Electron Inertial Length Research Articles (Page 1)

Abstract We use a two‐dimensional particle‐in‐cell simulation code to examine how the spatial scale evolves as the chorus wave is initially generated in the equatorial source region and then propagates to higher latitudes, experiencing growth or damping while propagating. The distinct rising‐tone chorus elements have been successfully excited self‐consistently near the magnetic equator within a limited radial region and propagate both outward and inward as the latitude increases. The wave normal angle increases as the latitude increases. We test two types of correlation analyses on both 2D spectra and 1D waveforms to determine the correlation scale of the single rising‐tone chorus element. The results indicate that the parallel spatial scale of the chorus element is more than 500 ( is the electron inertial length at the center of the simulation domain) and the transverse spatial scale increases from near the equator to at high latitude. The parallel correlation scale is much larger than the transverse (radial) spatial scale of individual chorus elements, which is consistent with the results of simultaneous multi‐satellite observations.

Abstract Recently, electron‐only reconnection, in which there is no obvious ion bulk flow and ion heating, has been pervasively observed in the Earth's magnetosphere. In this Letter, we realize electron‐only reconnection with a guide field in the Keda Linear Magnetized Plasma (KLMP) device. By measuring the magnetic field, we identify unambiguously a distorted quadrupolar structure of the magnetic field in the out‐of‐plane direction. At the same time, electrons are obviously heated in the current sheet with the half‐width about 0.8 electron inertial length. The maximum velocity of the estimated electron flow in the reconnection plane is about eight Alfvén speed.

We use multispacecraft Magnetospheric Multiscale observations to investigate electric fields and ion reflection at a nonstationary collisionless perpendicular plasma shock. We identify subproton scale (5-10 electron inertial lengths) large-amplitude normal electric fields, balanced by the Hall term (J×B/ne), as a transient feature of the shock ramp related to nonstationarity (rippling). The associated electrostatic potential, comparable to the energy of the incident solar wind protons, decelerates incident ions and reflects a significant fraction of protons, resulting in more efficient shock-drift acceleration than a stationary planar shock.

The present study has investigated the statistical distribution of the current sheet width across the reconnection diffusion region by means of the 3D particle-in-cell simulations. The 3D reconnection layers are unstable to the flow shear instabilities, which results in electromagnetic (EM) turbulence generating effective magnetic dissipation around the x-line. The simulations are performed for several ion-to-electron mass ratios and computational domain sizes, which determine the fastest-growing mode in each simulation run. When the turbulence is weak, the current sheet width increases with the turbulence intensity, following a theoretical curve independent of the mass ratio and domain size. However, when the turbulence is stronger, the width saturates at a low level around 2 times the local electron inertia length, i.e., much smaller than the ion kinetic scales. It is found that the intense inductive electric field due to the EM turbulence is partly canceled out by the eddy viscous effect. As a result, the reconnection electric field is almost unchanged during the quasi-steady phase, regardless of the turbulence intensity. The result implies that the magnetohydrodynamic turbulence models are unlikely to be applicable to the reconnection diffusion region.

The tearing mode instabilities were numerically studied in two distinct models: the finite electron inertial magnetohydrodynamics (MHD) and the electron MHD (EMHD). The finite electron inertial MHD model employed a modified Hall-MHD model that incorporated the electron inertial effects in the generalized Ohm’s Law. On the other hand, the electron dynamics were described by the EMHD model. It is found that both electron inertial effects and electron dynamics significantly influence the linear and nonlinear growth of tearing mode instabilities, with electron dynamics playing a more dominant role. The dependence of the linear growth rate of tearing modes on the electron inertial length de was investigated. The results show that electron inertial effects enhance the growth rate but resemble the behavior of resistivity η. Whereas, in the EMHD model, electron inertia plays a dominant role in tearing mode instabilities. Additionally, a study on the nonlinear saturation of (2,1) tearing modes was conducted, demonstrating consistency with relevant analytical theories. The study indicates that, in both models, the magnetic island exhibits faster growth and achieves a larger saturated island width as de increases.

A recently published analysis of current sheets has updated the classic Harris 1D static solution by considering multiple classes of charged particle trajectories in a generalized and dynamic current sheet. It uses a 1D PIC simulation to describe dynamic pinching and bifurcation of the current sheet. These 1D results strongly suggest that properties of the inflowing plasma, including the plasma beta, have an important effect on the equilibrium thickness of the pinched current sheet. Since 1D studies cannot describe magnetic reconnection, the time appears right to carry such 1D studies over to 2D or 3D simulations to explore current sheet thickness effects on reconnection. The Magnetospheric Multiscale Mission (MMS), with its well-resolved multipoint measurements of collisionless plasma and fields, has found that collisionless reconnection is accompanied by non-adiabatic motions of electrons that only occur in magnetic structures with a narrow scale comparable to electron inertial lengths (de). The recent 1D studies suggest that a plasma pinch to such scales may only occur for inflowing magnetized plasmas with relatively low plasma beta. We conclude that a parametric exploration of simulated and observed reconnection inflow conditions, particularly plasma beta, should shed light on the enablement of reconnection in collisionless plasmas.

Magnetic reconnection driven by a capacitor coil target is an innovative way to investigate low-β magnetic reconnection in the laboratory, where β is the ratio of particle thermal pressure to magnetic pressure. Low-β magnetic reconnection frequently occurs in the Earth’s magnetosphere, where the plasma is characterized by β ≲ 0.01. In this paper, we analyze electron acceleration during magnetic reconnection and its effects on the electron energy spectrum via particle-in-cell simulations informed by parameters obtained from experiments. We note that magnetic reconnection starts when the current sheet is down to about three electron inertial lengths. From a quantitative comparison of the different mechanisms underlying the electron acceleration in low-β reconnection driven by coil targets, we find that the electron acceleration is dominated by the betatron mechanism, whereas the parallel electric field plays a cooling role and Fermi acceleration is negligible. The accelerated electrons produce a hardened power-law spectrum with a high-energy bump. We find that injecting electrons into the current sheet is likely to be essential for further acceleration. In addition, we perform simulations for both a double-coil co-directional magnetic field and a single-coil one to eliminate the possibility of direct acceleration of electrons beyond thermal energies by the coil current. The squeeze between the two coil currents can only accelerate electrons inefficiently before reconnection. The simulation results provide insights to guide future experimental improvements in low-β magnetic reconnection driven by capacitor coil targets.

ABSTRACT Three-dimensional kinetic-scale turbulence is studied numerically in the regime where electrons are strongly magnetized (the ratio of plasma species pressure to magnetic pressure is βe = 0.1 for electrons and βi = 1 for ions). Such a regime is relevant in the vicinity of the solar corona, the Earth’s magnetosheath, and other astrophysical systems. The simulations, performed using the fluid-kinetic spectral plasma solver (sps) code, demonstrate that the turbulent cascade in such regimes can reach scales smaller than the electron inertial scale, and results in the formation of electron-scale current sheets (ESCS). Statistical analysis of the geometrical properties of the detected ESCS is performed using an algorithm based on the medial axis transform. A typical half-thickness of the current sheets is found to be on the order of electron inertial length or below, while their half-length falls between the electron and ion inertial length. The pressure–strain interaction, used as a measure of energy dissipation, exhibits high intermittency, with the majority of the total energy exchange occurring in current structures occupying approximately 20 per cent of the total volume. Some of the current sheets corresponding to the largest pressure–strain interaction are found to be associated with Alfvénic electron jets and magnetic configurations typical of reconnection. These reconnection candidates represent about 1 per cent of all the current sheets identified.

The Hall Magnetohydrodynamic (MHD) equations are an extension of the standard MHD equations that include the “Hall” term from the general Ohm’s law. The Hall term decouples ion and electron motion physically on the ion inertial length scales. Implementing the Hall MHD equations in a numerical solver allows more physical simulations for plasma dynamics on length scales less than the ion inertial scale length but greater than the electron inertial length. The present effort is an important step towards producing physically correct results to important problems, such as the Geospace Environmental Modeling (GEM) Magnetic Reconnection problem. The solver that is being modified is currently capable of solving the resistive MHD equations on unstructured grids using the spectral difference scheme which is an arbitrarily high-order method that is relatively simple to parallelize. The GEM Magnetic Reconnection problem is used to evaluate whether the Hall MHD equations have been correctly implemented in the solver using the spectral difference method with divergence cleaning (SDDC) algorithm by comparing against the reconnection rates reported in the literature.

On electron kinetic scales, ions and electrons decouple, and electron velocity shear on electron inertial length ∼de can trigger electromagnetic (EM) electron Kelvin–Helmholtz instability (EKHI). In this paper, we present an analytic study of EM EKHI in an inviscid collisionless plasma with a step-function electron shear flow. We show that in incompressible collisionless plasma, the ideal electron frozen-in condition E+ve×B/c=0 must be broken for the EM EKHI to occur. In a step-function electron shear flow, the ideal electron frozen-in condition is replaced by magnetic flux conservation, i.e., ∇×(E+ve×B/c)=0, resulting in a dispersion relation similar to that of the standard ideal and incompressible magnetohydrodynamics KHI. The magnetic field parallel to the electron streaming suppresses the EM EKHI due to magnetic tension. The threshold for the EM mode of the EKHI is (k·ΔUe)2>ne1+ne2ne1ne2[ne1(vAe1·k)2+ne2(vAe2·k)2], where vAe=B/(4πmene)1/2, ΔUe, and ne are the electron streaming velocity shear and densities, respectively. The growth rate of the EM mode is γem∼Ωce, which is the electron gyro-frequency.

Abstract The magnetic pile‐up region and its front, which plays a crucial role in electron energization during magnetic reconnection, has been widely studied at fluid and ion scales. However, there have been few studies on electron‐scale front of magnetic pile‐up regions so far. Here, we present detailed observations of electron‐scale front in a tailward reconnection exhaust. With a thickness of ∼5.5 de (electron inertial length), the front propagated along its normal direction, mainly along the reconnection outflow direction. At this front, the strong energy conversion observed was mainly driven by the perpendicular electron current. The front can lead to adiabatic electron heating and acceleration. The front hosts an intense and highly structured electric field, reaching up to ∼120 mV/m and predominantly attributed to the electron convection term. Electrostatic waves with frequencies higher than the electron gyrofrequency and parallel normal angles (WRT background magnetic field) were detected adjacent to the front. Our study can provide insight into the roles of fronts and electron‐scale physics in magnetic reconnection.

Abstract We present Magnetospheric Multiscale observations of electrostatic double layers in quasi‐perpendicular Earth's bow shock. These double layers have predominantly parallel electric field with amplitudes up to 100 mV/m, spatial widths of 50–700 m, and plasma frame speeds within 100 km/s. The potential drop across a single double layer is 2%–7% of the cross‐shock potential in the de Hoffmann‐Teller frame and occurs over the spatial scale of 10 Debye lengths or one tenth of electron inertial length. Some double layers can have spatial width of 70 Debye lengths and potential drop up to 30% of the cross‐shock potential. The electron temperature variation observed across double layers is roughly consistent with their potential drop. While electron heating in the Earth's bow shock occurs predominantly due to the quasi‐static electric field in the de Hoffmann‐Teller frame, these observations show that electron temperature can also increase across Debye‐scale electrostatic structures.

A wave turbulence theory is developed for inertial electron magnetohydrodynamics (IEMHD) in the presence of a relatively strong and uniform external magnetic field $\boldsymbol {B_0} = B_0 \hat {\boldsymbol {e}}_\|$ . This regime is relevant for scales smaller than the electron inertial length $d_e$ . We derive the kinetic equations that describe the three-wave interactions between inertial whistler or kinetic Alfvén waves. We show that for both invariants, energy and momentum, the transfer is anisotropic (axisymmetric) with a direct cascade mainly in the direction perpendicular ( $\perp$ ) to $\boldsymbol {B_0}$ . The exact stationary solutions (Kolmogorov–Zakharov spectra) are obtained for which we prove the locality. We also found the Kolmogorov constant $C_K \simeq 8.474$ . In the simplest case, the study reveals an energy spectrum in $k_\perp ^{-5/2} k_\|^{-1/2}$ (with k the wavenumber) and a momentum spectrum enslaved to the energy dynamics in $k_\perp ^{-3/2} k_\|^{-1/2}$ . These solutions correspond to a magnetic energy spectrum ${\sim }k_\perp ^{-9/2}$ , which is steeper than the EMHD prediction made for scales larger than $d_e$ . We conclude with a discussion on the application of the theory to space plasmas.

We perform a high-resolution, 2D, fully kinetic numerical simulation of a turbulent plasma system with observation-driven conditions, in order to investigate the interplay between turbulence, magnetic reconnection, and particle heating from ion to subelectron scales in the near-Sun solar wind. We find that the power spectra of the turbulent plasma and electromagnetic fluctuations show multiple power-law intervals down to scales smaller than the electron gyroradius. Magnetic reconnection is observed to occur in correspondence of current sheets with a thickness of the order of the electron inertial length, which form and shrink owing to interacting ion-scale vortices. In some cases, both ion and electron outflows are observed (the classic reconnection scenario), while in others—typically for the shortest current sheets—only electron jets are present (“electron-only reconnection”). At the onset of reconnection, the electron temperature starts to increase and a strong parallel temperature anisotropy develops. This suggests that in strong turbulence electron-scale coherent structures may play a significant role for electron heating, as impulsive and localized phenomena such as magnetic reconnection can efficiently transfer energy from the electromagnetic fields to particles.

Electromagnetic (EM) instabilities and turbulence driven by the electron-temperature gradient (ETG) are considered in a local slab model of a tokamak-like plasma. Derived in a low-beta asymptotic limit of gyrokinetics, the model describes perturbations at scales both larger and smaller than the electron inertial length$d_e$, but below the ion Larmor scale$\rho _i$, capturing both electrostatic and EM regimes of turbulence. The well-known electrostatic instabilities – slab and curvature-mediated ETG – are recovered, and a new instability is found in the EM regime, called the thermo-Alfvénic instability (TAI). It exists in both a slab version (sTAI, destabilising kinetic Alfvén waves) and a curvature-mediated version (cTAI), which is a cousin of the (electron-scale) kinetic ballooning mode. The cTAI turns out to be dominant at the largest scales covered by the model (greater than$d_e$but smaller than$\rho _i$), its physical mechanism hinging on the fast equalisation of the total temperature along perturbed magnetic field lines (in contrast to kinetic ballooning mode, which is pressure balanced). A turbulent cascade theory is then constructed, with two energy-injection scales:$d_e$, where the drivers are slab ETG and sTAI, and a larger (parallel system size dependent) scale, where the driver is cTAI. The latter dominates the turbulent transport if the temperature gradient is greater than a certain critical value, which scales inversely with the electron beta. The resulting heat flux scales more steeply with the temperature gradient than that due to electrostatic ETG turbulence, giving rise to stiffer transport. This can be viewed as a physical argument in favour of near-marginal steady-state in electron-transport-controlled plasmas (e.g. the pedestal). While the model is simplistic, the new physics that is revealed by it should be of interest to those attempting to model the effect of EM turbulence in tokamak-relevant configurations with high beta and large ETGs.

Possible mode conversion from kinetic Alfvén wave to modified electron acoustic wave is examined based on a multi-fluid model involving two electron populations. The mode conversion transpires when a kinetic Alfvén wave propagates through a transition between a hot-electron-dominant region and a cold-electron-dominant region. It is shown that the mode conversion and the kinetic Alfvén wave reflection depend strongly on the hot electron inertial length, the hot electron temperature, and the perpendicular wavelength. The results suggest that such conversion is ubiquitous whenever a steep gradient of electron temperature exists, for example, in the planetary auroral acceleration regions or at the boundary of the solar corona.

On 6 July 2017, the four Magnetospheric Multiscale spacecrafts were positioned within an electron diffusion region (EDR) just northward of a reconnection X line. The EDR was identified by electron crescent distributions, out-of-plane current, and energy conversion. From this position, the three spacecrafts closest to the X line (within about three electron inertial lengths) were able to accurately measure the reconnection electric field and the electron inflow velocity. The reconnection rates derived from the electric field and inflow velocity measurements agree with theoretical estimates (0.11–0.17) and a previous measurement of EM in a tail reconnection event on 11 July 2017.

We study the nonlinear interaction of three parallel Alfvén wave packets (AWPs) in an initially uniform plasma using 2.5-dimensional particle-in-cell (PIC) numerical simulations. We aim to help to explain the observation of suprathermal electrons by the collision of multiple Alfvén waves in regions where these waves are trapped like the IAR (Ionospheric Alfvén Resonator), Earth radiation belts or coronal magnetic loops. In the context of the acceleration by the parallel Alfvén waves interactions (APAWI) process that has been described by Mottez (Ann. Geophys., vol. 30, issue 1, 2012, pp. 81–95; J. Plasma Phys., vol. 81, issue 1, 2015, p. 325810104), the interaction of two parallel Alfvén waves (AWs) generates longitudinal density modulations and parallel electric fields at the APAWI crossing region that can accelerate particles effectively in the direction of the background magnetic field. Our simulations show that when a third parallel AWP of different initial position arrives at the APAWI crossing region, it gives rise to a strong parallel electron beam ( $V \sim 5\text {--}7 V_{Te}$ ) at longitudinal cavity density gradients. We suggest that velocity drift from an outgoing AW generates interface waves in the transverse direction, which allows propagating waves to develop parallel electric fields by the phase mixing process when $k_{\perp }^{-1}$ of the wavy density gradient (oblique gradient) is in the range of the electron inertial length $c/\omega _{p0}$ .

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.

Abstract The Martian bow shock is a rich example of a supercritical, mass‐loaded collisionless shock that coexists with ultra‐low frequency upstream waves that are generated by the pick‐up of exospheric ions. The small size of the bow shock stand‐off distance (comparable with the solar wind ion convective gyroradius) raises questions about the nature of the particle acceleration and energy dissipation mechanism at work. The study of the Martian shock structure is crucial to understand its microphysics and is of special interest to understand the solar wind—planet interaction with a virtually unmagnetized body. We report on a complete identification and first characterization of the supercritical substructures of the Martian quasi‐perpendicular shock, under the assumption of a moving shock layer, using MAVEN magnetic field and solar wind plasma observations for two examples of shock crossings. We obtained substructures length‐scales comparable to those of the Terrestrial shock, with a narrow shock ramp of the order of a few electron inertial lengths. We also observed a well defined foot (smaller than the proton convected gyroradius) and overshoot that confirm the importance of ion dynamics for dissipative effects.