W. Guttenfelder

Simulation of microtearing turbulence in national spherical torus experimenta)

Thermal energy confinement times in National Spherical Torus Experiment (NSTX) dimensionless parameter scans increase with decreasing collisionality. While ion thermal transport is neoclassical, the source of anomalous electron thermal transport in these discharges remains unclear, leading to considerable uncertainty when extrapolating to future spherical tokamak (ST) devices at much lower collisionality. Linear gyrokinetic simulations find microtearing modes to be unstable in high collisionality discharges. First non-linear gyrokinetic simulations of microtearing turbulence in NSTX show they can yield experimental levels of transport. Magnetic flutter is responsible for almost all the transport (∼98%), perturbed field line trajectories are globally stochastic, and a test particle stochastic transport model agrees to within 25% of the simulated transport. Most significantly, microtearing transport is predicted to increase with electron collisionality, consistent with the observed NSTX confinement scaling....

Scaling of linear microtearing stability for a high collisionality National Spherical Torus Experiment discharge

Linear gyrokinetic simulations are performed based on a high collisionality NSTX discharge that is part of dimensionless confinement scaling studies. In this discharge, the microtearing mode is predicted to be unstable over a significant region of the plasma (r/a = 0.5–0.8), motivating comprehensive tests to verify the nature of the mode and how it scales with physical parameters. The mode is found to be destabilized with sufficient electron temperature gradient, collisionality, and beta, consistent with previous findings and simple theoretical expectations. Consistent with early slab theories, growth rates peak at a finite ratio of electron-ion collision frequency over mode frequency, νe/i/ω ∼ 1–6. Below this peak, the mode growth rate decreases with reduced collisionality, qualitatively consistent with global confinement observations. Also, in this region, increased effective ionic charge (Zeff) is found to be destabilizing. Experimental electron beta and temperature gradients are two to three times lar...

Internal electron transport barrier due to neoclassical ambipolarity in the helically symmetric experiment

Electron cyclotron heated plasmas in the Helically Symmetric Experiment (HSX) feature strongly peaked electron temperature profiles; central temperatures are 2.5 keV with 100 kW injected power. These measurements, coupled with neoclassical predictions of large “electron root” radial electric fields with strong radial shear, are evidence of a neoclassically driven thermal transport barrier. Neoclassical transport quantities are calculated using the PENTA code [D. A. Spong, Phys. Plasmas12, 056114 (2005)], in which momentum is conserved and parallel flow is included. Unlike a conventional stellarator, which exhibits strong flow damping in all directions on a flux surface, quasisymmetric stellarators are free to rotate in the direction of symmetry, and the effect of momentum conservation in neoclassical calculations may therefore be significant. Momentum conservation is shown to modify the neoclassical ion flux and ambipolar ion root radial electric fields in the quasisymmetric configuration. The effect is much smaller in a HSX configuration where the symmetry is spoiled. In addition to neoclassical transport, a model of trapped electron mode turbulence is used to calculate the turbulent-driven electron thermal diffusivity. Turbulenttransport quenching due to the neoclassically predicted radial electric field profile is needed in predictive transport simulations to reproduce the peaking of the measured electron temperature profile [Guttenfelder et al. , Phys. Rev. Lett.101, 215002 (2008)].

Suppressing electron turbulence and triggering internal transport barriers with reversed magnetic shear in the National Spherical Torus Experiment

The National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] can achieve high electron plasma confinement regimes that are super-critically unstable to the electron temperature gradient driven (ETG) instability. These plasmas, dubbed electron internal transport barriers (e-ITBs), occur when the magnetic shear becomes strongly negative. Using the gyrokinetic code GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)], the first nonlinear ETG simulations of NSTX e-ITB plasmas reinforce this observation. Local simulations identify a strongly upshifted nonlinear critical gradient for thermal transport that depends on magnetic shear. Global simulations show e-ITB formation can occur when the magnetic shear becomes strongly negative. While the ETG-driven thermal flux at the outer edge of the barrier is large enough to be experimentally relevant, the turbulence cannot propagate past the barrier into the plasma interior.

Resolving electron scale turbulence in spherical tokamaks with flow shear

This paper presents nonlinear gyrokinetic simulations of electron temperature gradient (ETG) turbulence based on spherical tokamak (ST) parameters. Most significantly the simulations include the strong toroidal flow and flow shear present in STs that suppress ion-scale turbulence while using kinetic ions at full mass ratio (mi/me=3600). The flow shear provides a physical long-wavelength cutoff mechanism that aids saturation of the simulations, which has previously been demonstrated to be problematic depending on magnetic shear. As magnetic shear varies widely in STs we systematically demonstrate saturation and convergence of the ETG simulations with respect to grid resolution, physical domain size, and boundary conditions. While using reduced ion mass or adiabatic ions can lessen computational expense they do not always provide reliable results. The resulting spectra from converged simulations are anisotropic everywhere in contrast to previous ETG simulations without flow shear. These results have implica...

Characterization and parametric dependencies of low wavenumber pedestal turbulence in the National Spherical Torus Experimenta)

The spherical torus edge region is among the most challenging regimes for plasma turbulence simulations. Here, we measure the spatial and temporal properties of ion-scale turbulence in the steep gradient region of H-mode pedestals during edge localized mode-free, MHD quiescent periods in the National Spherical Torus Experiment. Poloidal correlation lengths are about 10 ρi, and decorrelation times are about 5 a/cs. Next, we introduce a model aggregation technique to identify parametric dependencies among turbulence quantities and transport-relevant plasma parameters. The parametric dependencies show the most agreement with transport driven by trapped-electron mode, kinetic ballooning mode, and microtearing mode turbulence, and the least agreement with ion temperature gradient turbulence. In addition, the parametric dependencies are consistent with turbulence regulation by flow shear and the empirical relationship between wider pedestals and larger turbulent structures.

Experimental study of parametric dependence of electron-scale turbulence in a spherical tokamaka)

Electron-scale turbulence is predicted to drive anomalous electron thermal transport. However, experimental study of its relation with transport is still in its early stage. On the National Spherical Tokamak Experiment (NSTX), electron-scale density fluctuations are studied with a novel tangential microwave scattering system with high radial resolution of ±2 cm. Here, we report a study of parametric dependence of electron-scale turbulence in NSTX H-mode plasmas. The dependence on density gradient is studied through the observation of a large density gradient variation in the core induced by an edge localized mode (ELM) event, where we found the first clear experimental evidence of density gradient stabilization of electron-gyro scale turbulence in a fusion plasma. This observation, coupled with linear gyro-kinetic calculations, leads to the identification of the observed instability as toroidal electron temperature gradient (ETG) modes. It is observed that longer wavelength ETG modes, k⊥ρs≲10 (ρs is the i...

Correlations between quasi-coherent fluctuations and the pedestal evolution during the inter-edge localized modes phase on DIII-Da)

Direct measurements of the pedestal recovery during an edge-localized mode cycle provide evidence that quasi-coherent fluctuations (QCFs) play a role in the inter-ELM pedestal dynamics. Using fast Thomson scattering measurements, the pedestal density and temperature evolutions are probed on sub-millisecond time scales to show a fast recovery of the density gradient compared to the temperature gradient. The temperature gradient appears to provide a drive for the onset of quasi-coherent fluctuations (as measured with the magnetic probe and the density diagnostics) localized in the pedestal. The amplitude evolution of these QCFs tracks the temperature gradient evolution including its saturation. Such correlation suggests that these QCFs play a key role in limiting the pedestal temperature gradient. The saturation of the QCFs coincides with the pressure gradient reaching the kinetic-ballooning mode (KBM) critical gradient as predicted by EPED1. Furthermore, linear microinstability analysis using GS2 indicates that the steep gradient is near the KBM threshold. Thus, the modeling and the observations together suggest that QCFs are consistent with dominant KBMs, although microtearing cannot be excluded as subdominant.

Observation of ion scale fluctuations in the pedestal region during the edge-localized-mode cycle on the National Spherical Torus Experimenta)

Characterization of the spatial structure of turbulence fluctuations during the edge localized mode cycle in the pedestal region is reported. Using the beam emission spectroscopy and the correlation reflectometry systems, measurements show spatial structure—k⊥ρiped—ranging from 0.2 to 0.7 propagating in the ion diamagnetic drift direction at the pedestal top. These propagating spatial scales are found to be anisotropic and consistent with ion-scale microturbulence of the type ion temperature gradient and/or kinetic ballooning modes.

Reduced model prediction of electron temperature profiles in microtearing-dominated National Spherical Torus eXperiment plasmas

A representative H-mode discharge from the National Spherical Torus eXperiment is studied in detail to utilize it as a basis for a time-evolving prediction of the electron temperature profile using an appropriate reduced transport model. The time evolution of characteristic plasma variables such as βe, νe∗, the MHD α parameter, and the gradient scale lengths of Te, Ti, and ne were examined as a prelude to performing linear gyrokinetic calculations to determine the fastest growing micro instability at various times and locations throughout the discharge. The inferences from the parameter evolutions and the linear stability calculations were consistent. Early in the discharge, when βe and νe∗ were relatively low, ballooning parity modes were dominant. As time progressed and both βe and νe∗ increased, microtearing became the dominant low-kθ mode, especially in the outer half of the plasma. There are instances in time and radius, however, where other modes, at higher-kθ, may, in addition to microtearing, be i...