Non-equilibrium Statistical Mechanics Treatment of Nonlinear Modal Networks for Prediction of Observables in Instability Driven Turbulence

In toroidal ion temperature gradient (ITG) driven turbulence, it remains a challenge to understand heat flux reduction at and above the threshold of linear instability for a range of driving gradients called the Dimits regime. A known but unexplained feature of this regime is the observation of temporally intermittent turbulent fluctuations and resulting transport. Preexisting theory for the Dimits shift successfully attributed heat flux reduction to resonance in mode coupling, but this analysis was based on a cumulant-discard method which neglected intermittency. In this work, mode coupling network schematics are developed to statistically predict various aspects of gradient driven turbulence due to the underlying nonlinearity that is accessible by some dynamical system, ideally a fusion plasma manipulable by machine controls. These schematics correspond to construction of sets of interacting modes consistent with ITG turbulence phenomenology which may then be associated to statistical distributions that make predictions of transport, zonal flow spectra, and the presence of spatiotemporal intermittency. The composite analysis then yields novel insight into the underlying nature of the Dimits Shift.