MHD Scales Research Articles

Verification of electromagnetic simulation capabilities in global gyrokinetic particle-in-cell code GTS

Recently, the numerical scheme presented by Mishchenko et al. [Phys. Plasmas 21, 052113 (2014); 21, 092110 (2014)] enabled explicit gyrokinetic simulations of low-frequency electromagnetic instabilities in tokamaks at experimentally relevant values of plasma β. This scheme resolved the long-standing cancellation problem that previously hindered gyrokinetic particle-in-cell code simulations of magnetohydrodynamic phenomena with inherently small parallel electric fields. Moreover, the scheme did not employ approximations that eliminate critical tearing-type instabilities. Here, we report on the implementation of this numerical scheme in the global gyrokinetic particle-in-cell code GTS. This implementation allows for a more complete and accurate picture of interaction between small scale turbulence and MHD modes in tokamaks. Additionally, we present a comprehensive set of verification simulations of numerous electromagnetic instabilities relevant to present-day tokamaks. These simulations encompass the kinetic ballooning mode, the internal kink mode, the tearing mode, the micro-tearing mode, and the toroidal Alfven eigenmode destabilized by energetic ions, which are all instrumental in understanding tokamak physics. We will also showcase the preliminary nonlinear simulations of kinetic ballooning instabilities and (2,1) island formation due to tearing mode instability. These simulations validate the accuracy of the scheme implementation and pave the way for studying how these instabilities affect plasma confinement and performance.

Spectral properties of solar wind plasma flux and magnetic field fluctuations across fast reverse interplanetary shocks

We have analyzed spectra of fluctuations in the solar wind plasma flux and the magnetic field magnitude near the front of a fast reverse shocks, using data from the BMSW device (Bright Monitor of Solar Wind) operating on the SPEKTR-R satellite. Its time resolution made it possible to study plasma flux fluctuations up to a frequency of 16 Hz. Magnetic field data was taken mainly from the WIND satellite, for which the frequency of the fluctuations considered was up to 5.5 Hz. The slope of the spectra of the solar wind flux fluctuations on MHD scales has been shown to be close to the slope of the spectrum of magnetic field fluctuations in the disturbed region. On kinetic scales, the difference can be significant. For the region ahead of the front, the difference in the slope of the spectrum can be quite large both in the MHD and in the kinetic region. The frequency of the break of the flux spectrum ranges from 0.6 to 1.3 Hz, which corresponds to the scale of the proton inertial length. In a number of events, however, the shape of the spectrum indicates the influence of the proton gyroradius frequency, which is usually 0.05–0.15 Hz. The break in the power spectrum of magnetic field fluctuations also more often ranges from 0.7 to 1.2 Hz. In this case, the slope of the MHD part of the spectrum changes little, but in the kinetic part it increases slightly when moving to the disturbed region.

Анализ спектров флуктуаций величины потока плазмы и модуля магнитного поля на обратных ударных волнах

We have analyzed spectra of fluctuations in the solar wind plasma flux and the magnetic field magnitude near the front of a fast reverse shocks, using data from the BMSW device (Bright Monitor of Solar Wind) operating on the SPEKTR-R satellite. Its time resolution made it possible to study plasma flux fluctuations up to a frequency of 16 Hz. Magnetic field data was taken mainly from the WIND satellite, for which the frequency of the fluctuations considered was up to 5.5 Hz. The slope of the spectra of the solar wind flux fluctuations on MHD scales has been shown to be close to the slope of the spectrum of magnetic field fluctuations in the disturbed region. On kinetic scales, the difference can be significant. For the region ahead of the front, the difference in the slope of the spectrum can be quite large both in the MHD and in the kinetic region. The frequency of the break of the flux spectrum ranges from 0.6 to 1.3 Hz, which corresponds to the scale of the proton inertial length. In a number of events, however, the shape of the spectrum indicates the influence of the proton gyroradius frequency, which is usually 0.05–0.15 Hz. The break in the power spectrum of magnetic field fluctuations also more often ranges from 0.7 to 1.2 Hz. In this case, the slope of the MHD part of the spectrum changes little, but in the kinetic part it increases slightly when moving to the disturbed region.

Embedded Coherent Structures from Magnetohydrodynamics to Sub-ion Scales in Turbulent Solar Wind at 0.17 au

We study intermittent coherent structures in solar wind turbulence from MHD to kinetic plasma scales using Parker Solar Probe data during its first perihelion (at 0.17 au) in the highly Alfvénic slow solar wind. We detect coherent structures using Morlet wavelets. For the first time, we apply a multiscale analysis in physical space. At MHD scales within the inertial range, times scales τ ∈ (1, 102) s, we find (i) current sheets including switchback boundaries and (ii) Alfvén vortices. Within these events are embedded structures at smaller scales: typically Alfvén vortices at ion scales, τ ∈ (0.08, 1) s, and compressible vortices at sub-ion scales, τ ∈ 8(10−3, 10−2) s. The number of coherent structures grows toward smaller scales: we observe ∼200 events during a 5 hr time interval at MHD scales, ∼103 at ion scales, and ∼104 at sub-ion scales. In general, there are multiple structures of ion and sub-ion scales embedded within one MHD structure. There are also examples of ion and sub-ion scale structures outside MHD structures. To quantify the relative importance of different types of structures, we do a statistical comparison of the observed structures with the expectations of models of the current sheets and vortices. The results show the dominance of Alfvén vortices at all scales in contrast to the widespread view of the dominance of current sheets. This means that Alfvén vortices are important building blocks of Alfvénic solar wind turbulence.

Anisotropy of Magnetohydrodynamic and Kinetic Scale Fluctuations through Correlation Tensor in Solar Wind at 0.8 au

Space plasma turbulence is inherently characterized by anisotropic fluctuations. The generalized k-th order correlation tensor of magnetic field increments allow us to separate the mixed isotropic and anisotropic structure functions from the purely anisotropic ones. In this work, we quantified the relative importance of anisotropic fluctuations in solar wind turbulence using two Alfvénic data samples gathered by the Solar Orbiter at 0.8 astronomical units. The results based on the joined statistics suggest that the anisotropic fluctuations are ubiquitous in solar wind turbulence and persist at kinetic scales. Using the RTN coordinate system, we show that their presence depends on the anisotropic sector under consideration, e.g., the RN and RT sectors exhibit enhanced anisotropy toward kinetic scales, in contrast with the TN. We then study magnetic field fluctuations parallel and perpendicular to the local mean magnetic field separately. We find that perpendicular fluctuations are representative of the global statistics, resembling the typical picture of magnetohydrodynamic turbulence, whereas parallel fluctuations exhibit a scaling law with slope ∼1 for all the joined isotropic and anisotropic components. These results are in agreement with predictions based on the critical balance phenomenology. This topic is potentially of interest for future space missions measuring kinetic and MHD scales simultaneously in a multi-spacecraft configuration.

Are Switchback Boundaries Observed by Parker Solar Probe Closed?

Switchbacks are sudden and large deflections in the magnetic field that Parker Solar Probe frequently observes in the inner heliosphere. Their ubiquitous occurrence has prompted numerous studies to determine their nature and origin. Our goal is to describe the boundary of these switchbacks using a series of events detected during the spacecraft’s first encounter with the Sun. Using FIELDS and SWEAP data, we investigate different methods for determining the boundary normal. The observed boundaries are arc-polarized structures with a rotation that is always contained in a plane. Classical minimum variance analysis gives misleading results and overestimates the number of rotational discontinuities. We propose a robust geometric method to identify the nature of these discontinuities, which involves determining whether or not the plane that contains them also includes the origin ( B = 0). Most boundaries appear to have the same characteristics as tangential discontinuities in the context of switchbacks, with little evidence for having rotational discontinuities. We find no effect of the size of the Parker spiral deviation. Furthermore, the thickness of the boundary is within MHD scales. We conclude that most of the switchback boundaries observed by Parker Solar Probe are likely to be closed, in contrast to previous studies. Our results suggest that their erosion may be much slower than expected.

Non-universality of the Turbulent Spectra at Sub-ion Scales in the Solar Wind: Dispersive Effects versus the Doppler Shift

Large surveys of the power spectral density of the magnetic fluctuations in the solar wind have reported different slope distributions at MHD, sub-ion and sub-electron scales: the smaller the scale, the broader the distribution. Here, we review briefly some of the most relevant explanations of the broadening of the slopes at sub-ion scales. Then, we present a new one that has been overlooked in the literature, which is based on the relative importance of the dispersive effects with respect to the Doppler shift due to the mean flow speed. We build a toy model based on a dispersion relation of a linear mode that matches at high frequency (ω ≳ ω ci) the Alfvén (respectively whistler) mode at high oblique (respectively quasi-parallel) propagation angles θ kB . Starting with a double power-law spectrum of turbulence in the inertial range and at the sub-ion scales, the transformed spectrum (in frequency f) as it would be measured in the spacecraft reference frame shows a broad range of slopes at the sub-ion scales that depend both on the angle θ kB and the flow speed V. Varying θ kB in the range 4°–106° and V in the range 400−800 km s−1 the resulting distribution of slopes at the sub-ion scales reproduces quite well the observed one in the solar wind. Fluctuations in the solar wind speed and the wavevector anisotropy of the turbulence may explain (or at least contribute to) the variability of the spectral slopes reported from spacecraft observations in the solar wind.

Observations of Kolmogorov Turbulence in Saturn's Magnetosphere

AbstractThe Kolmogorov scaling in the inertial range of scales is a distinct characteristic of fully developed turbulence, and studying it offers valuable insights into the evolution of turbulence. In this work, we perform a statistical survey of the power spectra with the Kolmogorov scaling in Saturn's magnetosphere using Cassini measurements. Two cases study show that both magnetic‐field and electron density spectra exhibit f −5/3 at the MHD scales. The statistical analysis reveals a wide‐ranging and abundant presence of Kolmogorov spectra throughout magnetosphere, observed across all local times. Interestingly, the occurrence rate of these Kolmogorov‐like events within Saturn's magnetosphere surpasses that observed in the planetary magnetosheath. The measurements of magnetic compressibility for the Kolmogorov‐like events show the dominance of incompressible Alfvénic turbulence (44.64%) with respect to magnetosonic‐like one (6.94%). In addition, the source and evolution of the turbulent fluctuations are further discussed.

Data-driven Uncertainty Quantification of the Wave Telescope Technique: General Equations and Demonstration Using HelioSwarm

The upcoming NASA mission HelioSwarm will use nine spacecraft to make the first simultaneous multipoint measurements of space plasmas spanning multiple scales. Using the wave telescope technique, HelioSwarm’s measurements will allow for both the calculation of the power in wavevector and frequency space and the characterization of the associated dispersion relations of waves present in the plasma at MHD and ion-kinetic scales. This technique has been applied to the four-spacecraft Cluster and Magnetospheric Multiscale missions, and its effectiveness has previously been characterized in a handful of case studies. We expand this uncertainty quantification analysis to arbitrary configurations of four through nine spacecraft for three-dimensional plane waves. We use Bayesian inference to learn equations that approximate the error in reconstructing the wavevector as a function of relative wavevector magnitude, spacecraft configuration shape, and number of spacecraft. We demonstrate the application of these equations to data drawn from a nine-spacecraft configuration to both improve the accuracy of the technique, as well as expand the magnitudes of wavevectors that can be characterized.

Ion Dynamics in the Meso-scale 3-D Kelvin–Helmholtz Instability: Perspectives From Test Particle Simulations

Over three decades of in-situ observations illustrate that the Kelvin–Helmholtz (KH) instability driven by the sheared flow between the magnetosheath and magnetospheric plasma often occurs on the magnetopause of Earth and other planets under various interplanetary magnetic field (IMF) conditions. It has been well demonstrated that the KH instability plays an important role for energy, momentum, and mass transport during the solar-wind-magnetosphere coupling process. Particularly, the KH instability is an important mechanism to trigger secondary small scale (i.e., often kinetic-scale) physical processes, such as magnetic reconnection, kinetic Alfvén waves, ion-acoustic waves, and turbulence, providing the bridge for the coupling of cross scale physical processes. From the simulation perspective, to fully investigate the role of the KH instability on the cross-scale process requires a numerical modeling that can describe the physical scales from a few Earth radii to a few ion (even electron) inertial lengths in three dimensions, which is often computationally expensive. Thus, different simulation methods are required to explore physical processes on different length scales, and cross validate the physical processes which occur on the overlapping length scales. Test particle simulation provides such a bridge to connect the MHD scale to the kinetic scale. This study applies different test particle approaches and cross validates the different results against one another to investigate the behavior of different ion species (i.e., H+ and O+), which include particle distributions, mixing and heating. It shows that the ion transport rate is about 1025 particles/s, and mixing diffusion coefficient is about 1010 m2 s−1 regardless of the ion species. Magnetic field lines change their topology via the magnetic reconnection process driven by the three-dimensional KH instability, connecting two flux tubes with different temperature, which eventually causes anisotropic temperature in the newly reconnected flux.

Linking the Sun to the Heliosphere Using Composition Data and Modelling

Our understanding of the formation and evolution of the corona and the heliosphere is linked to our capability of properly interpreting the data from remote sensing and in-situ observations. In this respect, being able to correctly connect in-situ observations with their source regions on the Sun is the key for solving this problem. In this work we aim at testing a diagnostics method for this connectivity. This paper makes use of a coronal jet observed on 2010 August 2nd in active region 11092 as a test for our connectivity method. This combines solar EUV and in-situ data together with magnetic field extrapolation, large scale MHD modeling and FIP (First Ionization Potential) bias modeling to provide a global picture from the source region of the jet to its possible signatures at 1AU. Our data analysis reveals the presence of outflow areas near the jet which are within open magnetic flux regions and which present FIP bias consistent with the FIP model results. In our picture, one of these open areas is the candidate jet source. Using a back-mapping technique we identified the arrival time of this solar plasma at the ACE spacecraft. The in-situ data show signatures of changes in the plasma and magnetic field parameters, with FIP bias consistent with the possible passage of the jet material. Our results highlight the importance of remote sensing and in-situ coordinated observations as a key to solve the connectivity problem. We discuss our results in view of the recent Solar Orbiter launch which is currently providing such unique data.

Recent progress on turbulence and multi-scale interactions in tokamak plasmas

Studies on nonlinear interactions and multi-scale physics are crucial in the physical understanding of the turbulence and transport in the complex nonlinear system of fusion plasmas. This paper reviews recent studies on the turbulence and the related transport. The prominent results are mainly from tokamaks, such as HL-2A, Tore Supra and J-TEXT. First, turbulence behaviors and its role in transport will be introduced. Critical gradients in heat and particle transports have been observed and reproduced by simulations. Turbulence modes and its role in the transport are identified using advanced diagnostics. The measured turbulence transition is consistent with the observation of particle convection reversal and the simulation prediction. In addition, the excitation of an electromagnetic turbulence by either edge self-accumulated or externally seeded impurities has been observed. The impurity-driven turbulence plays an essential role in regulating the impurity transport. Then, the effect of plasma flows on turbulence and multi-scale interactions (micro-turbulence, meso-scale fluctuations, and large scale MHD activities) will be presented. Moreover, a new meso-scale electrostatic fluctuation has been observed. The results indicate that geodesic acoustic modes and magnetic fluctuations can transfer energy through nonlinear synchronization. At last, the enhancement of nonlinear interactions by external actuators will be reported. Theoretical studies in comparisons with experimental findings will be discussed.

Solar wind turbulence: Connections with energetic particles

For the solar wind, a wealth of observational evidence indicates that turbulence is an important dynamical process for velocity (v), magnetic (b), and other related fluctuations at MHD (fluid) scales. Here we review such observations and turbulence features, including discussion of when wave or turbulence descriptions can (or cannot) explain the observations. The relevance of properties of MHD turbulence to the acceleration and transport of energetic particles is emphasized. A summary of different classes of models for solar wind fluctuations is presented, followed by reviews of transport models for (i) solar wind fluctuations and (ii) cosmic rays. In connection with cosmic ray transport models, recent developments in terms of cosmic ray transport coefficients, as well as their application in cosmic ray modulation models, are discussed in detail.

Analysis of Turbulence Properties in the Mercury Plasma Environment Using MESSENGER Observations

Abstract Turbulence is ubiquitous in space and astrophysical plasmas, such as the solar wind, planetary magnetospheres, and the interstellar medium. It plays a key role in converting electric and magnetic energies into kinetic energy of the plasma particles. Here, the properties of MHD and kinetic-scale magnetic fluctuations in the Mercury environment are investigated using data collected by the MESSENGER spacecraft from 2011 March 23 to 2015 April 28. It is found that spectral indices at MHD scales vary from ∼−5/3 in the near-Planet solar wind (possibly the foreshock) to ∼−1.3 within the magnetosheath close to bow shock. The spectra steepen further in the magnetosheath close to magnetopause, and reach ∼−2.2 within the magnetosphere. Only 15% of events were found to have the Kolmogorov scaling ∼−5/3 in the magnetosheath. The high variability of the spectral indices implies that the scaling of turbulent fluctuations in the magnetosheath is not universal, and it emphasizes the role of the bow shock on the turbulence dynamics, at least at the largest scales. Analysis of the magnetic compressibility shows that only ∼30% of events with Kolmogorov inertial range in the magnetosheath are dominated by (shear) Alfvénic fluctuations, which contrasts with well-known features of solar wind turbulence. At kinetic scales, the steepest spectra (slopes ∼−2.8) occur in the solar wind, before flattening to ∼−2 near the bow shock, then steepening again to ∼−2.8 in the magnetosheath. The spectral indices at kinetic scales are close to the ones at large scales in the magnetosphere, which may be caused by the presence of heavy ions in the latter. The statistical results are compared with previous observations reported in other planetary plasma environments.

Magnetotail dipolarization fronts and particle acceleration: A review

In this paper, the particle acceleration processes around magnetotail dipolarization fronts (DFs) were reviewed. We summarize the spacecraft observations (including Cluster, THEMIS, MMS) and numerical simulations (including MHD, test-particle, hybrid, LSK, PIC) of these processes. Specifically, we (1) introduce the properties of DFs at MHD scale, ion scale, and electron scale, (2) review the properties of suprathermal electrons with particular focus on the pitch-angle distributions, (3) define the particle-acceleration process and distinguish it from the particle-heating process, (4) identify the particle-acceleration process from spacecraft measurements of energy fluxes, and (5) quantify the acceleration efficiency and compare it with other processes in the magnetosphere (e.g., magnetic reconnection and radiation-belt acceleration processes). We focus on both the acceleration of electrons and ions (including light ions and heavy ions). Regarding electron acceleration, we introduce Fermi, betatron, and non-adiabatic acceleration mechanisms; regarding ion acceleration, we present Fermi, betatron, reflection, resonance, and non-adiabatic acceleration mechanisms. We also discuss the unsolved problems and open questions relevant to this topic, and suggest directions for future studies.

Testing of the Taylor Frozen-in-flow Hypothesis at Electron Scales in the Solar Wind Turbulence

Abstract In single-spacecraft observations the Taylor frozen-in-flow hypothesis is usually used to infer wavenumber spectra of turbulence from the frequency ones. While this hypothesis can be valid at MHD scales in the solar wind because of the small phase speeds of the fluctuations in comparison with the solar wind flow speed, its validity at electron scales is questionable. In this paper, we use Cluster data to verify the validity of the Taylor hypothesis in solar wind turbulence using the test proposed in Sahraoui et al. based on the assumption that the spectral breaks occur at ρ i and ρ e. Using a model based on the dispersion relation of the linear whistler mode and the estimated ratios of the spectral breaks of the magnetic energy observed in the free-streaming solar wind, we find that 32% of the events would violate the Taylor hypothesis because of their high frequency (in the plasma rest frame) compared to the Doppler shift · (∣ω plas/k·V ∣ > 0.5). Furthermore, the model shows that those events would correspond to whistler modes with propagation angles θ kB ≤ 68°. The limitations of the method used and the implications of the results on future spacecraft measurements of electron-scale turbulence are discussed.

Dynamical evolution of magnetic fields in the intracluster medium

We investigate the evolution of magnetic fields in galaxy clusters starting from constant primordial fields using highly resolved ($\approx \rm 4 ~kpc$) cosmological MHD simulations. The magnetic fields in our sample exhibit amplification via a small-scale dynamo and compression during structure formation. In particular, we study how the spectral properties of magnetic fields are affected by mergers, and we relate the measured magnetic energy spectra to the dynamical evolution of the intracluster medium. The magnetic energy grows by a factor of $\sim$ 40-50 in a time-span of $\sim 9$ Gyr and equipartition between kinetic and magnetic energy occurs on a range of scales ($< 160 \rm ~kpc$ at all epochs) depending on the turbulence state of the system. We also find that, in general, the outer scale of the magnetic field and the MHD scale are not simply correlated in time. The effect of major mergers is to shift the peak magnetic spectra to it smaller scales, whereas the magnetic amplification only starts after $\lesssim$ 1 Gyr. In contrast, continuous minor mergers promote the steady growth of the magnetic field. We discuss the implications of these findings in the interpretation of future radio observations of galaxy clusters.

Can Hall Magnetohydrodynamics Explain Plasma Turbulence at Sub-ion Scales?

Abstract We investigate the properties of plasma turbulence by means of two-dimensional Hall-magnetohydrodynamic (HMHD) and hybrid particle-in-cell (HPIC) numerical simulations. We find that the HMHD simulations exhibit spectral properties that are in most cases in agreement with the results of the HPIC simulations and with solar wind observations. The energy spectra of magnetic fluctuations exhibit a double power law with spectral index −5/3 at MHD scales and −3 at kinetic scales, while for velocity fluctuations the spectral index is −3/2 at MHD scales. The break between the MHD and the kinetic scales occurs at the same scale in both simulations. In the MHD range the slopes of the total energy and residual energy spectra satisfy a fast Alfvén-dynamo balance. The development of a turbulent cascade is concurrently characterized by magnetic reconnection events taking place in thin current sheets that form between large eddies. A statistical analysis reveals that reconnection is qualitatively the same and fast in both the HMHD and HPIC models, characterized by inverse reconnection rates much smaller than the characteristic large-eddy nonlinear time. The agreement extends to other statistical properties, such us the kurtosis of the magnetic field. Moreover, the observation of a direct energy transfer from the large vortices to the small sub-ion scales, triggered by magnetic reconnection, further supports the existence of a reconnection-mediated turbulent regime at kinetic scales. We conclude that the HMHD fluid description captures to a large extent the transition of the turbulent cascade between the large MHD scales and the sub-ion scales.

On the magnetic field topology in reconnection region

Magnetic reconnection is generally accompanied by large and quasi-turbulent spatio-temporal fluctuations from the MHD scales down to the kinetic ones. The study of these turbulent fluctuations is generally based on the investigation of spectral and scaling features. In a recent paper by Consolini et al. [1] it has been shown how the statistics of geometrical invariants of coarse-grained gradient tensor of plasma velocity is able to provide valuable information on the topology of the turbulent structures. Here, we present a preliminary study of the topology of magnetic field structures at kinetic scales in the X-line/dissipation region of a reconnection event observed by MMS constellation [2]. The analysis evidenced vortex sheet Ohmic-dissipation.

Magnetic Reconnection as a Driver for a Sub-ion-scale Cascade in Plasma Turbulence

Abstract A new path for the generation of a sub-ion-scale cascade in collisionless space and astrophysical plasma turbulence, triggered by magnetic reconnection, is uncovered by means of high-resolution two-dimensional hybrid-kinetic simulations employing two complementary approaches, Lagrangian and Eulerian, and different driving mechanisms. The simulation results provide clear numerical evidence that the development of power-law energy spectra below the so-called ion break occurs as soon as the first magnetic reconnection events take place, regardless of the actual state of the turbulent cascade at MHD scales. In both simulations, the reconnection-mediated small-scale energy spectrum of parallel magnetic fluctuations exhibits a very stable spectral slope of , whether or not a large-scale turbulent cascade has already fully developed. Once a quasi-stationary turbulent state is achieved, the spectrum of the total magnetic fluctuations settles toward a spectral index of in the MHD range and of at sub-ion scales.