Damping of zonal modes through turbulent momentum transport

It is shown that the radial transport of parallel momentum provides a damping mechanism for the zonal flow relevant for plasma turbulence close to the nonlinear threshold. The damping mechanism is confirmed by a “Rosenbluth-Hinton” test with a model radial momentum diffusion, in which the decay rate of the residual potential is found to be proportional to the model diffusion coefficient and in good agreement with the analytical result. Nonlinear simulations show that, when momentum transport is suppressed, stronger long wavelength zonal flow shearing occurs. The suppression of momentum transport then allows for the development of fully developed staircase structures in the E × B shear, which can suppress turbulence completely for a finite time window. No impact on shorter wavelength zonal flows is observed, in contrast to the analytical prediction which suggests a high damping rate. The latter result raises the question of the relevance the residual zonal flow plays in turbulence saturation.