Stability and control of iterated non-linear transport solvers for fusion edge plasmas

The application of numerical transport solvers for the steady state plasma boundary of magnetic fusion devices is related to the iterative approximation of a fixed-point of a non-linear map. Although 2D (axisymmetric) or even 3D transport solvers are routinely applied for the quantification of steady state plasma flows, unstable behavior can occur under certain conditions. A simple two-point model is applied to demonstrate the generic nature of this kind of unstable behavior which can occur when the fixed-point loses its stability and resulting in a period doubling route to chaos. Furthermore, it is demonstrated that wavelike oscillations can occur at low divertor temperatures. An adaptive relaxation scheme is presented which allows to suppress discrete and wavelike oscillations in order to stabilize the fixed-point iteration.