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Density limits in stellarators are caused mainly by enhanced impurity radiation leading to a collapse of the temperature on the time scale of the energy confinement time rather than on a fast MHD time scale, which is characteristic for a loss of equilibrium. 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. Radiative collapse occurs when the high-temperature branch merges with an unstable temperature branch. The bifurcation point is a function of the heating power and the plasma density. Thus a density limit can be defined by the existence of the upper bifurcation point, where the stable high-temperature branch ceases to exist. 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. Some numerical examples are given, one with radiation centred in the plasma core and the other one with boundary radiation. The scaling of the density limit is dependent on the localization of the radiation. 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 compared with experimental findings in Wendelstein 7-AS and Wendelstein 7-A.

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Authors: WOBIG H, Max-Plank-Institut fur Plasmaphysik,EURATOM-Association, Boltzmannstrasse 2, D-85748 Garching (DE)
Bibliographic Reference: Article: Plasma Phys. Control. Fusion, Vol. 42 (2000), pp. 931-948
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