P. Bachmann

Bifurcation of temperature and anomalous transport in the boundary region of Wendelstein 7-X

This paper discusses some problems of the island divertor in the Wendelstein \mbox{7-X} configuration. These islands exist on the ? = 1 surface at the plasma boundary and will be utilized for impurity control in the Wendelstein \mbox{7-X} experiment. The structure of this island region depends on the plasma pressure and the tendency is to become more and more ergodic with rising plasma pressure. Thermal transport in the divertor region is described by the transport equation, which is inherently three-dimensional. By averaging along the helical geometry of the island, this equation can be reduced to a two-dimensional one describing the temperature distribution in the poloidal plane. In this approximation a strong similarity to tokamak geometry exists. Since the plasma currents modify the islands, a finite-? equilibrium is computed as the basis of a geometric analysis of divertor action. Anomalous transport strongly affects the width of the scrape-off layer and the width of the wetted area on the divertor target plates; therefore it is investigated how anomalous transport modifies the transport equation. The non-linearity of the radiation losses in the divertor region and the non-linearity of the boundary conditions can lead to a bifurcation of the temperature distribution and to multiple solutions. Some numerical examples of one-dimensional temperature profiles and bifurcated solutions are given.

Chaos in 1D Radiative Edge Plasmas

Bifurcation and chaos in radiative edge plasmas are investigated on the basis of a periodically driven reaction-diffusion equation which results from the time dependent 1d heat conduction equation including a given periodically time-modulated impurity density. The temporal problem shows the transition to chaos through the Feigenbaum route. In 1d and time dependent plasmas Hopf bifurcation and intermittency phenomena exist. The application to a carbon seeded plasma shows the existence of different oscillation regimes.

Bifurcation of Temperature in Edge Plasmas

Multiple solutions and bifurcation phenomena of the 1d heat conduction equation are caused by the non-monotonic dependence of the impurity radiation function on the temperature [1], [2], or nonlinear boundary conditions for the heat flux to the target plates in the high-recycling regime [3]. This paper deals with temperature bifurcations in radiative edge plasmas. The starting point is the 3-dimensional heat conduction equation. At first general existence, stability and bifurcation conditions of multiple steady solutions of the 3d heat conduction equation are discussed. Then the 2d energy balance for the edge plasma both of a axisymmetric plasma device and a limiter tokamak is analyzed. Numerical solutions to the derived stationary 2d heat conduction equation demonstrate different aspects of temperature bifurcations.