The excitation of stable eigenmodes in unstable plasma turbulence, previously documented in collisionless trapped electron mode turbulence, is shown to be a generic behavior of local (quasihomogeneous) systems. A condition is derived to indicate when such excited eigenmodes achieve a sufficient level in saturation to affect the turbulence, and produce changes in saturation levels, instability drive, and transport. The condition is shown to be consistent with the results of collisionless and dissipative trapped electron turbulence, and is further illustrated by an entirely different model describing simple ion turbulence driven by the ion temperature gradient. The condition suggests that all eigenmodes of the ion model affect saturation, but none dominates. This is consistent with the results of simulations, which show nonlinear modifications to eigenmode structure, growth rate, and transport that occur intermittently in time, despite fixed driving gradients.

A two-field model for collisionless trapped electron mode turbulence has both finite amplitude-induced stability and instability, depending on wave number. Effects usually identified with nonlinear plasma instability (self-trapping, kinetics, 3D mode structure, magnetic shear) are absent. Nonlinear stability and instability reside in ExB advection of density. It drives modes of a purely damped branch of the dispersion relation to finite amplitude and changes the rate at which free energy is released into the turbulence by shifting the density-potential cross phase. Analysis shows that modes of the purely damped branch cannot be ignored in saturation, and that the linear growth rate is a poor indicator of driving at finite amplitude, invalidating mixing length and quasilinear approximations. Using statistical closure theory, the nonlinear eigenmode and growth rate are determined from the saturation level of modes on all branches, stable and unstable, and the nonlinear cross phase that governs finite-amplitude instability

The mission of the spherical tokamak NSTX-U is to explore the physics that drives core and pedestal transport and stability at high- and low collisionality, as part of the development of the spherical tokamak (ST) concept towards a compact, low-cost ST-based pilot plant. NSTX-U will ultimately operate at up to 2 MA and 1 T with up to 12 MW of neutral beam injection power for 5 s. NSTX-U will operate in a regime where electromagnetic instabilities are expected to dominate transport, and beam-heated NSTX-U plasmas will explore a portion of energetic particle parameter space that is relevant for both -heated conventional and low aspect ratio burning plasmas. NSTX-U will also develop the physics understanding and control tools to ramp-up and sustain high performance plasmas in a fully-noninductive fashion. NSTX-U began research operations in 2016, but a failure of a divertor magnetic field coil after ten weeks of operation resulted in the suspension of operations and initiation of recovery activities. During this period, there has been considerable work in the area of analysis, theory and modeling of data from both NSTX and NSTX-U, with a goal of understanding the underlying physics to develop predictive models that can be used for high-confidence projections for both ST and higher aspect ratio regimes. These studies have addressed issues in thermal plasma transport, macrostability, energetic particlet-driven instabilities at ion-cyclotron frequencies and below, and edge and divertor physics.

This paper presents the first observation of divertor localized turbulence in the NSTX-Upgrade spherical tokamak. Previous work in NSTX discharges (Maqueda et al 2010 Nucl. Fusion 50 075002) described fluctuations on the divertor target due to blobs generated on the low field side midplane. In the region that shows disconnection from upstream turbulence (private flux region and proximity of the strike point), divertor-localized fluctuations are observed via imaging of C III and D-α emission in diverted L-mode discharges and are characterized in this paper. Field-aligned filaments connected to the divertor target plate are radially localized at the separatrix on the outer divertor leg and in the private flux region on the inner divertor leg. These are limited to the region below the X-point with fluctuation levels up to 10%–20%. The filaments have comparable poloidal and radial correlation lengths (10–100 ion gyroradii ) and parallel correlation lengths of several meters. Toroidal mode numbers are in the range of 10–30 and 2–10 for outer and inner leg filaments. The poloidal motion of outer leg filaments has the same direction and comparable magnitude to advection due to drift calculated by the multi-fluid edge transport code UEDGE with inclusion of cross field drifts. Disconnection between inner and outer leg filaments as well as the absence of correlation with upstream turbulence support the hypothesis of X-point disconnection for divertor leg filaments. Simulations with the ArbiTER linear eigenvalue solver and a resistive-balooning model were performed with a simulation grid limited to the divertor legs. Instabilities localized to the bad curvature side of the divertor legs were observed, in qualitative agreement with the experiment.

Plasma zonal-flow excitation and saturation in fluid electron-drift-wave turbulence are studied spectrally. The zonal flow is a spectral condensation onto the zero-frequency linear-wave structure. In the representation diagonalizing the wave coupling that dominates interactions at long wavelengths, nonlinear triad interactions involving zero-frequency waves are greatly enhanced. Zonal modes are excited on both unstable and purely stable eigenmode branches. Coupling to the latter introduces robust, finite amplitude-induced damping of zonal flows, providing saturation.