Ignia: Lawson Criterion
Electromagnetism & Plasma arc, page 85 of 193. Back to The Pixelated Physics Universe
Who they are
Ignia holds a star in a bottle. To light it, she needs it dense enough, hot enough, for long enough.
Ignia is a character of the Electromagnetism & Plasma arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
For a deuterium–tritium plasma to ignite, the product of density, temperature and energy confinement time must pass a threshold, lowest near 14 keV. Each fusion makes a 3.5 MeV helium nucleus, which stays to heat the plasma, and a 14.1 MeV neutron. J. D. Lawson set out the criterion in 1957; on 5 Dec 2022 the National Ignition Facility put 2.05 MJ of laser light on a target and got 3.15 MJ out, a target gain of about 1.5.
$$ \begin{gathered} n\,T\,\tau_E \gtrsim 3\times10^{21}\ \mathrm{keV\,s\,m^{-3}} \quad (\text{D-T ignition; lowest near } T \approx 14\ \mathrm{keV}) \\ \mathrm{D} + \mathrm{T} \rightarrow {}^{4}\mathrm{He}\ (3.5\ \mathrm{MeV}) + n\ (14.1\ \mathrm{MeV}) \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $n$ | ion density | 1/m³ |
| $T$ | plasma temperature in energy units (1 keV ≈ 1.16 × 10⁷ K) | keV |
| $\tau_E$ | energy confinement time | s |
| $\mathrm{D},\ \mathrm{T}$ | deuterium and tritium nuclei | 1 |
| ${}^{4}\mathrm{He},\ n$ | helium-4 nucleus and neutron (fusion products) | 1 |
Honest caveat: The lasers drew about 100 times more energy from the grid. That was target gain, not net or wall-plug gain.
Sources
- Lawson (1957) Some Criteria for a Power Producing Thermonuclear Reactor, Proc. Phys. Soc. B 70, 6
- Wurzel & Hsu (2022) Progress toward fusion energy breakeven and gain as measured against the Lawson criterion, Phys. Plasmas 29, 062103
- Abu-Shawareb et al. (2024) Achievement of Target Gain Larger than Unity in an Inertial Fusion Experiment, Phys. Rev. Lett. 132, 065102
Crossovers
Ignia meets Plasma Drift (Ionized Gas / Plasma). Plasma Drift's E × B drift and other particle motions in magnetic fields decide how well a plasma is confined. Ignia needs that confinement to be good enough to pass the Lawson triple product for fusion.
Ignia meets Stellar Core (Nuclear Fusion). Ignia confines a plasma with magnets. Stellar Core confines it with gravity. Both need high density, temperature and confinement time for fusion to pay its way.
Wear the lore
- Ignia – The Lawson Criterion Physics T-Shirt
- Related infographic poster: The Magnetic Bottle – Plate 078 Physics Poster
Concept keywords: Lawson Criterion, Ignia, Electromagnetism & Plasma, physics lore, Pixelated Physics