On radiative density limits in stellarators

Density limits in stellarators are caused mainly by enhanced impurity radiation leading to a collapse of the temperature. A simple model can be established, which computes the temperature in the plasma with a fixed heating profile and a temperature-dependent radiation profile. If the temperature-dependent radiation function has one or several extrema, multiple solutions of the transport equation exist and radiative collapse occurs when the high temperature branch merges with the unstable temperature branch. At this bifurcation point the temperature decreases to a stable low temperature solution. The bifurcation point is a function of the heating power and the plasma density. Thus a density limit can be defined as the point where bifurcation occurs. It is shown that bifurcation and sudden temperature collapse does not occur below a power threshold. Anomalous thermal conductivity and the details of the impurity radiation, which in the present model is assumed to be in corona equilibrium, determine the scaling of the density limit. A model of the anomalous transport is developed, which leads to Gyro-Bohm scaling of the confinement time. The density limit based on this transport model is close to experimental findings in Wendelstein 7-AS. (author)