On Radiative Density Limits and Anomalous Transport 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.

[1]  M. Rosenbluth,et al.  Electron heat transport in a tokamak with destroyed magnetic surfaces , 1978 .

[2]  B. Steffen,et al.  An ergodic divertor for tore supra , 1984 .

[3]  Resistive ballooning modes near the edge of toroidal configurations , 1999 .

[4]  L. Giannone,et al.  Physics of the density limit in the W7-AS stellarator , 2000 .

[5]  Y. Takeiri,et al.  Scalings of energy confinement and density limit in stellarator/heliotron devices , 1990 .

[6]  E. Strumberger,et al.  Finite-β magnetic field line tracing for Helias configurations , 1997 .

[7]  K. Lackner,et al.  Tokamak Confinement in Relation to Plateau Scaling , 1990 .

[8]  P. Ghendrih,et al.  Radiative instability in a diverted plasma , 1992 .

[9]  Y. Andrew,et al.  Sensitivity of calculated neutral helium line intensities and their ratios to uncertainties in excitation rate coefficients , 2000 .

[10]  K. Itoh,et al.  Detached and attached plasma in stellarators , 1988 .

[11]  W. Schneider,et al.  Thermal instabilities and poloidal asymmetries in the tokamak edge plasma , 1986 .

[12]  N. Ohyabu,et al.  One-dimensional simulation on stability of detached plasma in a tokamak divertor , 1999 .

[13]  P. Ghendrih,et al.  Thermal equilibrium in a diverted plasma , 1990 .

[14]  W. Stacey.  Explanation for MARFE formation and subsequent evolution into a detached symmetric plasma edge , 1996 .

[15]  Ralf Kaiser,et al.  Resistive ballooning modes in W7-AS and W7-X , 1993 .

[16]  W Vii-A Team,et al.  Impurity transport in the wendelstein VII-A stellarator , 1985 .

[17]  J. Connor.  Invariance principles and plasma confinement , 1988 .

[18]  M. Goossens,et al.  Multifaceted asymmetric radiation from the edge (MARFE's): A general magnetohydrodynamic study in a one-dimensional tokamak model , 1994 .