AcademyNuclear Physics
Academy
Fusion
Level 1 - Physics topic page in Nuclear Physics.
Principle
Fusion releases energy when light nuclei combine into products with greater total binding energy.
Notation
\(Q\)
fusion energy release
J, MeV
\(Z_1,Z_2\)
charges of reacting nuclei
1
\(r\)
nuclear separation
\(\mathrm{m}\)
\(U_C\)
Coulomb barrier energy
J, MeV
\(T\)
plasma temperature
\(\mathrm{K}\)
\(n\)
particle number density
\(\mathrm{m^{-3}}\)
Method
Derivation 1: Energy release
Fusion is favorable for light nuclei below the binding-energy-per-nucleon peak.
Q value
\[Q=(m_i-m_f)c^2\]
Binding form
\[Q=B_f-B_i\]
Derivation 2: Coulomb barrier
Nuclei must approach closely enough for the strong force to act.
Barrier scale
\[U_C\approx\frac{1}{4\pi\epsilon_0}\frac{Z_1Z_2e^2}{r}\]
Thermal scale
\[K\sim k_BT\]
Derivation 3: Tunneling
Fusion can occur below the classical barrier because nuclear wave functions tunnel.
Barrier penetration
\[P\sim e^{-2\int\kappa(r)dr}\]
Rate sensitivity
\[\text{fusion rate depends strongly on temperature}\]
Rules
Fusion Q
\[Q=(m_i-m_f)c^2\]
Coulomb barrier
\[U_C\approx\frac{1}{4\pi\epsilon_0}\frac{Z_1Z_2e^2}{r}\]
Thermal scale
\[K\sim k_BT\]
Examples
Question
Why is deuterium-tritium fusion easier than proton-carbon fusion?
Answer
Lower charge product
\[Z_1Z_2\]
gives a smaller Coulomb barrier.Checks
- Fusion of light nuclei releases energy up to the iron-region binding peak.
- The Coulomb barrier rises with \(Z_1Z_2\).
- High temperature increases collision energy and tunneling probability.
- Stellar fusion depends on quantum tunneling, not only classical barrier crossing.