Earth's Plasma Research Articles

Suppression of Nonlinear Chorus Wave Growth by Active Control of Gyroresonant Interactions With Electron Hole Deformation

AbstractNonlinear gyroresonant acceleration is an essential mechanism for the formation of relativistic electrons in Earth's radiation belts, yet we still have only limited knowledge of how electron motion interacts nonlinearly with plasma waves. Here we demonstrate the compelling suppression of whistler‐mode chorus emissions as a resonant wave with energetic electrons by tuning an external transmitter signal in space plasmas. Through forcible modification of electron motions via phase trapping by the external waves, the nonlinear gyroresonant current is suppressed along with the electron hole deformation. Moreover, this can decrease the population of relativistic electrons due to the lack of coherent resonant waves seen by the phase‐organized electrons. Understanding such nonlinear wave suppression effects is crucial for a potential active control of Earth's plasma environment.

Beam‐Driven Electron Cyclotron Harmonic and Electron Acoustic Waves as Seen in Particle‐In‐Cell Simulations

AbstractRecent study has demonstrated that electron cyclotron harmonic (ECH) waves can be excited by a low energy electron beam. Such waves propagate at moderately oblique wave normal angles (∼70°). The potential effects of beam‐driven ECH waves on electron dynamics in Earth's plasma sheet is not known. Using two‐dimensional Darwin particle‐in‐cell simulations with initial electron distributions that represent typical plasma conditions in the plasma sheet, we explore the excitation and saturation of such beam‐driven ECH waves. Both ECH and electron acoustic waves are excited in the simulation and propagate at oblique wave normal angles. Compared with the electron acoustic waves, ECH waves grow much faster and have more intense saturation amplitudes. Cold, stationary electrons are first accelerated by ECH waves through cyclotron resonance and then accelerated in the parallel direction by both the ECH and electron acoustic waves through Landau resonance. Beam electrons, on the other hand, are decelerated in the parallel direction and scattered to larger pitch angles. The relaxation of the electron beam and the continuous heating of the cold electrons contribute to ECH wave saturation and suppress the excitation of electron acoustic waves. When the ratio of plasma to electron cyclotron frequency ωpe/ωce increases, the ECH wave amplitude increases while the electron acoustic wave amplitude decreases. Our work reveals the importance of ECH and electron acoustic waves in reshaping sub‐thermal electron distributions and improves our understanding on the potential effects of wave‐particle interactions in trapping ionospheric electron outflows and forming anisotropic (field‐aligned) electron distributions in the plasma sheet.

Energy Dissipation in Electron-only Reconnection

Magnetic reconnection is a fundamental process in space and astrophysical plasmas that converts magnetic energy to particle energy. Recently, a novel kind of reconnection, called electron-only reconnection, has been observed in Earth's magnetosheath plasma. A defining characteristic of electron-only reconnection is that electron jets are observed but ion jets are absent. This is in contrast with traditional ion-coupled reconnection, where both ions and electrons exhibit outflowing velocity jets. Findings from the Magnetospheric Multiscale mission observations and particle-in-cell simulations show clear signatures of electron heating in electron-only reconnection events, while ions are not heated or cooled in these events. This result is unlike ion-coupled reconnection, where both ions and electrons are heated to varying degrees. The ratio of electron to ion dissipation increases with the local magnetic curvature, indicating that the partition of heat into ions and electrons is dependent on the current-sheet thickness.

Characteristics of dust plasma environment at lunar south pole

Unlike the Earth, the Moon lacks is not protected from the atmosphere and global magnetic field, and will be directly exposed to complex radiation environments such as high-energy cosmic rays, solar wind, and the Earth’s magnetotail plasma. The surface of the Moon is covered with a thick layer of lunar soil, and the particles in the soil with a diameter between 30 nm–20 μm are called lunar dust. In the complex environments such as solar wind or magnetotail plasma, lunar dust carries an electric charge and becomes charged lunar dust. Charged lunar dust is prone to migration under the action of the electric field on the lunar surface. Charged migrated lunar dust is easy to adhere to the surface of instruments and equipment, resulting in visual impairment, astronauts’ movement disorders, equipment mechanical blockage, sealing failure, and material wear, which affects the lunar exploration mission. As an important lunar exploration landing site, the lunar south pole receives special solar radiation and produces a special dust plasma environment due to its special location. In order to provide an environmental reference for lunar south pole exploration, it is necessary to explore the characteristics of the dust plasma environment in the lunar south pole and its impact. In view of the lunar south pole environment, The Spacecraft Plasma Interactions Software (SPIS) software developed by the European Space Agency is used to carry out modelling and simulation in this work. Through the simulation, the logarithmic distribution of the lunar dust space density in a range of 0–200 m at the lunar south pole, the potential distribution near the lunar surface, and the spatial distribution characteristics of plasma electrons and ions are obtained. The obtained lunar dust space density and lunar surface potential are similar to the previous theoretical derivation and field detection data, so the simulation results have high reliability. The spatial potential distribution and the spatial density distribution of electrons and ions in the lunar environment with and without lunar dust are compared. Finally, the conclusions can be drawn as follows. The space potential increases with altitude increasing. The potential at 0–10 m near the lunar south pole is about –40 V, and the space potential at 100 m is about –20 V. The density of lunar dust in an altitude range below 10 m is 10<sup>7.22</sup> m<sup>–3</sup>–10<sup>4.66</sup> m<sup>–3</sup>. The electron density in the dust plasma near the lunar surface is 10<sup>5.47</sup> m<sup>–3</sup>, and the ion density is 10<sup>6.07</sup> m<sup>–3</sup>, and both increase with altitude increasing. Charged lunar dust affects the spatial distribution of lunar dust, mainly through affecting the distribution of the space electric field, which leads to difference in electron distribution, but has little effect on ions.

An Updated Geomagnetic Index‐Based Model for Determining the Latitudinal Extent of Energetic Electron Precipitation

AbstractEnergetic Electron Precipitation (EEP) from the Earth's plasma sheet and the radiation belts is an important feature of atmospheric dynamics through their destruction of ozone in the lower thermosphere and mesosphere. Therefore, understanding the magnitude of the atmospheric impact of the Sun‐Earth interaction requires a comprehensive understanding of the intensity and location of EEP. This study improves the accuracy of a previous pressure‐corrected Dst model that predicts the equatorward extent of >43, >114, and >292 keV EEP using the measurements from the Medium Energy Proton Electron Detector detector of six National Oceanic and Atmospheric Administration/Polar Orbiting Environmental Satellites and EUMETSAT/METOP satellites. The improvement is achieved through multiple linear regression of pressure‐corrected Dst and pressure‐corrected Ring Current (RC) indices. The RC index mitigates the baseline variation of the Dst index that created an inherent solar cycle bias in the previous model. The new model is then extended to the Southern Hemisphere (SH) after removing the South Atlantic Anomaly longitudes from the data. More than 80% of the residuals lie within ±1.8° Corrected Geomagnetic Latitude (CGMLat) in the Northern Hemisphere and within ±1.98° CGMLat in the SH.

Langmuir and Upper Hybrid Waves in Earth's Magnetotail

AbstractWaves at the electron plasma frequency are found throughout the heliosphere. They provide indicators of unstable electron distributions, are routinely used to estimate the local electron number density, and can lead to radio wave emission at the plasma frequency and its harmonics. Although they have been studied extensively in various solar and heliospheric plasma regions, there is a lack of statistical studies of plasma frequency waves in Earth's magnetotail. Here, the occurrence and properties of plasma frequency waves, namely Langmuir and upper hybrid (UH) waves, are investigated in Earth's magnetotail using the four Magnetospheric Multiscale spacecraft. In Earth's magnetotail plasma frequency waves are observed about 1% of the time. About 80% of the waves are identified as Langmuir waves, while about 20% are identified as UH waves. The waves are primarily found in the plasma sheet boundary layer. By comparing with the local electron distributions it is shown that the Langmuir waves are generated by the bump‐on‐tail instability, while UH waves are typically associated with broad electron beams or loss‐cone‐like distributions. The majority of the waves are found in close proximity to ion outflow regions associated with magnetic reconnection in the magnetotail. The waves are likely generated by plasma sheet electrons escaping along newly reconnected magnetic field lines or electron beams propagating toward the distant magnetotail.

Observations of Locally Generated Whistler-mode Waves in the Martian Magnetotail Current Sheet

The whistler-mode wave is an electromagnetic wave that commonly occurs in space plasma and has been extensively studied, especially within the Earth's magnetosphere. They have also been reported in the near-Mars space, such as Martian upstream solar wind, crustal magnetic field, ionopause, and the magnetic reconnection ion diffusion region. However, the generation of whistler-mode waves in the Martian magnetotail current sheet is still unclear. Based on observations made by Mars Atmosphere and Volatile Evolution spacecraft, we report whistler-mode waves observed within a train of proton-scale magnetic dips during a Martian magnetotail current sheet crossing. The linear growth rate analyses demonstrate that the whistler-mode waves are locally generated within the magnetic dips. Unlike in Earth's plasma environment, the train of magnetic dips in the Martian plasma sheet is attributed to electron mirror-mode instability. Our finding suggests that the mirror-mode structure in the Martian magnetotail can be an important source region for generating whistler-mode waves. This provides a new insight into how whistler-mode waves are generated in unmagnetized planets.

Observations of plasma waves generated by charged space objects

A sampling of the environment around inert space objects has determined, which linear and nonlinear waves are created by moving space debris of all sizes. Plasma waves excited by satellites and space debris moving through the Earth's plasma in low earth orbit have been measured with in situ electric field sensors on other satellites. These orbit driven plasma waves are of interest for proximity detection of space debris and sources of electrostatic and electromagnetic noise on spacecraft. Satellites and other space objects moving through the near-earth ionosphere between 200 and 1000 km altitude become electrically charged by both electron collection and photo emission in sunlight. These hypersonic, charged objects can excite a wide range of plasma waves. Measurements with the Radio Receiver Instrument (RRI) on the Swarm-E satellite have shown that electromagnetic plasma waves from known objects can be observed out to ranges of tens of kilometers. The amplitude, spectral, and polarization changes of the RRI data are consistent with electromagnetic, compressional Alfvén waves launched by charged space objects traveling across magnetic field lines. In addition, electrostatic lower hybrid waves or nonlinear ion acoustic pinned oscillations may have been self-generated and measured on the Swarm-E satellite. It is proposed that measurements of these waves with local electric field measurements or remote electromagnetic wave scatter may be useful to design systems for the location of orbiting objects. Spatial and temporal details of spacecraft charging are key to understanding the extent of waves associated with the object motion in space plasmas.

Coexistence of positive and negative polarity solitons, double layers and supersolitons in electron-positron multi-ion plasmas

In order to analyze the nonlinear propagation of arbitrary amplitude ion-acoustic waves, the Sagdeev pseudopotential formalism is used to a four-component multi-ion plasma made up of inertial light positive ions, heavy negative ions, inertialess nonextensive electrons, and positrons. At first, we derived the expression of Sagdeev Pseudopotential for our plasma model and then numerically investigated the condition for the existence of several nonlinear structures such as solitons, double layers, supersolitons, etc. Based on numerical simulation, it is observed that within a certain range of parameters, our plasma model allows compressive as well as a rarefactive soliton, flat-top soliton, double layer, and supersoliton solutions. Great emphasis is placed on the determination of the existence regions for both solitons and supersolitons in the parameter space. Also, various nonlinear structures are explored to examine the effects of various plasma properties, such as the nonextensivity parameter, Mach number, etc. The findings of the current investigations may be helpful for comprehending significant features of ion-acoustic wave structures in space plasmas such as earth's ionosphere, cometary tails, etc., and laboratory plasmas like laser-plasma interaction research.

RCM Modeling of Bubble Injections Into the Inner Magnetosphere: Spectral Properties of Plasma Sheet Particles

AbstractCollisionless astrophysical plasmas are correlated systems in which particles are often not in thermal equilibrium and can be characterized by power‐law distributions. The kappa distribution function, which is a more generalized form of the power‐law function, is often used to describe acceleration and production of high‐energy particles in different space plasma environments. The spectra of particles in the Earth's plasma sheet constructed using Time History of Events and Mesoscale Interactions during Substorms data show that the kappa index exhibits a strong dawn‐dusk asymmetry and a clear dependence on both geocentric distance and magnetic local time. Furthermore, statistics indicate that spectrum hardening, or softening is expected during geomagnetically disturbed periods. To understand how the shape of the particle distribution function evolves and what factors affect the kappa index, we simulate earthward plasma transport using a kinetic drift model. In the simulations, the plasma distribution is initially considered to be a kappa function with . However, with time, both protons and electrons' distribution functions evolve and deviate from their initial shapes. We demonstrate that by implementing transient low‐entropy plasma injections, the Rice Convection Model average distribution functions can reasonably agree with observations. We also discuss the relative impact of gradient/curvature drift, particle loss, and bubble injections, based on controlled numerical experiments.

Properties and Acceleration Mechanisms of Electrons Up To 200keV Associated With a Flux Rope Pair and Reconnection X-Lines Around It in Earth's Plasma Sheet.

The properties and acceleration mechanisms of electrons (<200keV) associated with a pair of tailward traveling flux ropes and accompanied reconnection X-lines in Earth's plasma sheet are investigated with MMS measurements. Energetic electrons are enhanced on both boundaries and core of the flux ropes. The power-law spectra of energetic electrons near the X-lines and in flux ropes are harder than those on flux rope boundaries. Theoretical calculations show that the highest energy of adiabatic electrons is a few keV around the X-lines, tens of keV immediately downstream of the X-lines, hundreds of keV on the flux rope boundaries, and a few MeV in the flux rope cores. The X-lines cause strong energy dissipation, which may generate the energetic electron beams around them. The enhanced electron parallel temperature can be caused by the curvature-driven Fermi acceleration and the parallel electric potential. Betatron acceleration due to the magnetic field compression is strong on flux rope boundaries, which enhances energetic electrons in the perpendicular direction. Electrons can be trapped between the flux rope pair due to mirror force and parallel electric potential. Electrostatic structures in the flux rope cores correspond to potential drops up to half of the electron temperature. The energetic electrons and the electron distribution functions in the flux rope cores are suggested to be transported from other dawn-dusk directions, which is a 3-dimensional effect. The acceleration and deceleration of the Betatron and Fermi processes appear alternately indicating that the magnetic field and plasma are turbulent around the flux ropes.

Energetic electron scattering by kinetic Alfvén waves at strong magnetic field gradients of dipolarization front

Energetic electron scattering and precipitation from the Earth's plasma sheet to the ionosphere is an important contributor to magnetosphere–ionosphere coupling. In this study, we investigate the role of one of the most intense wave emissions, kinetic Alfvén waves (KAWs), in energetic electron scattering. We have evaluated the effect of KAWs on energetic electrons within a curved magnetic field configuration exhibiting sharp cross field gradients. The magnetic field in Earth's magnetotail plasma sheet with an embedded dipolarization front is used as a working example. Taking into account electron bounce motion and perpendicular guiding-center drifts, we have shown that electrons with energies of tens to hundreds of keV can be scattered by KAWs in pitch angle and momentum through Doppler-shifted Landau resonance near the magnetic equator. The bounce-averaged pitch-angle diffusion coefficients for near-loss-cone (∼2°) electrons are on the order of 10–7–10–6 rad2/s for a characteristic KAW amplitude of 1 mV/m and approach the strong diffusion limit of ∼10–4 rad2/s for amplitudes of greater than 10 mV/m. These results suggest that under such ambient conditions, KAWs can pitch-angle scatter energetic electron population into the loss cone. In Earth's plasma sheet, this scattering is, thus, very likely to cause significant precipitation during active times. The diffusion coefficients of energetic electrons at large pitch angles (∼45°–∼80°) are more than two orders of magnitude larger than those of electrons near the loss cone, suggesting that KAWs contribute to isotropization of anisotropic electrons due to adiabatic heating should they drift into the vicinity of the magnetic field gradient.

A high-fidelity high-efficiency model for electrodynamic tether system based on recursive algorithm

The electrodynamic tether (EDT) system is used as one of the end-of-life disposal technologies to deorbit defunct satellites with the benefit of Earth's magnetic field and plasma environment. However, due to the flexibility of the conductive tether, the orbit-attitude coupling effects as well as the influence of Multiphysics fields, this system suffers from time-consuming computations using complicated mathematical model in long-term simulations. Therefore, this paper proposes a high-fidelity high-efficiency dynamics model for the EDT system, in which the tether libration and transverse motions are described by the articulated model, and the system equations are formulated using recursive dynamics algorithm. Computational cost of the recursive method is compared with a nonrecursive method, and the result shows that with the number of tether elements larger than 15, the recursive method would show better computational efficiency. Since the conductive tether tends to be kilometers long in application, this new model would definitely contribute to the numerical efficiency. In addition, simulations are conducted with 2 and 16 tether elements solutions. By comparing the obtained results, it is found that the two cases show large differences over time. For a long tether, it is reasonable to use a larger number of elements in the dynamics analysis. Besides, in order to suppress the libration motion and avoid unstable states in the EDT system, a current control strategy is proposed and verified by a deorbit simulation in low Earth orbit.

Direct Observation of Acceleration and Thermalization of Beam Electrons Caused by Double Layers in the Earth's Plasma Sheet

AbstractWe report direct observations of the detailed processes for the acceleration and thermalization of beam electrons in the plasma sheet (PS) of the Earth's magnetotail. With observations from the four magnetospheric multiscale (MMS) satellites, the potential of a double layer (DL) structure is found to be mostly consistent with enhancements of the averaged parallel energy of the beam electrons passing through the DL structure, demonstrating that beam electrons are accelerated by the DL structure. Thereafter, Debye‐scale parallel electric field turbulences and an increase of the parallel temperature are simultaneously observed, implying that electrostatic parallel turbulences thermalize beam electrons. These observations imply that the DL is a key process controlling the acceleration and thermalization of beam electrons in the PS of the Earth's magnetotail.

Multisatellite Observations of Ion Holes in the Earth's Plasma Sheet

AbstractWe present the first observations of electrostatic solitary waves with electrostatic potential of negative polarity around a fast plasma flow in the Earth's plasma sheet. The solitary waves are observed aboard four Magnetospheric Multiscale spacecraft, which allowed accurately estimating solitary wave properties. Based on a data set of 153 solitary waves, we show that they are locally one‐dimensional Debye‐scale structures with amplitudes up to 20% of local electron temperature and they propagate at plasma frame speeds ranging from a tenth to a few ion‐acoustic speeds at arbitrary angles to the local magnetic field. The solitary waves are associated with multi‐component proton distributions and their velocities are around those of a beam‐like proton population. We argue that the solitary waves are ion holes, nonlinear structures produced by ion‐streaming instabilities, and conclude that once ions are not magnetized, ion holes can propagate oblique to local magnetic field.

Magnetospheric response to solar wind forcing: ultra-low-frequency wave–particle interaction perspective

Abstract. Solar wind forcing, e.g., interplanetary shock and/or solar wind dynamic pressure pulses impacting Earth's magnetosphere, manifests many fundamental important space physics phenomena, including producing electromagnetic waves, plasma heating, and energetic particle acceleration. This paper summarizes our present understanding of the magnetospheric response to solar wind forcing in the aspects of radiation belt electrons, ring current ions and plasmaspheric plasma physics based on in situ spacecraft measurements, ground-based magnetometer data, magnetohydrodynamics (MHD) and kinetic simulations. Magnetosphere response to solar wind forcing is not just a “one-kick” scenario. It is found that after the impact of solar wind forcing on Earth's magnetosphere, plasma heating and energetic particle acceleration started nearly immediately and could last for a few hours. Even a small dynamic pressure change in interplanetary shock or solar wind pressure pulse can play a non-negligible role in magnetospheric physics. The impact leads to generation of a series of waves, including poloidal-mode ultra-low-frequency (ULF) waves. The fast acceleration of energetic electrons in the radiation belt and energetic ions in the ring current region response to the impact usually contains two contributing steps: (1) the initial adiabatic acceleration due to the magnetospheric compression, (2) followed by the wave–particle resonant acceleration dominated by global or localized poloidal ULF waves excited at various L-shells. Generalized theory of drift and drift–bounce resonance with growth- or decay-localized ULF waves has been developed to explain in situ spacecraft observations. The wave-related observational features like distorted energy spectrum, “boomerang” and “fishbone” pitch angle distributions of radiation belt electrons, ring current ions and plasmaspheric plasma can be explained in the framework of this generalized theory. It is worth pointing out here that poloidal ULF waves are much more efficient at accelerating and modulating electrons (fundamental mode) in the radiation belt and charged ions (second harmonic) in the ring current region. The results presented in this paper can be widely used in solar wind interacting with other planets such as Mercury, Jupiter, Saturn, Uranus and Neptune and other astrophysical objects with magnetic fields.

Ion Convection as a Function of Distance to the Neutral Sheet in Earth's Magnetotail

AbstractWe utilized 33 years of data obtained by the Geotail, THEMIS, Cluster and MMS missions to investigate the slow (&lt;200 km/s) ion flows perpendicular to the magnetic field in Earth's magnetotail plasma sheet. By using plasma β as a proxy of distance to the neutral sheet, we find that the ion flow patterns vary systematically within the plasma sheet. Particularly, in regions farther from the neutral sheet, earthward (tailward) flows exhibit a strong tendency to diverge (converge) quasi‐symmetrically, with respect to the midnight meridional plane. As the distance becomes closer toward the neutral sheet, this tendency to diverge and converge gradually weakens. Moreover, duskward flows become the dominant components in both the earthward and tailward flows. These variations in ion flow patterns with distance to neutral sheet are hemispherically independent. We suggest that the spatial profiles of the electric and diamagnetic drift vary with distance to the neutral sheet and are therefore responsible for the varying ion flow patterns.

Regulation of ionospheric plasma velocities by thermospheric winds.

Earth's equatorial ionosphere exhibits substantial and unpredictable day-to-day variations in density and morphology. This presents challenges in preparing for adverse impacts on geopositioning systems and radio communications even 24 hours in advance. The variability is now theoretically understood as a manifestation of thermospheric weather, where winds in the upper atmosphere respond strongly to a spectrum of atmospheric waves that propagate into space from the lower and middle atmosphere. First-principles simulations predict related, large changes in the ionosphere, primarily through modification of wind-driven electromotive forces: the wind-driven dynamo. Here we show the first direct evidence of the action of a wind dynamo in space, using the coordinated, space-based observations of winds and plasma motion made by the National Aeronautics and Space Administration Ionospheric Connection Explorer. A clear relationship is found between vertical plasma velocities measured at the magnetic equator near 600 km and the thermospheric winds much farther below. Significant correlations are found between the plasma and wind velocities during several successive precession cycles of the Ionospheric Connection Explorer's orbit. Prediction of thermospheric winds in the 100-150 km altitude range emerges as the key to improved prediction of Earth's plasma environment.

Can Earth's Magnetotail Plasma Sheet Produce a Source of Relativistic Electrons for the Radiation Belts?

AbstractSimultaneous observations from Van Allen Probes in Earth's outer radiation belt (∼4–6 RE) and Magnetospheric Multiscale (MMS) in the magnetotail plasma sheet at &gt;20 RE geocentric distance are used to compare relative levels of relativistic electron phase space density (PSD) for constant values of the first adiabatic invariant, M. We present new evidence from two events showing: (a) at times, there is sufficient PSD in the central plasma sheet to provide a source of &gt;1 MeV electrons into the outer belt; (b) the most intense levels of relativistic electrons are not accelerated in the solar wind or transported from the inner magnetosphere and thus must be accelerated rapidly (within ∼minutes or less) and efficiently across a broad region of the magnetotail itself; and (c) the highest intensity relativistic electrons observed by MMS were confined within only the central plasma sheet. The answer to the title question here is: yes, it can, however whether Earth's plasma sheet actually does provide a source of several 100s keV to &gt;1 MeV electrons to the outer belt and how often it does so remain important outstanding questions.

Influence of MHD Turbulence on Ion Kappa Distributions in the Earth's Plasma Sheet as a Function of Plasma β Parameter

The possible influence of MHD turbulence on the energy distributions of ions in the Earth's plasma sheet was studied using data taken by the THEMIS satellites. Turbulence levels were traced using eddy diffusion coefficients (D), of which we measured one for each Geocentric Solar Magnetospheric (GSM) coordinates every 12 min. Ion fluxes between 1.75 and 210.5 keV during the same time windows that correspond to mainly suprathermal populations were fitted to Kappa distribution functions, which approximate a Maxwellian distribution when theκ-index (κ) is large. We found that the distribution of the eddy diffusion coefficients is bimodal, independently of both the eddy diffusion component and the plasma beta (β) parameter, which is defined as the ratio between plasma and magnetic pressures. The main peak corresponds to turbulent plasma flows withD&amp;gt; 103km2s−1. In such cases, the impact of turbulence on theκindex depends on the value ofβand also on the direction of the turbulent transport. For eddy diffusion perpendicular to the neutral sheet, the values ofκdecrease asDzzincreases forβ&amp;lt; 2; while for higher values ofβ,κincreases withDzz. For the other two directions, the values ofκdecrease asDincreases. This last tendency is stronger forβ~ 1 but almost null forβ~ 10. The secondary peak in the distribution ofDvalues might represent quasi-laminar flows forming part of very large vortices, correct detection and description of which is beyond the scope of this study.