VOLUME 78, NUMBER 8 PHYSICAL REVIEW LETTERS 24 FEBRUARY 1997 Dynamics of Transition to Enhanced Confinement in Reversed Magnetic Shear Discharges P. H. Diamond, 1, * V. B. Lebedev, 1 D. E. Newman, 2 B. A. Carreras, 2 T. S. Hahm, 3 W. M. Tang, 3 G. Rewoldt, 3 and K. Avinash 4 1 Dept. of Physics, University of California at San Diego, La Jolla, California 92093-0319 2 Fusion Energy Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 3 Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08544 4 Institute for Plasma Research, Bhat, Gandhinagar, 382 424, India (Received 5 March 1996) A simple model of the transition to enhanced confinement in reversed shear discharges is presented. The proposed transition mechanism relies on a synergism between electric field shear suppression of turbulence aided by reduced curvature drive due to magnetic shear reversal or reduction. Profile structure and transport barrier propagation dynamics are predicted. A novel analytical theory for the time evolution of the barrier foot-point location is presented. The model predicts that the transition threshold has favorable dependence on pretransition temperature ratio T i T e , in-out asymmetry in the E 3 B shearing rate (i.e., lower for larger Shafranov shift), density profile peakedness, and unfavorable scaling with density. Optimal confinement occurs in discharges where deposition is peaked within the magnetic shear reversal radius. [S0031-9007(97)02457-5] PACS numbers: 52.55.Fa Achieving understanding and control of turbulent trans- port is a necessary prerequisite for the design of an eco- nomical advanced tokamak fusion reactor. Significant progress toward enhanced performance has been made by exploiting the spontaneous transition to high confinement regimes, such as H mode [1] or VH mode [2] induced by increased radial electric field shear. Such E r shear [3], which is produced by the onset of sheared rotation and the steepening of the ion pressure profile, suppresses tur- bulence and transport [4], thus initiating a self-reinforcing feedback [5,6] which results in a bifurcation to a state with significant local reduction of fluctuations and trans- port. In H mode and VH mode, the transport barrier is initiated at the plasma edge. Recently, a new regime of enhanced core confinement has been discovered in discharges with reversed mag- netic shear [7,8]. In such discharges, formed by intense auxiliary heating of prelude (pretransition) plasmas dur- ing current ramp-up, confinement is observed to increase dramatically when a critical power input level is surpassed. Stored energy content builds rapidly, and a transport bar- rier forms at r * r min , where r min is the location of the minimum of qr . Typically, particle, ion thermal and momentum transport in the core of such ERS (enhanced reversed shear) [7] and NCS (negative central shear) [8] plasmas is reduced to levels below that of conventional neoclassical theory. This is consistent with the long stand- ing predictions that negative magnetic shear will reduce geodesic curvature drive of microinstabilities [such as the toroidal ion temperature gradient (ITG) driven mode, vari- ous trapped particle modes, and high-n ballooning modes] and that peaked density profiles will quench ITG modes [9,10]. Nevertheless, the theoretical predictions that resid- ual ITG turbulence and collisionless trapped electron mode turbulence should persist in prelude discharges [11], as well as the experimental indications of a clear bifurca- tion in particle, energy and momentum content evolution (as shown by a discontinuity in the time derivative of lo- cal density, ion temperature, and toroidal rotation velocity) subsequent to establishment of reversed shear all together suggest that magnetic shear reversal is not sole cause of the remarkable confinement improvements observed in ERSNCS-mode plasmas. This is consistent with the ob- servation of internal transport barriers in weakly negative shear discharges, where geodesic curvature drive is not fully eliminated [8]. Here, we propose a simple model of ERSNCS tran- sition dynamics. The model consists of an electric field shear driven transport bifurcation which develops in the radially inhomogeneous ambient transport environment characteristic of the prelude phase plasmas. The strong radial inhomogeneity is a consequence of the qr  profile structure. The essential mechanism intrinsic to the model is a local transport bifurcation which occurs when a lo- cal profile gradient threshold (entering the determination of E 0 r ) is exceeded. Magnetic shear reversal lowers the lo- cal threshold, thus facilitating transition and localizing the region of barrier formation to the region of shear reversal. Thus, a synergism between the reduced curvature drive of the pretransition reversed shear plasma and the E 0 r -driven transport bifurcation is fundamental to this model. The transition front is predicted to propagate [12] outward in ra- dius until it reaches a radius at which the power, particle, or momentum input is insufficient to exceed the local thresh- old criterion. Note that within the scope of this model, the obvious question of why the electric field shear bifurcation is spatially pinned to the region of magnetic shear reversal is straightforwardly resolved, since (even weakly) negative shear significantly reduces geodesic curvature drive, thus lowering the local (electric field-shear-driven) bifurcation 1472 0031-9007 97 78(8) 1472(4)$10.00 © 1997 The American Physical Society