Ion-scale Turbulence Research Articles

Multifractal analysis of high resolution solar wind proton density measurements

The solar wind is a highly turbulent medium, with a high level of field fluctuations throughout a broad range of scales. These include an inertial range where a turbulent cascade is assumed to be active. The solar wind cascade shows intermittency, which however may depend on the wind conditions. Recent observations have shown that ion-scale magnetic turbulence is almost self-similar, rather than intermittent. A similar result was observed for the high resolution measurements of proton density provided by the spacecraft Spektr-R. Intermittency may be interpreted as the result of the multifractal properties of the turbulent cascade. In this perspective, this paper is devoted to the description of the multifractal properties of the high resolution density measurements. In particular, we have used the standard coarse-graining technique to evaluate the generalized dimensions Dq, and from these the multifractal spectrum f(α), in two ranges of scale. A fit with the p-model for intermittency provided a quantitative measure of multifractality. Such indicator was then compared with alternative measures: the width of the multifractal spectrum, the peak of the kurtosis, and its scaling exponent. The results indicate that the small-scale fluctuations are multifractal, and suggest that different measures of intermittency are required to fully understand the small scale cascade.

Design of tangential viewing phase contrast imaging for turbulence measurements in JT-60SA.

A tangential viewing phase contrast imaging system is being designed for the JT-60SA tokamak to investigate microturbulence. In order to obtain localized information on the turbulence, a spatial-filtering technique is applied, based on magnetic shearing. The tangential viewing geometry enhances the radial localization. The probing laser beam is injected tangentially and traverses the entire plasma region including both low and high field sides. The spatial resolution for an Internal Transport Barrier discharge is estimated at 30%-70% of the minor radius at k = 5 cm-1, which is the typical expected wave number of ion scale turbulence such as ion temperature gradient/trapped electron mode.

The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence

The 2D spectrum of the saturated electric potential from gyrokinetic turbulence simulations that include both ion and electron scales (multi-scale) in axisymmetric tokamak geometry is analyzed. The paradigm that the turbulence is saturated when the zonal (axisymmetic) ExB flow shearing rate competes with linear growth is shown to not apply to the electron scale turbulence. Instead, it is the mixing rate by the zonal ExB velocity spectrum with the turbulent distribution function that competes with linear growth. A model of this mechanism is shown to be able to capture the suppression of electron-scale turbulence by ion-scale turbulence and the threshold for the increase in electron scale turbulence when the ion-scale turbulence is reduced. The model computes the strength of the zonal flow velocity and the saturated potential spectrum from the linear growth rate spectrum. The model for the saturated electric potential spectrum is applied to a quasilinear transport model and shown to accurately reproduce the electron and ion energy fluxes of the non-linear gyrokinetic multi-scale simulations. The zonal flow mixing saturation model is also shown to reproduce the non-linear upshift in the critical temperature gradient caused by zonal flows in ion-scale gyrokinetic simulations.

E × B flow velocity deduced from the poloidal motion of fluctuation patterns in neutral beam injected L-mode plasmas on KSTAR

A method for direct assessment of the equilibrium E × B flow velocity (E×B flow shear is responsible for the turbulence suppression and transport reduction in tokamak plasmas) is investigated based on two facts. The first one is that the apparent poloidal rotation speed of density fluctuation patterns is close to the turbulence rotation speed in the direction perpendicular to the local magnetic field line within the flux surface. And the second “well-known” fact is that the turbulence rotation velocity consists of the equilibrium E × B flow velocity and intrinsic phase velocity of turbulence in the E × B flow frame. In the core region of the low confinement (L-mode) discharges where a strong toroidal rotation is induced by neutral beam injection, the apparent poloidal velocities (and turbulence rotation velocities) are good approximations of the E×B flow velocities since linear gyrokinetic simulations suggest that the intrinsic phase velocity of the dominant turbulence is significantly lower than the apparent poloidal velocity. In the neutral beam injected L-mode plasmas, temporal and spatial scales of the measured turbulence are studied by comparing with the local equilibrium parameters relevant to the ion-scale turbulence.

Isotope effects on particle transport in the Compact Helical System

The hydrogen isotope effects of particle transport were studied in the hydrogen and deuterium dominant plasmas of the Compact Helical System (CHS). Longer decay time of electron density after the turning-off of the gas puffing was observed in the deuterium dominant plasma suggesting that the recycling was higher and/or the particle confinement was better in the deuterium dominant plasma. Density modulation experiments showed the quantitative difference of the particle transport coefficients. Density was scanned from 0.8 × 1019 m−3 to 4 × 1019 m−3 under the same magnetic field and almost the same heating power. In the low density regime (line averaged density < 2.5 × 1019 m−3), the lower particle diffusivity and the larger inwardly directed core convection velocity was observed in the deuterium dominant plasma, while in the high density regime (line averaged density >2.5 × 1019 m−3) no clear difference was observed. This result indicates that the isotope effects of particle transport exist only in the low density regime. Comparison with neoclassical transport coefficients showed that the difference of particle transport is likely to be due to the difference of turbulence driven anomalous transport. Linear character of the ion scale turbulence was studied. The smaller linear growth rate qualitatively agreed with the reduced particle transport in the deuterium dominant plasma of the low density regime.

ION-SCALE TURBULENCE IN THE INNER HELIOSPHERE: RADIAL DEPENDENCE

The evolution of the ion-scale plasma turbulence in the inner heliosphere is studied by associating the plasma parameters for hybrid-code turbulence simulations to the radial distance from the Sun via a Solar wind model based mapping procedure. Using a mapping based on a one-dimensional solar wind expansion model, the resulting ion-kinetic scale turbulence is related to the solar wind distance from the Sun. For this purpose the mapping is carried out for various values of ion beta that correspond to the heliocentric distance. It is shown that the relevant normal modes such as ion cyclotron and ion Bernstein modes will occur first at radial distances of about 0.2–0.3 AU, i.e., near the Mercury orbit. This finding can be used as a reference, a prediction to guide the in situ measurements to be performed by the upcoming Solar Orbiter and Solar Probe Plus missions. Furthermore, a radial dependence of the wave-vector anisotropy was obtained. For astrophysical objects this means that the spatial scales of filamentary structures in interstellar media or astrophysical jets can be predicted for photometric observations.

Cross-Scale Interactions between Electron and Ion Scale Turbulence in a Tokamak Plasma.

Multiscale gyrokinetic turbulence simulations with the real ion-to-electron mass ratio and β value are realized for the first time, where the β value is given by the ratio of plasma pressure to magnetic pressure and characterizes electromagnetic effects on microinstabilities. Numerical analysis at both the electron scale and the ion scale is used to reveal the mechanism of their cross-scale interactions. Even with the real-mass scale separation, ion-scale turbulence eliminates electron-scale streamers and dominates heat transport, not only of ions but also of electrons. Suppression of electron-scale turbulence by ion-scale eddies, rather than by long-wavelength zonal flows, is also demonstrated by means of direct measurement of nonlinear mode-to-mode coupling. When the ion-scale modes are stabilized by finite-β effects, the contribution of the electron-scale dynamics to the turbulent transport becomes non-negligible and turns out to enhance ion-scale turbulent transport. Damping of the ion-scale zonal flows by electron-scale turbulence is responsible for the enhancement of ion-scale transport.

Improved strong scaling of a spectral/finite difference gyrokinetic code for multi-scale plasma turbulence

Abstract Optimization techniques of a plasma turbulence simulation code GKV for improved strong scaling are presented. This work is motivated by multi-scale plasma turbulence extending over multiple spatio-temporal scales of electrons and ions, whose simulations based on the gyrokinetic theory require huge calculations of five-dimensional (5D) computational fluid dynamics by means of spectral and finite difference methods. First, we present the multi-layer domain decomposition of the multi-dimensional and multi-species problem, and segmented MPI-process mapping on 3D torus interconnects, which fully utilizes the bi-section bandwidth for data transpose and reduces the conflicts of simultaneous point-to-point communications. These techniques reduce the inter-node communication cost drastically. Second, pipelined computation-communication overlaps are implemented by using the OpenMP/MPI hybrid parallelization, which effectively mask the communication cost. Careful regulations of the pipeline length and of the thread granularity respectively suppress latencies of MPI, load imbalance and scheduling overheads of OpenMP. Thanks to the above optimizations, GKV achieves excellent strong scaling up to ∼600k cores with high computational performance 782.4 TFlops (8.29% of the theoretical peak) and high effective parallelization rate ∼99.99994% on K, which demonstrates its applicability and efficiency toward a million of cores. The optimized code realizes multi-scale plasma turbulence simulations covering electron and ion scales, and reveals cross-scale interactions of electron- and ion-scale turbulence.

Dispersion relation as a channel of plasma turbulence evolution

Abstract We present evidence from ion-scale plasma turbulence simulations that normal-mode waves and sideband waves co-exist when a plasma evolves from wave fields into turbulence. Ion-scale fluctuations represent normal-mode fluctuations such as Bernstein and cyclotron modes, accompanied by sideband waves having moderate frequency mismatch with the normal modes. The evolution process is studied using the method of energy partition and frequency broadening. Wave evolution into turbulence exhibits distinct stages: growth phase of normal modes, saturation, and decay. The saturation time is of the order of 1000 ion gyroperiods, which is delayed at higher values of the plasma parameter beta. We conclude that the dispersion relations play the central role in plasma turbulence evolution, serving as the energy flux channel in the spectral domain.

Wavevector anisotropy of plasma turbulence at ion kinetic scales: solar wind observations and hybrid simulations

Abstract. Wavevector anisotropy of ion-scale plasma turbulence is studied at various values of ion beta. Two complementary methods are used. One is multi-point measurements of magnetic field in the near-Earth solar wind as provided by the Cluster spacecraft mission, and the other is hybrid numerical simulation of two-dimensional plasma turbulence. Both methods demonstrate that the wavevector anisotropy is reduced with increasing values of ion beta. Furthermore, the numerical simulation study shows the existence of a scaling law between ion beta and the wavevector anisotropy of the fluctuating magnetic field that is controlled by the thermal or hybrid particle-in-cell simulation noise. Likewise, there is weak evidence that the power-law scaling can be extended to the turbulent fluctuating cascade. This fact can be used to construct a diagnostic tool to determine or to constrain ion beta using multi-point magnetic field measurements in space.

Synergistic cross-scale coupling of turbulence in a tokamak plasma

For the first time, nonlinear gyrokinetic simulations spanning both the ion and electron spatio-temporal scales have been performed with realistic electron mass ratio ((mD∕me)1∕2 = 60.0), realistic geometry, and all experimental inputs, demonstrating the coexistence and synergy of ion (kθρs∼O(1.0)) and electron-scale (kθρe∼O(1.0)) turbulence in the core of a tokamak plasma. All multi-scale simulations utilized the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] to study the coupling of ion and electron-scale turbulence in the core (r/a = 0.6) of an Alcator C-Mod L-mode discharge shown previously to exhibit an under-prediction of the electron heat flux when using simulations only including ion-scale turbulence. Electron-scale turbulence is found to play a dominant role in setting the electron heat flux level and radially elongated (kr ≪ kθ) “streamers” are found to coexist with ion-scale eddies in experimental plasma conditions. Inclusion of electron-scale turbulence in these simulations is found to increase both ion and electron heat flux levels by enhancing the transport at the ion-scale while also driving electron heat flux at sub-ρi scales. The combined increases in the low and high-k driven electron heat flux may explain previously observed discrepancies between simulated and experimental electron heat fluxes and indicates a complex interaction of short and long wavelength turbulence.

Comparison of BES measurements of ion-scale turbulence with direct gyro-kinetic simulations of MAST L-mode plasmas

Observations of ion-scale (kyρi ⩽ 1) density turbulence of relative amplitude ≳0.2% are available on the Mega Amp Spherical Tokamak (MAST) using a 2D (8 radial × 4 poloidal channel) imaging beam emission spectroscopy diagnostic. Spatial and temporal characteristics of this turbulence, i.e., amplitudes, correlation times, radial and perpendicular correlation lengths and apparent phase velocities of the density contours, are determined by means of correlation analysis. For a low-density, L-mode discharge with strong equilibrium flow shear exhibiting an internal transport barrier in the ion channel, the observed turbulence characteristics are compared with synthetic density turbulence data generated from global, non-linear, gyro-kinetic simulations using the particle-in-cell code NEMORB. This validation exercise highlights the need to include increasingly sophisticated physics, e.g., kinetic treatment of trapped electrons, equilibrium flow shear and collisions, to reproduce most of the characteristics of the observed turbulence. Even so, significant discrepancies remain: an underprediction by the simulations of the turbulence amplitude and heat flux at plasma periphery and the finding that the correlation times of the numerically simulated turbulence are typically two orders of magnitude longer than those measured in MAST. Comparison of these correlation times with various linear timescales suggests that, while the measured turbulence is strong and may be ‘critically balanced’, the simulated turbulence is weak.

Overview of physics results from MAST towards ITER/DEMO and the MAST Upgrade

New diagnostic, modelling and plant capability on the Mega Ampère Spherical Tokamak (MAST) have delivered important results in key areas for ITER/DEMO and the upcoming MAST Upgrade, a step towards future ST devices on the path to fusion currently under procurement. Micro-stability analysis of the pedestal highlights the potential roles of micro-tearing modes and kinetic ballooning modes for the pedestal formation. Mitigation of edge localized modes (ELM) using resonant magnetic perturbation has been demonstrated for toroidal mode numbers n = 3, 4, 6 with an ELM frequency increase by up to a factor of 9, compatible with pellet fuelling. The peak heat flux of mitigated and natural ELMs follows the same linear trend with ELM energy loss and the first ELM-resolved Ti measurements in the divertor region are shown. Measurements of flow shear and turbulence dynamics during L–H transitions show filaments erupting from the plasma edge whilst the full flow shear is still present. Off-axis neutral beam injection helps to strongly reduce the redistribution of fast-ions due to fishbone modes when compared to on-axis injection. Low-k ion-scale turbulence has been measured in L-mode and compared to global gyro-kinetic simulations. A statistical analysis of principal turbulence time scales shows them to be of comparable magnitude and reasonably correlated with turbulence decorrelation time. Te inside the island of a neoclassical tearing mode allow the analysis of the island evolution without assuming specific models for the heat flux. Other results include the discrepancy of the current profile evolution during the current ramp-up with solutions of the poloidal field diffusion equation, studies of the anomalous Doppler resonance compressional Alfvén eigenmodes, disruption mitigation studies and modelling of the new divertor design for MAST Upgrade. The novel 3D electron Bernstein synthetic imaging shows promising first data sensitive to the edge current profile and flows.

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

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.

Multiscale gyrokinetics for rotating tokamak plasmas: II. Reduced models for electron dynamics

In this paper, we extend the multiscale approach developed in Abel et al (2012 Rep. Prog. Phys. submitted) by exploiting the scale separation between ions and the electrons. The gyrokinetic equation is expanded in powers of the electron to ion mass ratio, which provides a rigorous method for deriving the reduced electron model. We prove that ion-scale electromagnetic turbulence cannot change the magnetic topology, and argue that to lowest order the magnetic field lies on fluctuating flux surfaces. These flux surfaces are used to construct magnetic coordinates, and in these coordinates a closed system of equations for the electron response to ion-scale turbulence is derived. All fast electron timescales have been eliminated from these equations. We also use these magnetic surfaces to construct transport equations for electrons and for electron heat in terms of the reduced electron model.

Subcritical fluctuations and suppression of turbulence in differentially rotating gyrokinetic plasmas

Differential rotation is known to suppress linear instabilities in fusion plasmas. However, numerical experiments show that even in the absence of growing eigenmodes, subcritical fluctuations that grow transiently can lead to sustained turbulence, limiting the ability of the velocity shear to suppress anomalous transport. Here transient growth of electrostatic fluctuations driven by the parallel velocity gradient (PVG) and the ion temperature gradient (ITG) in the presence of a perpendicular (E × B) velocity shear is considered. The maximally simplified (but, as numerical simulations suggest, most promising for transport reduction) case of zero magnetic shear is treated in the framework of a local shearing box approximation. In this case there are no linearly growing eigenmodes, so all excitations are transient. In the PVG-dominated regime, the maximum amplification factor is found to be eN with N ∝ q/ϵ (safety factor/inverse aspect ratio), the maximally amplified wavenumbers perpendicular and parallel to the magnetic field are related by kyρi ≈ (ϵ/q)1/3k∥vthi/S, where ρi is the ion Larmor radius, vthi the ion thermal speed and S the E × B shear. In the ITG-dominated regime, N is independent of wavenumber and N ∝ vthi/(LTS), where LT is the ion-temperature scale length. Intermediate ITG–PVG regimes are also analysed and N is calculated as a function of q/ϵ, LT and S. Analytical results are corroborated and supplemented by linear gyrokinetic numerical tests. Regimes with N ≲ 1 for all wavenumbers are possible for sufficiently low values of q/ϵ (≲7 in our model); ion-scale turbulence is expected to be fully suppressed in such regimes. For cases when it is not suppressed, an elementary heuristic theory of subcritical PVG turbulence leading to a scaling of the associated ion heat flux with q, ϵ, S and LT is proposed; it is argued that the transport is much less ‘stiff’ than in the ITG regime.

Gyrokinetic turbulent transport simulation of a high ion temperature plasma in large helical device experiment

Ion temperature gradient turbulent transport in the large helical device (LHD) is investigated by means of gyrokinetic simulations in comparison with the experimental density fluctuation measurements of ion-scale turbulence. The local gyrokinetic Vlasov simulations are carried out incorporating full geometrical effects of the LHD configuration, and reproduce the turbulent transport levels comparable to the experimental results. Reasonable agreements are also found in the poloidal wavenumber spectra of the density fluctuations obtained from the simulation and the experiment. Numerical analysis of the spectra of the turbulent potential fluctuations on the two-dimensional wavenumber space perpendicular to the magnetic field clarifies the spectral transfer into a high radial wavenumber region which correlates with the regulation of the turbulent transport due to the zonal flows. The resultant transport levels at different flux surfaces are expressed in terms of a simple linear relation between the transport coefficient and the ratio of the squared turbulent potential fluctuation to the averaged zonal flow amplitude.

Beam emission spectroscopy turbulence imaging system for the MAST spherical tokamak

A new beam emission spectroscopy turbulence imaging system has recently been installed onto the MAST spherical tokamak. The system utilises a high-throughput, direct coupled imaging optics, and a single large interference filter for collection of the Doppler shifted D(α) emission from the ~2 MW heating beam of ~70 keV injection energy. The collected light is imaged onto a 2D array detector with 8 × 4 avalanche photodiode sensors which is incorporated into a custom camera unit to perform simultaneous 14-bit digitization at 2 MHz of all 32 channels. The array is imaged at the beam to achieve a spatial resolution of ~2 cm in the radial (horizontal) and poloidal (vertical) directions, which is sufficient for detection of the ion-scale plasma turbulence. At the typical photon fluxes of ~10(11) s(-1) the achieved signal-to-noise ratio of ~300 at the 0.5 MHz analogue bandwidth is sufficient for detection of relative density fluctuations at the level of a few 0.1%. The system is to be utilised for the study of the characteristics of the broadband, ion-scale turbulence, in particular its interaction with flow shear, as well as coherent fluctuations due to various types of MHD activity.

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 implications for interpreting turbulence measurements, and represent an important step in determining when and where ETG turbulence is expected to be relevant in ST plasmas. They are also important in the context of validating simulations with both experimental transport analysis and turbulence measurements.

Gyrokinetic simulations of spherical tokamaks

This paper reviews transport and confinement in spherical tokamaks (STs) and our current physics understanding of this that is partly based on gyrokinetic simulations. Equilibrium flow shear plays an important role, and we show how this is consistently included in the gyrokinetic framework for flows that greatly exceed the diamagnetic velocity. The key geometry factors that influence the effectiveness of turbulence suppression by flow shear are discussed, and we show that toroidal equilibrium flow shear can sometimes entirely suppress ion scale turbulence in today's STs. Advanced nonlinear simulations of electron temperature gradient (ETG) driven turbulence, including kinetic ion physics, collisions and equilibrium flow shear, support the model that ETG turbulence can explain electron heat transport in many ST discharges.