KAHIBARO
Table of Contents
What a Fusion Reaction Is
A fusion reaction happens when two light atomic nuclei join together to make a heavier nucleus. In the process, energy can be released. Fusion is the opposite of fission, where a heavy nucleus splits into smaller parts.
Light nuclei are the best candidates for fusion because joining them can produce a nucleus with a greater binding energy per nucleon. That means the final nucleus is more tightly bound than the initial nuclei, and the difference in energy appears as released energy.
A general fusion reaction can be written as
$$
A + B \rightarrow C + D + Q
$$
where $A$ and $B$ are the initial nuclei, $C$ and $D$ are the products, and $Q$ is the energy released. Sometimes only one final nucleus is produced, but often fusion creates a nucleus plus another particle such as a neutron or proton.
In any nuclear reaction, important conservation laws must hold. In fusion reactions, the total charge and the total number of nucleons must be the same before and after the reaction.
Why Fusion Releases Energy
The energy released in fusion comes from mass difference. If the total mass of the initial nuclei is greater than the total mass of the final products, the missing mass is converted into energy through
$$
E = mc^2
$$
The energy released is called the $Q$ value:
$$
Q = \left(m_{\text{initial}} - m_{\text{final}}\right)c^2
$$
If $Q > 0$, the reaction is exothermic and releases energy. Many fusion reactions involving very light nuclei have positive $Q$ values.
A fusion reaction releases energy only if the final products have less total mass than the starting nuclei.
Common Fusion Reactions
Several fusion reactions are especially important in physics because they are relevant in stars or in human attempts to produce controlled fusion energy.
Deuterium Tritium Fusion
One of the most important fusion reactions is
$$
{}^{2}_{1}\mathrm{H} + {}^{3}_{1}\mathrm{H} \rightarrow {}^{4}_{2}\mathrm{He} + {}^{1}_{0}\mathrm{n} + 17.6 \, \mathrm{MeV}
$$
Here, deuterium and tritium combine to form helium 4 and a neutron. This reaction releases a large amount of energy and is the easiest fusion reaction to achieve in laboratories compared with many alternatives.
Deuterium Deuterium Fusion
Another possible reaction is
$$
{}^{2}_{1}\mathrm{H} + {}^{2}_{1}\mathrm{H} \rightarrow {}^{3}_{2}\mathrm{He} + {}^{1}_{0}\mathrm{n} + 3.27 \, \mathrm{MeV}
$$
or
$$
{}^{2}_{1}\mathrm{H} + {}^{2}_{1}\mathrm{H} \rightarrow {}^{3}_{1}\mathrm{H} + {}^{1}_{1}\mathrm{p} + 4.03 \, \mathrm{MeV}
$$
So deuterium deuterium fusion can proceed through more than one channel.
Deuterium Helium 3 Fusion
A further example is
$$
{}^{2}_{1}\mathrm{H} + {}^{3}_{2}\mathrm{He} \rightarrow {}^{4}_{2}\mathrm{He} + {}^{1}_{1}\mathrm{p} + 18.3 \, \mathrm{MeV}
$$
This reaction is attractive because it produces a proton rather than a neutron, but it is harder to achieve.
Proton Proton Fusion
In stars like the Sun, the basic long term fusion process begins with proton proton fusion. A simplified first step is
$$
{}^{1}_{1}\mathrm{H} + {}^{1}_{1}\mathrm{H} \rightarrow {}^{2}_{1}\mathrm{H} + e^{+} + \nu_e
$$
This reaction is much slower than laboratory fusion reactions because it involves the weak interaction.
Reading Fusion Equations
Fusion equations must satisfy conservation of nucleon number and charge. For example, in deuterium tritium fusion:
$$
{}^{2}_{1}\mathrm{H} + {}^{3}_{1}\mathrm{H} \rightarrow {}^{4}_{2}\mathrm{He} + {}^{1}_{0}\mathrm{n}
$$
Before the reaction, the total mass number is
$$
2 + 3 = 5
$$
After the reaction, the total mass number is
$$
4 + 1 = 5
$$
Before the reaction, the total atomic number is
$$
1 + 1 = 2
$$
After the reaction, the total atomic number is
$$
2 + 0 = 2
$$
So the reaction is balanced.
To check a nuclear fusion equation, always verify both mass number and atomic number.
Comparison of Important Fusion Reactions
| Reaction | Main Products | Energy Released | Notes |
|---|---|---|---|
| ${}^{2}\mathrm{H}+{}^{3}\mathrm{H}$ | ${}^{4}\mathrm{He}+n$ | $17.6 \, \mathrm{MeV}$ | Most practical for present fusion research |
| ${}^{2}\mathrm{H}+{}^{2}\mathrm{H}$ | ${}^{3}\mathrm{He}+n$ or ${}^{3}\mathrm{H}+p$ | $3.27$ or $4.03 \, \mathrm{MeV}$ | Multiple channels |
| ${}^{2}\mathrm{H}+{}^{3}\mathrm{He}$ | ${}^{4}\mathrm{He}+p$ | $18.3 \, \mathrm{MeV}$ | Harder to ignite |
| $p+p$ | ${}^{2}\mathrm{H}+e^+ + \nu_e$ | Small per step | Dominant in the Sun |
Energy Distribution in Fusion Products
The released energy does not appear as a single lump of energy sitting somewhere. It becomes kinetic energy of the reaction products. In deuterium tritium fusion, the helium nucleus and neutron fly away at high speeds.
Because the neutron has no electric charge, it can escape magnetic confinement systems easily. That is why neutron production is such an important feature of many fusion reactions.
Example of a Fusion Energy Calculation
Suppose a fusion reaction has initial total mass $m_i$ and final total mass $m_f$. Then
$$
Q = (m_i - m_f)c^2
$$
If
$$
m_i - m_f = 0.0189 \, u
$$
then using
$$
1u \approx 931.5 \, \mathrm{MeV}/c^2
$$
we get
$$
Q = 0.0189 \times 931.5 \, \mathrm{MeV} \approx 17.6 \, \mathrm{MeV}
$$
This is the energy released in the deuterium tritium reaction.
A small loss of mass in nuclear reactions corresponds to a very large release of energy.
Simple Reaction Diagram
What Makes Fusion Reactions Special
Fusion reactions are special because they involve light nuclei and can release enormous energy compared with chemical reactions. The energy scale is measured in millions of electron volts, $\mathrm{MeV}$, rather than a few electron volts.
They are also central to both astrophysics and energy research. In stars, fusion reactions power the emission of light and heat. In laboratories, scientists seek fusion reactions that produce more energy than is required to sustain them.
Final Idea
A fusion reaction is a nuclear joining process in which light nuclei combine to form heavier nuclei, often releasing large amounts of energy because the products are more tightly bound and have less total mass. The reaction equation must conserve charge and nucleon number, and the released energy is given by the mass defect through $E = mc^2$.