The Reynolds stress induced by weakly up-down asymmetric ion temperature gradient mode
A weakly up-down asymmetric ion temperature gradient (ITG) mode (formed in the up-down symmetric equilibrium), localized in the bad curvature region, may contribute dominantly to the nonlinear Reynolds stress because its growth rate is higher than the competing modes: the strongly up-down asymmetric modes, and other modes peaked (poloidally) away from the outboard mid-plane. Based on the fluid ITG model, the parameterized analytic wave function is constructed in the two dimensional (2D) Fourier-ballooning representation, and numerically verified by making use of the finite difference methods. Analytic expressions for the poloidal Reynolds stresses, defined on a rational surface, are given for both the weakly and the strongly up-down asymmetric ITG modes. It is shown here that the poloidal stresses of both modes can be interpreted as a superposition of a monopole and a dipole structure. For comparison with the experiment, the stresses are calculated for L-mode discharge parameters on five machines. Analytic expressions for the total parallel Reynolds stresses (contributed from all rational surfaces) are also derived for both modes: they are also exhibited, graphically, using a Gaussian wave intensity model.