43-4 Thermonuclear Fusion: The Basic Process#
Prompts
Why does fusion of light nuclei release energy? Connect your answer to the binding-energy-per-nucleon curve (section 42-2). How does this contrast with fission?
Nuclei repel each other via the Coulomb force. Why must fusion occur at very high temperature? What does “thermonuclear” mean?
The deuterium-tritium reaction \(d + t \to {}^4\text{He} + n + 17.6\,\text{MeV}\) has the largest cross section at achievable temperatures. Why is D–T favored over p–p or D–D for Earth-based fusion?
How do you calculate the Q-value (energy released) for a fusion reaction from atomic masses?
Deuterium is abundant in seawater; tritium is rare and decays. What are the implications for fusion fuel?
Lecture Notes#
Overview#
Thermonuclear fusion is the combining of light nuclei into heavier ones. It releases energy when the product lies below iron on the binding-energy-per-nucleon curve (section 42-2) — the mirror of fission, which splits heavy nuclei.
Nuclei must overcome the Coulomb barrier to get close enough for the strong force to bind them. High temperature (keV–MeV) gives nuclei enough kinetic energy for fusion — hence thermonuclear.
The deuterium–tritium (D–T) reaction has the largest cross section at achievable temperatures and releases 17.6 MeV per fusion.
Why Fusion Releases Energy#
The binding energy per nucleon \(E_b/A\) is lower for light nuclei (\(A\) small) and rises toward a peak near iron (section 42-2). When two light nuclei fuse into a heavier one below the iron peak, the total binding energy increases — energy is released.
Process |
Direction |
Energy |
|---|---|---|
Fusion |
Light \(\to\) heavier (below iron) |
Released |
Fission |
Heavy \(\to\) lighter (above iron) |
Released |
The Coulomb Barrier#
Nuclei are positively charged and repel each other. To fuse, they must get within ~1 fm for the strong force to act. The Coulomb barrier is the potential energy that must be overcome.
Classically, nuclei would need kinetic energy \(\sim\) MeV to surmount the barrier. Quantum tunneling helps, but high temperature is still required: \(k_B T \sim\) keV to MeV. “Thermonuclear” means fusion driven by thermal motion in a hot plasma (section 43-5: Sun; section 43-6: Earth-based attempts).
The Deuterium–Tritium Reaction#
The D–T reaction has the largest fusion cross section at temperatures achievable on Earth (~10–100 keV):
where \(d\) = deuterium (\(^2\text{H}\)), \(t\) = tritium (\(^3\text{H}\)). The 17.6 MeV appears as kinetic energy of the alpha particle and neutron.
Why D–T? Both nuclei have charge \(+e\) (low Coulomb barrier); the product \(^4\text{He}\) is tightly bound. The p–p reaction (Sun) has a much smaller cross section and requires higher temperatures or longer confinement.
Reaction |
\(Q\) (MeV) |
Cross section |
Note |
|---|---|---|---|
D–T |
17.6 |
Largest at ~10–100 keV |
Preferred for Earth |
D–D |
~3.6 |
Smaller |
No tritium needed |
p–p |
~0.4 |
Very small |
Dominates in Sun (slow) |
Q-Value and Fuel#
The Q-value is the energy released: \(Q = (m_{\text{reactants}} - m_{\text{products}})c^2\). For D–T, \(Q = 17.6\) MeV.
Deuterium is abundant (~0.015% of hydrogen in seawater). Tritium is rare and radioactive (\(T_{1/2} \approx 12\) y); it must be bred (e.g., from lithium by neutron capture) or produced in the fusion device.
Energy per nucleon
Fusion releases ~3.5 MeV per nucleon for D–T (17.6 MeV / 5 nucleons), compared to ~0.8 MeV per nucleon for fission (200 MeV / 235). Fusion is more energy-dense per unit mass of fuel.
Summary#
Fusion: light nuclei combine; energy released when product is below iron on \(E_b/A\) curve.
Coulomb barrier requires high temperature (thermonuclear).
D–T: \(d + t \to {}^4\text{He} + n + 17.6\) MeV; largest cross section at achievable \(T\).
D abundant; T must be bred. Q-value from mass defect.