Ignia
The Lawson Criterion Physics
Size guide S–5XL · inches
Ignia holds a star in a bottle. To light it, she needs it dense enough, hot enough, for long enough.
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.
n T τ_E ≳ 3 × 10²¹ keV·s·m⁻³, D + T → ⁴He (3.5 MeV) + n (14.1 MeV)
- n: ion density (m⁻³)
- T: temperature (keV; 1 keV ≈ 11.6 million K)
- τ_E: energy confinement time (s)
- D, T: deuterium, tritium
- n (in the reaction): 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.
Honest caveat: The lasers drew about 100 times more energy from the grid. That was target gain, not net or wall-plug gain.
On the shirt
Front: Ignia, the pixel-art character, with the title. Back: the triple product, the D–T reaction, the NIF 2022 result and the wall-plug caveat. Printed on a unisex tee.
Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days
Details
Size & fitS–5XL
Unisex heavy cotton (Gildan 5000), classic fit.
| Size | Width | Length | Sleeve |
|---|---|---|---|
| S | 18 | 28 | 15.1 |
| M | 20 | 29 | 16.5 |
| L | 22 | 30 | 18 |
| XL | 24 | 31 | 19.5 |
| 2XL | 26 | 32 | 21 |
| 3XL | 28 | 33 | 22.4 |
| 4XL | 30 | 34 | 23.7 |
| 5XL | 32 | 35 | 25 |
スケール感の目安：サイズ M の幅は 20 in（50.80 cm）で、プランク長のおよそ 3.143 × 1034 倍です（lP = 1.616255 × 10−35 m）。メジャーで測るほうが早いです。
Measurements in inches, ±1.5 in tolerance.
ShippingBy destination
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Returns & replacements21 days
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Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.
The physics
Equations
| Symbol | Meaning | Unit |
|---|---|---|
| \(n\) | ion density | \(\mathrm{1/m³}\) |
| \(T\) | plasma temperature in energy units (1 keV ≈ 1.16 × 10⁷ K) | \(\mathrm{keV}\) |
| \(\tau_E\) | energy confinement time | \(\mathrm{s}\) |
| \(\mathrm{D},\ \mathrm{T}\) | deuterium and tritium nuclei | \(\mathrm{1}\) |
| \({}^{4}\mathrm{He},\ n\) | helium-4 nucleus and neutron (fusion products) | \(\mathrm{1}\) |
Sources
- Lawson (1957) Some Criteria for a Power Producing Thermonuclear Reactor, Proc. Phys. Soc. B 70, 6 (opens in a new tab)
- Wurzel & Hsu (2022) Progress toward fusion energy breakeven and gain as measured against the Lawson criterion, Phys. Plasmas 29, 062103 (opens in a new tab)
- Abu-Shawareb et al. (2024) Achievement of Target Gain Larger than Unity in an Inertial Fusion Experiment, Phys. Rev. Lett. 132, 065102 (opens in a new tab)
Field notes
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