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 x(b)(t) similar to [D(n)t(P - P-c)/P-c](1/2), where P-c is the local transition power threshold and D-n 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. (C) 1997 American Institute of Physics.