P.W. Terry and R. Gatto

Department of Physics, University of Wisconsin-Madison

Transport barriers in fusion plasmas occur in regions where the turbulence level is reduced by the action of a localized shear flow. Although many mechanisms have been proposed to explain the formation of shear flows, the problem is not yet understood. In this respect, the turbulent Reynolds stress (RS) has been postulated to generate shear flow both in tokamaks [1] where it is mainly electrostatic, and in Reversed-Field Pinches (RFPs) [2] where, on the contrary, it is predominantly magnetic. Noting that in the Madison Symmetric Torus (MST) the transition to the spontaneous enhanced confinement regime occurs at a sawtooth crash and is characterized by a shear layer near the edge of the plasma [3] it is conceivable that initially shear flow is created by the RS due to the excitation of diamagnetic edge modes by the cascade from the core resonant unstable tearing modes. After the crash, when the edge modes relax to their pre-crash magnitudes, shear flow is maintained by the RS due to the steepened pressure gradient created by suppression of turbulence.

To analyze such a scenario we study the generation of the RS associated with m=0 (low-n) and m=1 (high-n) tearing modes at rational surfaces at the edge of the RFP. We consider the tearing mode equations in slab geometry and solve them using a conductivity model which includes pressure-gradient effects (non-zero electron diamagnetic frequencies, omega*_n and omega*_T) and a linear shear flow localized near the resistive layer of the mode. The equations are solved by using a perturbative approach based on the smallness of a parameter proportional to the shear flow intensity.

We have analyzed the influence of the stability parameter Delta'
and omega* on the amplitude of
the RS.
The shear flow introduces asymmetries in the eigenfunctions leading to a linear variation
of the RS with shear strength.
The results of the calculations are compared with experimental measurements
of the magnetic RS in MST.
We conclude by considering a set of three coupled equations which model the
transition dynamics to the enhanced confinement regime.

Work supported by US DOE

[1] P. H. Diamond, Y.-M. Liang, B. A. Carreras, P. W. Terry, Phys. Rev. Lett., 72,
2565 (1994).

[2] R. Gatto, P. W. Terry, C. McKay and C. C. Hegna, US-EU TTF Meeting, Portland, OR,
1999.

[3] B. E. Chapman, A. F. Almagri, J. K. Anderson, et al., Phys. Plasmas 5, 1848 (1998).