neutron must have energy above about 1 MeV
Fission may take place in any of the heavy nuclei after capture of a neutron. However, low‑energy (slow or thermal) neutrons are able to cause fission only in those isotopes of uranium and plutonium whose nuclei contain odd numbers of neutrons (e.g. U‑233, U‑235, and Pu‑239).
For nuclei containing an even number of neutrons, fission can only occur if the incident neutrons have energy above about one million electron volts (MeV).

7. Fission
The probability that fission or any another neutron‑induced reaction will occur is described by the cross‑section for that reaction. The cross‑section may be imagined as an area surrounding the target nucleus and within which the incoming neutron must pass if the reaction is to take place. The fission cross sections increase greatly as the neutron velocity decreases. In nuclei with an odd‑number of neutrons, such as U‑235, the fission cross‑section becomes very large at thermal energies.
As you can see on this graph, both scales are logarithmic.

8. Fission Neutron Name/Title Energy (eV) Cold Neutrons 0 < 0.025
Thermal Neutrons
0.025
Epithermal Neutrons
0.025 < 0.4
Cadmium Neutrons
0.4 < 0.6
Epicadmium Neutrons
0.6 < 1
Slow Neutrons
1 < 10
Resonance Neutrons
10 < 300
Intermediate Neutrons
300 < 1,000,000
Fast Neutrons
1,000,000 < 20,000,000
Relativistic Neutrons
>20,000,000
A neutron is said to have thermal energy when it has slowed down to be in thermal equilibrium with its surroundings. In other words, the kinetic energy of the neutrons is similar to the kinetic energy of the surrounding atoms due to their random thermal motion.
As can be seen from this table, neutrons can range in energy from 2.5 x 10-2 eV to over 2 x 107 eV, nine orders of magnitude.
To promote fission in reactions where thermal neutrons are required, moderators such as water are used to slow the neutrons down.

9. Fission
The fission chain reaction must be initiated by introducing some neutrons into the fissile material. This can be done by inserting an Am-Be, Pu-Be, Po-Be or Ra-Be source. The Am, Pu, Po or Ra emits alpha particles which release neutrons from the beryllium as it turns to carbon‑12.
Using U‑235 in a thermal reactor as an example, when a neutron is captured, the total energy is distributed amongst the 236 nucleons (protons & neutrons) now present in the compound nucleus. This nucleus is relatively unstable and it is likely to break into two fragments of around half the mass. These fragments are nuclei found near the middle of the Periodic Table and the probabilistic nature of the break‑up leads to several hundred possible combinations as seen in this figure. Creation of the fission fragments is followed almost instantaneously by emission of a number of neutrons (typically 2 or 3, average 2.5), which enable the chain reaction to be sustained.

10. transuranics from neutron capture
fission products
and
transuranics from neutron capture
The graph shows the decay of fission products after removal from a reactor.

11. Fission Source of energy released during fission:
Kinetic energy of fission fragments
Gamma rays
Kinetic energy of neutrons emitted
Prompt
Delayed
About 85% of the energy released is initially the kinetic energy of the fission fragments. However, in solid fuel they can only travel a microscopic distance, so their energy becomes converted into heat. The balance of the energy comes from gamma rays emitted during or immediately following the fission process and from the kinetic energy of the neutrons. Some of the latter are immediate (so‑called prompt neutrons), but a small proportion (0.7% for U‑235, 0.2% for Pu‑239) is delayed, as these are associated with the radioactive decay of certain fission products. The longest delayed neutron group has a half‑life of about 56 seconds.

12. Criticality Neutrons ejected during fission equal
neutrons producing more fissions
+ neutrons absorbed
+ neutrons lost from system
Criticality is constant if balance exists. Fission rate (power) can be changed by varying the number of neutrons absorbed and/or controlling the number lost
The delayed neutron release is the crucial factor enabling a chain reacting system (or reactor) to be controllable and to be able to be held precisely critical. At criticality the chain reacting system is exactly in balance, such that the number of neutrons produced in fissions remains constant. This number of neutrons may be completely accounted for by the sum of those causing further fissions, those otherwise absorbed, and those leaking out of the system. Under these circumstances the power generated by the system remains constant. To raise or lower the power, the balance must be changed (using the control system) so that the number of neutrons present (and hence the rate of power generation) is either reduced or increased. The control system is used to restore the balance when the desired new power level is attained.

13. Criticality Multiplication Factor (4 factor formula) Nf+1 Keff = Nf
Nf+1 is the number of neutrons produced in the “f+1” generation by the Nf neutrons of the previous “f” generation

14. Criticality
Sub-Critical (keff < 1) – more neutrons lost by escape from system and/or non-fission absorption by impurities or “poisons” than produced by fission.
Critical (keff = 1) – one neutron per fission available to produce another fission
Super-Critical (keff > 1) – rate of fission neutron production exceeds rate of loss

15. Criticality
Keff depends on the availability of neutrons with the required energy and the availability of fissile atoms
As a result, keff depends on composition, arrangement and size of fissile material
If assembly is infinitely large, no neutrons are lost and Keff = L x k , where L is the non-leakage probability and K depends on 4 factors

16. Fission Control of Fission
Fission typically releases 2-3 neutron (average 2.5)
One is needed to sustain the chain reaction at a steady level of controlled criticality
The other 1.5 leak from the core region or are absorbed in non‑fission reactions
Fission of U‑235 nuclei typically releases 2 or 3 neutrons with an average of about 2.5. One of these neutrons is needed to sustain the chain reaction at a steady level of controlled criticality; on average, the other 1.5 leak from the core region or are absorbed in non‑fission reactions.

17. Fission Control of Fission
Boron or cadmium control rods absorb neutrons
When slightly withdrawn the number of neutrons available for fission exceeds unity and the power level increases
When the power reaches the desired level, the control rods are returned to the critical position
Neutron‑absorbing control rods are used to adjust the power output of a reactor. These typically use boron and/or cadmium (both are strong neutron absorbers) and are inserted among the fuel assemblies. When they are slightly withdrawn from their position at criticality, the number of neutrons available for ongoing fission exceeds unity (i.e. criticality is exceeded) and the power level increases. When the power reaches the desired level, the control rods are returned to the critical position and the power stabilises.

18. Fission Control of Fission
fission neutrons initially fast (energy above 1 MeV)
fission in 235U most readily caused by slow neutrons (energy about 0.02 eV)
moderator slows fast neutrons by elastic collisions
For natural (unenriched) U only graphite and “heavy” water suitable moderators
For enriched uranium “light” water may be used
Neutrons released in fission are initially fast (velocity about 109 cm/sec, or energy above 1 MeV), but fission in U‑235 is most readily caused by slow neutrons (velocity about 105 cm/sec, or energy about 0.02 eV). A moderator material comprising light atoms thus surrounds the fuel rods in a reactor. Without absorbing too many, it must slow down the neutrons in elastic collisions (compare it with collisions between billiard balls on an atomic scale). In a reactor using natural (unenriched) uranium the only suitable moderators are graphite and heavy water (these have low levels of unwanted neutron absorption). With enriched uranium (i.e. increased concentration of U‑235), ordinary (light) water may be used as moderator. (Water is also commonly used as a coolant, to remove the heat and generate steam.)

19. Fission Control of Fission
fuel gradually accumulates fission products and transuranic elements which increases neutron absorption (control system has to compensate)
after about three years, fuel is replaced due to:
build‑up in absorption
metallurgical changes from constant neutron bombardment
burn‑up effectively limited to about half of the fissile material
While fuel is in use in the reactor, it is gradually accumulating fission products and transuranic elements which cause additional neutron absorption. The control system has to be adjusted to compensate for the increased absorption. When the fuel has been in the reactor for three years or so, this build‑up in absorption, along with the metallurgical changes induced by the constant bombardment of the fuel materials, dictates that the fuel should be replaced. This effectively limits the burn‑up to about half of the fissile material, and the fuel assemblies must then be removed and replaced with fresh fuel.

20. Fission Summary
Note that the 235U atom at the bottom of the picture can’t capture the fast neutron, however, the atom at the top can capture the neutron after it has been moderated.

21. Fusion
In 1920 Arthur Eddington suggested that the energy of the sun and stars was a product of the fusion of hydrogen atoms into helium
In the core of the sun at temperatures of 10‑15 million degrees Celsius, hydrogen is converted to Helium
Since the 1950's, great progress has been made in nuclear fusion research however, the only practical application of fusion technology to date has been the "hydrogen" or thermonuclear bomb
Nuclear Fusion is the energy‑producing process which takes place continuously in the sun and stars. In the core of the sun at temperatures of 10‑15 million degrees Celsius, Hydrogen is converted to Helium providing enough energy to sustain life on earth.
The dream of harvesting energy from the same reaction that powers our sun has been around since 1920, when Arthur Eddington suggested that the energy of the sun and stars was a product of the fusion of hydrogen atoms into helium. Since the 1950's, great progress has been made in nuclear fusion research. However, the only practical application of fusion technology to date has been the "hydrogen" or thermonuclear bomb.

22. Fusion Fusion has an almost unlimited potential
The hydrogen isotopes in one gallon of water have the fusion energy equivalent of 300 gallons of gasoline
A fusion power plant would have no greenhouse gas emissions and would not generate high level radioactive waste
Experts predict the world is still at least 50 years and billions of dollars away from having fusion generated electricity largely due to the enormous size and complexity of a fusion reactor
Researchers stress that nuclear fusion has an almost unlimited potential to supply electricity. The hydrogen isotopes in one gallon of water have the fusion energy equivalent of 300 gallons of gasoline. A nuclear fusion power plant would also have no greenhouse gas emissions, and would generate none of the long lived, high level radioactive waste associated with conventional nuclear fission power plants.
Despite its theoretical potential, leading experts predict that the world is still at least 50 years and billions of research dollars away from having electricity generated from nuclear fusion. This is largely due to the enormous size and complexity of a reactor that would be capable of sustaining nuclear fusion.

23. Fusion Hydrogen atoms merged to create helium
Helium mass is slightly less (1%) than the original mass with the difference being given off as energy
Rather than using hydrogen atoms, it is easier to promote fusion by using two isotopes of hydrogen, deuterium and tritium
Deuterium is a naturally occurring isotope of hydrogen which has one extra neutron
One hydrogen atom in 6700 occurs as deuterium and can be separated from the rest
Nuclear fusion involves the binding together of hydrogen atoms, creating helium. The total mass of the final products is slightly less, one percent, than the original mass, with the difference being given off as energy. If this energy can be captured, it could be used to generate electricity.
Rather than using normal hydrogen atoms, it has been found that it is easier to promote fusion by using two isotopes of hydrogen, deuterium and tritium. Isotopes are forms of the same chemical element which have the same number of protons in their nuclei, but a different number of neutrons. Deuterium is a naturally occurring isotope of hydrogen which has one extra neutron.
One hydrogen atom in 6700 occurs as deuterium and can be separated from the rest.

24. Fusion
Deuterium and tritium combine to produce helium and energy.

25. Fusion
Tritium very rare because it is naturally radioactive and decays quickly
Tritium can be made by bombarding the naturally occurring element lithium with neutrons
Tritium could be created by having a "blanket" made of lithium surrounding a fusion containment vessel (this would result in a breeder reactor)
Fusion can only be accomplished at temperatures typical of the centre of stars, (of the order of 100 million degrees Celsius)
Tritium has two extra neutrons and is very rare, because it is naturally radioactive and decays quickly. Tritium can be manufactured by bombarding the naturally occurring element lithium with neutrons from either a fission or fusion reactor. Current thinking is that tritium would be created by having a "blanket" made of lithium surrounding a containment vessel. A reactor such as this, which "breeds" its own fuel, is called a breeder reactor.
Unlike nuclear fission used in conventional nuclear power plants, there is no convenient method of starting a nuclear fusion reaction. Fusion can only be accomplished at temperatures typical of the centre of stars, about 100 million degrees Celsius.

26. Fusion Fuels
Deuterium can be extracted from water (If all the world's electricity were provided by fusion, deuterium would last for millions of years)
Tritium does not occur naturally and will be manufactured from lithium within the machine
Lithium, the lightest metal, is plentiful in the earth's crust (if all the world's electricity were to be provided by fusion, known reserves would last for at least 1000 years)
Even though fusion occurs between Deuterium and Tritium, the consumables are Deuterium and Lithium
Fuels
Deuterium is abundant as it can be extracted from all forms of water. If all the world's electricity were to be provided by fusion power stations, Deuterium supplies would last for millions of years.
Tritium does not occur naturally and will be manufactured from Lithium within the machine.
Lithium, the lightest metal, is plentiful in the earth's crust. If all the world's electricity were to be provided by fusion, known reserves would last for at least 1000 years.
Once the reaction is established, even though it occurs between Deuterium and Tritium, the consumables are Deuterium and Lithium.

27. Fusion Fuels
For example, 10 grams of Deuterium which can be extracted from 500 litres of water and 15g of Tritium produced from 30g of Lithium would produce enough fuel for the lifetime electricity needs of an average person in an industrialised country
Quantities
For example, 10 grams of Deuterium which can be extracted from 500 litres of water and 15g of Tritium produced from 30g of Lithium would produce enough fuel for the lifetime electricity needs of an average person in an industrialised country.

28. Fusion Power Plants
A fusion reactor capable of generating 1000 MW of electricity would be very large and complex
While fission reactors can be made small enough to be used in submarines or satellites, the minimum size of a fusion reactor would be similar to that of today's largest commercial nuclear plants
the difficult part is creating a sustainable fusion reaction - capturing the energy to generate electricity is very similar to a fission reactor
A 1000 MW fusion generator would consume only 150 kg of deuterium and 400 kg of lithium annually
Fusion Power Plants
A full scale fusion reactor capable of generating 1000 MW (1 MW = 1 million watts) of electricity, comparable to conventional nuclear power plants, would be a very large and complex machine. While fission reactors can be made small enough to be used in submarines or satellites, the minimum size and output of a fusion reactor would be similar to that of today's largest nuclear plants.
Although a fusion reactor capable of generating electricity has never been built, the difficult part is creating a sustainable fusion reaction. Capturing the energy given off by the reaction in the form of heat and transforming the heat to electricity is very similar to generating electricity from a conventional fission reactor.
A 1000 MW fusion generator would have a yearly fuel consumption of only 150 kg of
deuterium and 400 kg of lithium.

29. Advantages and Disadvantages of Fusion
The fuels required for fusion reactors, deuterium and lithium, are so abundant that the potential for fusion is virtually unlimited
Oil and gas fired power plants as well as nuclear plants relying on uranium will eventually run into fuel shortages as these non‑renewable resources are consumed
Unlike fossil plants, fusion reactors have no emission of carbon dioxide (contributor to global warming) or sulphur dioxide (cause of acid rain)
Advantages/Disadvantages of Fusion
Nuclear fusion, if it can be developed, would have several advantages over conventional fossil fuel and nuclear fission power plants. The fuels required for fusion reactors, deuterium and lithium, are so abundant that the potential for fusion is virtually unlimited. Oil and gas fired power plants as well as nuclear plants relying on uranium will eventually run into fuel shortages as these non‑renewable resources are consumed. Like conventional nuclear plants, fusion reactors have no emission of carbon dioxide, the major contributor to global warming or sulphur dioxide, the main cause of acid rain. Fossil fuel power plants burning coal, oil and natural gas are large contributors to global warming and acid rain.

30. Advantages and Disadvantages of Fusion
Barriers to the widespread use of nuclear power have been public concern over operational safety, and the disposal of radioactive waste
Accidents such as Chernobyl and Fukushima are virtually impossible with a fusion reactor because only a small amount of fuel is in the reactor at any time
It is also so extremely difficult to sustain a fusion reaction (should anything go wrong, the reaction would invariably stop)
One of the barriers to the widespread use of conventional nuclear power plants has been public concern over operational safety, and the disposal of radioactive waste. Major accidents, such as Chernobyl, are virtually impossible with a fusion reactor because only a small amount of fuel is in the reactor at any time. It is also so extremely difficult to sustain a fusion reaction, that should anything go wrong, the reaction would invariably stop.

31. Advantages and Disadvantages of Fusion
Long lived highly radioactive wastes are generated by conventional nuclear plants
Although the quantity of radioactive waste produced by a fusion reactor might be slightly greater than that from a conventional nuclear plant, the wastes would have low levels of short lived radiation, decaying almost completely within 100 years.
The major disadvantages of nuclear fusion are the vast amounts of time and money which will be required before any electricity is generated by fusion
Long lived highly radioactive wastes are generated by conventional nuclear plants; these must be safely disposed of and represent a hazard to living things for thousands of years. The radioactive wastes generated by a fusion reactor are simply the walls of the containment vessel which have been exposed to neutrons. Although the quantity of radioactive waste produced by a fusion reactor might be slightly greater than that from a conventional nuclear plant, the wastes would have low levels of short lived radiation, decaying almost completely within 100 years.

32. Where to Get More Information
Cember, H., Johnson, T. E, Introduction to Health Physics, 4th Edition, McGraw-Hill, New York (2009)
International Atomic Energy Agency, Postgraduate Educational Course in Radiation Protection and the Safety of Radiation Sources (PGEC), Training Course Series 18, IAEA, Vienna (2002)