The Role of Magnetic Shear for Zonal Flow Generation and Transport Barriers

The role of magnetic shear for zonal flow generation by ion-temperature-gradient (ITG-) and trapped electron (TE-) mode turbulence is studied analytically using fluid descriptions. The scaling of the zonal flow (ZF) growth rate with magnetic shear is examined and compared with linear growth rates for typical tokamak parameter values. The results indicate that large levels of ZF are obtained in regions of negative magnetic shear, in particular for ZF driven by TE mode turbulence. The strong magnetic shear scaling obtained for TE mode driven zonal flows originates from the bounce average of the electron magnetic drifts. The study of turbulence suppression and generation in magnetically confined fusion plasma research has attracted much interest recently. It is well established that the interaction between small scale turbulence and zonal flows, which are radially localized flows propagating mainly in the poloidal direction, can reduce the radial transport by shearing the eddies of the driving background turbulence. The purpose of the present paper is to extend previous analytical studies (1)-(2) to investigate the effects of magnetic shear on the zonal flow generation by ion-temperature-gradient (ITG-) and trapped electron (TE-) mode turbulence, respectively. The ITG- and TE-mode driven cases will be considered separately and the corresponding ZF generation by ITG and TE mode turbulence will be calculated and compared. For the ITG mode description, a reduced version of the standard Weiland model (3) is utilized. In this formulation the ITG model includes the ion continuity and the ion temperature equations, neglecting the influence of parallel ion momentum and electromagnetic effects, while the electrons are assumed to be Boltzmann distributed. The TEM model is based on the bounce averaged electron continuity and electron temperature equations for the trapped electron fluid (4). The ion and trapped electron mode fluid models are fairly symmetric except for the FLR terms which are included in the ion fluid model and the bounce average which is performed on the electron quantities. The zonal flow evolution is treated by the vorticity equation. The generation of ZF by ITG- and TE-modes are studied