Nuclear Energy
3. Nuclear Fusion
Learning outcomes
- I can describe nuclear fusion.
- I can compare fusion and fission.
- I can explain why fusion powers the Sun.
- I can describe the conditions required for fusion.
- I can explain why controlled fusion is difficult.
Nuclear Fusion
Nuclear fusion is a nuclear reaction in which two light atomic nuclei combine to form a heavier nucleus.
Fusion can release enormous amounts of energy because the products can have a greater binding energy per nucleon than the original light nuclei.
Fusion is the main process that powers:
- the Sun
- other main-sequence stars
Scientists are also working to develop controlled fusion as a possible source of electricity on Earth.
Light Nuclei Combine
Fusion involves:
small nuclei → larger nucleus
For example, hydrogen isotopes can combine to form helium.
Two hydrogen isotopes important in experimental fusion research are:
deuterium (²H)
and:
tritium (³H)
Deuterium contains:
- 1 proton
- 1 neutron
Tritium contains:
- 1 proton
- 2 neutrons
Deuterium-Tritium Fusion
An important fusion reaction for terrestrial fusion research is:
²₁H + ³₁H → ⁴₂He + ¹₀n + energy
The products are:
- helium-4 nucleus
- neutron
- energy
Approximately:
17.6 MeV
of energy is released per deuterium-tritium fusion reaction.
Checking the Fusion Equation
Consider:
²₁H + ³₁H → ⁴₂He + ¹₀n
Check nucleon number.
Left:
2 + 3 = 5
Right:
4 + 1 = 5
Check atomic number.
Left:
1 + 1 = 2
Right:
2 + 0 = 2
Therefore, nucleon number and electric charge are conserved.
Why Fusion Releases Energy
Fusion releases energy because light nuclei can combine to form nuclei that are more tightly bound.
The key idea is:
binding energy per nucleon
For light nuclei, combining nuclei can increase the average binding energy per nucleon.
The resulting nucleus has slightly less total rest mass than the original particles.
This difference is the:
mass defect
Mass-Energy Equivalence
The mass difference is converted into other forms of energy according to:
E = Δmc²
where:
- E = energy released
- Δm = mass defect
- c = speed of light
Because:
c = 3.0 × 10⁸ m/s
even a tiny amount of mass can correspond to a substantial amount of energy.
Binding Energy Curve
The relationship between binding energy and nuclear mass helps explain both fusion and fission.
The binding energy per nucleon generally increases as very light nuclei combine.
It reaches high values around the:
iron/nickel region
This means energy can be released by:
fusion of light nuclei
and by:
fission of very heavy nuclei
Both processes move nuclei toward more tightly bound configurations.
Fusion vs Fission
Fusion and fission are both nuclear reactions, but they work in opposite ways.
| Feature | Fusion | Fission |
|---|---|---|
| Basic process | Light nuclei combine | Heavy nucleus splits |
| Typical nuclei | Hydrogen isotopes | Uranium-235, plutonium-239 |
| Energy source | Increased binding energy | Increased binding energy |
| Powers | Stars | Nuclear reactors |
| Conditions | Extremely high temperature | Neutron-induced in many reactors |
| Chain reaction | Not a neutron-driven chain reaction like fission | Can form neutron chain reaction |
| Main challenge | Maintaining suitable plasma conditions | Controlling fission and managing heat/waste |
Fusion and Fission Have Something in Common
Although fusion combines nuclei and fission splits them, both release energy for the same fundamental reason:
the products are more tightly bound than the original nuclei.
In both cases:
mass of products < mass of original system
The mass difference appears as released energy.
Why Fusion Powers the Sun
The Sun is mostly composed of:
- hydrogen
- helium
At the Sun's core, extremely high temperatures and pressures allow hydrogen nuclei to participate in fusion reactions.
Overall, hydrogen is gradually converted into:
helium
and energy is released.
Conditions in the Sun's Core
The Sun's core has a temperature of roughly:
15 million K
The enormous gravitational force of the Sun also produces extremely high:
pressure and density
These conditions allow nuclei to interact frequently enough for fusion to occur.
Hydrogen Nuclei Repel Each Other
Atomic nuclei containing protons have:
positive electric charge
Like charges repel.
Therefore, two hydrogen nuclei approaching each other experience:
electrostatic repulsion
This creates an energy barrier that makes fusion difficult.
The Coulomb Barrier
The electrostatic repulsion between positively charged nuclei is often described as the:
Coulomb barrier
For fusion to occur, nuclei must approach extremely closely.
At larger distances:
electrostatic repulsion dominates
At extremely short nuclear distances:
the strong nuclear interaction can bind the nuclei
The challenge is getting the nuclei close enough.
Why High Temperature Is Needed
Temperature is related to the average kinetic energy of particles.
At very high temperatures, nuclei move rapidly.
This increases the probability that colliding nuclei can approach sufficiently closely for fusion to occur.
Therefore:
higher temperature → greater particle kinetic energy → greater probability of fusion
However, even at stellar temperatures, quantum tunnelling is also crucial.
Quantum Tunnelling
Classically, many nuclei would not have enough energy to overcome the Coulomb barrier completely.
Quantum mechanics allows a particle to have some probability of passing through a barrier that it could not cross according to classical physics.
This is called:
quantum tunnelling
Quantum tunnelling is extremely important in stellar fusion.
Without it, fusion in the Sun would occur far too slowly under the conditions present in its core.
The Strong Nuclear Interaction
Once nuclei become extremely close, the:
strong nuclear interaction
becomes dominant.
This attractive interaction can bind protons and neutrons together.
Therefore:
electrostatic force keeps nuclei apart
while:
strong nuclear interaction can bind them when sufficiently close
Fusion in the Sun
The main fusion process in the Sun is the:
proton-proton chain
The full process occurs through several stages.
The overall result can be simplified as:
4 hydrogen nuclei → helium-4 nucleus + other particles + energy
The actual reaction sequence includes:
- positrons
- neutrinos
- gamma radiation
Solar Energy
The energy released by fusion begins deep inside the Sun.
Energy travels outward through the solar interior before eventually being emitted from the surface as electromagnetic radiation.
This energy reaches Earth as:
- visible light
- infrared radiation
- ultraviolet radiation
- other electromagnetic radiation
Nearly all energy driving Earth's climate and most ecosystems ultimately comes from solar energy.
Mass Loss in the Sun
The helium nucleus and other final products have slightly less mass than the original particles involved in the overall fusion process.
The difference becomes energy.
Again:
E = Δmc²
The Sun therefore converts a small amount of mass into energy continuously.
Why the Sun Does Not Explode Immediately
Fusion in the Sun is naturally regulated.
Gravity pulls the Sun inward.
Thermal pressure produced by the hot gas and energy generation pushes outward.
For most of its main-sequence lifetime, these effects produce an approximate balance called:
hydrostatic equilibrium
Fusion on Earth
Scientists are attempting to reproduce controlled fusion on Earth.
A major goal is to use fusion energy to generate:
electricity
One promising reaction is:
deuterium + tritium → helium-4 + neutron + energy
But creating the conditions necessary for sustained controlled fusion is extremely difficult.
Plasma
At ordinary temperatures, matter may exist as:
- solid
- liquid
- gas
At extremely high temperatures, atoms become ionized.
Electrons separate from nuclei.
The resulting state of matter is called:
plasma
A fusion fuel therefore exists as an extremely hot plasma.
Conditions Required for Fusion
Controlled fusion requires three important conditions:
High temperature
Nuclei need very high kinetic energies.
Sufficient particle density
There must be enough nuclei available to collide.
Sufficient confinement time
The plasma must remain hot and dense long enough for enough fusion reactions to occur.
These ideas are sometimes summarized by the:
triple product
of temperature, density, and confinement time.
Why Earth Requires Extremely High Temperatures
The Sun benefits from enormous gravitational confinement.
Earth-based reactors cannot reproduce the Sun's enormous gravitational pressure.
Instead, experimental fusion systems generally compensate by using extremely high temperatures.
Fusion plasmas used in terrestrial experiments can reach temperatures of:
tens to hundreds of millions of degrees
At such temperatures, no ordinary solid container could directly hold the plasma.
The Containment Problem
Suppose plasma at more than 100 million °C touched an ordinary reactor wall.
The wall could not simply contain the plasma like a conventional metal tank.
Scientists therefore need methods to keep the plasma:
away from the walls
One major approach uses:
magnetic fields
Magnetic Confinement
Plasma contains electrically charged particles.
Charged particles experience forces in magnetic fields.
Strong magnetic fields can therefore be used to guide and confine the plasma.
One major magnetic-confinement device is the:
tokamak
Tokamaks
A tokamak uses powerful magnetic fields to confine hot plasma inside a toroidal, or doughnut-shaped, chamber.
The goal is to:
- heat the plasma
- keep it stable
- prevent excessive contact with reactor walls
- maintain suitable density
- sustain fusion reactions
Why Magnetic Fields Can Confine Plasma
Plasma consists of:
- positively charged nuclei
- negatively charged electrons
Moving charged particles experience magnetic forces.
Magnetic fields can therefore make charged particles follow curved or spiral paths.
Carefully designed magnetic fields can help confine the plasma inside the reactor.
Plasma Instabilities
Plasma is difficult to control.
It can develop:
- waves
- turbulence
- instabilities
- sudden changes in shape
- energy losses
If confinement deteriorates:
plasma energy escapes → plasma cools → fusion rate decreases
Maintaining stable plasma is one of the major challenges of controlled fusion.
Inertial Confinement Fusion
Another approach is:
inertial confinement fusion
Instead of using magnetic fields to confine plasma for relatively long periods, powerful energy pulses rapidly compress a tiny fusion-fuel target.
Lasers are one method used to achieve this.
The fuel is compressed and heated rapidly enough that fusion can occur before the material expands.
Magnetic vs Inertial Confinement
Magnetic confinement
Uses:
magnetic fields
to confine hot plasma.
Examples include:
- tokamaks
- stellarators
Inertial confinement
Uses rapid compression and heating.
One approach uses:
powerful lasers
Both aim to create suitable fusion conditions, but they use very different methods.
The Fusion Energy Challenge
Producing fusion reactions is possible.
The much harder challenge is creating a system that can reliably produce useful energy.
The system must provide enough fusion energy to justify the energy required for:
- plasma heating
- magnetic systems
- lasers or other drivers
- cooling
- fuel handling
- reactor operation
This is why demonstrations of fusion reactions are not automatically equivalent to a commercial fusion power station.
Fusion Gain
Scientists use different measures of:
fusion gain
A simple idea is:
energy produced by fusion / energy supplied to the fusion fuel or system
The exact definition matters because some measurements compare fusion energy only with energy delivered directly to the plasma or target, while a complete power plant must also account for the energy consumed by the entire facility.
Ignition
In fusion research, ignition describes a condition where fusion heating becomes sufficient to help sustain the fusion process without requiring the same level of external heating.
Achieving and maintaining such conditions in a practical power-producing system is extremely challenging.
Deuterium
Deuterium is a stable isotope of hydrogen.
It contains:
- 1 proton
- 1 neutron
Deuterium occurs naturally in water.
This makes it a potentially abundant fusion fuel.
Tritium
Tritium contains:
- 1 proton
- 2 neutrons
Unlike deuterium, tritium is:
radioactive
It has a half-life of about:
12.3 years
Large natural supplies of tritium are not readily available.
Future deuterium-tritium fusion reactors would therefore need systems for obtaining and managing tritium.
Producing Tritium
One proposed strategy is to produce tritium using:
lithium
Neutrons produced by deuterium-tritium fusion can interact with lithium-containing material surrounding the reactor.
This could help produce replacement tritium fuel.
Such a system is often called a:
breeding blanket
Fusion Neutrons
The neutron produced by deuterium-tritium fusion carries a large fraction of the released energy.
Because neutrons have no electric charge, magnetic fields cannot confine them.
They escape the plasma and enter surrounding materials.
Their kinetic energy can then be converted into:
thermal energy
Generating Electricity from Fusion
A future fusion power station could use fusion neutrons to heat surrounding material.
The approximate energy pathway would be:
nuclear fusion → neutron kinetic energy → thermal energy → steam/turbine or other heat engine → generator → electrical energy
In this respect, the later stages could resemble other thermal power stations.
Neutron Damage
High-energy fusion neutrons create engineering challenges.
They can interact with reactor materials and cause:
- atomic displacement
- structural damage
- material embrittlement
- activation of materials
Therefore, future fusion reactors require materials capable of surviving intense neutron bombardment for long periods.
Fusion and Radioactive Waste
Fusion does not produce the same mixture of fission products and transuranic elements associated with conventional fission reactors.
However, it would be incorrect to say:
"fusion produces no radioactive waste."
High-energy neutrons can activate reactor materials, making some components radioactive.
Tritium is also radioactive and requires careful management.
Fusion Safety
Fusion has several potential safety advantages.
A fusion reactor would not rely on the same type of self-sustaining fission chain reaction used in a fission reactor.
If the necessary plasma conditions are lost:
fusion rapidly decreases or stops
because the required temperature, density, and confinement conditions are no longer maintained.
However, fusion facilities would still require careful management of:
- tritium
- activated materials
- powerful magnetic systems
- high-energy neutrons
- large thermal loads
Why Controlled Fusion Is Difficult
The difficulty can be summarized as several connected problems.
Temperature
The plasma must reach extremely high temperatures.
Confinement
The plasma must be prevented from losing energy too quickly.
Stability
The plasma must remain sufficiently stable.
Density
Enough nuclei must be present to produce useful fusion rates.
Materials
Reactor components must survive intense heat and neutron exposure.
Fuel
Tritium must be produced, contained, and managed.
Energy balance
The entire system must eventually produce useful net electrical energy reliably.
The Lawson Criterion
Fusion conditions can be described using relationships between:
- plasma temperature
- particle density
- energy confinement time
This is associated with the:
Lawson criterion
A fusion system must achieve sufficiently favorable combinations of these quantities for fusion energy production to become useful.
This is why temperature alone is not enough.
A plasma could be extremely hot but still produce little useful fusion energy if it is:
- too thin
- poorly confined
- losing energy too quickly
Fusion in Stars vs Fusion on Earth
| Feature | Sun | Earth-Based Fusion |
|---|---|---|
| Confinement | Gravity | Magnetic fields or inertial compression |
| Temperature | ~15 million K core | Often tens to hundreds of millions K |
| Pressure | Enormous gravitational pressure | Much lower than stellar core pressure |
| Main fuel process | Proton-proton chain | D-T fusion is a major research focus |
| Duration | Billions of years | Experimental confinement |
| Main challenge | Naturally sustained by gravity | Artificial control and energy gain |
Why the Sun Can Fuse at a Lower Temperature
The Sun's core is extraordinarily dense compared with laboratory fusion plasmas and is confined continuously by the gravity of the entire star.
It also has:
billions of years
over which fusion can occur.
Earth-based fusion systems need much higher reaction rates in a much smaller volume.
This is one reason terrestrial fusion research uses temperatures considerably higher than the Sun's core temperature.
Fusion Does Not Mean "Unlimited Free Energy"
Fusion fuel resources could be substantial, but a fusion power plant would still require:
- expensive infrastructure
- advanced materials
- maintenance
- fuel processing
- cooling systems
- electricity-generating equipment
- radiation protection
- waste management
Fusion could potentially become an important energy source, but it would not make energy literally free or unlimited.
Advantages of Fusion
Potential advantages include:
- very high energy density
- abundant deuterium resources
- no carbon dioxide produced by the fusion reaction itself
- no neutron-driven runaway chain reaction like fission
- less long-lived high-level waste than conventional fission is expected to produce
- potentially large fuel resources
Challenges of Fusion
Major challenges include:
- extremely high plasma temperatures
- maintaining confinement
- plasma instability
- energy losses
- neutron damage
- tritium production and handling
- complex reactor materials
- achieving reliable net electricity production
- economic competitiveness
- maintaining equipment exposed to extreme conditions
Worked Example: Nuclear Equation
Suppose:
²₁H + ³₁H → ⁴₂He + X
Find X.
Mass number:
2 + 3 = 4 + A
5 = 4 + A
A = 1
Atomic number:
1 + 1 = 2 + Z
2 = 2 + Z
Z = 0
Therefore:
X = ¹₀n
The missing particle is a:
neutron
Worked Example: Fusion Energy
One D-T fusion reaction releases approximately:
17.6 MeV.
Convert to joules.
1 eV = 1.60 × 10⁻¹⁹ J
17.6 MeV:
= 17.6 × 10⁶ eV
Energy:
= 17.6 × 10⁶ × 1.60 × 10⁻¹⁹
≈ 2.82 × 10⁻¹² J
This is the energy from just one fusion reaction.
A large number of reactions can therefore release enormous amounts of energy.
Worked Example: Comparing Fission and Fusion
Suppose a student says:
"Fission and fusion release energy because atoms are destroyed."
This is incorrect.
A better explanation is:
Both reactions rearrange nuclei into configurations with greater binding energy per nucleon.
The products have slightly less rest mass than the original system.
The difference appears as energy according to:
E = Δmc²
Common Mistakes
Mistake: Saying fusion splits atoms.
Fusion combines light nuclei. Fission splits heavy nuclei.
Mistake: Saying fusion joins complete atoms together.
Fusion involves atomic nuclei.
Mistake: Saying fusion occurs because nuclei attract each other electrically.
Positively charged nuclei electrically repel each other.
Mistake: Saying temperature removes the Coulomb barrier.
High temperature increases kinetic energy and the probability of nuclei approaching closely enough; quantum tunnelling is also important.
Mistake: Saying the Sun uses uranium fusion.
The Sun primarily converts hydrogen into helium.
Mistake: Saying the Sun uses deuterium-tritium fusion as its main process.
The Sun's main process is the proton-proton chain.
Mistake: Saying plasma is simply a very hot gas.
Plasma contains significant numbers of free charged particles.
Mistake: Saying fusion reactors require no confinement.
Maintaining suitable confinement is one of fusion's biggest challenges.
Mistake: Saying fusion creates no radioactive material.
D-T fusion produces energetic neutrons that can activate reactor materials, and tritium itself is radioactive.
Mistake: Assuming producing fusion once means commercial fusion electricity has been achieved.
A practical power station must repeatedly and reliably produce useful net electrical energy.
Key Terms
Nuclear fusion — process in which light nuclei combine to form heavier nuclei.
Deuterium — hydrogen isotope containing one proton and one neutron.
Tritium — radioactive hydrogen isotope containing one proton and two neutrons.
Plasma — ionized state of matter containing free charged particles.
Coulomb barrier — electrostatic energy barrier caused by repulsion between positively charged nuclei.
Strong nuclear interaction — interaction that binds nucleons together at very short distances.
Quantum tunnelling — quantum effect allowing particles some probability of crossing barriers they could not classically overcome.
Binding energy — energy associated with holding a nucleus together.
Binding energy per nucleon — average binding energy for each proton or neutron in a nucleus.
Mass defect — difference in rest mass associated with nuclear binding or a nuclear reaction.
Magnetic confinement — use of magnetic fields to confine hot plasma.
Tokamak — toroidal magnetic-confinement device used in fusion research.
Stellarator — another magnetic-confinement device designed to confine fusion plasma.
Inertial confinement — fusion approach using rapid compression and heating of a small fuel target.
Fusion gain — comparison between fusion energy output and an appropriate measure of supplied energy.
Ignition — condition in which fusion heating substantially sustains the fusion process.
Lawson criterion — condition relating temperature, density and confinement time required for useful fusion performance.
Breeding blanket — reactor structure intended partly to produce tritium from lithium using fusion neutrons.
Key Takeaways
- Nuclear fusion combines light atomic nuclei into heavier nuclei.
- Fusion releases energy because the products can have greater binding energy per nucleon.
- A small mass difference is converted into energy according to E = Δmc².
- Deuterium and tritium are important fuels in terrestrial fusion research.
- D-T fusion produces helium-4, a neutron and approximately 17.6 MeV of energy.
- Fusion powers the Sun and other stars.
- The Sun mainly converts hydrogen into helium through the proton-proton chain.
- Positively charged nuclei repel each other electrically.
- Nuclei must approach extremely closely before the strong nuclear interaction can bind them.
- High temperature increases nuclear kinetic energy and the probability of fusion.
- Quantum tunnelling is important in stellar fusion.
- Fusion fuel on Earth exists as extremely hot plasma.
- Useful fusion requires suitable temperature, density and confinement time.
- Tokamaks use magnetic fields to confine plasma.
- Inertial confinement can use powerful lasers to compress fusion fuel.
- Plasma instability and energy loss make controlled fusion difficult.
- D-T fusion produces energetic neutrons that create engineering challenges.
- Fusion materials can become radioactive through neutron activation.
- Tritium is radioactive and would need careful production and handling.
- Fusion does not involve the same neutron-driven chain reaction as fission.
- If suitable plasma conditions are lost, fusion rapidly decreases.
- Fusion and fission both release nuclear binding energy, but fusion combines light nuclei while fission splits heavy nuclei.
- Controlled fusion is scientifically possible, but developing reliable and economically practical fusion electricity remains an engineering challenge.
Check Your Understanding
- Define nuclear fusion.
- How does fusion differ from nuclear fission?
- Name the two hydrogen isotopes commonly considered for terrestrial fusion reactors.
- How many protons and neutrons are found in deuterium?
- How many protons and neutrons are found in tritium?
- Write the nuclear equation for deuterium-tritium fusion.
- Approximately how much energy is released in one D-T fusion reaction?
- Explain why fusion can release energy.
- What is the relationship between fusion and binding energy per nucleon?
- What process provides most of the Sun's energy?
- Why do positively charged nuclei resist being brought together?
- What is the Coulomb barrier?
- Why are extremely high temperatures needed for fusion?
- Explain the importance of quantum tunnelling in stellar fusion.
- What is plasma?
- Identify the three major conditions required for useful controlled fusion.
- Explain how a tokamak attempts to confine fusion plasma.
- What is the difference between magnetic confinement and inertial confinement?
- Why are high-energy neutrons a challenge for D-T fusion reactors?
- Explain why achieving fusion reactions in a laboratory is not the same as operating a practical fusion power station.