Fusion (AQA A-Level Physics): Revision Notes

Fusion

Understanding nuclear fusion

Nuclear fusion is the process in which two lighter nuclei combine to form a heavier nucleus. During fusion, energy is released to the surroundings because the product nucleus is more tightly bound than the original lighter nuclei that created it. This increased stability means the nucleus formed has less mass than its constituents, and this mass difference corresponds to the energy released.

The key to understanding fusion lies in binding energy per nucleon - the average energy that holds each nucleon within a nucleus. When lighter nuclei fuse, the resulting nucleus has a higher binding energy per nucleon, indicating greater stability. The difference in binding energy between products and reactants is transferred to the surroundings as released energy.

Conditions for energy release through fusion

For a fusion process to release energy, a specific condition must be satisfied: the two lighter nuclei undergoing fusion must have lower binding energy per nucleon values than the nucleus they form.

Examining the binding energy per nucleon graph reveals that only nuclei positioned to the left of the peak can satisfy this condition. The peak occurs at iron-56 ($^{56}$Fe), which possesses the highest binding energy per nucleon at approximately $8.7$ MeV/nucleon, making it the most stable nucleus. Therefore, fusion can only release energy when involving nuclei with mass numbers less than 56.

When lighter nuclei fuse, both the binding energy per nucleon and the nucleon number increase, producing a more stable configuration.

Deuterium-tritium fusion reaction

A frequently studied fusion reaction involves two hydrogen isotopes: deuterium ($^2$H) and tritium ($^3$H). These isotopes have binding energy per nucleon values of $1.11$ MeV/nucleon and $2.83$ MeV/nucleon respectively. When fused, they produce helium-4 ($^4$He) with a significantly higher binding energy per nucleon of $7.07$ MeV/nucleon.

The nuclear reaction equation is:

$^2\text{H} + ^3\text{H} \rightarrow ^4\text{He} + ^1_0\text{n}$

This reaction also produces a neutron. The substantial increase in binding energy per nucleon when forming helium-4 results in considerable energy transfer to the surroundings, making this reaction particularly useful for potential fusion energy applications.

Calculating energy released in fusion

Two equivalent methods exist for determining the energy released during fusion: calculating the change in binding energy or determining the mass defect. Both approaches will yield the same result when applied correctly.

Method 1: Change in binding energy

The energy released equals the difference between total binding energies of products and reactants:

$\text{Change in binding energy} = (\text{total binding energy of products}) - (\text{total binding energy of reactants})$

Method 2: Mass defect calculation

Energy release can alternatively be determined through mass loss during the reaction. The mass defect represents the difference between the initial and final masses, which is converted into energy.

Using atomic mass unit values:

• Deuterium nucleus: $2.01355$ u
• Tritium nucleus: $3.01550$ u
• Helium-4 nucleus: $4.00150$ u
• Neutron: $1.00867$ u

Challenges of fusion on Earth

Achieving controlled fusion on Earth faces substantial technical obstacles. Understanding these challenges helps explain why fusion power, despite its immense potential, has not yet been commercially realized.

The primary challenge is overcoming electrostatic repulsion between positively charged nuclei. Since nuclei carry the same positive charge, they naturally repel each other according to Coulomb's law.

At these elevated temperatures, nuclei move rapidly enough to collide with sufficient force, allowing the attractive strong nuclear force to overcome the repulsive electrostatic force. The plasma created at these temperatures must also be confined for sufficient time and at sufficient density for fusion reactions to occur at a useful rate.

These extreme temperature requirements present the main engineering challenge for developing practical fusion power generation on Earth. Current experimental reactors like ITER are designed to achieve and maintain these conditions using powerful magnetic fields to confine the superheated plasma.

Fusion in stars

Stars generate their heat and light through fusion reactions occurring in their cores. These natural fusion reactors have been operating for billions of years, providing a model for human attempts at controlled fusion.

Massive stars can fuse nuclei progressively to produce elements as heavy as iron through successive fusion processes. This process, called stellar nucleosynthesis, is responsible for creating most of the elements in the universe.

In our Sun, the dominant fusion process converts hydrogen nuclei into helium through a series of reactions known as the proton-proton chain. These stellar fusion reactions constitute the energy source that powers stars, producing the electromagnetic radiation they emit throughout their lifetimes.

The energy released through fusion creates an outward pressure that balances the inward pull of gravity, maintaining the star's stable structure for billions of years.