Reactivity Versus Temperature

The rate-averaged cross-section for D–He-3 rises steeply through the tens of keV and broadens past ~100 keV, framing the operating window.

The reactivity curve

Fusion power density scales with n₁ n₂ ⟨σv⟩, where ⟨σv⟩ is the reaction rate averaged over the ion velocity distribution. For D–³He, ⟨σv⟩ is small below 20 keV, climbs steeply through 30–80 keV, and flattens beyond ~100 keV. The burner sits on the upper shoulder of this curve near 90 keV.

D–T (dashed) peaks near 64 keV and is larger at every temperature; D–³He (gold) peaks higher and later. The gap is why D–³He needs a higher temperature and a higher triple product to reach the same power density.

Reading the window

The practical window is bounded below by insufficient reaction rate and above by radiation and confinement penalties. The ~90 keV design point is chosen inside that window, accepting that D–³He will always be reactivity-limited relative to D–T.

The averaging that produces ⟨σv⟩ matters as much as the peak: because reactions are dominated by the fast tail of the distribution, the reactivity is sensitive to how well the plasma stays Maxwellian and how hot the ions run relative to the electrons. A hot-ion mode, where T_i exceeds T_e, both raises ⟨σv⟩ and eases the bremsstrahlung balance, which is why the burner targets it.

• Power density ∝ n₁n₂⟨σv⟩
• D–³He reactivity peaks higher and later than D–T
• Steep rise through 30–80 keV
• Operating window sits on the upper shoulder