Influence of the tritium ${\beta }^{-}$ decay on low-temperature thermonuclear burn-up in deuterium-tritium mixtures

Low-temperature $(T<~15\mathrm{keV})$ thermonuclear burn-up in deuterium-tritium mixtures with various deuterium–tritium–helium-3 ratios is considered. The general dependence is studied for the critical burn-up parameter $x_c=\rho r_c$ upon the initial temperature T, density ${\rho }_0,$ and tritium molar concentration y for the $\left[\mathrm{D}\right]:y\left[\mathrm{T}\right]:\left(1\mathrm{}-y\right){[}^3\mathrm{He}]$ mixture. In particular, it is shown that, if the tritium concentration y decreases, then the critical burn-up parameter $x_c(T,{\rho }_0,y)$ grows very quickly (at fixed T and ${\rho }_0).\mathrm{}$ This means that tritium ${\beta }^{-}$ decay significantly complicates thermonuclear burn-up in deuterium-tritium mixtures.