Some Divertor Scaling Considerations

A case is advanced for ``divertor non-scaling'', viz that absolute values of divertor density $n_d \sim 10^{21}$ m$^{-3}$ and temperature $T_d \sim$ 5 eV need to be achieved for optimal demo/reactor-relevant studies. For $T_d >$ 10 eV sputtering is very strong; for $T_d <$ 2 eV there is risk of detachment and density limit. High $n_d$ is required for high power, high duty cycle devices so that net erosion $\ll$ gross erosion via prompt local re-deposition of sputtered material. This occurs when impurity neutral ionization mean free path $\ll$ fuel ion gyro-radius (magnetic pre-sheath thickness); for $B\sim$ 5~T this requires $n_d\stackrel {>} {\sim} 10^{21}$ m$^{-3}$. Thus peak parallel power flux density $\sim 0.1 - 0.5$ GW/m$^2$. Modified two-point modeling then gives that: (a) ``upstream'' (e.g. outside midplane, separatrix), conditions, $n_{eu}$, $T_u$, are almost fixed, independent of R (device size) and P$_{\rm SOL}$ (power entering the SOL), and (b) the required P$_{\rm SOL}\sim$ R$^1$, R$^{1.5}$ or R$^2$, depending on assumptions about target power width; the latter are discussed. A test device with these absolute $n_d$, $T_d$ values will reproduce the most critical edge aspects of demo/reactors including power handling and material erosion/migration.