On the Murakami density limit in tokamaks and reversed-field pinches

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Abstract
A theoretical upper limit for the density in an Ohmically heated tokamak discharge follows from the requirement that the Ohmic heating power deposited in the current‐carrying channel exceed the impurity radiative cooling in this critical region. A compact summary of our results gives this limit nM for the central density as nM =[Ze/(Ze−1)]1/2 ne0 (BT /1T) (1m/R), where ne0 depends strongly on the impurity species and is remarkably independent of the central electron temperature Te(0). For Te(0) ∼1 keV, ne0 =1.5×1014 cm−3 for beryllium, ne0 =5.5×1013 cm−3 for oxygen, ne0 =1.0×1013 cm−3 for iron and, ne0 =0.5×1013 cm−3 for tungsten. The results agree quantitatively with Murakami’s original observations. A similar density limit, known as the I/N limit, exists for reversed‐field pinch devices and this limit has also been evaluated for a variety of impurity species.