A Simple Relation Between Plasma Density and Temperature in the Scrape-Off Layer of High Recycling Divertors

It has been found that values of neu and Teu in the SOL of single null, high recycling divertor discharges in JET and Alcator C-MOD are related approximately as Teu ∝ neu1/2, where (Teu, neu) are the values of plasma temperature and density on any given flux tube at the 'upstream' end, e.g., halfway between the two targets. Using the standard Two Point Model for the high recycling (Conduction-Limited) divertor, this result is shown to be directly related to criteria based on plasma collisionality that have to be satisfied if the flux tube is to be in the Conduction-Limited (high recycling) Regime rather than the Sheath-Limited (low recycling) Regime or the Detached Regime. Further, a tendency for the collisionality as calculated for upstream conditions to remain constant across the SOL is noted and explanations are given. The latter then implies the tendency for Teu ∝ neu1/2, to hold, not just at the separatrix, but across the SOL. This also implies that the upstream radial decay lengths can be expected to satisfy λn/λT0.5, in the Conduction-Limited Regime. Other simple correlations, such as between target ion saturation current density, Jsat,t, and neu are also implied, and are found to hold for the data base considered. These findings are, however, tendencies, and not universal relationships.