Session CO5: Turbulence and Transport

Simultaneous 2D Doppler backscattering from edge turbulence

The Synthetic Aperture Microwave Imaging (SAMI) diagnostic (previously at MAST and now at NSTX-U) actively probes the plasma edge using a wide (80 degree beam width) and broadband (10-34.5 GHz) beam. It digitizes the phase and amplitude of the Doppler backscattered signal using a receiving array of eight antennas which can be focused in any direction post shot to an angular range of 6-24 degree FWHM. This allows Doppler BackScattering (DBS) experiments to be conducted in every direction within the field of view simultaneously. This capability is unique to SAMI and is a novel way of conducting DBS experiments. SAMI has measured the magnetic pitch angle in the edge for the first time using a backscattering diagnostic. This is possible with simultaneous 2D DBS because the maximum backscattered power is perpendicular to the turbulence and turbulence is elongated along the magnetic field. SAMI has also studied the effect of NBI and the L-H transition on turbulent velocity, and turbulence suppression in the edge during H-mode. Initial results from all of these studies will be presented.   

Stochastic model of Rayleigh-Taylor mixing with time-dependent acceleration

We report the stochastic model of Rayleigh-Taylor (RT) mixing with time-dependent acceleration. RT mixing is a statistically unsteady process, where the means values of the flow quantities as well as the fluctuations around these means are time-dependent. A set of nonlinear stochastic differential equations with multiplicative noise is derived on the basis of rigorous momentum model and group theory analyses to account for the randomness of RT mixing. A broad range of parameter regime is investigated; self-similar asymptotic solutions are found; new regimes of RT mixing dynamics are identified. We show that for power-law asymptotic solutions describing RT mixing the exponent is relatively insensitive and pre-factor is sensitive to the fluctuations, and find the statistic invariants of the dynamics in each of the new regimes.   

3D Gyrokinetic simulation of the relaxation of magnetized temperature filaments

An electromagnetic, 3D gyrokinetic particle simulation model is used to study the relaxation of magnetized electron temperature filaments embedded in a large, uniform plasma of lower temperature. The study provides insight into the role of unstable drift-Alfv\'{e}n waves observed in a basic electron heat transport experiment [D.C. Pace et al. Phys. Plasmas \textbf{15}, 122304 (2008)]. At saturation onset, the unstable temperature-gradient-driven drift-Alfv\'{e}n fluctuations display a spiral spatial pattern, similar to laboratory measurements, which causes the rearrangement of the temperature profile. After linear instability saturation the system exhibits very different behavior depending on the inclusion of modes without variation along the magnetic field. In their absence the initial filament evolves into a broadened temperature profile, self-consistent with undamped, finite amplitude drift-Alfv\'{e}n waves, however, their inclusion causes the destruction of the filament and damping of the drift-Alfv\'{e}n modes leading to a final state consisting of undamped convective cells and multiple smaller-scale filaments. Simulation particle tracking and permutation entropy analysis reveal an underlying chaotic dynamics associated with the anomalous transport.   

Modeling full radial electric field and flow shears in gyrokinetic simulations

The radial electric field ($E_r$) is important in the turbulence of tokamak plasmas. It affects the growth rate of instabilities through the $E\times B$ shear and changes the real frequency of drift waves by adding a Doppler shift. The modeling of $E_r$ in simulations, however, was usually not complete. The full profiles of the main ion toroidal and poloidal flows were not implemented. In the gyrokientic electromagnetic particle code GEM, the poloidal flow was assumed to be zero by introducing a parallel flow. However, recent experiments show that the poloidal flow could be important.\footnote{B.A. Grierson et al., Nucl. Fusion 53 (2013) 063010.} In this study we add the full main ion rotation flows to GEM, following the comprehensive procedures of Sugama and Horton.\footnote{H. Sugama and W. Horton, Phys. Plasmas 5, 2560 (1998).} The major contribution to the $E_r$ from the ion toroidal flow is used as $E_{r0}$, and the result as $E_{r1}$. The effects to the growth rate and Doppler shift of all terms in the force balance equation are demonstrated using linear simulations of edge and core tokamak plasmas.   

Microturbulent transport of alpha particles, coupled in radius and energy

Previous work\footnote{Wilkie, Abel, Highcock, Dorland. ``Validating modelling assumptions of alpha particles in electrostatic turbulence.'' \emph{Journal of Plasma Physics}, \textbf{81}:905810306 (2015)} has shown that, to reliably estimate the turbulent flux of alpha particles, one must use the correct equilibrium distribution function. Futhermore, even the assumption that transport and collisions occur on seperate timescales is called into question, especially around the critical speed. Transport-modification to the distribution of alpha particles can therefore have a significant effect on the alpha-ion heating rate, essential for a burning plasma. We have developed a novel technique that takes advantage of the linearity of the gyrokinetic equation for trace species, allowing one to obtain the global coupled radius-energy transport of fusion-born alpha particles. Here, we show the adjustment to the alpha heating profile as modified by microturbulence for an ITER-like H-mode, and compare to several other transport models.   

Gyrokinetic simulations of microturbulence in DIII-D tokamak pedestal

The characteristics of H-mode pedestal are generally believed to be constrained by current-driven peeling-ballooning modes and pressure-driven instabilities, such as kinetic ballooning mode (KBM). In this work we use global gyrokinetic code (GTC) to identify and study the edge pressure-driven instabilities in the H-mode pedestal using realistic geometry and plasma profiles of DIII-D shot 131997. In our simulations we observe the KBM mode marginally dominant in the steep gradient region ($\psi_N=0.98$), in the range of $k_\theta\sim 1cm^{-1}$ which corresponds to the most unstable mode number in the nonlinearly saturated state. For shorter wavelengths the trapped electron mode becomes dominant since its linear growth rate increases with the mode number, while the KBM gets saturated. In the pedestal top region ($\psi_N=0.95$) the ITG dominates. Resonant magnetic perturbations (RMP) are widely applied for ELM mitigation. During RMP suppression, the increase of edge turbulence is often observed. To understand this phenomena we use gyrokinetic simulations to address the direct effect of magnetic perturbations on the microturbulence. Simulations with 3D equilibrium reconstructed by VMEC code have been compared with toroidally averaged equilibrium, using identical pressure profiles.   

Mode-coupling in Upper-hybrid Turbulence: Vlasov Simulations

Turbulence in a magnetized plasma near the upper-hybrid frequency involves coupling among the upper hybrid, electron Berstien and lower-hybrid waves, and the interactions are dominantly by parametric coupling and strong turbulence. These processes in the case of turbulence excited by high intensity electromagnetic waves in a density cavity are simulated using a Vlasov code. In the three-wave processes the upper hybrid wave excited by the external pump wave undergoes parametric decay in two decay processes. In the first decay mode, which is excited when the amplitudes of the waves trapped in the density cavity reaches a threshold, the upper hybrid wave decays in to another upper hybrid wave and a lower-hybrid wave. Sudsequently in a second decay mode parametric coupling into electron Bernstein and lower-hybrid waves are excited. In the four-wave process modulational (oscillating two-stream) instability of the upper hybrid waves, leads to wave collapse and strong turbulence. The simulations correspond to ionospheric heating experiments, which provide a unique and natural laboratory for the study of plasma turbulence.   

Particle diffusion in strong field-guided magnetohydrodynamic turbulence

We consider three-dimensional incompressible magnetohydrodynamic turbulence in the presence of a strong mean background magnetic field. We examine the Lagrangian statistics and characterize the transport properties of the system by numerically tracking a large number of passive massless particles. Previous studies demonstrated that in two dimensions, the presence of a weak background guiding field can suppress turbulent transport in the field-perpendicular direction. The situation in three dimensions is less clear. Here, we measure the single-particle diffusion along different directions with respect to the background magnetic field. By varying the background field strength, we quantify the effect of such guiding field on turbulent diffusion and interpret the results in terms of the Lagrangian velocity function.   

An analysis of methods of determining the effective eddy viscosity of an Implicit LES for mixing simulations

The Implicit large-eddy simulations (ILES) have been utilized as an effective approach for calculating many complex flows at high Reynolds number flows. Richtmyer--Meshkov (RM) instability induced flow can be viewed as a homogeneous decaying turbulence (HDT) after the passage of the shock. In this article, a critical evaluation of three methods for estimating the effective Reynolds number and the effective kinematic viscosity is undertaken utilizing high resolution ILES data. Effective Reynolds numbers based on the vorticity and kinetic energy decay rate, or the integral length and dissipation scale are found to be the most self-consistent when compared to the expected phenomenology and wind tunnel experiments.   

Quantification of anisotropy in quasi-static magnetohydrodynamic turbulence

We perform a numerical and analytical study of quasi-static magnetohydrodynamic (MHD) turbulence for moderate and large interaction parameters $N$. The kinetic energy is concentrated near the equator (plane perpendicular to the mean magnetic field) due to the strong dissipation in the polar regions. This distribution is conveniently quantified using the ring spectrum, which provides more details than the one-dimensional shell spectrum. We also show that for large $N$ the energy spectrum is exponential in wavenumbers.\footnote{K. S. Reddy and M. K. Verma, Phys. Fluids, {\bf 26}, 025109 (2014)} The direct computation of energy flux reveals an inverse cascade of energy of the perpendicular component of the velocity at low wavenumbers (similar to that in two-dimensional turbulence), but a forward energy cascade for the parallel component of velocity. We quantify these using ring-to-ring energy transfers. We show that the rings with higher polar angles transfer energy to ones with lower polar angles. For large interaction parameters, the dominant energy transfer takes place near the equator (polar angle $\theta \approx \pi/2$). These energy transfer are consistent with the anisotropic energy spectrum.\footnote{K. S. Reddy, R. Kumar, and M. K. Verma, Phys. Plasmas, {\bf 21}, 2014}   

Ion kinetic instabilities and turbulence of a parallel shearing flow of a plasma with hot ions

The results of the analytical and numerical investigations of the shear flow driven ion kinetic instabilities, excited due to the inverse ion Landau damping in the parallel shearing flow of plasmas with comparable ion and electron temperatures, that is the case relevant to a tokamak and space plasma, are presented. The levels of turbulence and the turbulent heating rates of ions and ion turbulent viscosity, resulted from the development of the electrostatic ion-temperature gradient and electromagnetic drift-Alfven turbulence, are determined and their consequences are discussed.   

Emission of ion acoustic waves by acceleration of Langmuir solitons in inhomogeneous plasmas

Emission of ion acoustic waves by acceleration of Langmuir solitons in inhomogeneous plasmas Y.Nishimura, Y.A.Chen, C.Z. Cheng, and Y.Nishida Institute of Space and Plasma Sciences, National Cheng Kung University, Taiwan New phenomena in Langmuir solitons1 are observed by numerical experiments. Incorporating background density gradient, the Langmuir solitons are accelerated. Ion acoustic waves are emitted during the acceleration phase of the Langmuir solitions which can be regarded as an analogy of charged particles emitting photons by acceleration.2 When the electric field rapidly spreads in the presence of the density gradient above the threshold, the density cavity lose the sustaining mechanism by ponderomotive force. The solitons collapse into two ion density clumps.This work is supported by Ministry of Science and Technology of Taiwan, MOST 103-2112-M-006-007 and MOST 104-2112-M-006-019. [1] V.E. Zakharov. Sov. Phys. JETP 35, 908 (1972). [2] P.K.Kaw, Sov. Phys. JETP {\bf 55}, 839 (1982).   

Reverse trend in turbulent transport coefficient for H mode edge plasmas

It is generally accepted that the micro-scale turbulence leads to anomalous transport observed in tokamaks. We carry out gyrokinetic simulation using the GTC code to study the relationship between the turbulent transport and its pressure gradient drive. It is found in the weak gradient regime, the turbulent transport coefficient increases with the gradient drive, which is consistent with Dimits 2000 result. However, in strong gradient regime which corresponds to the edge profile for the H mode plasma, the turbulent transport shows a clear reverse trend, i.e., the turbulent transport coefficient decreases with the gradient drive increasing. This feature is found to be closely related to the reduction of radial correlation length in the strong gradient regime, which could be explained by the unconventional ballooning mode structures observed in the gyrokinetic simulations with strong gradients.   

Self-consistent computation of shear flow generation and energy transfer in plasma interchange turbulence

A flux-driven two-fluid model based on drift-reduced Braginskii equations is studied to simulate shear flow generation and energy transfer in plasma interchange turbulence. We find that two regimes exist during the evolution of interchange turbulence. In the first regime, large-scale convective cells are formed and the mean E$\times $B shear flow is low. Then the increased heat flux triggers a transition to the second regime. During the transition, the system responds with higher fluctuation level and the fluctuation-induced energy transfer is stronger. Finally a high mean E$\times $B flow shear is generated in the second regime.   

Immersed boundary methods for magnetically confined conducting fluids

Immersed boundary methods for computing confined fluid and plasma flows in complex geometries are reviewed. The mathematical principle of the volume penalization technique is explained, giving examples for imposing Dirichlet and Neumann boundary conditions. Applications for plasma turbulence in three space dimensions, solving the visco-resistive MHD equations in toroidal domains, illustrate the applicability and the efficiency of the method in computing flows in complex geometries. Examples for generating rotational flows in toroidal geometries and the emergence of quasi-single helicity states in RFP devices are presented. Ref.: K. Schneider. Immersed boundary methods for numerical simulation of confined fluid and plasma turbulence in complex geometries: a review. J. Plasma Phys., doi:10.1017/S0022377815000598, 2015, in press.