Understanding Saturation and Turbulence: the Impact of Stable Modes

Turbulent heat fluxes arising from plasma microinstabilities are a key limiting factor in modern fusion experiments. Unlike that of such instabilities, our understanding of nonlinear saturation often remains schematic, limiting our predictive abilities. Here, we discuss how to analyze and interpret linearly stable eigenmodes and cover several examples where the importance of such modes in saturation can be leveraged to gain deeper insights into nonlinear processes and to produce improved reduced models.Stable modes absorb much of the linearly injected energy, providing the mechanism by which turbulence saturates, be it ion-temperature-gradient-driven (ITG), trapped-electron-mode, or driven shear-flow turbulence. In gyrokinetics, a vast number of stable modes exists at each wavenumber; however, a single pseudospectral mirror mode can be used to account for the collective action of many stable modes. In shear-flow turbulence, removal of the stable mirror mode leads to the substantial excitation of small-scale fluctuations.It is shown that the inclusion of stable-mode physics in quasilinear transport models allows us to recover the nonlinear upshift of the critical gradient as well as nonlinear electromagnetic stabilization, both of which arise due to a resonance between the unstable mode, the stable (pseudo-)mode, and the zonal flow. By extending this approach to account for non-zonal couplings, first successes have been achieved towards turbulence-optimizing stellarators.Finally, at low plasma beta, flux surfaces become stochastic on small scales, producing magnetic flutter transport. In the case of ITG turbulence, this stochasticity stems from a linearly stable microtearing mode receiving energy from the ITG mode.Open questions include how saturation involving successive triplet interactions can be described and how stable modes may be extracted more efficiently from simulations.