Session CO03: Fundamental Plasmas: Turbulence I

Live

Motivated by recent observations that RMPs tend to raise the L-H Power Threshold, we revisit the classic problem of instability dynamics in a stochastic magnetic field. The resistive interchange, in the collisional regime, is examined as a simple prototypical case. This problem is intrinsically a multi-scale one, and must be dealt with by the method of averaging. A key point is that maintaining divergence-free current on all scales forces the appearance of perpendicular currents (and thus, convective cell flows) in order to maintain charge balance in the presence of parallel current convergences (due to small scale magnetic fields). This is in \textbf{marked} contrast to test particle theories, such as the classic by Rechester and Rosenbluth. The microscale cells drive turbulent viscosity and diffusion. These cells may be the cause of RMP pump-out. Turbulent transport and stochastic bending modify the large-scale cell. This analysis parts company with the extensive ancient history of this subject.   

Live

The density limit phenomenology follows from the collapse of edge shear layers, leading to increased turbulence, transport and edge cooling, et seq. The challenge is to understand how the robust Greenwald scaling \underline {n}$_{\mathrm{g}}\sim $I$_{\mathrm{p}}$ is related to the collapse physics. Neoclassical zonal flow screening is a natural mechanism for the emergence of the I$_{\mathrm{p}}$scaling. The current (I$_{\mathrm{p}})$scaling due to neoclassical screening survives in the plateau regime, characteristics of edge plasmas. A new model of the coupled drift wave-zonal flow system is presented. Neoclassical response is included in the zonal flow evolution while the drift waves follow the Hasegawa-Wakatani model. This model leads to two synergistic results. A spectral equation for zonal flow intensity shows that the zonal flow modulational growth rate scale as I$_{\mathrm{p}}$whereas the zonal noise exhibits the stronger scaling of I$_{\mathrm{p}}$. This assures stronger flow seeding with increasing current. Quasilinear vorticity flux reveal that the mean vorticity gradient increases with plasma current as I$_{\mathrm{p}}$. Both these results indicate that large I$_{\mathrm{p}}$favors stronger zonal flow production and stronger feedback on drift waves and transport. A reduced D transport modelling is in progress to study \underline {n}scaling with I$_{\mathrm{p}}$and other dimensionless parameters.   

Live

Computing turbulent fluxes is one of the central problems of turbulence modeling. In this work, we use a data-driven approach to infer a mean-field model for the fluxes. Starting from numerical solution of the 2-D Hasegawa-Wakatani system, we use deep supervised learning to train a deep neural network which outputs the local turbulent particle flux and Reynolds stress as a function of local mean gradients, flow properties, and turbulence intensity. The deep neural network detects a previously unreported, non-diffusive particle flux which is proportional to the gradient of vorticity. We recover this flux, which (in the presence of a zonal flow) tends to modulate the density profile, with a simple analytic calculation. Using the new method, we also uncover a Cahn-Hilliard-type model for the generation of zonal flow via Reynolds stress, which agrees with previous theoretical work. Together with the particle flux, we thus obtain a reduced 1-D model for the turbulent dynamics directly from numerical data. We solve this numerically and compare to direct numerical simulation of the full 2-D system. We discuss the importance of symmetry to the deep learning method, the method's portability to other applications, and its range of validity.   

Live

We have expanded our previous gyrokinetic L-H bifurcation study [1, 2] in the edge gyrokinetic code XGC to include the isotope and size ($a/\rho_i$)) effects. The interplay between the turbulence modes, Reynolds stress, and the neoclassical ExB shearing rate will be discussed in relation to the isotope and a/ρi effects. Two different neoclassical effects will be included in the study: the X-point orbit loss effect and the radial plasma gradient effect. Influence on the enhanced $E\times B$ shearing rate by reduction in the neutral particle recycling rate will also be discussed. [1] C.S. Chang, S. Ku, G.R. Tynan, R. Hager et al., Phys. Rev. Lett. 118, 175001 (2017) [2] S. Ku, C. S. Chang, R. Hager, R. M. Churchill et al. Phys. Plasmas 25, 056107 (2018)   

Live

Density and density peaking are crucial for the efficiency of future fusion power plants. The density peaking and the turbulent transport are modelled with GENE and TGLF for two collisionality scaling experiments at JET and DIII-D. Experimental data from these machines show a dissimilar dependence in the density peaking from the source and turbulent transport: for JET the source is dominant while the turbulent transport is dominant for DIII-D. This is studied by investigating the zero flux density gradient (peaking factor) and by calculating the particle balance diffusion and pinch. Simulations showed that the largest change in the density peaking came from the difference in the normalized temperature gradients. The perturbed diffusion and pinch were also simulated with TGLF and showed a good match with the experimentally measured values. The calculated ratio of the particle balance pinch and diffusion explained the difference in peaking from turbulent transport, a high ratio in DIII-D yielding high peaking and a low ratio for JET yielding low peaking. However, the particle balance diffusion, which suppresses the peaking from the source, was high for DIII-D and low for JET. Thus, explaining that the particle source has a larger impact for the peaking at JET.   

Live

This paper discusses the extension of the anti-symmetric formalism, which was successfully applied to the Braginskii and MHD models [1], to the drift-ordered models used in turbulence applications. The anti-symmetric representation is an alternative to the traditional Lagrangian and Eulerian representations. It exposes symmetries of the model that result in discrete conservation theorems, obtained by simple analogy between the continuous and discrete equations. In addition to the typical mass, momentum, and energy conservation theorems, we show it is possible to derive a discrete circulation theorem for the vorticity. These properties are demonstrated in simulations involving single-seeded blob propagation. Finally, we discuss possibilities for exact energy conservation in numerical applications, which is formally elusive and requires solving a complicated non-Boussinesq Poisson equation. [1] F.D Halpern and R.E. Waltz, Phys. Plasmas 25, 060703 and Phys. Plasmas 27, 042303.   

Live

Up-down asymmetric geometries enable turbulence to redistribute toroidal momentum in the radial direction [Camenen, et al. 2010]. The bulk toroidal rotation generated by this phenomenon can improve MHD stability, motivating recent work to optimise the magnetic geometry in order to maximise the plasma rotation [Ball, et al. 2014]. However, the impact that this asymmetric turbulence has on the plasma current had not yet been studied. To this end, we have coupled a $\delta $f local gyrokinetic code (STELLA) and a neoclassical code (SFINCS). We show that the elongated asymmetric geometries found to maximize intrinsic rotation yield higher plasma currents than symmetric configurations. Nevertheless, the asymmetric turbulence produces a negligible effect on the current when compared to the total increment observed. The up-down asymmetric configuration also affects the balance of trapped and passing particles. Scans in elongation and elongation tilt suggest that the trapped particle population can be increased, yielding potential enhancements to the current of the order of 10{\%} in originally symmetric geometries.   

Live

Nonlinear electrostatic gyrokinetic simulations of electron temperature gradient (ETG) turbulence in JET-ILW pedestals reveal statistical inhomogeneity in poloidal angle, in stark contrast with core ETG turbulence. The heat flux and fluctuations are confined to a region centered at the outboard midplane, and fall off at a characteristic poloidal cutoff angle. The cutoff angle is determined by the local flux surface separation and the local variation of the magnetic shear. The nonlinear heat flux distribution does not follow simple quasilinear estimates, which suggested that toroidal ETG generated turbulence could carry significant heat flux \footnote{J. F. Parisi et al. “Toroidal and slab ETG instability dominance in the linear spectrum of JET-ILW pedestals (Submitted)”. (2020)}. However, the heat flux is dominated by turbulence caused by the slab ETG instability and is comparable to experimental observations. We discuss the implications of this statistically inhomogeneous turbulence for transport.   

Live

Linear gyrokinetic simulations DIII-D discharge {\#}159243 find unstable reversed shear Alfven eigenmodes (RSAE) excited by fast ions with significant growth rate for toroidal mode number n$=$3-12 and strong driftwave instability excited by thermal plasma pressure gradients with significant growth rate n$=$10-32. Nonlinear simulations of microturbulence and AE have been first carried out separately to understand the numerical properties and physical dynamics of microturbulence and AE, respectively. The zonal flows are found to dominate the RSAE saturation process. Nonlinear coupling of multiple toroidal modes further reduces the RSAE turbulence intensity and EP diffusivity, and suppresses the intermittency. Nonlinear simulations of high-n driftwave instabilities find that turbulence is regulated by zonal flows and that turbulence spreads from edge to core. Nonlinear GTC simulations including both high-n microturbulence and low-n RSAE on the same footing are been carried out to study their nonlinear interactions and effects on EP transport.   

Live

We present a fully-Bayesian approach for the inference of radial profiles of experimental impurity transport coefficients [Sciortino et al. 2020, submitted] and examine the effect of charge exchange processes with background neutrals. Our forward model for laser blow-off injections of calcium (Z$=$20) is based on the pySTRAHL code, optimized for iterations in high-performance computing environments. Alcator C-Mod offers opportunities to examine high-performance cases where the only source of deuterium neutrals is due to wall recycling, thus avoiding complex modeling of neutral beams. Even in the C-Mod high-density, high neutral edge opacity conditions, charge exchange is demonstrated to be remarkably important in the outer confined regions. We present results from multiple operating regimes and compare to neoclassical, gyro-fluid and gyrokinetic models (both quasi-linear and non-linear) in each case, demonstrating quantitative agreement in diffusion profiles. Convection can be matched under certain assumptions, but is more weakly constrained; in particular, inferred pedestal profiles can be significantly modified by the inclusion of charge exchange in forward modeling.   

Live

Recent experiments indicate that RMP fields can reduce fluctuation-driven Reynolds forces and so inhibit the initiation of the L-H transition. We present a theory of vorticity flux decoherence and its implications for zonal flow evolution. This theory builds upon recent fundamental work on vorticity mixing in a tangled magnetic field. We calculate the decoherence of the vorticity flux due to stochastic magnetic field scattering in presence of a strong toroidal field. The three relevant rates are: (1) the bandwidth of the ambient electrostatic micro-instabilities ($\Delta \omega$), (2) the bandwidth of Alfv\'en waves excited by Drift-Alfv\'en coupling ($|v_A\Delta k_{\parallel}|$), and (3) the stochasticity-induced decorrelation rate ($1/\tau_c = max(k^2_{\perp} D, (k_{\theta}^2 v_A^2 D/L_s)^{1/3})$), where $D$ accounts for scattering by the stochastic field. Decoherence requires (3) $>$ (1) and (3) $>$ (2) (i.e. Kubo number $Ku \geq 1$). These inequalities define the critical value of $\langle (\delta B)^2 /B^2 \rangle$ for an effect on the transition. The analysis proceeds by considering the Els\"asser population responses. The implications for decoherence of the particle and heat flux are discussed, as well.   

Live

A strong isotope effect on transport has been observed in high-density FT-2 discharges, where changing the operating gas from hydrogen to deuterium improves confinement time up to a factor of 2 in the highest density regimes. Experimental evidence suggests formation of a transport barrier in the high confinement regimes with deuterium, while hydrogen plasmas retain their transport characteristics. We present GENE simulation results for four characteristic cases in this series of experiments: two low density cases where isotope effect is not seen, and two high density cases where significant effect is present. We also identify radially localized impurity modes observed in the simulations.   

Live

Turbulence and transport in H-mode pedestals tend to be of a different nature and harder to evaluate and understand than in the core. In particular, microtearing (MT) turbulence is a key mechanism in explaining pedestal evolution. For a pedestal scenario based on a DIII-D discharge, it is shown through nonlinear gyrokinetic simulations that MT saturates via zonal fields -- in a process analogous to zonal-flow-catalyzed energy transfer -- while simultaneously generating strong zonal flows. Coexisting with the ion-scale MT are multiple branches of electron-temperature-gradient (ETG) modes. When resolving only electron scales, intermediate-scale streamers produce significant heat flux. However, when both ion and electron scales are included, the zonal flows driven by MT partially suppress the electrostatic ETG transport. The rule that a constant ratio of growth rate and wavenumber across scales leads to an equal balance of large- and small-scale transport is confirmed. Resonant magnetic perturbations -- important in the suppression of edge-localized modes -- disrupt zonal flows through the breaking of flux surfaces, enabling a radial electron current channel. In the present scenario, this leads to an increase in electron-scale transport while leaving ion-scale fluxes unaffected.   

On Demand

We report a first study of time-dependent Probability Density Functions (PDFs) in the Low-to-High confinement mode (L-H) transition by extending the previous prey-predator-type model (Kim & Diamond, Phys. Rev. Lett. 91, 185006, 2003) to a stochastic model. We highlight the limited utility of mean value and variance in understanding the L-H transition by showing strongly non- Gaussian PDFs, with the number of peaks changing in time. We also propose a new information geometric method by using information length, dynamical time scale, and information phase portrait, and show their utility in forecasting transitions and self-regulation between turbulence and zonal flows. In particular, we demonstrate the importance of intermittency (rare events of large amplitude) of zonal flows that can play an important role in promoting the L-H transition. Implications for hysteresis in the L-H and H-L transition are discussed. Reference E. Kim and R. Hollerbach, Phys. Rev. Res. 2, 023077 (2020).