Simple relations between scrape-off layer parameters of high recycling divertors Part I: The relation between `upstream density and temperature

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 µ neu1/2, where (Teu,neu) are the values of plasma temperature and density on any given flux tube at the `upstreamʹ end, for example, 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 - which 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: the (Teu, neu) points for conduction limited flux tubes are predicted to fill a (somewhat narrow) band in the (Teu, neu) plane. Secondly, a tendency for the collisionality, as calculated for upstream conditions, to remain constant across the SOL is noted and an explanation is given. The latter then implies a tendency for Teu µ neu1/2, to hold, not just at the separatrix but across the SOL. Thirdly, for the JET data a further re-enforcing factor tending to cause a rather strong Teu µ neu1/2 correlation is identified in the dependence of cSOL^ on the plasma parameters. The values of cSOL^ were extracted from the JET data using an onion skin method analysis. The first effect is expected to be general to Atokamaks operated in the high recycling/conduction limited regime, although it only states that (Teu, neu) values will fall within a certain band, and a decreasing value of Teu with increasing neu is not ruled out. It is not known at this time how general the second two effects are.