Parameter of Merit for Experiments Aiming at DT Ignition

Given the importance of reaching ignition conditions in magnetically confined plasmas [1] it is appropriate to identify parameters of merits for the design of future machines. One considered for the Ignitor experiment is ${{P}_{mI}}=B_{p}^{2}{{I}_{T}}$, where ${{I}_{T}}$ is the toroidal plasma current and ${{B}_{p}}$ is the average poloidal field, aiming for about 100 (T2 MA). The starting point for ${{T}_{e}}\simeq {{T}_{i}}$, is $\Re \simeq {{\alpha }_{T}}nTD_{\bot }^{th}/{{a}^{2}}\ $ where $\Re $ is the D-T reactivity, $\Re \propto {{\alpha }_{F}}{{n}^{2}}{{T}^{2}}$ and a is the mean plasma radius. Assuming $D_{\bot }^{th}\propto {{\alpha }_{D}}/n\ $ and $n\propto {{\alpha }_{L}}J$, where $J$ is the current density,${{\alpha }_{F}}{{n}^{2}}{{T}^{2}}\simeq {{\alpha }_{T}}nT{{\alpha }_{D}}/\left( J{{a}^{2}}{{\alpha }_{L}} \right)\ $ and, for $nT\propto {{\alpha }_{c}}B_{p}^{2}$ we obtain $B_{p}^{2}{{I}_{p}}\propto \left( {{\alpha }_{D}}{{\alpha }_{T}} \right)/\left( {{\alpha }_{F}}{{\alpha }_{c}}{{\alpha }_{L}} \right)\ $. The introduced $\alpha $-parameters involve weaker dependences on plasma and machine characteristics than those given already. \\ $[1]$ B. Coppi and the Ignitor Team, Nucl. Fus. 55, 053001 (2015).