Effect of Radial Electric Field Shear on Tokamak Transport:
Flow Shear and Magnetic Field Scaling
S. H. Batha,† S. D. Scott,‡ D. R. Mikkelsen,‡ C. C. Petty,*
E. J. Synakowski,‡ G. Taylor,‡ and M. C. Zarnstorff‡
†Fusion Physics and Technology, Inc., Torrance, CA USA; ‡Princeton Plasma Physics
Laboratory, Princeton, NJ USA; *General Atomics, San Diego, CA USA
I. Introduction
Numerous recent tokamak experiments using reversed magnetic shear have renewed interest
in the connection between reduced energy and particle transport and large shearing rates of the
radial electric field.[1,2] A simple criterion has been suggested[3] for turbulence and transport
suppression. Transport is suppressed when the shearing rate, γExB, is larger than the linear
growth rate, γmax, of the fastest growing mode involved in the transport. The shearing rate is
defined as γExB ≡ RBp/Bt∂(Er/RBp)/∂r where Bp and Bt are the poloidal and toroidal magnetic
fields, respectively.[4] Force balance determines the radial electric field to be Er = ∇P/nZe +
VtBp - VpBt. In plasmas with small pressure gradients, such as in L-mode discharges, the ratio
γExB/γmax is expected to scale as MBp/Bt where M is the toroidal Mach number (M = Vt/Cs and Cs
is the ion sound speed).
Although complete turbulence suppression requires γExB ≈ γmax, nonlinear numerical
turbulence calculations have indicated that transport could be reduced even when γExB < γmax.
Thus, shear-flow effects could potentially affect confinement in a variety of plasma regimes
including L-mode and the H-mode core. For this reason, the dependence of the shearing rate on
the toroidal velocity may be a concern for the validity of ρ* and other scaling experiments that
use only uni-directional beam injection. The results of those scaling experiments may be
confused by a favorable scaling of transport with increased flow shear. Also, empirical
expressions for the global energy confinement time, τE, typically do not explicitly account for
rotation effects. Scalings deduced from rotating plasma