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

It has been found that values of n(eu) and T-eu in the SOL of single null, high recycling divertor discharges in JET and Alcator C-Mod are related app roximately as T-eu proportional to n(eu)(1/2), where (T-eu, n(eu)) are the values of plasma temperature and density on any given flux tube at the 'ups tream' end, for example, halfway between the two targets. Using the standar d two point model for the high recycling (conduction limited) divertor, thi s result is shown to be directly related to criteria based on plasma collis ionality - which have to be satisfied if the flux tube is to be in the cond uction limited (high recycling) regime rather than the sheath limited (low recycling) regime or the detached regime: the (T-eu, n(eu)) points for cond uction limited flux tubes are predicted to fill a (somewhat narrow) band in the (T-eu, n(eu)) plane. Secondly, a tendency for the collisionality, as c alculated for upstream conditions, to remain constant across the SOL is not ed and an explanation is given. The latter then implies a tendency for T-eu proportional to n(eu)(1/2), to hold, not just at the separatrix but across the SOL. Thirdly, for the JET data a further re-enforcing factor tending t o cause a rather strong T-eu proportional to n(eu)(1/2) correlation is iden tified in the dependence of chi(perpendicular to)(SOL) on the plasma parame ters. The values of chi(perpendicular to)(SOL) were extracted from the JET data using an onion skin method analysis. The first effect is expected to b e general to tokamaks operated in the high recycling/conduction limited reg ime, although it only states that (T-eu, n(eu)) values will fall within a c ertain band, and a decreasing value of T-eu with increasing n(eu) is not ru led out. It is not known at this time how general the second two effects ar e.