Fusion chain reaction-chain reaction with charged particles

Abstract

It is shown that in the case of a medium which is an exoergic nuclear mixture (a mixture of nuclei which can lead to an exoenergetic reaction) and which possesses a high temperature (\ensuremath{\sim}${10}^{7}$ \ifmmode^\circ\else\textdegree\fi{}K) or a relatively high density (\ensuremath{\sim}${10}^{4}$ g/cc), a fusion chain reaction can take place. This is due to the decrease in the stopping power of the medium under the conditions given above. Equations for determining the multiplication factor for a binary mixture under various physical conditions are derived. The multiplication factor is calculated for a DT mixture. It is concluded that for an exoergic nuclear mixture there exists a critical temperature or a critical density which limits the slow release of fusion nuclear energy. For an infinite medium of 50% DT mixture the critical temperature and the critical density are \ensuremath{\sim}${10}^{7}$ \ifmmode^\circ\else\textdegree\fi{}K and \ensuremath{\sim}${10}^{3}$ g/cc, respectively. In a finite medium the values are higher and there exists a critical mass which limits the possibility for the development of a fusion chain reaction. This critical mass was estimated and in first approximation is ${m}_{\mathrm{cr}} (\mathrm{in}\mathrm{grams})=1/{(\mathrm{density}\mathrm{of}\mathrm{the}\mathrm{medium}\mathrm{in} \mathrm{g}/\mathrm{cc})}^{2}$.