Session NO4: Basic: Turbulence and Transport

On the Origin of Current Scaling of the Density Limit

Density limits impose a fundamental limit on tokamak operation. Recent work has identified shear layer collapse as the fundamental dynamics of the rise in particle transport associated with density limit behavior. Shear layer collapse occurs when electrons become nonadiabatic (i.e. hydrodynamic). The origin of current scaling --- ubiquitous in density limit dynamics --- remains. Here, we explore the implications of zonal flow screening (or inertia) for the current scaling. Simple arguments show that shear perturbations are more resilient at high density, in accord with Greenwald scaling. We will discuss further developments of the theory.   

When does turbulence spreading matter?

Turbulence spreading studies looking at spatiotemporal evolution of a slug of turbulence do not address how spreading affects profile evolution and thus miss the key question. Hence we study turbulence spreading effect on plasma profiles. Turbulence spreading is most active in the region of strong turbulence intensity gradient i.e., L mode edge with a strong edge localized turbulence source and in No Man's Land which connects the pedestal to the stiff core in H mode. Spreading reduces local intensity and steepens the pressure gradient to maintain steady state flux balance. In general, without an edge intensity source, the turbulence intensity profile is almost flat and spreading has a weak effect on plasma profiles in L mode. Interaction of turbulence spreading and avalanching is studied. Spreading weakly affects the avalanche distribution. In H mode, the strong intensity gradient at No Man's Land induces a flux of intensity from the unstable core to the stable pedestal where it is suppressed and ultimately dissipated by strong ExB shear. We find that turbulence spreading actually elevates the pedestal height by reducing turbulence intensity in No Man's Land. Hence surprisingly turbulence spreading actually increases energy content in H mode.   

Rossby Wave-Zonal Flow Turbulence in a Tangled Magnetic Field

Rossby wave-zonal flow turbulence frequently occurs in the presence of a tangled stochastic magnetic field. Tangled fields that coexist with an ordered mean field play a key role in turbulence in the solar tachocline and in magnetic confinement devices. Simulations show that interaction of the tangled field with Rossby turbulence is multi-faceted. We are interested in how tangled small-scale stochastic magnetic fields might affect the waves and the zonal flow by modifying the transport of mean potential vorticity. To understand the physics of this nonlinear system, we consider a model with the prescribed tangled fields. This tangled-field dominated system with high Kubo number cannot be treated by standard quasilinear theory. We develop a “double averaged” theory and construct quasilinear-type expressions for the vorticity flux and stresses. Our principal results are that the random-field induced stresses damp the Rossby waves, and that the phase relation in vorticity flux is modified by the tangled field. This leads to a suppression of zonal flows which occurs at levels of field intensities well below that of Alfvnization, where Maxwell stress balances the Reynolds stress. Ongoing work is focused on understanding the feedback of shears on the small scale field.   

Electron-scale turbulence in fusion plasmas: direct measurements and simulation validation

A lot of indirect evidence suggests that electron temperature gradient (ETG) turbulence is a key player in magnetized fusion plasmas. ETG turbulence is considered to contribute to the overall electron heat flux and to affect ion-scale turbulence by reducing the effectiveness of shear-flow stabilization. The FT-2 tokamak provides unique opportunities for making direct measurements of electron-scale density fluctuations via enhanced microwave scattering. Here, we present experimental data of this type, together with direct comparisons with high-realism gyrokinetic simulations using the GENE code. Simulated fluctuation wavenumber spectra at electron scales, subjected to synthetic diagnostics, are found to be in good agreement with the observations. Interestingly, the ETG turbulence in the simulations exhibits a spontaneous symmetry breaking as a result of the presence of a low-Z impurity species at significant density, and the experimental data supports the existence of this effect. We also address the effect of significant dilution on linear mode structure.   

Drift-Alfven Fluctuations and Transport in Multiple Interacting Magnetized Electron Temperature Filaments

Steep thermal gradients in a magnetized plasma can induce a variety of spontaneous low frequency excitations such drift-Alfven waves and vortices. We present results from basic experiments on heat transport in magnetized plasmas with multiple heat sources in close proximity. The setup consists of three biased probe-mounted CeB6 crystal cathodes that inject low energy electrons along a strong magnetic field into a pre-existing cold afterglow plasma forming three electron temperature filaments. A triangular spatial pattern is chosen for the thermal sources and multiple axial and transverse probe measurements allow for determination of the cross-field mode patterns and axial filament length. When the three sources are placed within a few collisionless electron skin depths a non-azimuthally symmetric wave pattern emerges due to the overlap of drift-Alfven modes forming around each filament. This leads to enhanced cross-field transport from chaotic mixing (E×B) and profile collapse of the inner triangular region and steepened thermal gradients in the outer triangular region which spontaneously generates quasi-symmetric higher azimuthal mode number drift-Alfven fluctuations. In addition a sheared azimuthal flow is present from the emissive cathode that modifies the Alfvenic eigenmodes.   

Learning mean field dynamics for drift wave turbulence

Drift wave turbulence in confined plasma features the nonlinear interaction and self-consistent evolution of the pressure profile, zonal flow field, and turbulence intensity field. The profile drives the turbulence via linear instability, which then both drives the zonal flow via modulational instability and evolves the profile via turbulent transport. The zonal flow, in turn, feeds back on the turbulence via shear suppression. Closing a mean-field model for this system requires the challenging task of evaluating the turbulent fluxes due to cross-correlations between fluctuating quantities. In this work, we examine this system in the context of a Hasegawa-Wakatani model and use a supervised learning approach to learn a mean-field model for the turbulent fluxes. Results are presented and compared to analytical calculation. The results demonstrate the importance of the frequency shift due to the mean vorticity gradient, which is neglected in most studies.   

Bispectral analysis of broadband and quasi-coherent oscillations (geodesic-acoustic modes) to interpret wave-wave interactions in the T-10 Tokamak

Local fluctuations of poloidal electric field \~{ }E\textunderscore pol and density \~{ }n\textunderscore e were simultaneously measured by a heavy ion beam probe [Demers et al., 2001; Dnestrovskij et al., 1994; Melnikov et al., 2017] having a 5-slit energy analyzer that allows an estimate of the turbulent particle flux and E \texttimes B rotation velocity in the gradient zone of plasma column (r/a $=$ 0.8) [Eliseev et al., 2018]. High spatial and temporal resolution of the modern multichannel HIBP makes the HIBP an effective tool to study plasma oscillations. Previous work documented time-resolved interactions between measured plasma parameters using correlation analysis (of \~{ }E\textunderscore pol and \~{ }n\textunderscore e and cross-phase). This talk documents time-resolved interactions between measured plasma disparate-frequency modes using bicorrelation analysis (of \~{ }E\textunderscore pol and \~{ }n\textunderscore e and bi-phase) [Stauber, 1995; Riggs, 2019]. The intention is to identify the direction of energy transfer between modes (broadband, quasi-coherent).   

Transition from drift wave turbulence to coherent zonal structures using a flux-balanced fluid model for plasma edge turbulence

We investigate the drift wave – zonal flow interaction mechanism in plasma edge turbulence using the recent two-field flux-balanced Hasegawa-Wakatani model, whose particularity is an improved treatment of the electron response on magnetic flux surfaces. A sharp transition is observed from a turbulence dominated regime to a zonal jet dominated regime. The robust zonal jets are further enhanced with multi-scale dynamics when the numerical domain is elongated in the radial direction. We analyze the generation and stability of the zonal state based on the selective decay principle and the secondary instability analysis. The generation of zonal jets is displayed from the secondary instability analysis via nonlinear interactions with a linearly unstable drift base mode, while stabilizing damping effect is shown from a zonal flow base state. The selective decay process can be characterized by transient visits to several metastable states, then final convergence to a purely zonal state. We rely on detailed statistical analysis of our numerical experiments to highlight the energy transfer mechanisms. The insights gained from investigating the properties of our simple model can lead to guidelines for the development of model reduction methods for more complicated systems.   

ELM triggering by impurity pellet injection basing on ELM-suppressed H-mode on EAST.

The first results of edge-localized mode (ELM) triggering basing on ELM-suppressed H-mode on EAST using submillimeter granules (lithium and carbon) horizontal injection from the low field side midplane are reported. The ELM-suppression was achieved by active boron powder injection. In this scenario, robust ELM triggering was obtained with the nominal 0.9±0.1mm diameter lithium granules, with the triggering efficiency \textasciitilde 100{\%}. The triggered ELM frequency was varied between 10-120Hz. The particle flux from the triggered ELM results in impacts on a wide spatial region of the outer target; and preliminary analysis suggests triggered ELM amplitude is reduced with increasing ELM frequency. The core radiation from heavy impurities decreased during the lithium granule injection, while the edge radiation increases due to low-Z impurities. This implies that the core impurities are effectively driven out. The ELM triggering probability is below 50{\%} for nominal 0.7mm±0.1mm diameter carbon granules. Ablation behavior differs between carbon and lithium granules. High speed camera data indicated that some carbon granules split into many small pieces and sometimes resulted in the disruption.   

Spectral Approach to Particle Transport in Turbulent Dusty Plasma

Here we present a recently developed analytical approach where the onset of turbulence in dusty plasma is investigated using mathematical methods from spectral theory and fractional calculus. Specifically, we compute the time-evolved distribution of the system energy as a function of disorder concentration and strength of nonlocal interactions within the medium. In this study, disorder is determined from the stochastic fluctuations of the dust charge, while the nonlocal effects are obtained from the density distributions of the plasma species. The predictions from the proposed spectral analysis are compared against results from molecular dynamics simulations and laboratory experiments of dusty plasmas generated under similar system conditions. We also discuss the application of the spectral approach to dust particle transport in edge plasma turbulence.   

Time-dependent study of anisotropy in Rayleigh-Taylor instability induced turbulent flows with a variety of density ratios

This study focuses on understanding the time-dependent aniso\-tropy, mixing, scaling of flows induced by Rayleigh-Taylor instability (RTI), complementing the late-time snapshots reported by Cabot \&\ Zhou [\textit{Phys.\ Fluids}, \textbf{25}, 015107 (2013)]. In particular, we utilize three large datasets with different Atwood numbers (density ratios) from well resolved direct numerical simulations (DNS) at moderate Reynolds number with the goal of determining the degree of departure of this inhomogeneous flow from that of homogeneous, isotropic turbulence (HIT). Three key time-dependent statistical measurements are considered in detail to delineate the role played by the acceleration. First, a number of directional length scales in this anisotropic turbulence are inspected. Second, the relationship among the outer-scale, turbulence length, and the Taylor-microscale based Reynolds numbers is also clarified. Finally, the normalized dissipation rate is employed to inspect the distinctive features of the flow in inhomogeneous direction parallel to gravity and in the homogeneous perpendicular directions.   

Multi-component Mutual Diffusion in the Warm, Dense Matter Regime

We present the formulation of ternary and higher mixtures in the warm, dense matter regime. Binary mixtures have received considerable attention for mass transport, but few studies have addressed the complexities of ternary and higher mixtures. We explicitly examine ternary systems utilizing the Maxwell-Stefan formulation that relates diffusion to gradients in the chemical potential. Trajectories characterized by positions and velocities yield Onsager coefficients, which connect macroscopic diffusion to microscopic particle motions, through various autocorrelation functions (ACF). We use both classical (Yukawa pair-potentials) and orbital-free density functional molecular dynamics simulations to generate long trajectories. We employ the reference-mean form of the ACFs and determine the center-of-mass coefficients through a simple reference-frame-dependent similarity transformation. From the Onsager terms we determine the mutual diffusion coefficients. We compare to the Darken approximation and show that the self-diffusion constants determined in the full mixture (as opposed to the infinite dilution limit) get closer to the Onsager derived value. We present results from mixtures with only light elements (D-Li-C) and highly-asymmetric mass components (H-C-Ag).   

Experimental Validation of Dense Plasma Transport Models using the Z-Machine

Mixing of cold, higher-Z elements into the fuel region of an inertial confinement fusion target spoils the fusion burn efficiency. Recently, there has been a surge in the development of dense plasma transport modeling and the associated transport coefficients; however, experimental validation remains in its infancy. To address this gap, Sandia National Laboratories is developing a new experimental platform at the Z-facility to investigate plasma transport in dense plasmas that span the entire warm dense matter regime. This platform is being developed to measure species transport across a V/CH interface. In order to interpret measurements made using this experimental platform, modeling tools that incorporate transport effects in strongly coupled plasmas are required. Our team have utilized new advances in multi-species kinetic theory, collision models applicable to strongly coupled plasmas and modeling of degenerate electron plasmas to develop such a capability. The resulting kinetic transport code has been applied, along with state-of-the-art radiation hydrodynamic codes, to model the experiments. Results from this modeling effort highlight the importance of strong electric fields in driving interfacial mixing.