Intermittency and the Fourth Order Cumulant of Toroidal Ion Temperature Gradient Driven Turbulence

Intermittency in the turbulent fluctuations associated with the Dimits regime of toroidal ion temperature gradient (ITG) driven turbulence is investigated via weak turbulence closure. The fourth order cumulant is calculated perturbatively and employed as a primitive metric to quantify both the strength of a system's departure from Gaussianity as well as the timescales associated with this behavior. Intermittency is of interest as it is observed that the turbulent fluctuation probability distribution features a significant non-Gaussian tail in the Dimits regime, where there exists a discrepancy between instability growth rate and heat flux both as a function of temperature gradient. In a phenomenon known as the Dimits shift, the heat flux is considerably suppressed at and above the linear critical gradient until sufficiently large values of temperature gradient are imposed upon the system. This increase in the critical gradient above the threshold predicted by linear theory has recently been attributed to resonance in mode coupling, but the intermittent behavior of fluctuations was not included in that analysis. The weak turbulence closure calculates fourth order cumulants which express non-Gaussian behavior due to the presence of correlation and resonant interactions amongst tetrads of fluctuations. The intermittency arising from consideration of said cumulants is evaluated numerically and compared with preexisting theory and simulation to assess the approximate influence of non-Gaussian statistics on features of toroidal ITG driven turbulence.