Theory of the spatiotemporal dynamics of transport bifurcations

The development and time evolution of a transport barrier in a magnetically confined plasma with nonmonotonic, nonlinear dependence of the anomalous flux on mean gradients is analyzed in the context of a one-field model. Upon consideration of both the spatial inhomogeneity and the gradient nonlinearity of the transport coefficient, it is shown that the transition develops as a bifurcation front with radially propagating discontinuity in the local gradient. The spatial location of the transport barrier as a function of input flux is calculated. The analysis indicates that for powers slightly above threshold, the barrier location $xb(t)∼[Dnt(P−Pc)/Pc]1/2$⁠, where $Pc$ is the local transition power threshold and $Dn$ is the neoclassical diffusivity. This result suggests a simple explanation for the high disruptivity observed in reversed shear plasmas. The basic conclusions of this theory are insensitive to the details of the local transport model.