Dynamics of spatiotemporally propagating transport barriers

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Abstract
A simple dynamic model of spatiotemporally propagating transport barriers and transition fronts from low (L) to high (H) confinement regimes is presented. The model introduces spatial coupling (via transport) into the coupled evolution equations for flow shear and fluctuation intensity, thus coupling the supercritical L to H bifurcation instability to turbulent transport. Hence, fast spatiotemporal front propagation and evolutionary behavior result. The theory yields expressions for the propagation velocity and termination point of an L–H transition front and transport barrier. When the evolution of the pressure gradient, ∇Pi, and the contribution of ∇Pi to sheared electric field, Er′, is included, the ambient pretransition pressure gradient acts as a local source term that drives the evolution of the poloidal velocity shear. The transition may then evolve either as a spatiotemporally propagating front or as a uniform (i.e., nonlocal) fluctuation reduction or quench. The precise route to transition adopted depends on the relative magnitudes of the front transit time, τT, and the fluctuation reduction time, τf, respectively. The relevance of spatiotemporally propagating L–H transition fronts to the very high confinement regime (VH mode) evolution in DIII‐D [R. I. Pinsker and the DIII‐D Team, Plasma Physics and Controlled Nuclear Fusion Research 1992 (International Atomic Energy Agency, Vienna, 1993), Vol. 1, p. 683] and in the Joint European Torus (JET) [Plasma Physics and Controlled Nuclear Fusion Research 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 27] is discussed.