On secondary and tertiary instability in electromagnetic plasma microturbulence

Zonal flows, widely accepted to be the secondary instability process leading to the nonlinear saturation of ion temperature gradient modes, are shown to grow at higher rates relative to the linear mode amplitude as the plasma pressure β is increased—thus, confirming that zonal flows become increasingly important in the turbulent dynamics at higher β. At the next level of nonlinear excitation, radial corrugations of the distribution function (zonal flow, zonal density, and zonal temperature) are demonstrated to modify linear growth rates moderately through perturbed-field, self-consistent gradients: on smaller scales, growth rates are reduced below the linear rate. In particular, excitation of kinetic ballooning modes well below their usual threshold is not to be expected under normal conditions. These findings strengthen the theory of the non-zonal transition M. J. Pueschel et al., Phys. Rev. Lett. 110, 155005 (2013).