Electron Pressure Tensor Research Articles

Electron Heating in 2D Particle-in-cell Simulations of Quasi-perpendicular Low-beta Shocks

We measure the thermal electron energization in 1D and 2D particle-in-cell simulations of quasi-perpendicular, low-beta (β p = 0.25) collisionless ion–electron shocks with mass ratio m i/m e = 200, fast Mach number Mms=1 –4, and upstream magnetic field angle θ Bn = 55°–85° from the shock normal nˆ . It is known that shock electron heating is described by an ambipolar, B -parallel electric potential jump, Δϕ ∥, that scales roughly linearly with the electron temperature jump. Our simulations have Δϕ∥/(0.5miush2)∼0.1 –0.2 in units of the pre-shock ions’ bulk kinetic energy, in agreement with prior measurements and simulations. Different ways to measure ϕ ∥, including the use of de Hoffmann–Teller frame fields, agree to tens-of-percent accuracy. Neglecting off-diagonal electron pressure tensor terms can lead to a systematic underestimate of ϕ ∥ in our low-β p shocks. We further focus on two θ Bn = 65° shocks: a Ms=4 ( MA=1.8 ) case with a long, 30d i precursor of whistler waves along nˆ , and a Ms=7 ( MA=3.2 ) case with a shorter, 5d i precursor of whistlers oblique to both nˆ and B ; d i is the ion skin depth. Within the precursors, ϕ ∥ has a secular rise toward the shock along multiple whistler wavelengths and also has localized spikes within magnetic troughs. In a 1D simulation of the Ms=4 , θ Bn = 65° case, ϕ ∥ shows a weak dependence on the electron plasma-to-cyclotron frequency ratio ω pe/Ωce, and ϕ ∥ decreases by a factor of 2 as m i/m e is raised to the true proton–electron value of 1836.

Numerical study of the suppression of magnetic reconnection onset with injected plasma

In this study, we perform two simulations with different plasma injection times. These simulations use the experimental setup of double-coil target-driven magnetic reconnection. The injected plasma is introduced as an external factor influencing the suppression of magnetic reconnection. Under the influence of the injected plasma, the magnetic field cannot pile up in the current sheet because the magnetic force and thermal pressure on both sides have decreased. As a result, under the combined influence of these factors, the current sheet cannot become sufficiently thin and reconnection is suppressed. Consequently, the terms for electron inertia and the non-diagonal components of the electron pressure tensor, which contribute to the reconnection electric field, are all smaller due to a reduction of the magnetic flux in the current sheet. The study provides a plausible experimental scheme for studying the onset of magnetic reconnection in the laboratory. It may also potentially provide new ideas for investigating the onset of magnetic reconnection in different environments, such as turbulent magnetic reconnection in Earth's magnetosheath.

Distribution of Negative J·E′ in the Inflow Edge of the Inner Electron Diffusion Region During Tail Magnetic Reconnection: Simulations Vs. Observations

AbstractMagnetic reconnection is a universal phenomenon existing in the space. Energy conversion is one of the essential parts of reconnection discussed for decades. Positive energy conversion (J·E′ > 0) is usually regarded as the sign of electron diffusion region (EDR), while the negative one (J·E′ < 0) turns out to gather in the outer EDR. Here we report the negative J·E′ appearing in the inflow edge of the inner EDR, based on Magnetospheric Multiscale mission observations and particle‐in‐cell simulations. Both observations and simulations verify that this negative J·E′ is mainly contributed from the electron pressure tensor term in generalized Ohm's law. The energy loss of electrons plays the dominant effect in the electron pressure tensor, and this energy decline is caused by the electric field which is induced by the decreasing magnetic field. Our results provide significant insights to expand the understanding of the reconnection regimes.

EVALUATION OF RECONNECTION PARAMETERS FOR COLLISIONLESS DISPENSATION IN SOLAR CORONA

In the present paper, we have obtained an analytical solution for the thickness of current sheet in the dissipation region of the solar corona, reconnection time and reconnection rate for collisionless magnetic reconnection occuring in the solar corona. For our analysis we have used the length scale of the electron dissipation region based on field reversals. The reconnection electric field and component of the electron pressure tensor used in the Sweet-Parker model have been utilised to finally determine the exact numerical value of the thickness of current sheet, reconnection time and reconnection rate. It is shown that the thickness of the current sheet in the collisionless reconnection model is directly proportional to the electron mass and inversely proportional to the length scale of the electron dissipation region. Also, it is shown that the reconnection time is inversely proportional to the cube of the magnetic field and directly proportional to length scale, whereas reconnection rate is inversely proportional to the length scale of the electron dissipation region.

Reconstruction of the Electron Diffusion Region With Inertia and Compressibility Effects.

A method based on electron magnetohydrodynamics (EMHD) for the reconstruction of steady, two‐dimensional plasma and magnetic field structures from data taken by a single spacecraft, first developed by Sonnerup et al. (2016), https://doi.org/10.1002/2016ja022430, is extended to accommodate inhomogeneity of the electron density and temperature, electron inertia effects, and guide magnetic field in and around the electron diffusion region (EDR), the central part of the magnetic reconnection region. The new method assumes that the electron density and temperature are constant along, but may vary across, the magnetic field lines. We present two models for the reconstruction of electron streamlines, one of which is not constrained by any specific formula for the electron pressure tensor term in the generalized Ohm's law that is responsible for electron unmagnetization in the EDR, and the other is a modification of the original model to include the inertia and compressibility effects. Benchmark tests using data from fully kinetic simulations show that our new method is applicable to both antiparallel and guide‐field (component) reconnection, and the electron velocity field can be better reconstructed by including the inertia effects. The new EMHD reconstruction technique has been applied to an EDR of magnetotail reconnection encountered by the Magnetospheric Multiscale spacecraft on 11 July 2017, reported by Torbert et al. (2018), https://doi.org/10.1126/science.aat2998 and reconstructed with the original inertia‐less version by Hasegawa et al. (2019), https://doi.org/10.1029/2018ja026051, which demonstrates that the new method better performs in recovering the electric field and electron streamlines than the original version.

Hamiltonian kinetic-Hall magnetohydrodynamics with fluid and kinetic ions in the current and pressure coupling schemes

We present two generalized hybrid kinetic-Hall magnetohydrodynamics (MHD) models describing the interaction of a two-fluid bulk plasma, which consists of thermal ions and electrons, with energetic, suprathermal ion populations described by Vlasov dynamics. The dynamics of the thermal components are governed by standard fluid equations in the Hall MHD limit with the electron momentum equation providing an Ohm's law with Hall and electron pressure terms involving a gyrotropic electron pressure tensor. The coupling of the bulk, low-energy plasma with the energetic particle dynamics is accomplished through the current density (current coupling scheme; CCS) and the ion pressure tensor appearing in the momentum equation (pressure coupling scheme; PCS) in the first and the second model, respectively. The CCS is a generalization of two well-known models, because in the limit of vanishing energetic and thermal ion densities, we recover the standard Hall MHD and the hybrid kinetic-ions/fluid-electron model, respectively. This provides us with the capability to study in a continuous manner, the global impact of the energetic particles in a regime extending from vanishing to dominant energetic particle densities. The noncanonical Hamiltonian structures of the CCS and PCS, which can be exploited to study equilibrium and stability properties through the energy-Casimir variational principle, are identified. As a first application here, we derive a generalized Hall MHD Grad–Shafranov–Bernoulli system for translationally symmetric equilibria with anisotropic electron pressure and kinetic effects owing to the presence of energetic particles using the PCS.

Cluster After 20 Years of Operations: Science Highlights and Technical Challenges

AbstractThe Cluster mission was the first constellation using four identical spacecraft to study Sun‐Earth connection plasma processes. Using four spacecraft in a tetrahedron shape, it could measure, for the first time, 3D quantities such as electrical currents, plasma gradients or divergence of the electron pressure tensor and 3D structures such as boundaries, surface waves or vortices. Launched in pairs in July and August 2000, on two Soyuz rockets from Baikonur, the four spacecraft have been collecting data continuously for more than 20 years. The mission faced many challenges during the years of operations as some spacecraft subsystems had a lifetime of a few years beyond the initial two‐year mission. The major one was to operate without functioning batteries and to successfully pass short and long eclipses, up to 3 h long, without damaging the on‐board computers and transmitters and without freezing the fuel. More than 1,000 eclipses have been successfully passed since 2010 using a specially made procedure which switches off the complete spacecraft before entering into eclipse and switches it on when the Sun is again illuminating the solar panels. During 20 years, many discoveries and science results have been published in more than 2,700 scientific papers. A few highlights are presented here, focusing on how varying the spacecraft separation was essential to achieve the science goals of the mission. The Cluster Science Data System and the Cluster archive allows public access to all science data as well as spacecraft ancillary data.

Numerical study of non-gyrotropic electron pressure effects in collisionless magnetic reconnection

We investigate the time evolution of the six-component electron pressure tensor in a hybrid code studying consequences for the two-dimensional reconnection process in an initially perturbed Harris sheet. We put forward that two tensor components (a diagonal and a non-diagonal one) grow in an unstable way unless an isotropization operator is considered. This isotropization term is physically associated with an electron heat flux. As a consequence, we put forward that an enhanced value of a diagonal component is observed in the very middle of field reversal at sub-ion scale. Because of the increase in the kinetic pressure, the magnetic field is decreased in this electron layer, hence increasing the associated out-of-plane current at its edges and leading to its bifurcation. The bifurcation mechanism is based on the presence of electron pressure anisotropy, related to the gradient of inflow electron bulk velocity. The gradient in the inflow direction of the enhanced diagonal electron pressure tensor component results in the deceleration of the ions entering the X-point region. We suggest that bifurcated current sheets resulting from the anisotropies/agyrotropies of the six-component electron pressure tensor correspond to smaller reconnection rates compared to non-bifurcated ones.

Laboratory Verification of Electron‐Scale Reconnection Regions Modulated by a Three‐Dimensional Instability

AbstractDuring magnetic reconnection in collisionless space plasma, the electron fluid decouples from the magnetic field within narrow current layers, and theoretical models for this process can be distinguished in terms of their predicted current layer widths. From theory, the off‐diagonal stress in the electron pressure tensor is related to the thermal noncircular orbit motion of electrons around the magnetic field lines. This stress becomes significant when the width of the reconnecting current layer approaches the small characteristic length scale of the electron motion. To aid in situ spacecraft and numerical investigations of reconnection, the structure of the electron diffusion region is here investigated using the Terrestrial Reconnection Experiment. In agreement with the closely matched kinetic simulations, laboratory observations reveal the presence of electron‐scale current layer widths. Although the layers are modulated by a current‐driven instability, three‐dimensional simulations demonstrate that it is the off‐diagonal stress that is responsible for breaking the frozen‐in condition of the electron fluid.

The Inertia‐Based Model for Reconstruction of the Electron Diffusion Region

AbstractThe present study is focused on the problem of reconstruction of the magnetic configuration in the magnetic reconnection electron diffusion region (EDR). The problem is addressed in the frame of electron magnetohydrodynamics with kept electron inertia term. We introduce the new reconstruction model independent of divergence of the electron pressure tensor and reconnection electric field. The model is tested on the magnetotail reconnection event of July 11, 2017 observed by the Magnetospheric Multiscale (MMS) spacecraft in the course of crossing the very core part of the reconnection region, the internal EDR. This new model demonstrates considerably better accuracy of the longitudinal electron velocity reconstruction due to the lower sensitivity to the configuration deviation from the two‐dimensional time‐independent model adopted in our study. We suggest also a new technique to estimate the guide field, implementing the reconstruction of magnetic potential of the in‐plane magnetic field and relying on symmetric properties of magnetic reconnection.

Spontaneous growth of the reconnection electric field during magnetic reconnection with a guide field: A theoretical model and particle-in-cell simulations**Project supported by the National Natural Science of China (Grant Nos. 41527804 and 41774169), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB 41000000), and the Key Research Program of Frontier Sciences of the Chinese Academy

Reconnection electric field is a key element of magnetic reconnection. It quantifies the change of magnetic topology and the dissipation of magnetic energy. In this work, two-dimensional (2D) particle-in-cell (PIC) simulations are performed to study the growth of the reconnection electric field in the electron diffusion region (EDR) during magnetic reconnection with a guide field. At first, a seed electric field is produced due to the excitation of the tearing-mode instability. Then, the reconnection electric field in the EDR, which is dominated by the electron pressure tensor term, suffers a spontaneous growth stage and grows exponentially until it saturates. A theoretical model is also proposed to explain such a kind of growth. The reconnection electric field in the EDR is found to be directly proportional to the electron outflow speed. The time derivative of electron outflow speed is proportional to the reconnection electric field in the EDR because the outflow is formed after the inflow electrons are accelerated by the reconnection electric field in the EDR and then directed away along the outflow direction. This kind of reinforcing process at last leads to the exponential growth of the reconnection electric field in the EDR.

Pressure Tensor Elements Breaking the Frozen-In Law During Reconnection in Earth's Magnetotail.

Aided by fully kinetic simulations, spacecraft observations of magnetic reconnection in Earth's magnetotail are analyzed. The structure of the electron diffusion region is in quantitative agreement with the numerical model. Of special interest, the spacecraft data reveal how reconnection is mediated by off-diagonal stress in the electron pressure tensor breaking the frozen-in law of the electron fluid.

An Extended MHD Study of the 16 October 2015 MMS Diffusion Region Crossing

AbstractThe Magnetospheric Multiscale (MMS) mission has given us unprecedented access to high cadence particle and field data of magnetic reconnection at Earth's magnetopause. MMS first passed very near an X‐line on 16 October 2015, the Burch event, and has since observed multiple X‐line crossings. Subsequent 3‐D particle‐in‐cell (PIC) modeling efforts of and comparison with the Burch event have revealed a host of novel physical insights concerning magnetic reconnection, turbulence‐induced particle mixing, and secondary instabilities. In this study, we employ the Gkeyll simulation framework to study the Burch event with different classes of extended, multifluid magnetohydrodynamics (MHD), including models that incorporate important kinetic effects, such as the electron pressure tensor, with physics‐based closure relations designed to capture linear Landau damping. Such fluid modeling approaches are able to capture different levels of kinetic physics in global simulations and are generally less costly than fully kinetic PIC. We focus on the additional physics one can capture with increasing levels of fluid closure refinement via comparison with MMS data and existing PIC simulations. In particular, we find that the ten‐moment model well captures the agyrotropic structure of the pressure tensor in the vicinity of the X‐line and the magnitude of anisotropic electron heating observed in MMS and PIC simulations. However, the ten‐moment model is found to have difficulty resolving the lower hybrid drift instability, which plays a fundamental role in heating and mixing electrons in the current layer.

Mechanism of Reconnection on Kinetic Scales Based on Magnetospheric Multiscale Mission Observations

Abstract We examine the role that ions and electrons play in reconnection using observations from the Magnetospheric Multiscale (MMS) mission on kinetic ion and electron scales, which are much shorter than magnetohydrodynamic scales. This study reports observations with unprecedented high resolution that MMS provides for magnetic field (7.8 ms) and plasma (30 ms for electrons and 150 ms for ions). We analyze and compare approaches to the magnetopause in 2016 November, to the electron diffusion region in the magnetotail in 2017 July followed by a current sheet crossing in 2018 July. Besides magnetic field reversals, changes in the direction of the flow velocity, and ion and electron heating, MMS observed large fluctuations in the electron flow speeds in the magnetotail. As expected from numerical simulations, we have verified that when the field lines and plasma become decoupled a large reconnecting electric field related to the Hall current (1–10 mV m−1) is responsible for fast reconnection in the ion diffusion region. Although inertial accelerating forces remain moderate (1–2 mV m−1), the electric fields resulting from the divergence of the full electron pressure tensor provide the main contribution to the generalized Ohm’s law at the neutral sheet (as large as 200 mV m−1). In our view, this illustrates that when ions decouple electron physics dominates. The results obtained on kinetic scales may be useful for better understanding the physical mechanisms governing reconnection processes in various magnetized laboratory and space plasmas.

Nonideal Electric Field Observed in the Separatrix Region of a Magnetotail Reconnection Event

AbstractBased on the Magnetospheric Multiscale observations in the magnetotail, we present a complete crossing of the current sheet with ongoing magnetic reconnection. The field‐aligned inflowing electrons were observed in both separatrix regions (SRs) and their energy extended up to several times of the thermal energy. Along the SR, a net parallel electrostatic potential was estimated and could be the reason for the inflowing electron streaming. In the northern SR, the electron frozen‐in condition was violated and nonideal electric field was inferred to be caused by the gradient of the electron pressure tensor. The nongyrotropic electron distribution and significant energy dissipation were observed at the same region. The observations indicate that the inner electron diffusion region can extend along the separatrices or some electron‐scale instability can be destabilized in the SR.

Magnetospheric Multiscale Mission Observations of Reconnecting Electric Fields in the Magnetotail on Kinetic Scales

AbstractWe examine the role of ions and electrons in reconnection using the highest resolution observations from the Magnetospheric Multiscale mission on kinetic ion and electron scales. We report magnetic field and plasma observations from several approaches to the electron diffusion region in the current sheet in 2018. Besides magnetic field reversals, changes in the direction of flow velocity, ion and electron heating, Magnetospheric Multiscale observed large fluctuations in the electron flow speeds in the magnetotail. We have verified that when the field lines and plasma become decoupled, a large reconnecting electric field related to the Hall current (1–10 mV/m) is responsible for fast reconnection in the ion diffusion region. Although inertial acceleration forces remain moderate (1–2 mV/m), the electric fields resulting from the electron pressure tensor provide the main contribution to the generalized Ohm's law at the neutral sheet (as large as 200 mV/m). This illustrates that when ions decouple electron physics dominates.

Validation of Anisotropic Electron Fluid Closure Through In Situ Spacecraft Observations of Magnetic Reconnection

AbstractA valid fluid model for electrons in collisionless space plasmas is desirable for understanding the structure and evolution of magnetic reconnection geometries. Additionally, such a fluid model would be useful for the simulation of systems too large to be tractable in a fully kinetic model. Using Magnetospheric Multiscale spacecraft observations, we provide direct confirmation of the Lê et al., 2009 (https://doi.org/10.1103/PhysRevLett.102.085001) equations of state for the electron pressure tensor during guide field reconnection and demonstrate how the closure can be applied in efficient numerical simulation, yielding new physical insight to the electron heating problem. Furthermore, we use the Lê et al., 2009 equations of state to predict a scaling of electron heating in the exhaust comparable to the available observational data.

High‐Resolution Measurements of the Cross‐Shock Potential, Ion Reflection, and Electron Heating at an Interplanetary Shock by MMS

AbstractThe Magnetospheric Multiscale (MMS) spacecraft obtained unprecedented high‐time resolution multipoint particle and field measurements of an interplanetary shock event on 8 January 2018. The spacecraft encountered the supercritical forward shock of a forward/reverse shock pair in the pristine solar wind upstream of the bow shock near the subsolar point as they neared apogee at ~25 RE. The high‐time resolution measurements from the four spacecraft, separated by only ~20 km, allowed direct measurement of particle distributions revealing evidence of electron heating and near specularly reflected ions. The cross‐shock potential is calculated directly from 3‐D electric field measurements. This is the first reported direct high temporal resolution (<1 s) observation at an interplanetary shock of near specularly reflected ions. Calculation of the cross‐shock potential yields a potential jump significant enough to reflect at least some of the protons from the incident solar wind beam. The cross‐shock potential calculated here is consistent with previous estimations based on particle measurements and numerical/analytical simulations. The ambipolar contribution to the cross‐shock potential calculated from the four‐spacecraft divergence of the electron pressure tensor is somewhat higher than that inferred form the Liouville‐mapped electron energy gain across the shock. Furthermore, the high‐time‐resolution 3‐D electric field measurements reported here reveal small‐scale nonlinear structures embedded in the shock layer that contribute to the nonmonotonic shock transition.

Energy transfer and electron energization in collisionless magnetic reconnection for different guide-field intensities

Electron dynamics and energization are one of the key components of magnetic field dissipation in collisionless reconnection. In 2D numerical simulations of magnetic reconnection, the main mechanism that limits the current density and provides an effective dissipation is most probably the electron pressure tensor term, which has been shown to break the frozen-in condition at the x-point. In addition, the electron-meandering-orbit scale controls the width of the electron dissipation region, where the electron temperature has been observed to increase both in recent Magnetospheric Multiple-Scale (MMS) observations and in laboratory experiments, such as the Magnetic Reconnection Experiment (MRX). By means of two-dimensional full-particle simulations in an open system, we investigate how the energy conversion and particle energization depend on the guide field intensity. We study the energy transfer from the magnetic field to the plasma in the vicinity of the x-point and close downstream regions, and E·J and the threshold guide field separating two regimes where either the parallel component, E||J||, or the perpendicular component, E⊥·J⊥, dominate the energy transfer, confirming recent MRX results and also consistent with MMS observations. We calculate the energy partition between fields and kinetic and thermal energies of different species, from electron to ion scales, showing that there is no significant variation for different guide field configurations. Finally, we study possible mechanisms for electron perpendicular heating by examining electron distribution functions and self-consistently evolved particle orbits in high guide field configurations.

System of Kinetic Equations for Collisionless Space Plasma in the Approximation of Field-Aligned Force Equilibrium for Electrons

A system of kinetic equations describing relatively slow large-scale processes in collisionless magnetoplasma structures with a spatial resolution on the order of the proton thermal gyroradius is derived. The system correctly takes into account the electrostatic effects in the approximation of field-aligned force equilibrium for electrons. The plasma is considered quasineutral, and the magnetic field is described by the Ampere equation. The longitudinal component of the electric field is found explicitly from the equality of the field-aligned component of the electric force acting on plasma electrons and the divergence of the electron pressure tensor. The electric field component orthogonal to the magnetic field is determined by the distributions of the number densities, current densities, and stress tensors of all plasma species in the instantaneous long-range approximation described by a system of time-independent elliptic equations. Versions of the system of equations adapted to the case of magnetized electrons described by the Vlasov equation in the drift approximation, as well as to the case in which all plasma species are magnetized, are derived. The resulting systems of equations allow creating numerical models capable of describing large-scale processes in nonuniform collisionless space plasma.