Nonlinear damping of zonal modes in anisotropic weakly collisional trapped electron mode turbulence

Comprehensive spectral analysis of a fluid model for trapped electron mode (TEM) turbulence reveals that marginally stable zonal modes at infinitesimal amplitude become robustly damped at finite amplitude. Zonal-mode structure, anisotropy, excitation, and wave number spectra are shown to result from interaction of the zero-frequency drift wave with the density advection nonlinearity. Heuristic dimensional balances, closure theory, and simulations manifest the primacy of the interaction, and yield energy transfer rates, fluctuation levels, spectra and finite-amplitude-induced dissipation. Strong sensitivity to the zero-frequency wave induces a marked spectral energy-transfer anisotropy that preferentially drives zonal modes relative to nonzonal modes. Zonal-mode excitation is accompanied by the nonlinear excitation of a spectrum of damped eigenmodes. The mixing of unstable TEM eigenmodes with the damped spectrum subjects zonal modes to finite-amplitude-induced damping. The combination of anisotropic transfer to zonal wave numbers and their nonlinear damping is shown to make this the dominant saturation mechanism for TEM turbulence