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This paper discusses a strategy to initialize a two-dimensional (2D) Reynolds-averaged Navier–Stokes model [LANL's Besnard–Harlow–Rauenzahn (BHR) model] in order to describe an unsteady transitional Richtmyer–Meshkov (RM)-induced flow observed in on-going high-energy-density ensemble experiments performed on the OMEGA-EP facility. The experiments consist of a nominal single-mode perturbation (initial amplitude a 0 ≈ 10 and wavelength λ = 100 μ m) with target-to-target variations in the surface roughness subjected to the RM instability with delayed Rayleigh–Taylor in a heavy-to-light configuration. Our strategy leverages high-resolution three-dimensional (3D) implicit large eddy simulations (ILES) simulations to initialize BHR-relevant parameters and subsequently validate the 2D BHR results against the 3D ILES simulations. A suite of five 3D ILES simulations corresponding to five experimental target profiles is undertaken to generate an ensemble dataset. Using ensemble averages from the 3D simulations to initialize the turbulent kinetic energy in the BHR model (K0) demonstrates the ability of the model to predict the time evolution of the interface as well as the density-specific-volume covariance, b. To quantify the sensitivity of the BHR results to the choice of K0 and the initial turbulent length scale, S0, we execute a parameter sweep spanning four orders of magnitude for both S0 and K0, generating a parameter space consisting of 26 simulations. The Pearson's correlation coefficient is used as a measure of discrepancy between the 2D BHR and 3D ILES simulations and reveals that the ranges 8 ≲ S 0 ≲ 20 μ m and 109 ≲ K 0 ≲ 10 10 cm2/s2 produce predictions that agree best with the 3D ILES results. [ABSTRACT FROM AUTHOR]

Yoon and Fang [Phys. Plasmas 15, 122312 (2008)] formulated a second-order nonlinear kinetic theory that describes the turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field. Their theory also includes discrete-particle effects, or the effects due to spontaneously emitted thermal fluctuations. However, terms associated with the spontaneous fluctuations in particle and wave kinetic equations in their theory contain proper dimensionality only for an artificial one-dimensional situation. The present paper extends the analysis and re-derives the dimensionally correct kinetic equations for three-dimensional case. The new formalism properly describes the effects of spontaneous fluctuations emitted in three-dimensional space, while the collectively emitted turbulence propagates predominantly in directions parallel/anti-parallel to the ambient magnetic field. As a first step, the present investigation focuses on linear wave-particle interaction terms only. A subsequent paper will include the dimensionally correct nonlinear wave-particle interaction terms. [ABSTRACT FROM AUTHOR]

This paper studies the turbulent kinetic energy ( k ⊥ ) in 2D isothermal electrostatic interchange-dominated E × B drift turbulence in the scrape-off layer and its relation to particle transport. An evolution equation for the former is analytically derived from the underlying turbulence equations. Evaluating this equation shows that the dominant source for the turbulent kinetic energy is due to interchange drive, while the parallel current loss to the sheath constitutes the main sink. Perpendicular transport of the turbulent kinetic energy seems to play a minor role in the balance equation. Reynolds stress energy transfer also seems to be negligible, presumably because no significant shear flow develops under the given assumptions of isothermal sheath-limited conditions in the open field line region. The interchange source of the turbulence is analytically related to the average turbulent E × B energy flux, while a regression analysis of TOKAM2D data suggests a model that is linear in the turbulent kinetic energy for the sheath loss. A similar regression analysis yields a diffusive model for the average radial particle flux, in which the anomalous diffusion coefficient scales with the square root of the turbulent kinetic energy. Combining these three components, a closed set of equations for the mean-field particle transport is obtained, in which the source of the turbulence depends on mean flow gradients and k ⊥ through the particle flux, while the turbulence is saturated by parallel losses to the sheath. Implementation of this new model in a 1D mean-field code shows good agreement with the original TOKAM2D data over a range of model parameters. [ABSTRACT FROM AUTHOR]

In this paper, we show that in some parameter range in gyrokinetic simulations, it is possible to apply a control method to stimulate the appearance of zonal flows while minimizing the duration of the control process and the impact on plasma parameters. For this purpose, a gyrokinetic code considering only trapped particles is used. The starting point of our work is a situation where zonal flows transiently appear after the nonlinear phase of saturation of trapped electron modes or trapped ion modes' micro-instabilities. These are observed to be strongly reduced in a later phase, permitting streamers to govern the plasma behavior in the steady-state. By intervening during this latter state (after this transient growth and decay of zonal flow), i.e., by increasing the ion/electron temperature ratio for a short time, it is found to be possible to bifurcate to a new steady-state, in which zonal flows are strongly present and are maintained indefinitely, thereby allowing a significant reduction in radial heat fluxes. [ABSTRACT FROM AUTHOR]

In hydrodynamic turbulence, the kinetic energy injected at large scales cascades to the inertial range, leading to a constant kinetic energy flux. In contrast, in magnetohydrodynamic (MHD) turbulence, a fraction of kinetic energy is transferred to the magnetic energy. Consequently, for the same kinetic energy injection rate, the kinetic energy flux in MHD turbulence is reduced compared to its hydrodynamic counterpart. This leads to relative weakening of the nonlinear term ⟨ | (u · ∇) u | ⟩ , (where u is the velocity field) and turbulent drag, but strengthening of the velocity field in MHD turbulence. We verify the above using shell model simulations of hydrodynamic and MHD turbulence. Quasi-static MHD turbulence too exhibits turbulent drag reduction similar to MHD turbulence. [ABSTRACT FROM AUTHOR]

To comprehensively understand the saturation of two-dimensional (2D) magnetized Kelvin–Helmholtz-instability-driven turbulence, energy transfer analysis is extended from the traditional interaction between scales to include eigenmode interactions, by using the nonlinear couplings of linear eigenmodes of the ideal instability. While both kinetic and magnetic energies cascade to small scales, a significant fraction of turbulent energy deposited by unstable modes in the fluctuation spectrum is shown to be re-routed to the conjugate-stable modes at the instability scale. They remove energy from the forward cascade at its inception. The remaining cascading energy flux is shown to attenuate exponentially at a small scale, dictated by the large-scale stable modes. Guided by a widely used instability-saturation assumption, a general quasi-linear model of instability is tested by retaining all nonlinear interactions except those that couple to the large-scale stable modes. These complex interactions are analytically removed from the magnetohydrodynamic equations using a novel technique. Observations are an explosive large-scale vortex separation instead of the well-known merger of 2D, a dramatic enhancement in turbulence level and spectral energy fluxes, and a reduced small-scale dissipation length scale. These show the critical role of the stable modes in instability saturation. Possible reduced-order turbulence models are proposed for fusion and astrophysical plasmas, based on eigenmode-expanded energy transfer analyses. [ABSTRACT FROM AUTHOR]

E x B shear and trapped electron precession shear induced suppression of micro-turbulence is studied in general tokamak geometry. A systematic derivation of a two-point equation for trapped electron related turbulence based on modern bounce kinetic formalism is performed. A two-point nonlinear analysis yields the new criterion for the turbulence suppression |ωExB + ωPS| > ΔωT, where DxT is decorrelation rate of the ambient turbulence, ωExB is E x B shearing rate in general tokamak geometry [Hahm and Burrell, Phys. Plasmas 2, 1648 (1995)], and xPS is precession shearing rate. Therefore, both E x B shear and trapped electron precession shear can contribute to suppression of turbulence, and these effects can either add up or subtract depending on their relative sign. This result provides a better understanding of electron thermal internal transport barrier formation under various conditions. [ABSTRACT FROM AUTHOR]

We study the evolution of one million test particles in a turbulent plasma simulation, using the gyrokinetic code Trapped Element REduction in Semi-Lagrangian Approach (TERESA), as a method to get insights into the type of transport governing the plasma. TERESA (Trapped Element REduction in Semi-Lagrangian Approach) is a collisionless global 4D code which treats the trapped particles kinetically, while the passing particles are considered adiabatic. The Vlasov-Poisson system of equations is averaged over the cyclotron and the trapped particle's bounce motion, and thus, the model focuses on slow phenomena of the order of the toroidal precession motion of the banana orbits. We initialize the test particles, which are de facto "test banana-centers," at a time of the simulation when the plasma is turbulent. We impose an initial temperature and density gradients, and only the Trapped Ion Mode (TIM) instability can develop in this system. We then calculate the Mean Squared Displacement of the test particles as a function of time in order to obtain a random walk diffusion coefficient. We observe that the radial diffusion of the test particles depends on their toroidal precession kinetic energy (E), in such a way that the transport of particles is dominated by a strong, relatively narrow peak at the resonant energies. A radial particle diffusion flux is then calculated and compared to the total radial particle flux accounting for all the transport processes such as diffusion and advection which is obtained directly from the TERESA code. We can thus compare the diffusive contribution to the particle flux against the nondiffusive contributions. The results show that the total flux is essentially diffusive which is consistent with our simulation setup aiming for "global turbulence." Both fluxes present a peak around a resonance energy E R ≈ 1.74 T i between the TIM and the particles. Both thermal and high-energy particles do not contribute significantly to radial transport. [ABSTRACT FROM AUTHOR]

Bulk ion toroidal velocity profiles, V||VD+, peaking at 40-60km/s are observed with Mach probes in a narrow edge region of DIII-D discharges without external momentum input. This intrinsic rotation can be well reproduced by a first principle, collisionless kinetic loss model of thermal ion loss that predicts the existence of a loss-cone distribution in velocity space resulting in a co-Ip directed velocity. We consider two kinetic models, one of which includes turbulence-enhanced momentum transport, as well as the Pfirsch-Schluter (P-S) fluid mechanism. We measure a fine structure of the boundary radial electric field, Er, insofar ignored, featuring large (10-20 kV/m) positive peaks in the scrape off layer (SOL) at, or slightly inside, the last closed flux surface of these low power L- and H-mode discharges in DIII-D. The Er structure significantly affects the ion-loss model, extended to account for a non-uniform electric field. We also find that V||VD+ is reduced when the magnetic topology is changed from lower single null to upper single null. The kinetic ion loss model containing turbulence-enhanced momentum transport can explain the reduction, as we find that the potential fluctuations decay with radius, while we need to invoke a topology-enhanced collisionality on the simpler kinetic model. The P-S mechanism fails to reproduce the damping. We show a clear correlation between the near core V||C6+ velocity and the peak edge V||VD+ in discharges with no external torque, further supporting the hypothesis that ion loss is the source for intrinsic torque in the present tokamaks. However, we also show that when external torque is injected in the core, it can complete with, and eventually overwhelm, the edge source, thus determining the near SOL flows. Finally, we show some additional evidence that the ion/electron distribution in the SOL is non-Maxwellian. [ABSTRACT FROM AUTHOR]

In situ measurements of solar wind have strongly implicated its turbulent behavior. The observed power spectra report a breakpoint around length scales of the order of ion scales. As one of the responsible mechanisms for the observed steepening in power spectrum, our approach includes a right circularly polarized dispersive Alfvén wave (DAW) with finite frequency correction which, when subjected to transverse collapse/filamentation instability, may possibly result in steepening of spectrum and progressive transfer of energy from larger scales to smaller scales. We have studied the nonlinear effects associated with coupling of DAW with kinetic Alfvén wave in solar wind at 1A.U. The formation of localized structures provides a clue about the emergence of turbulence. Numerical simulation is performed to study localization and power spectral density of the field and density fluctuations. The results show steeper spectrum indicating transfer of large scale turbulent energy down to small scales. [ABSTRACT FROM AUTHOR]

Magnetohydrodynamic (MHD) turbulence is an inherent feature of large-scale, energetic astrophysical and geophysical magnetofluids. In general, these are rotating and are energized through buoyancy and shear, while viscosity and resistivity provide a means of dissipation of kinetic and magnetic energy. Studies of unforced, rotating, ideal (i.e., non-dissipative) MHD turbulence have produced interesting results, but it is important to determine how these results are affected by dissipation and forcing. Here, we extend our previous work and examine dissipative, forced, and rotating MHD turbulence. Incompressibility is assumed, and finite Fourier series represent turbulent velocity and magnetic field on a 64³ grid. Forcing occurs at an intermediate wave number by a method that keeps total energy relatively constant and allows for injection of kinetic and magnetic helicity. We find that 3-D energy spectra are asymmetric when forcing is present. We also find that dynamo action occurs when forcing has either kinetic or magnetic helicity, with magnetic helicity injection being more important. In forced, dissipative MHD turbulence, the dynamo manifests itself as a large-scale coherent structure that is similar to that seen in the ideal case. These results imply that MHD turbulence, per se, may play a fundamental role in the creation and maintenance of large-scale (i.e., dipolar) stellar and planetary magnetic fields. [ABSTRACT FROM AUTHOR]

Main ion dilution has been predicted by gyrokinetic simulations to have a significant effect on ion thermal transport in C-Mod ohmic plasmas. This effect was verified experimentally with a specific set of experiments on C-Mod in which ohmic deuterium plasmas across the linear ohmic confinement (LOC) through the saturated ohmic confinement (SOC) regimes were diluted by seeding with nitrogen gas (Z=7) injection. The seeding was observed to increase the normalized ion temperature gradients (ITGs) by up to 30% without a corresponding increase in the gyrobohm normalized ion energy flux, indicating a change in either the stiffness or the critical ion temperature gradient associated with ITG turbulence. The seeding also reversed the direction of the intrinsic toroidal rotation in plasmas slightly above the normal intrinsic rotation reversal critical density. GYRO simulations of the seeded and unseeded plasmas show that the seeding affected both the critical gradient and the stiffness. For plasmas in the LOC regime, the dilution primarily increased the critical gradient, while for plasmas in the SOC regime the dilution primarily decreased the stiffness. At r/a=0.8, where the experimental fluxes were above marginal stability, local GYRO predicted and experimental energy fluxes agreed, except for Qi in the SOC regime where GYRO under-predicted the experimental energy flux. At r/a=0.6, where the experimental fluxes were close to marginally stable, local GYRO predicted ITG modes to be strongly unstable and are responsible for both Qi and Qe (with Qi >Qe), as opposed to the experiment where Qi e. In contrast, global GYRO in this region predicted the ITG modes to be closer to marginal stability, and accurately predict the experimental Qi when the Ti profile is modified within experimental uncertainties. The fact that Qe is always less than Qi in the r/a=0.6 simulations with kδ?s≤1 indicates that high-k electron temperature gradient driven (ETG) modes must be included in future simulations and may be responsible for the electron energy transport in this case. [ABSTRACT FROM AUTHOR]

The nature and level of turbulent transport in the outer core of low-confinement (L-mode) discharges performed at the ASDEX Upgrade tokamak [Kallenbach et al., Nucl. Fusion 51, 094012 (2011)] are examined. Previously, it was found that for an L-mode discharge of the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] gyrokinetic simulations were unable to reproduce the experimental ion heat flux, underestimating it by almost an order of magnitude. In the present work, employing the GENE gyrokinetic turbulence code, an extensive nonlinear study is performed for L-mode discharges of ASDEX Upgrade in order to cross-check this observation. It is shown that no systematic underprediction can be found in these simulations-instead, discrepancies with respect to experimental transport levels are small enough to be resolved within the uncertainties of the experimental profiles. Moreover, it is shown that some turbulence properties resemble closely those of the underlying linear microinstabilities at least out to 90% of the minor radius, so that quasilinear transport models remain, in principle, applicable even for these parameters, provided that appropriate nonlinear saturation rules can be developed. [ABSTRACT FROM AUTHOR]