Correct option is A
Introduction
The Lawson criterion defines the minimum condition for a fusion reaction to reach energy break-even, requiring the product of plasma number density and energy confinement time to exceed a threshold value.
For deuterium–tritium fusion, this threshold is the least demanding of the fusion fuels.
Information Booster
The correct answer is 0.1 millisecond. The Lawson criterion for the deuterium–tritium (D–T) reaction states that energy break-even is achieved when the product of the number density (n) of fusing nuclei and the confinement time (τ) meets or exceeds a critical value:
n × τ ≥ 10²⁰ s/m³ (approximately, for D–T fusion)
Rearranging to solve for the minimum confinement time:
τ = (nτ)_required / n
Given the number density of the fusing nuclei, dividing the Lawson threshold (≈ 10²⁰ s/m³ for D–T) by that density yields the minimum confinement time. For the density specified in this problem, the calculation gives:
τ ≈ 0.1 millisecond
This confirms option (a). The D–T reaction requires the shortest confinement time of the candidate fusion fuels because it has the highest reaction cross-section at achievable plasma temperatures (around 10–15 keV), making it the most accessible route to break-even and the fuel of choice for reactors such as ITER.
Additional knowledge
• 0.5 millisecond — Incorrect. This is five times the correct value, arising from using too low a number density or too high a Lawson threshold in the τ = (nτ)/n calculation.
• 1.0 millisecond — Incorrect. This overestimates the confinement time tenfold, likely from a decimal-scaling error in the density or the Lawson product.
• 2.0 millisecond — Incorrect. This is twenty times the correct value, compounding an order-of-magnitude error with an additional factor, and would imply a far less favourable confinement requirement than D–T fusion actually demands.
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