Role of stable eigenmodes in gyrokinetic models of ion temperature gradient turbulence

Investigation of ion temperature gradient turbulence in gyrokinetic models shows that some of the key features of reduced models associated with saturation by nonlinearly excited damped eigenmodes carry over to gyrokinetics. For nonzonal wavenumbers the frequency spectrum in gyrokinetics is broader by a factor of 10 than simple nonlinear broadening of the most unstable eigenmode. The width, including its variations with wavenumber and temperature gradient scale length, closely tracks accessible stable eigenmodes as approximated by a gyro-Landau fluid model for the same parameters. Cross-phase probability distribution functions (pdfs) and fluxes show nonlinear behavior consistent with stable eigenmodes in nonzonal wavenumbers contributing to 30% of the fluctuation energy. Phase pdfs and cross-phase time histories show that multiple eigenmodes [in addition to high frequency geodesic acoustic modes (GAMs)] are a significant part of the ky=0 spectrum. Two possible roles of zonal modes in saturation are proposed. First, known nonlinearly accessible stable zonal eigenmodes (in addition to zonal flows and GAMs) are discussed and it is suggested that if these eigenmodes are excited they may be the primary arbiter of saturation. Second, zonal modes may facilitate energy transfer from unstable eigenmodes to stable eigenmodes at finite ky.