In this work, we propose a reduced model with a dynamical critical gradient to study the formation, propagation, and conversion of the transport barriers. In contrast to the commonly adopted static critical gradient, an evolving critical gradient self-consistently softens the profile stiffness, so as to facilitate the generation of transport barriers. This is especially crucial to the internal transport barrier (ITB) formation. Numerically, we show that the inhomogeneity of turbulent and neoclassical diffusivities can induce the global wave front propagation of the transport barrier. When the heating power ramps quickly, the ITB propagates unidirectionally to the edge region and converts into an edge transport barrier. For slow power ramping, the propagating ITB will bifurcate into bidirectional wavefronts and finally convert into a steady double transport barrier state. Our model uncovers the vital role of a dynamical 'profile-stiffness' in depicting the global dynamics of the transport barrier.
This paper proposes a model to study the formation, propagation, and conversion of transport barriers in tokamak plasmas. Unlike the static critical gradient, the model uses a dynamical critical gradient that allows for the generation of transport barriers, especially internal transport barriers (ITBs). The model shows that inhomogeneity of turbulent and neoclassical diffusivities can induce global wave-front propagation of transport barriers, and the speed of power ramping can lead to different barrier conversion scenarios.