Propagating zonal flows and turbulence saturation in magnetised fusion plasmas

Toroidal fusion devices are plagued by drift-wave turbulence causing large heat fluxes and limiting the confinement time. It is therefore crucial to understand the mechanisms for turbulence saturation, which typically involve the interplay between drift waves and zonal flows shearing apart turbulent eddies. Toroidal geometry has long been known to affect the linear zonal flow physics, weakening stationary zonal flows and introducing the rapidly oscillating geodesic acoustic modes. In this talk, I will demonstrate that the toroidicity also plays a pivotal role for the nonlinear zonal flow dynamics, giving rise to the toroidal secondary, a new mode of radially propagating zonal flows. The theory and physical mechanism of the toroidal secondary will be presented and validated using gyrokinetic simulations. Furthermore, the toroidal secondary will be shown to set the saturation level of ion-temperature-gradient turbulence. By combining the new zonal flow physics with the critical balance conjecture, scaling laws are derived for the turbulent heat flux, the eddy scale lengths, and the zonal flow amplitude, which are in agreement both with turbulence simulations and with past experimental observations.