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Nuclear Fusion Energy

Source lecture(s): PC368 Lec 1

Intuition

Fusion is the reason plasma physics is funded. Light nuclei bound together release energy because iron sits at the bottom of the binding-energy curve and everything lighter can fall toward it. The catch is that nuclei are positively charged: to fuse they must be thrown at each other hard enough to climb the Coulomb barrier — and a gas whose particles carry kilo-electron-volts of kinetic energy is, by definition, fully ionised. A fusion fuel is necessarily a plasma. Every difficulty in this course follows from that sentence.

The reaction of choice

\[\mathrm{D} + \mathrm{T} \;\rightarrow\; {}^{4}\mathrm{He}\,(3.5\ \text{MeV}) + n\,(14.1\ \text{MeV})\]

Deuterium–tritium wins not because it releases the most energy but because its cross-section peaks at the lowest temperature — around 65 keV, with useful rates from about 10 keV. Competing reactions need far hotter plasma:

Reaction Energy released Rough ignition temperature
D + T → ⁴He + n 17.6 MeV ~10–20 keV
D + D → ³He + n / T + p 3.3 / 4.0 MeV ~50 keV
D + ³He → ⁴He + p 18.3 MeV ~100 keV
p + ¹¹B → 3 ⁴He 8.7 MeV ~200 keV

The 3.5 MeV alpha is charged, so the magnetic field keeps it — that is the self-heating that makes ignition possible. The 14.1 MeV neutron is not confined and carries 80% of the yield out to a lithium blanket, where it both raises steam and breeds the tritium the reaction consumes.

Why anyone bothers

  • Fuel: deuterium is 1 part in 6500 of seawater hydrogen; lithium for tritium breeding is abundant. The practical supply is measured in millennia.
  • Safety: the burning plasma holds seconds of fuel at a time. There is no chain reaction and no runaway configuration — every failure mode ends with the plasma going out.
  • Waste: no long-lived actinides. Activated structural steel dominates, on a ~100-year timescale rather than 10⁵ years.
  • Density: the energy in one gram of D–T equals roughly eight tonnes of oil.

Set against that: nothing in the list matters until the Lawson criterion is met, which after seventy years it has been only transiently.

The temperature, in context

Ignition needs \(T \sim 10^8\) K — about seven times the centre of the Sun. This sounds like a mistake until you notice the Sun's advantage: it is enormous and in no hurry. Its power density at the core is about 275 W/m³, comparable to a compost heap. The Sun succeeds by being \(10^{27}\) kg of compost. A reactor cannot borrow that trick, so it compensates with temperature — see the triple product.

Common mistakes

  • "Fusion is the opposite of fission, so it must be harder to start and easier to stop." Half right. Fusion is harder to start and it stops itself; there is no critical mass and no supercritical excursion.
  • Confusing ignition with breakeven. \(Q = 1\) (scientific breakeven) means fusion power equals heating power injected into the plasma; ignition (\(Q = \infty\)) means the alphas alone sustain it. NIF reached target gain \(Q > 1\) in 2022; no device has ignited in the self-sustaining magnetic-confinement sense.
  • Quoting wall-plug efficiency as if it were \(Q\). Engineering breakeven — net electricity out of the building — is a much steeper requirement than \(Q = 1\).

Knowledge graph position

Prerequisites: Plasma. Leads to: Lawson criterion, magnetic confinement, MHD stability.

Quiz

Q1 (conceptual). Why must a fusion fuel be a plasma rather than a hot gas?

Answer

The Coulomb barrier requires particle energies of order 10 keV. At that energy every atom is ionised many times over — no bound electrons survive. Ionisation is not a design choice, it is a consequence of the temperature fusion demands.

Q2 (computational). A D–T reaction releases 17.6 MeV. How much energy is in 1 g of an equimolar D–T mixture, and how does that compare with burning 1 g of coal (~30 kJ)?

Answer

Mean molar mass ≈ 2.5 g/mol, so 1 g ≈ 0.4 mol ≈ \(2.4\times10^{23}\) nuclei, i.e. \(1.2\times10^{23}\) reactions. At \(17.6\ \text{MeV} = 2.8\times10^{-12}\) J each, that is \(\approx 3.4\times10^{11}\) J — about ten million times the coal.

Q3 (MCQ). The 14.1 MeV neutron is essential to a reactor mainly because it:

  • (a) heats the plasma and sustains ignition
  • (b) is confined by the magnetic field
  • (c) carries energy to the blanket and breeds tritium from lithium
  • (d) triggers a chain reaction
Answer

(c). Being neutral it escapes immediately, which is a feature: it delivers 80% of the yield to the blanket where it both makes steam and regenerates the tritium fuel. The alpha does the self-heating (a).