Theory of ITG turbulent saturation in stellarators: Identifying mechanisms to reduce turbulent transport

Abstract

A three-field fluid model that allows for general three-dimensional equilibrium geometry is developed to describe ion temperature gradient turbulent saturation processes in stellarators. The theory relies on the paradigm of nonlinear transfer of energy from unstable to damped modes at comparable wavelength as the dominant saturation mechanism. The unstable-to-damped mode interaction is enabled by a third mode that for dominant energy transfer channels primarily serves as a regulator of the nonlinear energy transfer rate. The identity of the third wave in the interaction defines different scenarios for turbulent saturation with the dominant scenario depending upon the properties of the 3D geometry. The nonlinear energy transfer physics is quantified by the product of a turbulent correlation lifetime and a geometric coupling coefficient. The turbulent correlation time is determined by a three-wave frequency mismatch, which at long wavelength can be calculated from the sum of the linear eigenfrequencies of the three modes. Larger turbulent correlation times denote larger levels of nonlinear energy transfer and hence smaller turbulent transport. The theory provides an analytic prediction for how 3D shaping can be tuned to lower turbulent transport through saturation processes.

Turbulence, transport, and zonal flows in the Madison symmetric torus reversed-field pinch

“…When the shear is strengthened only enough to bring the parallel and curvature drift frequencies to comparable values, the zonal flow no longer dominates saturation. 35 Instead, removing the zonal flows results in only a slight increase in saturation level, much like the situation described here for the ITG turbulence in the RFP. Moreover, an analysis of the triplet wavenumber interactions further confirms that non-zonal couplings become dominant in the regime of comparable drifts.…”

Stellarator microinstabilities and turbulence at low magnetic shear

“…The extended ion modes may then play a prominent role in saturation, facilitating energy transfer to damped modes while exploiting efficient nonlinear coupling to zonal flows to explain the visual prominence of zonal structures in nonlinear simulations. In the context of stellarator optimization, this offers a tantalizing prospect that stellarator geometry can be manipulated in a way to enhance the capability of subdominant modes to transfer energy and affect saturation, and motivates continued development of the theories of Hegna et al (2018) with more comprehensive physics in the pursuit of a turbulence-optimized stellarator.…”

Advancing the physics basis for quasi-helically symmetric stellarators

“…High values of τ pst correspond to lowered turbulent fluctuation levels and correspondingly reduced turbulent transport. In Hegna et al (2018), the dominant saturation mechanism was shown to be energy transfer to stable modes through non-zonal, marginally stable drift waves. As such, the analysis presented here focuses on assessing the energy transfer through non-zonal modes as opposed to energy transfer through zonal flows, which is shown to be the dominant saturation mechanism in tokamaks (Terry et al 2018), the NCSX stellarator (Hegna et al 2018;McKinney et al 2019) and the W7-X stellarator (Plunk et al 2017).…”