Turbulence Amplitude Research Articles

Large-scale Control of Kinetic Dissipation in the Solar Wind

Abstract In this Letter, we study the connection between the large-scale dynamics of the turbulence cascade and particle heating on kinetic scales. We find that the inertial range turbulence amplitude ( measured in the range of 0.01–0.1 Hz) is a simple and effective proxy to identify the onset of significant ion heating, and when it is combined with , it characterizes the energy partitioning between protons and electrons (T p /T e ); proton temperature anisotropy ( ); and scalar proton temperature (T p ) in a way that is consistent with previous predictions. For a fixed δB i , the ratio of linear to nonlinear timescales is strongly correlated with the scalar proton temperature in agreement with Matthaeus et al., though for solar wind intervals with , some discrepancies are found. For a fixed , an increase of the turbulence amplitude leads to higher T p /T e ratios, which is consistent with the models of Chandran et al. and Wu et al. We discuss the implications of these findings for our understanding of plasma turbulence.

Shaken and stirred: the effects of turbulence and rotation on disc and outflow formation during the collapse of magnetized molecular cloud cores

We present the results of eighteen magnetohydrodynamical calculations of the collapse of a molecular cloud core to form a protostar. Some calculations include radiative transfer in the flux-limited diffusion approximation while others employ a barotropic equation of state. We cover a wide parameter space, with mass-to-flux ratios ranging from $\mu = 5$ to $20$; initial turbulent amplitudes ranging from a laminar calculation (i.e. where the Mach number, $\mathscr{M} = 0$) to transonic $\mathscr{M} = 1$; and initial rotation rates from $\beta_\mathrm{rot} = 0.005$ to $0.02$. We first show that using a radiative transfer scheme produces warmer pseudo-discs than the barotropic equation of state, making them more stable. We then `shake' the core by increasing the initial turbulent velocity field, and find that at all three mass-to-flux ratios transonic cores are weakly bound and do not produce pseudo-discs; $\mathscr{M} = 0.3$ cores produce very disrupted discs; and $\mathscr{M} = 0.1$ cores produce discs broadly comparable to a laminar core. In our previous paper (arXiv:1701.08741), we showed that a pseudo-disc coupled with sufficient magnetic field is necessary to form a bipolar outflow. Here we show that only weakly turbulent cores exhibit collimated jets. We finally take the $\mathscr{M} = 1.0$, $\mu = 5$ core and `stir' it by increasing the initial angular momentum, finding that once the degree of rotational energy exceeds the turbulent energy in the core the disc returns, with a corresponding (though slower), outflow. These conclusions place constraints on the initial mixtures of rotation and turbulence in molecular cloud cores which are conducive to the formation of bipolar outflows early in the star formation process.

Validation of gyrokinetic simulations with measurements of electron temperature fluctuations and density-temperature phase angles on ASDEX Upgrade

Measurements of turbulent electron temperature fluctuation amplitudes, δTe⊥/Te, frequency spectra, and radial correlation lengths, Lr(Te⊥), have been performed at ASDEX Upgrade using a newly upgraded Correlation ECE diagnostic in the range of scales k⊥<1.4 cm−1, kr<3.5 cm−1 (k⊥ρs<0.28 and krρs<0.7). The phase angle between turbulent temperature and density fluctuations, αnT, has also been measured by using an ECE radiometer coupled to a reflectometer along the same line of sight. These quantities are used simultaneously to constrain a set of ion-scale non-linear gyrokinetic turbulence simulations of the outer core (ρtor = 0.75) of a low density, electron heated L-mode plasma, performed using the gyrokinetic simulation code, GENE. The ion and electron temperature gradients were scanned within uncertainties. It is found that gyrokinetic simulations are able to match simultaneously the electron and ion heat flux at this radius within the experimental uncertainties. The simulations were performed based on a reference discharge for which δTe⊥/Te measurements were available, and Lr(Te⊥) and αnT were then predicted using synthetic diagnostics prior to measurements in a repeat discharge. While temperature fluctuation amplitudes are overestimated by >50% for all simulations within the sensitivity scans performed, good quantitative agreement is found for Lr(Te⊥) and αnT. A validation metric is used to quantify the level of agreement of individual simulations with experimental measurements, and the best agreement is found close to the experimental gradient values.

Disappearance of Anisotropic Intermittency in Large-amplitude MHD Turbulence and Its Comparison with Small-amplitude MHD Turbulence

Abstract Multi-order structure functions in the solar wind are reported to display a monofractal scaling when sampled parallel to the local magnetic field and a multifractal scaling when measured perpendicularly. Whether and to what extent will the scaling anisotropy be weakened by the enhancement of turbulence amplitude relative to the background magnetic strength? In this study, based on two runs of the magnetohydrodynamic (MHD) turbulence simulation with different relative levels of turbulence amplitude, we investigate and compare the scaling of multi-order magnetic structure functions and magnetic probability distribution functions (PDFs) as well as their dependence on the direction of the local field. The numerical results show that for the case of large-amplitude MHD turbulence, the multi-order structure functions display a multifractal scaling at all angles to the local magnetic field, with PDFs deviating significantly from the Gaussian distribution and a flatness larger than 3 at all angles. In contrast, for the case of small-amplitude MHD turbulence, the multi-order structure functions and PDFs have different features in the quasi-parallel and quasi-perpendicular directions: a monofractal scaling and Gaussian-like distribution in the former, and a conversion of a monofractal scaling and Gaussian-like distribution into a multifractal scaling and non-Gaussian tail distribution in the latter. These results hint that when intermittencies are abundant and intense, the multifractal scaling in the structure functions can appear even if it is in the quasi-parallel direction; otherwise, the monofractal scaling in the structure functions remains even if it is in the quasi-perpendicular direction.

Edge turbulence effect on ultra-fast swept reflectometry core measurements in tokamak plasmas

Ultra-fast frequency-swept reflectometry (UFSR) enables one to provide information about the turbulence radial wave-number spectrum and perturbation amplitude with good spatial and temporal resolutions. However, a data interpretation of USFR is quiet tricky. An iterative algorithm to solve this inverse problem was used in past works, Gerbaud (2006 Rev. Sci. Instrum. 77 10E928). For a direct solution, a fast 1D Helmholtz solver was used. Two-dimensional effects are strong and should be taken into account during data interpretation. As 2D full-wave codes are still too time consuming for systematic application, fast 2D approaches based on the Born approximation are of prime interest. Such methods gives good results in the case of small turbulence levels. However in tokamak plasmas, edge turbulence is usually very strong and can distort and broaden the probing beam Sysoeva et al (2015 Nucl. Fusion 55 033016). It was shown that this can change reflectometer phase response from the plasma core. Comparison between 2D full wave computation and the simplified Born approximation was done. The approximated method can provide a right spectral shape, but it is unable to describe a change of the spectral amplitude with an edge turbulence level. Computation for the O-mode wave with the linear density profile in the slab geometry and for realistic Tore-Supra density profile, based on the experimental data turbulence amplitude and spectrum, were performed to investigate the role of strong edge turbulence. It is shown that the spectral peak in the signal amplitude variation spectrum which rises with edge turbulence can be a signature of strong edge turbulence. Moreover, computations for misaligned receiving and emitting antennas were performed. It was found that the signal amplitude variation peak changes its position with a receiving antenna poloidal displacement.

The role of geodesic acoustic mode on reducing the turbulent transport in the edge plasma of tokamak

Three sets of triple probe arrays (four-tip) are applied to study the transport properties at the edge of a HL-2A tokamak. The Geodesic Acoustic Mode (GAM) exhibits intermittent characteristics during the discharge. The radial particle flux has been studied in different phases corresponding to the variable GAM intensity. The experimental results reveal that the radial particle flux contributed by the ambient turbulence (20 kHz–100 kHz) has been suppressed by 13% during the GAM bursts, contrasting weak GAM cases. Power of density fluctuations and coherence between density and potential fluctuations contribute to most reduction of the particle flux, while changing the cross phase between the density and potential fluctuations and the suppression of power of potential fluctuations hardly contribute to it. These results suggest that the GAM can regulate the turbulent transport mainly by changing the amplitude of ambient turbulence, rather than the cross phase between density and potential fluctuations.

Numerical investigation on the transient characteristics of sediment-laden two-phase flow in a centrifugal pump

The objective of this work was to determine pressure fluctuation and transient flow characteristics, which aims to provide references to improve noise and vibration performance for the pump design and optimization when delivering sediment-laden flow. The three-dimensional (3D) transient simulations were simulated by SST k-ω turbulence model combined with Homogeneous equilibrium model (HEM). The experimental and numerical data was compared to validate the numerical accuracy. The simulation results predicted that the concentration shows strong effects on the external performance, velocity, pressure, turbulent kinetic energy distribution and peak amplitude of pulsation frequency, which all perform increasing trend with the rise of concentration. Meanwhile, the effect of the diameter size of particles on the flow field was relatively minor, which can also evidently influence the internal flow, but the effect is not simply proportional to the diameter size. The effect of diameter size on silt flow needs to be taken into account associated with the concentration distribution. The dominant frequency of solid-liquid approximately equals 0.8 times that of pure water, and the transient characteristics of sediment-laden flow perform low frequency with high amplitude features.

Chimera States in Continuous Media: Existence and Distinctness.

The defining property of chimera states is the coexistence of coherent and incoherent domains in systems that are structurally and spatially homogeneous. The recent realization that such states might be common in oscillator networks raises the question of whether an analogous phenomenon can occur in continuous media. Here, we show that chimera states can exist in continuous systems even when the coupling is strictly local, as in many fluid and pattern forming media. Using the complex Ginzburg-Landau equation as a model system, we characterize chimera states consisting of a coherent domain of a frozen spiral structure and an incoherent domain of amplitude turbulence. We show that in this case, in contrast with discrete network systems, fluctuations in the local coupling field play a crucial role in limiting the coherent regions. We suggest these findings shed light on new possible forms of coexisting order and disorder in fluid systems.

Vortices and the saturation of the vertical shear instability in protoplanetary discs

If sufficiently irradiated by its central star, a protoplanetary disks falls into an equilibrium state exhibiting vertical shear. This state may be subject to a hydrodynamical instability, the `vertical shear instability' (VSI), whose breakdown into turbulence transports a moderate amount of angular momentum while also facilitating planet formation, possibly via the production of small-scale vortices. In this paper, we show that VSI modes (a) exhibit arbitrary spatial profiles and (b) remain nonlinear solutions to the incompressible local equations, no matter their amplitude. The modes are themselves subject to parasitic Kelvin-Helmholtz instability, though the disk rotation significantly impedes the parasites and permits the VSI to attain large amplitudes (fluid velocities < 10% the sound speed). This `delay' in saturation probably explains the prominence of the VSI linear modes in global simulations. More generally, the parasites may set the amplitude of VSI turbulence in strongly irradiated disks. They are also important in breaking the axisymmetry of the flow, via the unavoidable formation of vortices. The vortices, however, are not aligned with the orbital plane and thus express a pronounced $z$-dependence. We also briefly demonstrate that the vertical shear has little effect on the magnetorotational instability, whereas magnetic fields easily quench the VSI, a potential issue in the ionised surface regions of the disk and also at larger radii.

Nature of Stochastic Ion Heating in the Solar Wind: Testing the Dependence on Plasma Beta and Turbulence Amplitude

Abstract The solar wind undergoes significant heating as it propagates away from the Sun; the exact mechanisms responsible for this heating are not yet fully understood. We present for the first time a statistical test for one of the proposed mechanisms: stochastic ion heating. We use the amplitude of magnetic field fluctuations near the proton gyroscale as a proxy for the ratio of gyroscale velocity fluctuations to perpendicular (with respect to the magnetic field) proton thermal speed, defined as . Enhanced proton temperatures are observed when is larger than a critical value (∼0.019–0.025). This enhancement strongly depends on the proton plasma beta ( ); when only the perpendicular proton temperature T ⊥ increases, while for increased parallel and perpendicular proton temperatures are both observed. For smaller than the critical value and no enhancement of T p is observed, while for minor increases in T ∥ are measured. The observed change of proton temperatures across a critical threshold for velocity fluctuations is in agreement with the stochastic ion heating model of Chandran et al. We find that in 76% of the studied periods, implying that stochastic heating may operate most of the time in the solar wind at 1 au.

Turbulent transport reduction induced by transition on radial electric field shear and curvature through amplitude and cross-phase in torus plasma

Spatiotemporal evolutions of radial electric field and turbulence are measured simultaneously in the H-mode transition, which is a prototypical example of turbulence structure formation in high-temperature plasmas. In the dynamical phase where transport barrier is established abruptly, the time-space-frequency-resolved turbulent particle flux is obtained. Here we report the validation of the mechanism of transport barrier formation quantitatively. It is found that the particle flux is suppressed predominantly by reducing density fluctuation amplitude and cross phase between density fluctuation and potential fluctuation. Both radial electric field shear and curvature are responsible for the amplitude suppression as was predicted by theory. Turbulence amplitude reduction immediately responds to the growth of the radial electric field non-uniformity and saturates, while cross phase continuously approaches zero.

Effect of enhanced dissipation by shear flows on transient relaxation and probability density function in two dimensions

We report a non-perturbative study of the effects of shear flows on turbulence reduction in a decaying turbulence in two dimensions. By considering different initial power spectra and shear flows (zonal flows, streamers and zonal flows, and streamers combined), we demonstrate how shear flows rapidly generate small scales, leading to a fast damping of turbulence amplitude. In particular, a double exponential decrease in the turbulence amplitude is shown to occur due to an exponential increase in wavenumber. The scaling of the effective dissipation time scale τe, previously taken to be a hybrid time scale τe∝τΩ2/3τη, is shown to depend on types of shear flow as well as the initial power spectrum. Here, τΩ and τη are shearing and molecular diffusion times, respectively. Furthermore, we present time-dependent Probability Density Functions (PDFs) and discuss the effect of enhanced dissipation on PDFs and a dynamical time scale τ(t), which represents the time scale over which a system passes through statistically different states.

Experimental identification of nonlinear coupling between (intermediate, small)-scale microturbulence and an MHD mode in the core of a superconducting tokamak

In this paper, we present clear experimental evidence of core region nonlinear coupling between (intermediate, small)-scale microturbulence and an magnetohydrodynamics (MHD) mode during the current ramp-down phase in a set of L-mode plasma discharges in the experimental advanced superconducting tokamak (EAST, Wan et al (2006 Plasma Sci. Technol. 8 253)). Density fluctuations of broadband microturbulence () and the MHD mode (toroidal mode number , poloidal mode number ) are measured simultaneously, using a four-channel tangential laser collective scattering diagnostic in core plasmas. The nonlinear coupling between the broadband microturbulence and the MHD mode is directly demonstrated by showing a statistically significant bicoherence and modulation of turbulent density fluctuation amplitude by the MHD mode.

A Test of the Interstellar Boundary EXplorer Ribbon Formation in the Outer Heliosheath

Abstract NASA’s Interstellar Boundary EXplorer (IBEX) mission is imaging energetic neutral atoms (ENAs) propagating to Earth from the outer heliosphere and local interstellar medium (LISM). A dominant feature in all ENA maps is a ribbon of enhanced fluxes that was not predicted before IBEX. While more than a dozen models of the ribbon formation have been proposed, consensus has gathered around the so-called secondary ENA model. Two classes of secondary ENA models have been proposed; the first class assumes weak scattering of the energetic pickup protons in the LISM, and the second class assumes strong but spatially localized scattering. Here we present a numerical test of the “weak scattering” version of the secondary ENA model using our gyro-averaged kinetic model for the evolution of the phase-space distribution of protons in the outer heliosheath. As input for our test, we use distributions of the primary ENAs from our MHD-plasma/kinetic-neutral model of the heliosphere-LISM interaction. The magnetic field spectrum for the large-scale interstellar turbulence and an upper limit for the amplitude of small-scale local turbulence (SSLT) generated by protons are taken from observations by Voyager 1 in the LISM. The hybrid simulations of energetic protons are also used to set the bounding wavenumbers for the spectrum of SSLT. Our test supports the “weak scattering” version. This makes an additional solid step on the way to understanding the origin and formation of the IBEX ribbon and thus to improving our understanding of the interaction between the heliosphere and the LISM.

Solar wind magnetic field background spectrum from fluid to kinetic scales

The solar wind is highly structured in fast and slow flows. These two dynamical regimes remarkably differ not only for the average values of magnetic field and plasma parameters but also for the type of fluctuations they transport. Fast wind is characterized by large amplitude, incompressible fluctuations, mainly Alfv\'{e}nic, slow wind is generally populated by smaller amplitude and less Alfv\'{e}nic fluctuations, mainly compressive. The typical corotating fast stream is characterized by a stream interface, a fast wind region and a slower rarefaction region formed by the trailing expansion edge of the stream. Moving {between these two regions}, from faster to slower wind, we observe the following behavior: a) the power level of magnetic fluctuations within the inertial range largely decreases, keeping the typical Kolmogorov scaling; b) at proton scales, for about one decade right beyond the high frequency break, the spectral index becomes flatter and flatter towards a value around -2.7; c) at higher frequencies, before the electron scales, the spectral index remains around -2.7 and, {based on suitable observations available for $4$ corotating streams}, the power level does not change, irrespective of the flow speed. All these spectral features, characteristic of high speed streams, suggest the existence of a sort of magnetic field background spectrum. This spectrum would be common to both faster and slower wind but, any time the observer would cross the inner part of a fluxtube channeling the faster wind into the interplanetary space, a turbulent and large amplitude Alfv\'{e}nic spectrum would be superposed to it.

The development of magnetic field line wander by plasma turbulence

Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to plasma heat. But plasma turbulence also generically leads to a tangling of the magnetic field that threads through the plasma. The resulting wander of the magnetic field lines may significantly impact a number of important physical processes, including the propagation of cosmic rays and energetic particles, confinement in magnetic fusion devices and the fundamental processes of turbulence, magnetic reconnection and particle acceleration. The various potential impacts of magnetic field line wander are reviewed in detail, and a number of important theoretical considerations are identified that may influence the development and saturation of magnetic field line wander in astrophysical plasma turbulence. The results of nonlinear gyrokinetic simulations of kinetic Alfvén wave turbulence of sub-ion length scales are evaluated to understand the development and saturation of the turbulent magnetic energy spectrum and of the magnetic field line wander. It is found that turbulent space and astrophysical plasmas are generally expected to contain a stochastic magnetic field due to the tangling of the field by strong plasma turbulence. Future work will explore how the saturated magnetic field line wander varies as a function of the amplitude of the plasma turbulence and the ratio of the thermal to magnetic pressure, known as the plasma beta.

The effect of core-collapse supernova accretion phase turbulence on neutrino flavor evolution*

During the accretion phase of a core-collapse supernovae, large amplitude turbulence is generated by the combination of the standing accretion shock instability and convection driven by neutrino heating. The turbulence directly affects the dynamics of the explosion, but there is also the possibility of an additional, indirect, feedback mechanism due to the effect turbulence can have upon neutrino flavor evolution and thus the neutrino heating. In this paper we consider the effect of turbulence during the accretion phase upon neutrino evolution, both numerically and analytically. Adopting representative supernova profiles taken from the accretion phase of a supernova simulation, we find the numerical calculations exhibit no effect from turbulence. We explain this absence using two analytic descriptions: the stimulated transition model and the distorted phase effect model. In the stimulated transition model turbulence effects depend upon six different lengthscales, and three criteria must be satisfied between them if one is to observe a change in the flavor evolution due to stimulated transition. We further demonstrate that the distorted phase effect depends upon the presence of multiple semi-adiabatic MSW resonances or discontinuities that also can be expressed as a relationship between three of the same lengthscales. When we examine the supernova profiles used in the numerical calculations we find the three stimulated transition criteria cannot be satisfied, independent of the form of the turbulence power spectrum, and that the same supernova profiles lack the multiple semi-adiabatic MSW resonances or discontinuities necessary to produce a distorted phase effect. Thus, we conclude that even though large amplitude turbulence is present in supernova during the accretion phase, it has no effect upon neutrino flavor evolution.

An eight-channel Doppler backscattering system in the experimental advanced superconducting tokamak.

Doppler backscattering system can measure the perpendicular velocity and fluctuation amplitude of the density turbulence with intermediate wavenumber. An eight-channel Doppler backscattering system has been installed in the Experimental Advanced Superconducting Tokamak (EAST), which can probe eight different radial locations simultaneously by launching eight fixed frequencies (55, 57.5, 60, 62.5, 67.5, 70, 72.5, 75 GHz) into plasma. The quasi-optical system consists of circular corrugated waveguide transmission, a fixed parabolic mirror, and a rotatable parabolic mirror which are integrated with quasi-optics front-end of the profile reflectometer inside the vacuum vessel. The incidence angle can be chosen from 5° to 12°, and the wavenumber range is 2-15/cm with the wavenumber resolution Δk/k≤0.21. Ray tracing simulations are used to calculate the scattering locations and the perpendicular wavenumber. The dynamic range of this new eight-channel Doppler backscattering system can be as large as 40 dB in the EAST. In this article, the hardware design, the ray tracing, and the preliminary experimental results in the EAST will be presented.

Stratified Simulations of Collisionless Accretion Disks

Abstract This paper presents a series of stratified-shearing-box simulations of collisionless accretion disks in the recently developed framework of kinetic magnetohydrodynamics (MHD), which can handle finite non-gyrotropy of a pressure tensor. Although a fully kinetic simulation predicted a more efficient angular-momentum transport in collisionless disks than in the standard MHD regime, the enhanced transport has not been observed in past kinetic-MHD approaches to gyrotropic pressure anisotropy. For the purpose of investigating this missing link between the fully kinetic and MHD treatments, this paper explores the role of non-gyrotropic pressure and makes the first attempt to incorporate certain collisionless effects into disk-scale, stratified disk simulations. When the timescale of gyrotropization was longer than, or comparable to, the disk-rotation frequency of the orbit, we found that the finite non-gyrotropy selectively remaining in the vicinity of current sheets contributes to suppressing magnetic reconnection in the shearing-box system. This leads to increases both in the saturated amplitude of the MHD turbulence driven by magnetorotational instabilities and in the resultant efficiency of angular-momentum transport. Our results seem to favor the fast advection of magnetic fields toward the rotation axis of a central object, which is required to launch an ultra-relativistic jet from a black hole accretion system in, for example, a magnetically arrested disk state.

The Parametric Decay Instability of Alfvén Waves in Turbulent Plasmas and the Applications in the Solar Wind

Abstract We perform three-dimensional ideal magnetohydrodynamic (MHD) simulations to study the parametric decay instability (PDI) of Alfvén waves in turbulent plasmas and explore its possible applications in the solar wind. We find that, over a broad range of parameters in background turbulence amplitudes, the PDI of an Alfvén wave with various amplitudes can still occur, though its growth rate in turbulent plasmas tends to be lower than both the theoretical linear theory prediction and that in the non-turbulent situations. Spatial–temporal FFT analyses of density fluctuations produced by the PDI match well with the dispersion relation of the slow MHD waves. This result may provide an explanation of the generation mechanism of slow waves in the solar wind observed at 1 au. It further highlights the need to explore the effects of density variations in modifying the turbulence properties as well as in heating the solar wind plasmas.