Intrinsic thermal stability of a D–T burning point

A burning D–T plasma is normally stabilised against thermal excursions by external control. This note derives a threshold condition under which a burning point is intrinsically thermally stable, that is, self-correcting with no controller: nu < (1 + f) / 2 where nu = d ln / d ln T is the logarithmic slope of the D–T reactivity and f is the transport fraction of the total losses, the remainder being radiative. If the confinement degrades with power as tau_E ~ P^(-delta), the condition relaxes to nu < f(1 + delta*nu) + (1 - f)/2. Evaluated with the Bosch–Hale D–T parametrisation, the intrinsically stable branch begins between approximately 26 keV (transport-dominated losses) and 39 keV (radiation-dominated losses). Operating there costs power density at fixed beta — between 72% and 43% of the maximum, which lies at 13.5 keV — and the loss is recovered, since P_fus scales as B^4, by a toroidal field increase of between 9% and 24%. This premium is set against the field increase already delivered by high-temperature superconducting magnets. The limits of the criterion are stated explicitly: it is local, and it does not address the beta limit, synchrotron losses or impurity accumulation. The note closes with a request for references, on whether the criterion is already known in the burning-plasma literature under another name.