Degenerate Bogdanov-Takens bifurcations in Fusion Plasma models

Abstract

Experiments in tokamaks (nuclear fusion reactors) have shown two modes of operation: L-mode and H-mode. Transitions between these two modes have been observed in three types: sharp, smooth and oscillatory. The same modes of operation and transitions between them have been observed in simplified transport models of the fusion plasma in one spatial dimension.

We study the dynamics in such a one-dimensional transport model by numerical continuation techniques. To this end the MATLAB package cl_matcontL was extended with the continuation of (codimension-2) Bogdanov-Takens bifurcations in three parameters using subspace reduction techniques. By applying these techniques to the transport model, we are able to detect a degenerate Bogdanov-Takens bifurcation of codimension 4. The computed 1- and 2-parameter slices are in agreement with the presence of this codimension-4 degenerate Bogdanov-Takens bifurcation. All three types of L-H transitions can be recognized in these slices.