The tritium burn-fraction in DT fusion

Abstract: The fraction of the tritium that is burned during one pass through a DT fusion system, $f_{tb}$, is a central issue for success of fusion energy. Reducing the tritium fraction, $f_t$, in a $DT$ burning plasma below a half increases the burn fraction, $f_{tb}\propto1/f_t$ but also the required confinement to achieve a burn $nT\tau_E\propto1/f_t(1-f_t)$. A doubling of the fractional burn entails only a 4/3 enhancement of the required $nT\tau_E$. The energy confinement time $\tau_E$ in tokamaks and stellarators is empirically gyro-Bohm with an approximate factor of two between the best and worse results used to construct scaling laws. Gyro-Bohm is also the approximate level of transport needed in a power plant. What has received little study are $\tau_t/\tau_E$, the ratio of the tritium to the energy confinement time, and $\tau_\alpha/\tau_E$, the ratio of the alpha particle to the energy confinement time. The tritium burn fraction is proportional to $\tau_t/\tau_E$, so the larger the better. The contamination of the plasma by helium ash is proportional to $\tau_\alpha/\tau_E$, so the smaller the better.