The Fusion Triple Product

The single figure of merit n T tau_E that compresses the ignition requirement into one number.

Why three quantities combine

Fusion power density scales as n^2 , and over the relevant temperature range for D-T rises roughly as T^2. Losses scale as nT/tau_E. Balancing them makes the ignition condition depend on the product of density, temperature, and confinement time together, the triple product:

n T tau_E >= about 3 x 10^21 keV s / m^3  (D-T, near optimal temperature)

Because the three factors trade off, a device can compensate lower density with longer confinement, or vice versa. The triple product therefore lets very different machines be compared on one axis.

Units and conventions

The product is usually quoted in keV s per cubic meter (or the older keV s per cubic centimeter). The exact threshold depends on impurity content, profile shapes, and whether break-even or full ignition is meant, so quoted values vary by a factor of a few.

How it is computed

• Take the peak or volume-averaged n and T from a profile calculation
• Take tau_E from confinement scaling or from measured stored energy divided by loss power
• Multiply, and compare against the temperature-dependent threshold curve

In simulation, the triple product is a diagnostic output of the transport-plus-power-balance solve rather than an input.

Progress and honesty

Historical fusion progress is often plotted as triple product versus year. It is a necessary milestone, not proof of net electricity, which depends on engineering conversion efficiencies. The Hyperion breeder is a design study with a target plasma gain of 3.424; Kronos makes no hardware net-gain claim before first-of-a-kind operation.